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Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 Imperial Valley, California, earthquake
Abstract
We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relations for peak horizontal acceleration and velocity. This new analysis uses a magnitude-independent shape, based on geometrical spreading and anelastic attenuation, for the attenuation curve. An innovation in technique is introduced that decouples the determination of the distance dependence of the data from the magnitude dependence. The resulting equations are
log A = − 1.02 + 0.249 M − log r − 0.00255 r + 0.26 P r = ( d 2 + 7.3 2 ) 1 / 2 5.0 ≦ M ≦ 7.7 log V = − 0.67 + 0.489 M − log r − 0.00256 r + 0.17 S + 0.22 P r = ( d 2 + 4.0 2 ) 1 / 2 5.3 ≦ M ≦ 7.4
where A is peak horizontal acceleration in g, V is peak horizontal velocity in cm/ sec, M is moment magnitude, d is the closest distance to the surface projection of the fault rupture in km, S takes on the value of zero at rock sites and one at soil sites, and P is zero for 50 percentile values and one for 84 percentile values.
We considered a magnitude-dependent shape, but we find no basis for it in the data; we have adopted the magnitude-independent shape because it requires fewer parameters.
... Zróznicowanie w budowie geologicznej warstw przypowierzchniowych jest ważnym czynnikiem mającym wpływ na wielkość zarejestrowanych na powierzchni drgań z uwagi na wzrost ich amplitud w stosunku do twardego podłoża, określany jako amplifikacja drgań. Wartość współczynnika amplifikacji wzrasta wraz ze spadkiem prędkości fal sejsmicznych [7]. Występowanie skał słabo związanych lub spękanych także wpływa na wzrost amplitudy drgań. ...
... Występowanie skał słabo związanych lub spękanych także wpływa na wzrost amplitudy drgań. Do analizy wykorzystano powszechnie stosowany, niezależnie od wielkości źródła, zarówno w odniesieniu do trzęsień ziemi jak i wstrząsów indukowanych działalnością górniczą, model relacji tłumienia Joyner'a-Boore'a [7]. Estymację parametrów relacji tłumienia przeprowadzono metodą regresji wielokrotnej [4,11]. ...
... 3. RELACJA TŁUMIENIA Z UWZGLĘDNIENIEM AMPLIFIKACJI DRGAŃ Do analizy danych pomiarowych wykorzystano relację tłumienia, która określa zależność pomiędzy wybranym parametrem drgań takim jak szczytowa amplituda prędkości lub przyspieszenia drgań a czynnikami wpływającymi na ich wielkość: energią sejsmiczną, odległością hipocentralną i współczynnikiem amplifikacji drgań dla poszczególnych stanowisk pomiarowych. Do estymacji parametrów relacji tłumienia wykorzystano metodę analizy regresji wielokrotnej [4] oraz model Joyner'a-Boore'a [7]. W ogólnej postaci model ten wyrażony jest przez związek liniowy: ...
In the area of KWK Myslowice-Wesola, ground vibrations from seismic events induced by mining activity is being continuously monitoring since May 2007 using 3 three–component seismic stations. Based on the seismic data obtained from recording of high-energy tremors an attempt was made to estimate the parameters of seismic attenuation relations, including the site amplification factors related to near–surface geological layers. Site amplification is the effect of increasing the amplitude of seismic vibrations recorded on the surface that is de-pendent on the parameters of the subsurface layers such as density, thickness, seismic velocity and wave type. To the estimation of site amplification was made by multiple regression analy-sis based on the Joyner-Boore attenuation model.
... In seismology, attenuation relations that do not take into account the directionality of vibrations are generally used. Many examples of different forms of these dependencies can be found in the literature [3][4][5][6]. For mining problems in Poland, the model proposed in [4] is usually used. ...
... By accounting for uncertainties associated with various parameters such as ground acceleration velocity and distance from the measurement site to the tremor source, these relationships provide more accurate estimates of the mean and variance of ground attenuation [13]. Validation of these relationships is crucial to ensure their reliability in seismic hazard assessment-assessing the probability of earthquakes and induced shaking and their potential impact on building infrastructure, or for interpreting near-surface structures, as well as mapping seismic activity in volcanic areas and assessing the stability of faults in oil fields [5,[14][15][16][17]. On the laboratory scale, with regard to seismoacoustic emissions, the recognition of shear and tension signals can be found in [18]. ...
... The models which take into account the directionality of ground vibration attenuation proposed in global seismology, e.g., ref. [5], are often characterized by a relatively large number of parameters. This requires having measurement results from many surface monitoring stations. ...
Entrepreneurs carrying out mining works under seismic hazard conditions are obliged to conduct studies in the field of engineering geophysics, including measuring, interpreting and evaluating the effects of rock mass tremors on ground vibration parameters, and thus the occurrence of harmful impacts on surface objects. However, for technical reasons, this is a difficult task to implement at all points subject to the influence of mining activities. Therefore, it becomes expedient to look for solutions that would provide greater accuracy in forecasting the distribution of ground vibration parameters. This paper proposes a method for forecasting the distribution of peak ground accelerations (PGAs) induced by mining activities, taking into account the directionality of vibration attenuation. In many cases, the explanation of the variation in the magnitude of recorded ground surface vibrations after a rock mass tremor cannot always be explained by only the variation of epicentral distances and the value of the vibration amplification factor by quaternary formations. Therefore, it is reasonable to take into account the directionality of vibration attenuation. The authors analyzed and evaluated the accuracy of predicting the distribution of ground vibration accelerations induced by mining activities, taking into account the directionality of vibration attenuation, using three models: the first, a classical model assuming isotropic vibration attenuation; the second, a model taking into account the anisotropy of vibration attenuation with elliptical isolines; the third, a model without assuming the shape of the isolines of vibration intensity parameters. For both models that took into account anisotropy of vibration attenuation, better results (more accurate descriptions of observed ground vibration accelerations) were obtained than for the model assuming isotropy. The most accurate estimates of vibration magnitude were obtained using the latter model.
... Going forward, the pdf and cdf in Equations (19) and (20) are used to obtain the general statistical properties of the RXg-G family of distributions. ...
... (23) Substituting the expression in (19), the incomplete rth moment gives: ...
... The corresponding empirical cdf (ecdf) plot is presented in Figure 3. It has previously been analyzed by Joyner and Boore (1981) and the observations are as follows: 7.5, 8.8, 8.9, 9.4, 9.7, 9.7 The dataset was analyzed, and the result is presented in Table 3. ...
A new family of distributions, called the Right truncated Xgamma-G, was developed. Explicit expressions for some of its statistical properties including the Renyi entropy, moments and generating functions, stress-strength reliability, Lorenz and Benferroni curves were established. The model parameters were estimated using the maximum likelihood estimation method and real-life application was provided using three datasets. It was also demonstrated that the Right truncated Xgamma-G family of
distributions fits the datasets better than the Kumaraswamy-G, Beta-G, Exponentiated Generalized-G, Weibull-G, and Gompertz-G families of distributions.
... We evaluated and adjusted two different parametric forms of GMPE developed for transcurrent tectonic regimes that resemble the tectonic setting in the Gulf of California, along with an additional parametric form developed for central Mexico that incorporates the focal depth as an independent variable. All three adjustments exhibit appropriate behavior in terms of residual analysis and variables stability, with the adjusted parametrical form of Joyner and Boore (Bull Seismol Soc Am 71:2011-2038, 1981. https:// doi. ...
... Despite being a model that does not share similar tectonic conditions with our study region, it is attractive because it considers the focal depth as an independent variable. The models proposed by Joyner and Boore (1981) and by Ö zbey et al. (2004) include a fixed focal depth within their definitions of distance but do not contemplate the influence of this parameter. GA05 parametrical form has been used successfully for GMPE in previous studies (Villalobos-Escobar et al. 2023) in Northeastern Mexico where the incorporation of this variable improved the residual analysis. ...
... This model adjusted the parametrical form proposed by Joyner and Boore (1981). The definition of distance r depends on the epicentral distance d and on the average depth of the events as a fixed value (11.86 km). ...
We present a ground-motion prediction equation (GMPE) of peak ground acceleration (PGA) for the Gulf of California, Mexico, derived from 1326 PGA values of 720 earthquakes recorded between 2015 and 2018 by the Red Sismológica de Banda Ancha del Golfo de California (RESBAN), operated by the Centro de Investigación Científica y de Educación Superior de Ensenada, Baja California (CICESE). We evaluated and adjusted two different parametric forms of GMPE developed for transcurrent tectonic regimes that resemble the tectonic setting in the Gulf of California, along with an additional parametric form developed for central Mexico that incorporates the focal depth as an independent variable. All three adjustments exhibit appropriate behavior in terms of residual analysis and variables stability, with the adjusted parametrical form of Joyner and Boore (Bull Seismol Soc Am 71:2011–2038, 1981. https://doi.org/10.1785/BSSA0710062011) providing the best overall performance. The proposed GMPE is: , with . PGA is peak horizontal acceleration in cm/s2, M is magnitude and d is epicentral distance. σA = 0.18 and σE = 0.4 correspond to the intra-event and inter-event standard deviations, respectively. Although the inclusion of focal depth as an independent variable enhanced adjustments in various tectonic regions, it did not provide a specific advantage in this context. To account for depth variations, we incorporated a fixed value representing the average focal depth into the distance definition (11.86 km) effectively capturing the seismic characteristics of the region and emphasizing the importance of regional-specific factors in GMPE development and refinement.
... To calculate the death per capita of each earthquake, we first utilized Joyner and Boore's (1981) [12] attenuation relations that predict PGA (peak ground acceleration) using magnitude and the distance from the fault rupture, as shown in Formula 1. [12] log(P GA(gravity) ...
... To calculate the death per capita of each earthquake, we first utilized Joyner and Boore's (1981) [12] attenuation relations that predict PGA (peak ground acceleration) using magnitude and the distance from the fault rupture, as shown in Formula 1. [12] log(P GA(gravity) ...
Accurate damage prediction is crucial for disaster preparedness and response strategies, particularly given the frequent earthquakes in Turkey. Utilizing datasets on earthquake data, infrastructural quality metrics, and contemporary socioeconomic factors, we tested various machine-learning architectures to forecast death tolls and fatalities per affected population. Our findings indicate that the Random Forest model provides the most reliable predictions. The model highlights earthquake magnitude and building stability as the primary determinants of damage. This research contributes to the reduction of fatalities in future seismic events in Turkey.
... Notably, no faulting-induced surface rupture deformations were observed after the Hatay-Yayladag˘ı earthquake (MTA, 2023). Figure 6 presents the attenuation of the recorded PGA intensities with Joyner and Boore (1981) distances, R jb , for the events. Predicted PGA intensities estimated by Boore et al. (2014), referred to as BSSA14, are also included. ...
... PGA's recorded during (a) Pazarcık, (b) Ekinö zü-Elbistan, and (c) Yayladag˘ı events are plotted againstJoyner and Boore (1981) distances. ...
Hatay Airport was shaken by the M w 7.8 and M w 7.5 Pazarcık and Ekinözü-Elbistan Kahramanmaraş earthquake sequence on February 6, 2023. Two weeks after these events, M w 6.3 Yayladağı-Hatay earthquake shook the site again. This paper presents the results of the reconnaissance assessment of soil liquefaction at the site, focusing on mostly three aspects: (a) the seismic response of the Hatay Airport, particularly the surface manifestations of seismic soil liquefaction in the form of soil ejecta; (b) the findings of site investigation studies performed before and after the seismic events, and (c) assessments for soil liquefaction susceptibility. Among the soil ejecta samples collected, three out of five are classified as clayey sand and fall within or near the boundary of the “further studies required” region on the susceptibility charts. The remaining two ejecta samples, composed of low and high-plasticity clay soils with PI values of 31 and 36% fall within the “not susceptible” region. The deviation from the current state of knowledge might be attributed to liquefaction-induced seepage eroding clayey soils to the ground surface or limitations in the current liquefaction susceptibility assessment methods for fine-grained soils, which may not accurately delineate the boundaries between susceptible and not-susceptible zones. Determining the most likely explanation requires additional site investigation studies, including CPT soundings, extending beyond the scope of this reconnaissance study. The documented case history and assessment results are expected to enhance the understanding of seismic soil liquefaction in fine-grained soils and contribute to the development of predictive models based on case histories for assessing liquefaction susceptibility and triggering.
... However, in some cases, the scaling of seismic ground motion with distance could not be appropriately determined due to a lack of understanding or information about the correlation between observations at different sites for a given event (Campbell, 1981;. As a result, weighted nonlinear leastsquare regression methods, such as the two-stage maximum-likelihood and the random-effect methods, were introduced to improve the regression analysis (Draper & Smith, 1981;Campbell, 1981;Joyner & Boore, 1981;Brillinger & Preisler, 1985;Abrahamson & Youngs, 1992;Campbell, 1993;Boore et al., 1993). In such an approach, the distance-dependent coefficients are derived first, using individual amplitude-scaling factors for each earthquake. ...
... The dotted lines represent the range of model uncertainties (. ±1σ ) around the median predictions for .M w 5.2. Distance .R JB is given after (Joyner & Boore, 1981), which is the shortest distance to the surface projection of the fault plane to be influenced by this information. In other words, prior to the inference, we can propose a range of values that these two parameters are expected to take. ...
... In 1981, Joyner and Boore [13] proposed a new attenuation relationship based on the North American earthquakes. The catalog consisted of earthquakes with surface wave magnitude (M S ) from 5 to 7.7 and records were taken from stations less than 370 km from the epicenter. ...
... The catalog consisted of earthquakes with surface wave magnitude (M S ) from 5 to 7.7 and records were taken from stations less than 370 km from the epicenter. Also, soil type has been effective in estimating acceleration as a coefficient for both soil and rock [13]. ...
Earthquake is one of the natural disasters that has always influenced human life. It is not currently possible to predict exactly when and where an earthquake will occur, nor how large it will be. It is also impossible to prevent an earthquake. However, by designing seismic-resistant structures, the amount of financial losses and casualties can be reduced. This resistant design requires the use of earthquake risk analysis. By using the earthquake risk analysis, it will be possible to estimate the parameters of the strong ground motion, including acceleration, velocity, and displacement in each area. Estimating the parameters of strong ground motion will be possible just by obtaining the appropriate attenuation relationship. The aim of this paper is to present an appropriate attenuation relationship to estimate the horizontal component of the possible occurrence of peak ground acceleration in each region. Two methods were used to calculate attenuation relationship: gene expression programing (GEP) and group method of data handling (GMDH). In the first step, an up-to-date and comprehensive catalog consisting of 1,185 earthquake records that occurred around the world has been prepared. In the next step, the parameters of magnitude, hypocentral distance, and shear wave velocity of these records have been used as variables of the attenuation relationship. Then, the fitness function (f) was determined, and attenuation relationships were calculated using GEP and GMDH. The amount of fitness function (f) was obtained 766.12 from 1,000 in the GEP method and 767.77 from 1,000 in the GMDH method. The values of the fitness function, residuals and comparison plots showed a high-agreement between “the values predicted by the attenuation relationships” and “the actual values observed in the earthquakes.” Finally, according to the results of this research, it can be said that the use of GEP and GMDH methods has provided better results than the other similar researches. Also, the use of up-to-date records makes the results of this research more reliable than the previous researches.
... The results indicate that the CAE + k-means can accurately classify GM response spectra, correctly determine the number of clusters in GM response spectra. For comparison purposes, established clustering algorithms for GM responses spectra (or in general for time series data), including AE + k-means [28], time series k-means [6], spectral clustering [24][25][26], and k-means on GM influence factors [21] (magnitude and Joyne-Boore distance, Rjb, [40]), are also evaluated. The comparison results demonstrate that the CAE + k-means outperforms the above-mentioned established clustering algorithms (see Section 3). ...
Ground motion selection has become increasingly central to the assessment of earthquake resilience. The selection of ground motion records for use in nonlinear dynamic analysis significantly affects structural response. This, in turn, will impact the outcomes of earthquake resilience analysis. This paper presents a new ground motion clustering algorithm, which can be embedded in current ground motion selection methods to properly select representative ground motion records that a structure of interest will probabilistically experience. The proposed clustering-based ground motion selection method includes four main steps: 1) leveraging domain-specific knowledge to pre-select candidate ground motions; 2) using a convolutional autoencoder to learn low-dimensional underlying characteristics of candidate ground motions' response spectra-i.e., latent features; 3) performing k-means clustering to classify the learned latent features, equivalent to cluster the response spectra of candidate ground motions; and 4) embedding the clusters in the conditional spectra-based ground motion selection. The selected ground motions can represent a given hazard level well (by matching conditional spectra) and fully describe the complete set of candidate ground motions. Three case studies for modified, pulse-type, and non-pulse-type ground motions are designed to evaluate the performance of the proposed ground motion clustering algorithm (convolutional autoencoder + k-means). Considering the limited number of pre-selected candidate ground motions in the last two case studies, the response spectra simulation and transfer learning are used to improve the stability and reproducibility of the proposed ground motion clustering algorithm. The results of the three case studies demonstrate that the convolutional autoencoder + k-means can 1) achieve 100 % accuracy in classifying ground motion response spectra, 2) correctly determine the optimal number of clusters, and 3) outperform established clustering algorithms (i.e., autoencoder + k-means, time series k-means, spectral clustering, and k-means on ground motion influence factors). Using the proposed clustering-based ground motion selection method, an application is performed to select ground motions for a structure in San Francisco, Cali-fornia. The developed user-friendly codes are published for practical use.
... In equation (4) 2 is a coefficient that describes the higher-order magnitude dependency, while 2 266 and 3 are coefficients accounting for a magnitude dependent geometrical attenuation and the 267 anelastic attenuation effect, respectively (e.g., Joyner & Boore, 1981 were performed using a Levenberg-Marquardt iterative, linearized approach (Levenberg, 1944;274 Marquardt, 1963) with the initial solution set to be consistent with the TL16 and LL20 available 275 models, respectively. The parameter ℎ was constrained to be larger than zero as it represents an 276 average correction for depth of the source-to-site distance. ...
Ground Motion Prediction Equations (GMPEs) are semi-empirical models to relate ground motion intensity measures, such as peak ground acceleration (PGA), peak ground velocity (PGV), and pseudo-spectral acceleration (SA), to earthquake magnitude, source-to-site distance, geological local site conditions, and possibly other covariates. GMPEs are employed for applications such as probabilistic seismic hazard analysis and post-event rapid shaking estimation. Over the last decade, the densely populated Campi Flegrei caldera in Southern Italy has experienced increasing seismicity, related to the volcanic unrest and ground uplift, with over nine thousand recorded events, with duration magnitude larger than − 1.1. In the past two years, seismic activity has intensified, including approximately seventy events with duration magnitudes between 2.5 and 4.4, most of them widely felt, causing in some cases non-negligible structural actions close to the epicentre, and ultimately sparking large public concern. In this study, we calibrated site-specific GMPEs for PGA, PGV, and 21 SA values over periods T from 0.01 to 10 seconds. The dataset includes recordings from the largest events over the past two years, recorded by more than fifty accelerometric and velocimetric seismic monitoring stations at epicentral distances R epi <40 km . Moment magnitude, which is the scale used in the GMPEs, was derived for the events from their displacement Fourier amplitude spectrum. The GMPEs shows structurally non-negligible SAs at short periods ( T <0.2 s ), and the relatively faster attenuation with distance ( R epi ≥5 km ) as compared to some existing ground motion models for Italy.
... A general empirical GMM ( [10]) has been used for soil type -rock (equation 1) ...
Based on radius vectors, a verified new GMM with directly included azimuth has developed. It has been fitted into a generated databank computed by use of an originally developed method-generator of data for regression analysis. Records of strong earthquakes that occurred in 1977, 1986 and both earthquakes that took place in 1990 in the Vrancea zone in Romania have been used.
... According to Khattri et al. (1984), 0.05 g was the PGA for Lucknow (the western part of the study area) when 10% of the exceedance probability in 50 years was considered. The PSHA for the whole of India was established by Bhatia et al. (1999) using the FRISK88 computer program and the attenuation relationship derived by Joyner and Boore (1981) based on earthquakes in California. The Global Seismic Hazard Assessing Programme (GSHAP) (Zhang et al. 1999) estimated a 10% probability of exceedance in 50 years in the range of 0.05-0.10 ...
Seismic hazard maps have been developed for the Faizabad region of Uttar Pradesh state of India, utilizing deterministic and probabilistic methodologies. Maximum earthquake magnitudes were meticulously determined for each seismic source within a 500 km radius, considering region-specific seismotectonic parameters and rupture characteristics. Twenty-seven ground motion prediction equations were considered for the studied regions, and through an efficacy test, ground motion prediction equations (GMPEs) were selected for segmented hypocentral distances. The final hazard values were computed by applying varied weighting factors to the chosen GMPEs. The peak ground acceleration (PGA) and spectral acceleration (SA) were computed for 2 and 10% probabilities of exceedance in 50 years. The PGA values for the region were found to range between 0.01 and 0.14 g, as obtained from the deterministic analyses. It was inferred from the PSHA that the PGA values range between 0.05 to 0.20 g and 0.01 to 0.12 g for the 2 and 10% probability of exceedance, respectively, for 50 years. Blocks situated in the southeastern part of the city, encompassing Gonda, Faizabad Sultanpur, and Pratapgarh, have been singled out as particularly vulnerable to seismic hazards, thus warranting heightened attention and strategic planning in urban and infrastructure development.
... The traditional regression method performs a single regression of all data, which can easily lead to uncertainty owing to the correlation between distance and magnitude parameters, resulting in poor stability of the regression parameters. In response to this problem, researchers proposed the use of a distributed regression method to decouple the distance and magnitude terms (Joyner and Boore, 1981). This method introduces dummy variables. ...
The seismic attenuation relationship between ground motion parameters (such as peak acceleration and response spectra value) and seismic parameters (such as magnitude and epicentral distance) is an important foundation for seismic hazard analysis and the core of determining seismic input parameters for seismic resistance engineering. The acceleration envelope parameters, which describe the relationship between ground motion intensity and time variation, are primarily used for artificially synthesizing seismic motion. At present, little research has been performed on the attenuation relationship of acceleration envelope parameters in the Longmenshan fault zone on the eastern side of the Tibetan Plateau in China. Therefore, this study selected the Mw4-6 aftershock records of the 2008 Wenchuan earthquake that occurred on the Longmenshan fault zone and established a commonly used three segment envelope model parameter attenuation relationship. We classified aftershock records based on their source mechanisms and obtained attenuation relationship models for thrust slip aftershocks, thrust and strike slip aftershocks, and strike slip aftershocks. The results are as follows: (1) The thrust slip aftershock records had the longest rising stage which is the time difference from the arrival of P-waves to the beginning of the stable sustained stage of seismic motion. Thrust and strike slip aftershocks records had the longest stable sustained stage period and the slowest attenuation at the tail of the record. (2) The attenuation relationship of the acceleration envelope parameters commonly used in Chinese engineering for artificially synthesizing seismic motion is based on the strong earthquake records in the western United States. But, compared to the attenuation characteristics of the acceleration envelope function in the western United States, the Mw4-6 earthquake records on the Longmenshan fault zone had a slower attenuation rate at the tail of the record. So, accurately artificially synthesizing seismic motion through envelope parameter attenuation model requires the use of attenuation model established by earthquake records in this region.
... The selection of the most suitable GMPE was based on criteria proposed by Abrahamson and Litehiser (1989) and hybrid regression method introduced by Joyner and Boore (1981) and Campbell's (1981). Additionally, Iyengar and Ghosh (2004) developed a region-specific attenuation model by incorporating attenuation factors proposed by Shankar and Sharma (1998) and Campbell's (1981). ...
Over the past decade, the Delhi (National Capital Region, NCR) has witnessed significant growth and has emerged as a vital center for commerce and education. This rapid urbanization owes itself to its strategic location, connecting important cities like Gurugram, Faridabad, Noida, Sonipat, and Rohtak. However, its proximity to active geological features such as the Main Himalayan Thrust (MHT), Main Boundary Thrust (MBT), and Main Central Thrust (MCT), the city has been susceptible to devastating earthquakes, making it imperative to conduct a comprehensive probabilistic seismic hazard assessment for the Delhi NCR area. To perform this assessment, a homogenized earthquake database from 1720 to 2023 within a 300 km radius of the epicenter of Delhi was utilized. This data enabled the calculation of peak ground acceleration (PGA) and Spectral Acceleration (Sa) at different time periods, representing 50%, 20%, 10%, 5%, and 2% probabilities of exceedance in 50 years at the bedrock level. A logic tree approach, incorporating Ground Motion Prediction Equations (GMPEs) with appropriate weighted factors, was applied to ensure accuracy. The findings of the updated seismic hazard assessment reveal that Delhi and its neighboring cities are highly vulnerable to seismic hazards, with expected PGA values of 0.10 g, 0.18 g, 0.26 g, 0.33 g, and 0.48 g for the respective probabilities of exceedance. These results are comparable with the Indian code IS:1893 Part I and Malhotra’s (2005) standards that validate their reliability. Furthermore, the seismic hazard results have been used to create a deaggregation plot, which helps to quantify the contributions of seismic sources in terms of magnitude and epicentral distance. This comprehensive understanding of seismic hazards in Delhi and its adjoining regions will aid in implementing appropriate measures to enhance preparedness and mitigate potential risks.
... After determining the site factors for the S-net sites, we corrected the observed PGAs and PGVs by subtracting the corresponding site factors for each site, and a regression analysis was performed for the entire dataset using the following two steps (Eqs. (3) and (4)) to determine prediction models for PGA and PGV, e.g., [33,45,46]. where is a dummy variable (equal to 1 for the -th earthquake and 0 for others), and is a coefficient for the -th earthquake; 1 and 2 are coefficients that account for the saturation of PGAs and PGVs at short distances, respectively. ...
S-net is a seafloor observation network for earthquakes and tsunamis around the Japan Trench, comprising 150 observatories with seismometers and pressure gauges. The region has been known to experience massive earthquakes, and several magnitude 6 and 7 class earthquakes have occurred after the network was established in 2016. This study constructed ground motion prediction equations (GMPEs) for horizontal peak ground accelerations (PGAs) and peak ground velocities (PGVs) using the S-net data and revealed that the GMPEs can be used to predict the PGAs and PGVs at the land stations where measured S-wave velocities are available. We used a relatively short time window of the S-net records from the viewpoint of earthquake early warning but included S waves. Data from earthquakes of magnitudes between Mw 5.5 and Mw 7.4 were used. The construction of the GMPEs was achieved in two steps. First, regression analysis was conducted for each event data, and mean site residual was obtained over the available records at each S-net site. Second, the data were adjusted by the mean site residuals, and stratified regression analysis, which decouples the source and path factors, was performed. Finally, we applied the GMPEs to predict PGAs and PGVs at the KiK-net sites on land. We determined that the residuals at the KiK-net sites were systematically biased with Vs30 (average S-wave velocity in the upper 30 m). We obtained correction factors for the bias and demonstrated that the PGAs and PGVs at the KiK-net sites could be predicted reasonably well.
The full paper is available online (free): https://www.fujipress.jp/jdr/dr/dsstr001900050760/
... The model proposed by Joyner and Boore (1981) is adopted in his study. This model was selected because it is the most widely used attenuation law in Europe where the majority of the data set was recorded. ...
... It was obtained from Andersen et al.[25]. The third data set gives peak accelerations measured at various observation stations for 23 earthquakes in California and is referred to in[26] by Joyner and Boore. It consists of 5 variables and each variable consists of 182 observations, we studied the fourth variable [dist: numeric Station-hypocenter distance (km)]. ...
This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of estimation were presented to estimate the parameters for the proposed family, such as maximum likelihood, ordinary least square, weighted least square, Anderson Darling, right-tailed Anderson-Darling, Cramér-von Mises, and maximum product of spacing methods. A special sub-model with three parameters called extended Modi exponential distribution was derived along with different shapes of its density and hazard functions. Randomly generated data sets and different estimation methods were used to illustrate the behavior of parameters of the proposal sub-model. To illustrate the importance of the proposed family over the other well-known methods, applications to medicine and geology data sets were analyzed.
... By minimizing the overall difference between the corrected PGV and the measured value through a search for linear-rupture model parameters (rupture direction and length), the corresponding parameters are determined as the fault model parameters of the earthquake (Böse et al. 2012;Convertito et al. 2012). With reliable estimates of the fault model, a well-estimated SSZ can be obtained by utilizing the estimated source parameters, the GMPEs and the distance to the rupture (Joyner and Boore 1981). ...
The rapid and accurate prediction of earthquake Strong-Shaking Zone (SSZ) is crucial for issuing precise early warnings to regions at high risk of strong ground shaking. Generally, the SSZ is derived from the real-time spatial distribution of observed ground motions. However, during the initial stages of large earthquakes, the SSZ is often underestimated and provide alerts without enough lead-time (the time interval between the alert declaration and the S-wave arrival to the target area). In this study, we propose an innovative approach termed Near-epicenter-based Partial Matching Crossover. Leveraging the characteristic that reliable magnitude estimates for large earthquakes are available earlier than accurate predictions of the peak ground velocity (PGV) distribution, this approach utilizes near-epicenter station data to rapidly estimate the SSZ. It achieves this by matching a segment of the fault, defined by a predetermined length, with the predicted PGV map within a 120 km radius centered at the epicenter. Application of our method to strong motion data from China, Japan and Turkey demonstrates its efficacy in quickly anticipating the post-earthquake intensity distributions for large earthquakes. Specifically, it offers a lead time of 5 s or more for 51.5% (39,354 km²), 43.3% (5772 km²), 31%(47,107 km²) and 75.3% (81,966 km²) of the IMM = V region during the M 8 Wenchuan earthquake, the M 7.3 Kumamoto earthquake, the M 7.8 Syria earthquake and M 7.6 Turkey earthquake, respectively. The presented approach introduces a novel methodology to extend the lead time for earthquake early warnings.
... where f(M,R) represents the functional dependence on the logarithm of the ground motion from an earthquake of magnitude M at distance R, and E is uncertainty, which is assumed to be normally distributed and have an estimable standard deviation (Fig. 18). Ground-motion models are typically developed from ground-motion observations in regions with high seismicity, such as California (e.g., Campbell, 1981;Joyner and Boore, 1981). However, the models for regions with low seismicity, such as the central and eastern United States, are developed from or calibrated by simulated ground motions, with or without any observations. ...
This report summarizes the efforts by the Kentucky Geological Survey at the University of Kentucky in assessing seismic hazards, particularly using probabilistic seismic hazard analysis (PSHA) and deterministic seismic hazard analysis (DSHA), for engineering designs and other applications in Kentucky and central United States. It can be downloaded at https://uknowledge.uky.edu/kgs_b/12/.
... A real-life data set from the field of seismology is used to determine the performance of the GPED. The Strong-Motion data, taken from Joyner and Boore (1981), consist of 182 recordings of 23 earthquakes with magnitudes greater than 5 and depths less than 20 km from the fault rupture in western North America from 1940 to 1980. The data are provided in Table 2, where the variable of our interest is the distance of the epicenter of the earthquake (km) from the seismic station. ...
Natural hazards are the extreme events that significantly distress life on Earth. To mitigate the detrimental impacts of these extreme events, it is essential to examine and model them using a probabilistic approach. Probability distributions are competent enough to analyze the exponential behavior and estimate the pattern of randomness in these real-life phenomena. We use the generalized Pareto-exponential distribution (GPED) and find it to be an appropriate model for extreme events that involve exponentially decaying variables. Interestingly, the GPED also comprises the features of both the well-known exponential and Pareto distributions and approaches several other well-known distributions after certain transformations. We derive its various probabilistic characteristics and provide an empirical study for different parametric values to observe their behavior. We follow the maximum likelihood method to estimate the unknown model parameters and conduct a simulation study for different sample sizes and different combinations of the model parameters to examine their stability. We also demonstrate the applicability of our model by using a data set from the field of seismology and establish its better performance by comparing it with some extant distributions.
... 17 PGA measurements from fifty-one, out of sixty-four stations mentioned in the previous section, were considered herein. Two stations were excluded as it was not possible to retrieve recorded data, while eleven stations with Joyner & Boore distance 22 exceeding 200 km were also further ruled out, as beyond the applicability limit of the selected GMPE. Figure 3(A) shows the median PGAs, according to the chosen GMPE (considering normal faulting style for the event), at the sites with damage data used to compute the fragility function (to follow); § the figure also shows the PGAs at the stations in the epicentral region (i.e., some of those in Figure 2B). In other words, it is the geographical representation of the conditional mean vector { } ′ in Equation (8), which is equivalent to a (median) ShakeMap. ...
Calibrating parametric fragility curves via empirical damage data is one of the standard approaches to derive seismic structural vulnerability models. Fragilities based on empirical data require the characterization of the ground motion (GM) intensity at the building sites in the area affected by the earthquake producing the observed damages. This is commonly conducted via ShakeMap, that is, a map of the expected values of a Gaussian random field (GRF) of the logarithms of a GM intensity measure conditional to magnitude, location, and possibly a set of recordings of the earthquake. Once that intensity and damage data at the same sites are available, the typical approach calibrates a two‐parameter fragility model. However, ShakeMap estimates are affected by uncertainty deriving from that of the GM model used to characterize it. Furthermore, such an uncertainty can be reduced by building damage data, which provide information on the shaking intensity at the sites where damage is observed. It is shown herein that if this uncertainty is not addressed, also considering the shaking information provided by damage, the estimates of the fragility parameters obtained using a median ShakeMap only can be biased, and a recommended maximum likelihood estimation procedure – which exploits the expectation maximization algorithm – is provided. These arguments are illustrated via an application considering damage data from the 2009 L'Aquila earthquake in central Italy.
... Therefore, their original rate curve is set to λ a (m a ) = 0∀m a . All earthquakes are assumed to occur at the same location (or very close in space), such that the shortest Joyner-Boore distance (Joyner and Boore, 1981) of each earthquake from the location of interest is R jb = 20 km. ...
In the context of natural hazard risk quantification and modeling of hazard interactions, some literature separates “Level I” (or occurrence) interactions from “Level II” (or consequence) interactions. The Level I interactions occur inherently due to the nature of the hazards, independently of the presence of physical assets. In such cases, one hazard event triggers or modifies the occurrence of another (e.g., flooding due to heavy rain, liquefaction and landslides triggered by an earthquake), thus creating a dependency between the features characterizing such hazard events. They differ from Level II interactions, which instead occur through impacts/consequences on physical assets/components and systems (e.g., accumulation of physical damage or social impacts due to earthquake sequences, landslides due to the earthquake-induced collapse of a retaining structure). Multi-hazard life cycle consequence (LCCon) analysis aims to quantify the consequences (e.g., repair costs, downtime, casualty rates) throughout a system’s service life and should account for both Level I and II interactions. The available literature generally considers Level I interactions – the focus of this study – mainly defining relevant taxonomies, often qualitatively, without providing a computational framework to simulate a sequence of hazard events incorporating the identified interrelations among them. This paper addresses this gap, proposing modeling approaches associated with different types of Level I interactions. It describes a simulation-based method for generating multi-hazard event sets (i.e., a sequence of hazard events and associated features throughout the system’s life cycle) based on the theory of competing Poisson processes. The proposed approach incorporates the different types of interactions in a sequential Monte Carlo sampling method. The method outputs multi-hazard event sets that can be integrated into LCCon frameworks to quantify interacting hazard consequences. An application incorporating several hazard interactions is presented to illustrate the potential of the proposed method.
... The following table summarizes the metadata identifying the 35 ground motions adopted in the analyses. Table 8 Ground motion metadata: identification code of the record, event, date, moment magnitude, Joyner and Boore distance [55], and soil class of the recording station. ...
Seismic structural reliability is typically quantified in terms of the mean annual number of earthquakes causing the structure of interest to exceed, in a single shock, a performance threshold (conventionally referred to as failure). This requires the definition of a hazard curve, which probabilistically characterizes the ground motion intensity at the site of interest, and a fragility curve that provides the failure probability given the ground shaking intensity. Recently, research attempted to account for the possible failure due to subsequent earthquakes, that is, damage accumulation, an issue neglected in the mentioned (classical) approach. To this aim, the so-called state-dependent fragility functions are often used. They provide the probability of getting any intermediate damage condition as a function of the intensity of the earthquake and the damage state of the structure. Fragility functions can also be developed for structural typologies (i.e., matching a given taxonomy), rather than individual structures, for large-scale seismic risk assessment. The presented study developed, in a reproducible manner, state-dependent fragility functions for Italian building typologies derived via back-to-back incremental dynamic analyses of equivalent-single-degree-of-freedom systems. The latter are taken from the outcomes of the SERA project (Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe) and refer to existing reinforced concrete and masonry residential buildings.
... As shown in Figure 1c, GRAPES's GNN passes seismic vectors from a local to regional scale. GRAPES predicts ground motion using a DNN, as opposed to traditional Ground Motion Models (GMMs), which use a set of task-specific features, such as distance from the fault and earthquake magnitude, to predict earthquake shaking (Joyner & Boore, 1981). GRAPES' DNN has an easier task than most GMMs: predict future shaking at each station using a combination of amplitude and phase features at nearby stations ( Figure 1d; Figure S5 in Supporting Information S1). ...
Plain Language Summary
Have you ever heard something through the grapevine? It often takes you by surprise to hear a message from someone other than the original source. You might have felt an earthquake in a similar way: experiencing shaking (the message) at your location rather than movement along a fault (the source). We apply grapevine‐style communication to earthquake early warning (EEW). The goal of EEW is to warn people to prepare for earthquake shaking before damaging seismic waves arrive at their location. We build on recent work that used deep learning and large earthquake data sets to predict earthquake shaking. We developed a deep learning algorithm called GRAPES which predicts shaking in a manner similar to a game of seismic telephone: when a seismic sensor detects shaking, it sends a message to its neighboring sensors, warning them to expect shaking soon. These sensors then pass on the message to their more distant neighbors along the grapevine. We show that the messages GRAPES learned to send between sensors are like seismic status updates: “I'm seeing this type of seismic wave right now”. We applied GRAPES to the 2019 M7.1 Ridgecrest, CA earthquake and it predicted shaking accurately and quickly.
... Rrup, deprem nedeniyle meydana gelen kırık ile çalışma sahası arasındaki mesafe olarak tanımlanırken, Rjb, yani Joyner-Boore mesafesi ise kırığın düzlemdeki izdüşümü ile çalışma sahasındaki mesafe olarak tanımlanmaktadır. Bir diğer tanımlamada Joyner-Boore mesafesi, fay yüzeyine olan en kısa mesafe olarak tanımlanmaktadır [8]. Genel olarak çalışmalara bakıldığında Rrup ile Rjb değerleri eşit kabul edilmektedir [9]. ...
Earthquakes are one of the important natural disasters of our country from past to present. Our country suffered many losses with these earthquakes. On February 6, 2023, a new one was added to these earthquakes. First, a 7.7 Mw magnitude earthquake with the epicenter in Pazarcık occurred at 04:17, and only 9 hours later at 13:24, a 7.6 Mw magnitude earthquake occurred with the epicenter in Elbistan. When we look at the past earthquakes in Turkey and the world, these earthquakes have entered the list of the largest earthquakes in history, both in terms of the region they affected, the structural damage they caused and the loss of life. For this reason, the consequences of the earthquake have gained importance for researchers working in this field in order to minimize the damages in earthquakes that may occur in the future. In order to better explain the reasons for the degree of impact of the affected cities, the distance between the point where the earthquake occurred and the study area must be taken into account accurately. These distances have been defined with many different approaches. The most well-known of these are the distance to the fracture, Joyner-Boore distance, Epicenter distance and Hypocenter distance. This study aimed to evaluate the differences of these distances in terms of their relationship with the peak acceleration values of the measurement stations. In this context, the distribution between peak acceleration values and difference R distances was examined, and the R distance that showed the highest agreement with the acceleration values was determined. It was observed that the highest agreement was between the peak acceleration values and the Joyner-Boore distance, which takes into account the projection on the plane of the fracture. It was determined that this distance value, which is generally accepted as approximately equal to the distance to the fracture, showed higher compliance in this study.
... For developing IPEs from the datasets considered in the present study, we have used the two-stage regression analysis method by Joyner and Boore (1981) (hereafter referred to as TSRA) and a multiple regression analysis (MRA) procedure. TSRA has been used for GMPE development as it decouples the magnitude dependence of the dependent variable from the distance dependence. ...
This study has developed Intensity Prediction Equations (IPEs) for the Himalayas and its sub-regions (divided into North-West Himalaya, Central Himalaya, and North-East Himalaya). For this purpose, intensity data reported in previous studies using traditional methods (like field surveys, media reports, and newspapers) and internet-based questionnaires (such as USGS’s Did You Feel It? or DYFI) were used to catalogue two separate intensity datasets. Intensities of traditional datasets were also reassessed for some earthquake events by different studies in the different scales of assignment, which was homogenized for the same intensity scale. IPEs are derived for both datasets separately using a two-stage and one-stage regression technique. These IPEs are developed for a first- and second-order relation with respect to earthquake magnitude. A “maximum intensity vs. magnitude approximation of the IPE” approach relying on an optimal hypocentral depth has also been proposed to select the best-suited IPEs. The information-theoretic approach-based Log-likelihood method (Scherbaum et al. 2009) has been used to check and compare developed IPE performance for events not used for IPE development. These newly developed equations can be used to assess the damage potential of future earthquakes.
... The ground-motion is validated versus comparison with empirical GMM and in-situ records, in terms of spectral acceleration (SA) and time histories. The SA at periods 1.0 s and 3.0 s is shown in Fig. 5 versus R jb , where R jb is a widely used source-to-site distance in near-fault region, defined as the closest distance to surface projection of fault plane (Joyner and Boore 1981). The stations were placed at a uniform interval of 1.0 km over the whole model surface, and the horizontal component of greater SA was selected for each station. ...
A Mw 6.6 earthquake struck Luding county, in Sichuan province of China on September 5, 2022, causing severe damage of nearby infrastructures. The earthquake indicates an awakening of southeast branch of Xianshuihe fault since the last 1973 Mw 7.6 Luhuo earthquake in Sichuan, thus attracting attention from the public. A physics-based method, combining spectral element method (SEM) and finite element method (FEM), was presented in this paper to investigate the correlation between near-fault motions and response of a road tunnel, which has a closest distance of about 6.0 km to the fault. This method allows to incorporate the rupture details, geological irregularity, 3D velocity structure, as well as the underground tunnel. The ground motions simulated by SEM were validated by comparison to specific station records and empirical ground motion model (GMM), which were subsequently input into the tunnel to obtain its axial deformation and sectional inner forces. Parametric study on tunnel alignment was conducted, and wavelet transformation was used to extract dynamic pulses from the ground motions. The results show that the tunnel response is remarkably affected by dynamic pulse directivity, and the axial forces could be dominated by permanent fault displacement for tunnel of the strike-normal alignment.
... In the earthquake-resistant design of buildings, the change in these ground motions can be determined by the attenuation relationships (Kramer 1996). Attenuation relationships have been developed by many researchers using strong ground motion data, taking into account the geological conditions of the site, the earthquake source mechanism, and the source distance (Joyner and Boore 1981;Campbell 1989;Ambraseys and Bommer 1991;Akkar and Bommer 2007;Abrahamson et al. 2013;Boore et al. 2013;Campbell and Bozorgnia 2013). In this study, the new genera- The database has one of the most comprehensive datasets, including different distance measures, various site characterizations, and earthquake source data (Power et al. 2008). ...
The effect of seismic waves on structures during an earthquake varies depending on local ground conditions. This study is dedicated to determining the seismic site characterization of Kovancılar district in the city of Elazığ, Turkey, whose location is close (5 km) to the East Anatolian Fault Zone (EAFZ), one of the most active fault zones all around globe. For this purpose, 1-D equivalent linear soil behavior analyzes were performed using 28 geotechnical drilling and 20 multi-channel surface wave (MASW) test data in the study area. The results of these analyses indicated the peak ground acceleration (PGA) values in Kovancılar ranged between 0.41 and 0.68 g, while high PGA values were observed in the region of alluvial soils in the south of the district. The acceleration spectra obtained from the analyses on three different locations were compared to the Turkish Building Seismic Regulation 2018 (TBSR 2018) and Eurocode 8 (EC-8 2004) design spectra. For some periods, the acceleration values in the site-specific spectra were observed to exceed the related values in the TBSR 2018 ZC and ZD design spectra. In addition, ground amplification, PGA, and spectral acceleration (Sa) maps with 0.2–1 s periods were created for the study area. With the evaluation of the obtained parameters, the north of the region was established to be more suitable for multi-story buildings, while the northeast, east, and southeast regions being more suitable for low-rise buildings.
... Additionally, the earthquake magnitude provides a useful scale to determine the acceleration values in ground motion models (e.g., Joyner and Boore 1981;Sabetta and Pugliese 1987;Loh et al. 1991;Sadigh et al. 1997;Kayabalı and Akin 2003;Ulusay et al. 2004;Van Eck et al. 2006;Güllü 2012). Therefore, the classification of active faults should include fault-based geological (seismo-tectonic) data together with their field characteristics for estimating earthquake and ground motion parameters, such as maximum Mw and PGA in hazard analyses. ...
The correct estimation of seismic hazards is a touchstone of seismic risk assessments. However, there is no quantitative or standard methodology to include the impacts of geological (i.e., seismo-tectonic) features of active faults or fault zones, and current classification schemes are not useful in hazard evaluations. Therefore, an attempt has been made to develop a methodology that integrates seismo-tectonic parameters of active faults to better inform urban and regional planning decisions. Fault rating system (FRS) provides a comparative review of faults/fault zones using a rating-based approach. In this approach, seven seismo-tectonic parameters are used to classify the fault/fault zone. Each of the seven parameters is assigned a value corresponding to the seismo-tectonic characteristics. The sum of the seven seismo-tectonic parameters is the fault index (FI) value, which lies in the range 0–100. A total of 64 important faults/fault zones were statistically analyzed to determine the best correlations with FI and moment magnitude (Mw) and peak ground acceleration (PGA). It was found that the FI values provide strong correlations with maximum Mw and PGA. It is proposed urban and regional planners use FRS to ensure a consistent approach in characterizing key aspects of active faults in earthquake-prone regions and in estimating ground motion parameters.
Campi Flegrei is a densely populated volcanic area in Italy. Its inner caldera periodically experiences uplift and subsidence, known as bradyseism, also accompanied by seismic activity. In the last decade, with uplift rates up to 2 cm/month, about nine-thousand earthquakes were recorded. Upon request of the local administration, the most updated data were collected and analyzed to evaluate the risk management strategy consisting of structural retrofitting according to the building code. Here it is shown that the reference moment magnitude is in the range , based on fault mapping, geomorphological inference, earthquake relocation, stress-drop analysis, and ground motion modelling. Earthquake forecasting enabled computing the exceedance probabilities of these magnitudes. Earthquake engineering showed that the minimum magnitudes expected to cause exceedance of design ground motion, are larger than the reference magnitudes. Finally, the risk reduction implied by the safety levels of new constructions was assessed for reinforced concrete buildings.
This study presents anovel framework for ground motion modelling utilizing Physics-Guided Symbolic Neural Networks (PGSNN). Symbolic neural networks offer anew method for knowledge discovery, providing aunique perspective for automatically uncovering predictive functional forms from data. This approach differs from traditional methods as itdoes not rely on predefined equations. Instead, itemploys symbolic operators to freely combine input parameters inahigh-dimensional space. This method addresses the problem ofdata imbalance by incorporating physical guidance to ensure that the model produces results that are consistent with established physical principles. The resulting equations align with the expectations of the engineering seismology community, particularly within the magnitude-distance ranges, where classical equations are well calibrated. The prediction performance of the PGSNN, evaluated across different intensity measures (PGA, PGV, and PSA), was assessed by calculating the residuals between measured and predicted values and their standard deviations. The predictive capability ofthis model was verified using new event records. The results indicate that the prediction performance of the PGSNN is comparable to those of traditional methods.
Tehran, the capital of Iran, is widely recognized as one of the world's most earthquake-vulnerable cities. Since there are no recorded ground motions of large earthquakes in the Tehran area, for seismological and earthquake engineering purposes, simulated ground motions may be useful in understanding the earthquake characteristics. On the other hand, ground motion simulation validation is an important and necessary task toward establishing
the efficacy of physics-based ground motion simulations for seismic hazard analysis and earthquake engineering
applications. This article presents a validation of the hybrid broadband ground motion simulation methodology
through simulation of Baladeh 2004 earthquake (Mw 6.2). This earthquake occurred On May 28, 2004, in the
Baladeh region in the North of Iran. This earthquake is remarkable because it was the first instrumentally
recorded large earthquake near Tehran. In this paper, for the first time, we obtain slip distribution on the fault
plane by finite fault inversion based on the neuro-fuzzy finite-fault approach. Next a hybrid broadband simulation
of ground motion recorded during the main shock of the Baladeh earthquake is done. Then a combination
of the finite difference method (0.1–1.0 Hz) and the stochastic finite fault method (1.0–20.0 Hz) is used for
quantifying ground motion values. The validity of the results is checked by some empirical GMPEs, a quantitative
score of Anderson, 2004, and also model bias of Graves and Pitarka (2010).
In this study the seismic hazard in Northern Algeria is analyzed by using a probabilistic approach, and specifically the parametric-historic method. This method enables the incorporation of the entire accessible seismic history into the analysis and effectively addresses both the spatial heterogeneity and temporal variability of the seismicity parameters. The recently compiled earthquake catalog covering the region and spanning the period from 1658 to 2018 was used for estimating the seismicity parameters. The seismic hazard maps in terms of peak ground acceleration (PGA) were calculated for return period of 475 years for rock, stiff soil, and soft soil conditions. The uniform hazard spectra (UHS) for the major cities in Northern Algeria were calculated for the same conditions. The largest PGA values are observed near the cities of Chlef, Algiers, Blida, Medea, and Tipasa. Arguably the most important obtained result is evident in the seismic hazard estimates for the capital city of Algiers, which significantly exceed previously published estimates.
The 6 February 2023 Kahramanmaraş–Türkiye earthquake sequence (M7.8 and M7.6) presents an exceptional opportunity to investigate both the effects of local soil conditions on damage patterns under strong shaking conditions and the performance of building foundations in areas that experienced ground failure. The significant ground failure and structural damage in Adıyaman–Gölbaşı triggered an intensive series of detailed reconnaissance and field surveys. This article aims to present the resulting database of observations on ground failures, building, and foundation performances. The field reconnaissance of ground failures and their effects on building performances involved aerial and walk-down surveys, including high-quality photographs taken across the town. In addition, data on building damage statistics compiled by the Ministry of Environment, Urbanization, and Climate Change were accessed and analyzed. The subsurface characteristics of the town were characterized using available data from pre-earthquake site investigation campaigns employed for town planning purposes. It is concluded that the ground failures in the town primarily resulted from soil liquefaction and cyclic softening. Most of the poor building and foundation performances and ground failures were documented in the northern part of Atatürk Boulevard, closer to the lake of Gölbaşı, where soil site characteristics were unfavorable. This revealed once again the significant effects of local soil site conditions, particularly soil liquefaction, on the intensified ground failures, foundation, and structural damage levels.
Attaining explicit hazard estimates is a challenging task for data sparse regions such as the Peninsular India. Physics based probabilistic seismic hazard analysis (Pb-PSHA) has gained momentum in recent years as a viable solution to this issue. While performing a site-specific analysis in data-sparse regions, instead of incorporating ground motion models (GMMs) from other regions in the hazard methodology, the Pb-PSHA involves obtaining physics-based numerical simulations. In the present study, Pb-PSHA is carried out for the entire southern Peninsular India, with a detailed demonstration for the Kalpakkam site, Tamilnadu. Due to absence of any data on local fault characteristics and past rupture models, simulations are derived using the spectral element method, for several source rupture scenarios. Further, the stochastic seismological model is used to simulate for high frequency (1-100 Hz) ensemble ground motions. Broadband ground motions are then obtained by combining the results from the deterministic model i.e., low frequency (0.01-1 Hz) simulations and the stochastic model. Further, PSHA based on elliptical gridded seismicity is carried out to obtain hazard curves for spectral accelerations. The ensuing uniform hazard response spectra are compared against the outcome of traditional PSHA involving a global GMM. The results indicate that the PGA values obtained from the Pb-PSHA are slightly higher than that of the global GMM-based PSHA.
The Nilüfer district experienced the most recent urbanization among the central districts of Bursa in South Marmara region with the completion of rapid construction. Since 358 BCE, many destructive earthquakes were reported on the branches of the North Anatolian Fault (NAF) which caused extensive damage to buildings and loss of life near Bursa city. Besides some studies conducted to define the soil behavior in the vicinity of Bursa, a seismic hazard study in Nilüfer is still lacking. We, therefore, carried out a microzonation study including the following steps. First, an earthquake hazard analysis was conducted and the peak ground acceleration (PGA) values were determined for an expected earthquake. In the next step, MASW (Multi-Channel Analysis of Surface Wave) measurements conducted at 54 points in 28 neighbourhoods of Nilüfer district were evaluated. Soil mechanical parameters were determined at 11 boreholes to assess the liquefaction potential. It was found that almost half of the study area suffers from low damage considering only the vulnerability index (Kg) index, which depends on the site effect. Therefore, in addition to the Kg values, we created a microzonation map using the results of soil liquefaction, settlement, changes in groundwater level, and the average values of spectral accel- eration. The study area is classified by four damage levels changing from low to high. Using only the Kg index could not quantify the potential damage level in the study area, thus we showed that the districts of Altıns ̧ehir, Hippodrome, Ürünlü and Alaaddinbey, Ertug ̆rul, 29 Ekim, 23 Nisan, Ahmetyesevi and Minareliçavus ̧ were identified at potentially high-risk damage zones. The results of this study clearly showed that considering the Kg index, which depends only on the local site effect, may lead to inadequate damage values.
Post-earthquake safety assessment of buildings and infrastructure poses significant challenges, often relying on time-consuming visual inspections. To expedite this process, safety criteria based on a demand-capacity model are utilized. However, rapid assessment frameworks require accurate estimations of intensity measures (IMs) to estimate seismic demand and assess structural health. Unfortunately, post-earthquake IM values are typically only available at monitored locations equipped with sensors or monitoring systems, limiting broader assessments. Simple spatial interpolation methods, while possible, struggle to consider crucial physical factors such as earthquake magnitude, epicentral distance, and soil type, leading to substantial estimation errors, especially in areas with insufficient or non-uniform seismic station coverage. To address these issues, a novel framework, BN-GMPE, combining a Bayesian network (BN) and a ground motion prediction equation (GMPE), is proposed. BN-GMPE enables inference and prediction under uncertainty, incorporating physical parameters in seismic wave propagation. A further novelty introduced in this work regards separating the near and far seismic fields in the updating process to attain a clearer understanding of uncertainty and more accurate IM estimation. In the proposed approach, a GMPE is employed for the estimation, and the bias and standard deviation of the prediction error are updated after any new information is entered into the network. The proposed method is benchmarked against a classic Kriging interpolator technique, considering some recent earthquake shocks in Italy. The proposed BN framework can naturally extend for estimating the probability of failure of various structures in a targeted region, which represents the ultimate aim of this research.
A Partially linear mixed effects model relating a response Y to predictors (X, Z, T) with the mean function XTβ + Zb + g(T) is considered in this paper. When the parametric parts’ variable X are measured with additive error and there is ill conditioned data suffering from multicollinearity, a new kernel two-parameter prediction method using the kernel ridge and Liu regression approach is suggested. The kernel two parameter estimator of β and the predictor of b are derived by modifying the likelihood and Henderson methods. Matrix mean square error comparisons are calculated. We also demonstrate that under suitable conditions, the resulting estimator of β is asymptotically normal. The situation with an unknown measurement error covariance matrix is handled. A Monte Carlo simulation study, together with an earthquake data example, is compiled to evaluate the effectiveness of the proposed approach at the end of the paper.
Ground motions exhibiting pulse-like (PL) features present a distinct and significant threat to the structural
integrity of constructed environments, due to intense pulse, large amplitude, and rapid energy release. The lack
of recorded PL ground motion data in the Indian region presents a significant challenge for accurate seismic risk
assessment of the built environment. In the absence of recorded PL ground motions, the generation of synthetic
PL ground motions can provide earthquake acceleration time histories for seismic response analysis of structures
and also to evaluate ground motion prediction equations (GMPEs). Within this framework, the modified stochastic finite-fault approach based on the dynamic corner frequency is used to generate the synthetic ground
motions for the 2001 Gujarat earthquake. These artificially generated ground motions are validated using
available peak ground acceleration data from thirteen stations. After validation, the ground motions are
generated at locations equidistant from the fault in all four directions (i.e., east, west, north, south). The expected
acceleration time histories at specific sites, the spatial distribution of ground motion characteristics, and the
effect of site non-linearity are investigated. Based on the geographical positioning of sites for the 2001 event, it
was observed that 65.15 % of ground motions on the western side, relative to the epicenter, exhibited PL
characteristics, whereas 23.64 % of ground motions on the eastern side were observed to have PL properties. The
effect of uncertainty in the model input parameters on the simulated ground motions is examined by performing
a sensitivity analysis. The reliability and validity of the simulated ground motions are assessed by deriving an
empirical equation and compared with the results obtained from available GMPEs for the region.
Ground motion prediction models estimate ground motion intensities using parameters such as earthquake magnitude and fault distance. Gaussian process regression, one of the nonparametric methods, was used in this study to model the attenuation relations of peak ground acceleration (PGA). As an example of the analysis, the dataset of the 2016 Kumamoto earthquake sequence observed by K-NET and KiK-net was applied. The results show that the Gaussian process regression model underestimates the observed values in the near source area. This may be due to the difference in the density of observed values between the far field and the near field. In this paper, an original kernel function was proposed that can reflect the characteristics of seismic ground motion in the near source area. By using the proposed method, it is possible to construct a ground motion prediction model that can express the distribution of ground motion intensity in the whole field from near to far.
We examine how the choice of ground-motion-to-intensity conversion equations (GMICEs) in earthquake early warning (EEW) systems affects resulting alert regions. We find that existing GMICEs can underestimate observed shaking at short rupture distances or overestimate the extent of low-intensity shaking. Updated GMICEs that remove these biases would improve the accuracy of alert regions for the ShakeAlert EEW system for the West Coast of the United States. ShakeAlert uses ground-motion prediction equations (GMPEs), which calculate spatial distributions of peak ground acceleration (PGA) and peak ground velocity (PGV) from earthquake source estimates, combined with GMICEs to translate GMPE output into modified Mercalli intensity (MMI). We find significant epistemic uncertainty in alert distances; near-source MMI estimates from different GMICEs can differ by over 1 MMI unit, and MMI extents used for public EEW alerts can differ by hundreds of kilometers for larger magnitude earthquakes (M ∼6.5+). We use a catalog of “Did You Feel It?” shaking reports to evaluate how well GMICEs predict observed shaking. Our preferred GMICE is the one that computes MMI using PGV for high intensities and transitions to using PGA for nondamaging intensities. These results motivate updating GMICE relationships more generally, including in ShakeMap applications.
Ground-motion models (GMMs) are frequently used in engineering seismology to estimate ground motion intensities. The majority of GMMs predict the response spectral ordinates (such as spectral acceleration) of a single-degree-of-freedom oscillator because of their common application in engineering design practices. Response spectra show how an idealized structure reacts to applied ground motion; however, they do not necessarily represent the physics of ground motion. The functional forms of the response spectra GMMs are built around ideas taken from the Fourier spectral concept. Assuming the validity of Fourier spectral concepts in the response spectral domain could cause physically inexplainable effects. In this study, using a mixed-effects regression technique, we introduce four models capable of predicting the Fourier amplitude spectrum that investigates the impact of incorporating random-effect event and station terms and variations in using a mixed-effects regression technique in one or two steps using truncated dataset or all data (nontruncated dataset). All data consists of 2581 three-component strong ground motion data resulting from 424 events with magnitude ranging from 4.0 up to 7.4, from 1976 to 2020, and 706 stations. The truncated dataset’s records, events, and stations are reduced to 2071, 408, and 636, respectively. As part of this study, we develop GMMs to predict the Fourier amplitude spectrum for the Iranian plateau within the frequency range of 0.3–30 Hz. We adopted simple, functional forms for four models, and we included a limited number of predictors, namely Mw (moment magnitude), Rjb (Joyner–Boore distance), and VS30 (time-averaged shear-wave velocity in the top 30 m). Due to statistical analyses, the style-of-faulting term was excluded from the final functional forms. The robustness of the derived models is indicated by unbiased residual variation with predictor variables.
This work introduces a number of methods for estimating the parameters of the [0,1] Truncated Nadarajah-Haghighi exponential distribution. The percentile method, Cramer von Misses, maximum likelihood, ordinary least square, weighted least square, maximum product spaces, and Anderson darling are a few of these methods. Also, we find the quantile function, survival function, hazard function, cumulative hazard function, and odd function of the distribution, in addition to that, we find the entropy. To find the best method for estimating parameters for the new distribution, a simulation analysis is carried out. Table 3 shows that the new distribution has the highest p-value, indicating a better fit compared to the other distributions. In contrast, the Anderson value (A) and Cramer value (W) and K-S value for the new distribution are the lowest, suggesting a relatively poorer fit compared to the other distributions when fitted. According to Table 5, the new distribution exhibits the lowest values for information criteria such as AIC (Akaike Information Criterion), CAIC (Consistent Akaike Information Criterion), BIC (Bayesian Information Criterion), and HQIC (Hannan-Quinn Information Criterion). This suggests that the new distribution fits the data better than the other distributions being compared.
Ground motion models (GMM) incorporating proper epistemic uncertainty quantification are fundamental for seismic hazard analysis, structural seismic design, and earthquake risk management. However, this critical uncertainty has not been systematically addressed in recently prevalent machine learning (ML)-based GMMs. To rectify this gap, a straightforward and flexible framework based on bootstrapping is proposed for generic ML algorithms. Specifically, a group of datasets are generated through bootstrap resampling, each employed to develop an individual GMM. In the inference phase, the epistemic uncertainty is represented by the prediction samples from this ensemble of models. In case study, the Light Gradient Boosting Machine (LGBM), is applied to establish a GMM on the NGA-West2 database. Overfitting is mitigated by early-stopping, and its implications on uncertainty components and random-effect variability are thoroughly examined. Compared to artificial neural network (ANN) in literature, our work demonstrates a decrease in the standard deviation of inter- and intra-event variability by an average of 0.051 and 0.140, respectively. Moreover, our model adeptly captures the heteroscedasticity of epistemic uncertainty, particularly over different regions and within the range of the metadata with limited data. The significance of epistemic uncertainty is highlighted by its potential to diminish the statistical significance of seismic scaling effects at short-period pseudo spectral acceleration (PSA) for great events and at rock sites.
Site amplification is an important component of strong ground motion prediction as it differs among sites, reflecting its specific local subsurface geology. Here, we confirm that site amplifications are similar in a neighborhood area over a long period. However, few studies have investigated the spatial properties in a wide region (i.e., the whole of Japan). In this study, we explored the spatial properties of site amplifications based on the generalized inversion technique (GIT) using Fourier amplitude spectra (FAS) as well as pseudo-velocity response spectra (pSv) as the latter is an important index for engineering purposes and the most similar type of response spectra to FAS. The spatial distributions of S-wave site amplifications (SA-S), especially within large sediment basins (e.g., the Kanto and Osaka Basins in Japan), were found to be relatively similar in proximate areas for a long period ranging from 2 to 8 s. This suggests that we could easily predict the site amplifications using an empirical approach through spatial interpolation based on the properties obtained by the GIT. Furthermore, we propose a prediction procedure for site amplification for the whole duration from the SA-S at an arbitrary site. We used the correction function, which converts the SA-S to the site amplification for the whole duration (SA-W), including an S-wave portion and a subsequent portion. This function is called the whole-duration to S-wave spectral ratio (WSR) and is stable in terms of spatial properties. As we could estimate the SA-S either by theoretical transfer functions or observed microtremors, we can easily predict the SA-W based on the proposed WSR concept. We found that SA-S in pSv is more or less similar to SA-S in FAS, however, SA-W in pSv fails to capture the effects of the long duration of ground motions inside a large basin so that we cannot recommend to use pSv for the prediction of whole duration of ground motion.
On August 1, 1975, a magnitude 5.9 (mb) earthquake occurred approximately 8 km SSE of the town of Oroville, California. This earthquake and its associated foreshock-aftershock sequence are of particular interest because of their possible relation to the impounding of the 4.3 billion m3 Lake Oroville. Hypocenter locations for 336 aftershocks that occurred during August define a fault plane striking N3°E and dipping 60° to the west to a depth of 10 km. Dimensions of the epicentral area are approximately 7 km in an east-west direction by 15 km in a north-south direction. The fault plane passes beneath Oroville Dam at 5-km depth, and if projected up dip, would crop out beneath the reservoir to the east. The distribution in space and time of foreshocks and aftershocks suggests that rupture began at depth and progressed up dip and to the north and south.
Recordings from five strong-motion accelerograph stations have been used to derive a three-dimensional dislocation model for the Parkfield Earthquake. The model consists of a buried fault which extends from a depth of 3 km to a depth of 9 km below the ground surface. It appears from the analysis, which considers various fault lengths, that the zone of significant faulting was the 20-km-long northwestern section of the fault. The rupture velocity has been found to be between 2.4 and 2.5 km/sec and the dislocation amplitudes have been found to be about 120 cm. There have been comparisons made of the model results with geodetic data on static deformations and creep measurements following the event. In contrast with several other source mechanism studies of the Parkfield event, this model yields a picture which appears to be very consistent with both the dynamic strong-motion measurements as well as the available geodetic and creep data.
The pattern of energy release during the Imperial Valley, California, earth- quake of 1940 is studied by analyzing the El Centro strong motion seismograph record and records from the Tinemaha seismograph station, 546 km from the epicenter. The earthquake was a multiple event sequence with at least 4 events recorded at El Centro in the first 25 seconds, followed by 9 events recorded in the next 5 minutes. Clear P~ S, and surface waves were observed on the strong motion record. Although the main part of the earthquake energy was released during the first 15 seconds, some of the later events were as large as M = 5.8 and thus are important for earthquake engineering studies. The moment calcu- lated using Fourier analysis of surface waves agrees with the moment estimated from field measurements of fault offset after the earthquake. The earthquake engineering significance of the complex pattern of energy release is discussed. It is concluded that a cumulative increase in amplitudes of building vibration re- sulting from the present sequence of shocks would be significant only for struc- tures with relatively long natural period of vibration. However, progressive weak- ening effects may also lead to greater damage for multiple event earthquakes.
The Imperial Valley earthquake was a multiple sequence (Trifunac and Brune, 1970) with at least four events occurring during the main energy release. These four events, recorded on the strong-motion seismograph in El Centro, located about 10 km NW from the instrumentally determined epicenter, and nine after- shocks recorded in the next 5 rain are re-examined in this paper to test an approxi- mate source theory (Brune, 1970). This theory predicts the shape of the body-wave spectra in terms of the seismic moment and stress drop. By fitting theoretical spectra to the spectra calculated from the strong-motion accelerogram, moment and stress drop can be estimated for each of the multiple events. Inasmuch as the average displacements at the fault and the source dimensions can be derived from the known moment and stress drop, the pattern of average displacements along the fault was computed from the instrumental records. A test of the theory, then, consists of comparing the fault displacements derived from seismograms with the fault displacements observed at the surface (Buwalda, unpublished field notes). For the Imperial Valley earthquake, agreement between these two independent methods of measurement is good, suggesting that the above theory is an adequate first approximation for the spectra of body waves. The stress drop variations along the fault, inferred also from the above theory, indicate two areas of major stress concentration located near the northwestern and southeastern ends of the disloca- tion. The stress drops for various events varied from about ten to several hundred bars.
The exact Cagniard-de Hoop solutions for a point dislocation in half-space are used to construct models of the strong ground motion observed during the February 9, 1971 San Fernando earthquake (M_L = 6.4). By summing point dislocations distributed over the fault plane, three-dimensional models of a finite fault located in a half-space are constructed to study the ground motions observed at JPL (Pasadena), Palmdale, Lake Hughes, and Pacoima Dam. Since the duration of faulting is comparable to the travel times for various wave types, very complex interference of these arrivals makes a detailed interpretation of these wave forms difficult. By investigating the motion due to small sections of the fault, it is possible to understand how various wave types interfere to produce the motion due to the total fault. Rayleigh waves as well as S to P head waves are shown to be important effects of the free surface. Near-field source effects are also quite dramatic. Strong directivity is required to explain the difference in amplitudes seen between stations to the north and stations to the south. Faulting appears to have begun north of Pacoima at a depth of 13 km. The rupture velocity, which is near 2.8 km/sec in the hypocentral region, appears to slow to 1.8 km/sec at a depth of 5 km. Displacements on the deeper sections of the fault are about 2.5 m. Fault offsets become very small at depths near 4 km and then grow again to 5 m near the surface rupture. The large velocity pulse seen at Pacoima is a far-field shear wave which is enhanced by directivity. Peak accelerations at Pacoima are probably associated with the large shallow faulting. The total moment is 1.4 × 10^(26) ergs.
A reanalysis of the available data for the 1966 Parkfield, California, earthquake (ML=512) suggests that although the ground breakage and aftershocks extended about 40 km along the San Andreas Fault, the initial dynamic rupture was only 20 to 25 km in length. The foreshocks and the point of initiation of the main event locate at a small bend in the mapped trace of the fault. Detailed analysis of the P-wave first motions from these events at the Gold Hill station, 20 km southeast, indicates that the bend in the fault extends to depth and apparently represents a physical discontinuity on the fault plane. Other evidence suggests that this discontinuity plays an important part in the recurrence of similar magnitude 5 to 6 earthquakes at Parkfield.
Analysis of the strong-motion records suggests that the rupture stopped at another discontinuity in the fault plane, an en-echelon offset near Gold Hill that lies at the boundary on the San Andreas Fault between the zone of aseismic slip and the locked zone on which the great 1857 earthquake occurred. Foreshocks to the 1857 earthquake occurred in this area (Sieh, 1978), and the epicenter of the main shock may have coincided with the offset zone. If it did, a detailed study of the geological and geophysical character of the region might be rewarding in terms of understanding how and why great earthquakes initiate where they do.
Analyses of peak amplitudes of strong earthquake ground motion have been carried out with the emphasis on their dependence on earthquake magnitude, epicentral distance, and geological conditions at the recording site. Approximate empirical scaling functions have been developed which, for a selected confidence level, yield an estimate of an upper bound of peak accelerations, velocities, and displacements. The parameters in these scaling functions have been computed by least-squares fitting of the recorded data on peak amplitudes which are now available for a range of epicentral distances between about 20 and 200 km and are representative for the period from 1933 to 1971 in the Western United States.
The possibility of extrapolating the derived scaling laws to small epicentral distances where no strong-motion data are currently available has been tested by comparing predicted peak amplitudes with related parameters at the earthquake source. These source parameters (average dislocation and stress drop) can be derived from other independent studies and do not contradict the inferences presented in this paper. It has been found that for an approximate 90 per cent confidence level the presently available data suggest that peak accelerations, velocities, and displacements at the fault and for the frequency band between 0.07 and 25 Hz probably do not exceed about 3 to 5 g, 400 to 700 cm/sec, and 200 to 400 cm, respectively.
The logarithms of the peaks of strong ground motion seem to depend in a linear manner on earthquake magnitude only for small shocks. For large magnitudes this dependence disappears gradually and maximum amplitudes may be achieved for M ≈ 7.5. The influence of geological conditions at the recording site appears to be insignificant for peak accelerations but becomes progressively more important for peaks of strong-motion velocity and displacement.
At 19h00m09.46s UTC, on 24 January 1980, a strong earthquake (ML = 5.5) that caused a surprising amount of damage occurred north of Livermore Valley about 12 km to the southeast of Mt. Diablo, and was associated with surface rupture along the Greenville Fault. There was a foreshock (ML = 2.7) a minute and a half earlier and a sequence of 59 events (ML ≧ 2.5) in the ensuing 6 days. On 27 January at 02h33m35.96s, a larger magnitude earthquake occurred in the sequence (ML = 5.6). This second principal shock was located 14 km to the south of the first principal earthquake toward the southern end of the Greenville Fault. Preliminary estimates of the seismic moments of the two principal shocks are 5.3 × 1024 and 1.3 × 1024 dyne-cm, respectively. In addition to the lower seismic moment, the ML = 5.6 shock on 27 January exhibits a clearly focused radiation pattern, with large amplitudes toward the northeast.
Field investigations after the first principal shock indicated surfaced rupture along the Greenville fault zone for at least 6 km, with both right-lateral strike-slip and some dip-slip motion with the northeast side up. Variable offsets on surface cracks suggested displacements of a few centimeters (with evidence of increases in some places after the second 27 January earthquake). There were eight earthquakes with ML ≧ 4.0 in the sequence up to 5 February 1980. No foreshocks near the Greenville Fault (ML ≧ 1.5) were observed by the University of California Seismographic Stations in the prior 3 months.
Rapid deployment of field seismographs by a number of seismological organizations permitted precise locations and fault-plane solutions. Some results on seismicity are as follows.
The rupture propagated over 15 km to the southeast along the Marsh Creek-Greenville faults on 24 January and stopped in the vicinity of Highway 580. This southern progression may have had some causal connection with the relatively high intensities reported near the southwest end of the Greenville Fault. The two principal shocks of the sequence have slight but significant differences in the fault-plane solutions; both are predominantly right-lateral strike-slip, but the strike of the northern one is N13°W, whereas the strike of the southern one is N39°W. This change in strike is not evident in the mapped strikes of the Marsh Creek and the Greenville faults. In contrast to the second principal earthquake, the first principal shock was followed by two others (ML > 4.0) in rapid succession, one 53 sec and the other 97 sec after. This repetition gave a relatively long duration to the shaking on 24 January, and was commented on in felt reports. It may explain the greater intensity reported in many localities on 24 January compared to 27 January. The b value (0.64 ± 0.13) for the sequence is somewhat lower than the b = 0.70 ± 0.17 for the recent Coyote Lake earthquake sequence on the Calaveras Fault on 5 August 1979. There are fewer earthquakes than normal in the range 3.0 < ML < 4.0 in the Greenville sequence.
Fault parameters of the Ms 7.1 St. Elias, Alaska, earthquake of February 28, 1979, are determined from an analysis of P-wave first motions, fundamental-mode surface waves, and aftershock data. The preferred P-wave nodal plane has a shallow (12°) angle of dip and indicates underthrusting in a northerly (N13°W) direction, which is also close to the azimuth (N8°W) of the deviatoric compression (P) vector. Aftershock activity during the 24-hr interval immediately following the main shock extends over an area of 3200 km2, which is taken to represent the fault area of the main shock. Because aftershock activity outlines a fault area with nonrectangular geometry, fault length (50 to 80 km) and width (50 to 65 km) are not well defined. Estimates of focal depth from aftershock activity fall in the range 10 to 20 km, which surface-wave analysis is unable to restrict further. For the main shock, seismic moment, Mo, is 2.5 × 1027 dyne-cm (0.25 × 1021 N.m) and average dislocation, 2 meters. Average rupture velocity falls in the range 2.5 to 3 km/sec. Apparent stress, ησ, is 5 bars (0.5 MPa) and stress drop, Δσ, 35 bars (3.5 MPa). These values are considered typical of large-magnitude interplate earthquakes.
Improved hypocentral locations have been obtained for the San Fernando earthquake and its larger aftershocks through the use of data from portable stations installed in and around the aftershock area subsequent to the main shock. The main shock, at 14 00 41.8 GMT on 9 February 1971, is now assigned a magnitude (M_L) of 6.4 and a location at 34° 24.7' N, 118° 24.0' W, h = 8.4 km. Fifty-five aftershocks of magnitude 4.0 and greater had occurred through 31 December 1971. The lunate-shaped epicentral distribution of aftershocks is consistent with the idea of southward thrusting along a disc-shaped fault surface, and aftershock depths as well as aftershock focal mechanisms suggest that the thrust surface dips about 35° toward N 20° E. However, a distinct linear alignment of left-lateral strike-slip aftershocks parallel to the motion direction near the west boundary of activity suggests that the fault surface has a steep flexure along this line, down-stepped to the west, and both the planar distribution of aftershocks and the local geology support this concept.
The earthquake sequence of late February and March 1972 involved movement along the San Andreas fault and within the crustal wedge enclosed by the branching San Andreas and San Benito faults near Bear Valley, San Benito County, California. Activity was mainly confined to three distinct zones of strike-slip faulting: the short north-trending aftershock zone of the M 3.5 earthquake of February 22, 1972, the aftershock zone of the M 5.0 Bear Valley earthquake of February 24, 1972 located along the San Andreas fault, and the west-trending aftershock zone of the M 4.6 earthquake of February 27, 1972. The north-trending and west-trending zones lie between the two major splays of the branching fault system. Focal mechanism solutions from events in these zones are consistent with the transfer of horizontal, dextral displacement from the San Andreas fault to the San Benito, Paicines and Calaveras faults within the Bear Valley region. During the 18 months preceding the February 1972 sequence, the hypocentral regions of both the M 5.0 and M 4.6 shocks were characterized by concentrations of small earthquakes. Aftershock source areas of these two events progressively expanded during the course of the aftershock sequence. Estimates of the mainshock rupture surface for these events based on the distribution of aftershocks range over a factor of 4 owing to the irregular distribution of aftershocks and the rapid growth of the aftershock zone.
A comprehensive spectral analysis of Love and Rayleigh waves was made on the Parkfield earthquake of June 28, 1966. Using tentative Q values obtained by the usual two-station method for continental and oceanic paths, the observed spectra were corrected for dissipation, and used for obtaining a tentative source model. The resultant model, having the fault length 37 km, the strike direction N43°W and the rupture velocity 2.2 km/sec, is consistent with various near field measurements.
Based on this tentative source model, a least-squares method is applied to separate source, dissipation and interference effects on the spectra. The logarithm of the ratio of the observed to the theoretical spectra was plotted against the epicentral distance for various frequencies. The slope and zero-crossing value of the fitted straight line were used for revising the attenuation coefficient and the seismic moment respectively. The variability of individual station spectra was attributed to the interference effect. The revised value of the seismic moment of the Parkfield earthquake is e (0.33±0.40) ×10 25 dyne-cm. The revised attenuation coefficients indicate that Love waves have consistently higher dissipation than Rayleigh waves at periods 15 to 40 seconds. Both show marked minimum of dissipation (Q over 800 for Love and over 1000 for Rayleigh waves) at periods between 20 and 25 seconds.
We found that our Q data are consistent with a model which has a high-Q zone in the lower crust and uppermost mantle, overlying a low-Q zone which correlates well with the Gutenberg low-velocity zone. There is an indication that the intrinsic Q is dependent on period at depths shallower than 90 kilometers in such a way that it increases with period up to 20 seconds. For periods beyond 20 seconds, the intrinsic Q may be constant for all periods and all depths above 90 kilometers.
Strong motion data from western North America for earthquakes of magnitude greater than 5 are examined to provide the basis for estimating peak acceleration, velocity, displacement, and duration as a function of distance for three magnitude classes. A subset of the data (from the San Fernando earthquake) is used to assess the effects of structural size and of geologic site conditions on peak motions recorded at the base of structures. Small but statistically significant differences are observed in peak values of horizontal acceleration, velocity and displacement recorded on soil at the base of small structures compared with values recorded at the base of large structures. Some consideration is given to the prediction of ground motions at close distances where there are insufficient recorded data points. As might be expected from the lack of data, published relations for predicting peak horizontal acceleration give widely divergent estimates at close distances. Refs.
Teleseismic determinations of body-wave (P, S) spectra, interpreted in terms of the Brune (1970) seismic-source model, are used to estimate the parameters seismic moment (M_o) and source dimension (r) for three large, shallow, strike-slip earthquakes occurring on nearly vertical fault planes and for which the same parameters can be determined from field (F) data. These earthquakes are (1) the Borrego Mountain, California, earthquake (April 9, 1968) for which [M̅_o(P) = 10, M̅_o(S) = 6.6, and M_o(F) = 3.6] × 10^(25) dyne-cm and [r̅(p) = 14, r̅(S) = 23, and L/2(F) = 17] km; (2) the Mudurnu Valley, Turkey, earthquake (July 22, 1967) for which [M̅_o(P) = 9.1, M̅_o(S) = 8.5, and M_o(F) = 7.4] × 10^(26) dyne-cm, and [r̅(P) = 39, r̅(S) = 48, and L/2(F) = 40] km; and (3) the Dasht-e-Bayāz, Iran, earthquake (August 31, 1968) for which [M̅_o(P) = 4.8, M̅_o(S) = 8.6, and M_o(F) = 18] × 10^(26) dyne-cm, and [r̅(P) = S1, r̅(S) = 48, and L/2(F) = 40] km. The Brune (1970) model is well-calibrated with respect to the determination of these parameters for the earthquakes considered. A minimum estimate for the radiated energy can be expressed in terms of M_o and r; this estimate is low by a factor of 10 with respect to the estimate obtained from energy-magnitude relations for these three earthquakes. The stress drops of these events are of the order of 10 bars.
A method is presented for determining the local magnitude, M_L, from records from seismoscopes and similar instruments. The technique extrapolates the maximum response of the standard Wood-Anderson seismograph, which determines M_L, from the maximum response of the seismoscope. The standard deviation of the steady-state response of an oscillator subjected to white noise excitation is used to derive a relation correcting for the different periods, dampings, and gains of the two instruments. The accuracy of the method is verified by application to data from the San Fernando and Parkfield earthquakes wherein both accelerograph and seismoscope records are available from the same sites. The accelerograms are used to synthesize Wood-Anderson responses whose maxima are compared to those extrapolated from the seismoscope data. In both earthquakes, the average magnitudes and standard deviations determined by the two approaches are very nearly equal.
The method is then applied to the strong-motion data from the Managua, Nicaragua earthquake of December 23, 1972 (M_S = 6.2, mb = 5.6). A value of M_L = 6.2 is indicated from the seismoscope and accelerograph data. The next application is to the Guatemala earthquake of February 4, 1976 (M_S = 7.5, mb = 5.8). The only seismic instrumentation available for determining M_L is a seismoscope record from Guatemala City, which indicates M_L = 6.9 when a representative distance of about 35 km is used. As a final example, the records obtained during the 1906 San Francisco earthquake Formula from the Ewing duplex pendulum seismograph at Carson City, Nevada and the simple pendulum at Yountville, California are analyzed. After restoring the Carson City instrument, its period and damping were determined experimentally as were the period and damping of a similar instrument in the London Science Museum. On the basis of the strong-motion records from Carson City and Yountville, it is estimated that the local magnitude of the 1906 earthquake lies in the range Formula to 7.
The use of seismoscope data further extends the instrumental base from which M_L can be determined and allows the rapid determination of M_L in earthquakes where seismoscope data are available. The applications in this study provide further instrumental evidence for the saturation of M_L in the 7 to Formula range, with the value of 7.2 for the Kern County earthquake of 1952, the largest so far determined.
The ML 5.1 Santa Barbara earthquake of August 13, 1978, occurred at 34o22.2'N., long. 119o43.0'4km south of Santa Barbara, California, at a depth of 12.5km in the northeast Santa Barbara Channel, part of the western Transverse Ranges geomorphic-structural province. This part of the province is characterized by seismically active, east-trending reverse faults and rates of coastal uplift that have averaged up to about 10m/1000 yr over the last 45 000 yr. No surface rupture was detected onshore. Subsurface rupture propagated northwest from the main shock toward Goleta, 15km west of Santa Barbara, where a maximum acceleration of 0.44 g was measured at ground level and extensive minor damage occurred; only minor injuries were reported. A fairly well constrained fault plane solution of the main shock and distribution of the aftershocks indicate that left-reverse-oblique slip occurred on west-northwest-trending, north-dipping reverse faults; inadequate dip control precludes good correlation with any one of several mapped faults.-Authors
Long-period teleseismic P and S waves from the WWSS and Canadian networks are modeled to determine the focal parameters for the main shock in the Oroville earthquake series. Using the techniques of P first motions, wave-form synthesis, and phase identification, the focal parameters are determined as follows: dip 65°; rake −70°; strike 180°; depth 5.5 ± 1.5km; moment 5.7 ± 2.0 × 10^(24) dyne-cm; and a symmetric triangular time function 3 sec in duration. This is a north-south striking, westward dipping, normal fault with a small component of left-lateral motion. The time separation between the small foreshock and mainshock appears to be 6.5 sec at teleseismic distances, rather than 8.1 sec as observed at short distances.
The relationships among spectral velocity for 0. 5 hz and 1. 0 hz frequencies, peak ground acceleration, and peak ground velocity of earthquake-induced ground motion are investigated using the horizontal components of motion from 70 California strong-motion records and accounting for event size, source-to-site distance, and geologic conditions at the recording site. These strong motion records indicate that the estimation of intermediate-frequency spectral response using ground acceleration and typical design spectra is unconservative for a large, distant event (magnitude-8 plus , 120-km epicentral distance) by a factor of about 2 to 6, depending on the site geology. Ground velocity can be used to estimate intermediate frequency spectral response; however, expected spectral response will exceed these estimates during the motion from large, distant events by a factor of about 1. 4 to 2. 5. Because of the large variabilities associated with strong motion data, these results are tentative.
The ML 6.0 Point Mugu, California earthquake of February 21, 1973 and its aftershocks occurred within the complex fault system that bounds the southern front of the Transverse Ranges province of southern California. P-wave fault plane solutions for 51 events include reverse, strike slip and normal faulting mechanisms, indicating complex deformation within the 10-km broad fault zone. Hypocenters of 141 aftershocks fail to delineate any single fault plane clearly associated with the main shock rupture. Most aftershocks cluster in a region 5 km in diameter centered 5 km from the main shock hypocenter and well beyond the extent of fault rupture estimated from analysis of body-wave radiation. Strain release within the imbricate fault zone was controlled by slip on preexisting planes of weakness under the influence of a NE-SW compressive stress.
At 1705 UTC on August 6, 1979, a strong earthquake (ML = 5.9) occurred along the Calaveras fault zone south of Coyote Lake about 110 km southeast of San Francisco. This strong earthquake had an aftershock sequence of 31 events (2.4 ≦ ML ≦ 4.4) during August 1979. No foreshocks (ML ≧ 1.5) were observed in the 3 months prior to the main shock.
The local magnitude (ML = 5.9) and the seismic moment (Mo = 6 × 1024 dyne-cm from the SH pulse) for the main shock were determined from the 100 × torsion and 3-component ultra-long period seismographs located at Berkeley. Local magnitudes are determined for the aftershocks from the maximum trace amplitudes on the Wood-Anderson torsion seismograms recorded at Berkeley (Δ ≊ 110 km).
Temporal and spatial characteristics of the aftershock sequence are presented and discussed. Some key observations are: (1) the first six aftershocks (ML ≧ 2.4) proceed along the fault zone progressively to the south of the main shock; (2) all of the aftershocks (ML ≧ 2.4) to the south of the largest aftershock (ML = 4.4) have a different focal mechanism than the aftershocks to the north; (3) no aftershocks (ML ≧ 2.4) were observed significantly to the north of the main shock for the first 5 days of the sequence; and (4) the b-value (0.70 ± 0.17) for the aftershock sequence is not significantly different from the average b-value (0.88 ± 0.08) calculated for the Calaveras fault zone from 16 yr of data.
The characteristics of the Parkfield, California earthquake sequence of 1966 are presented. Historically, the epicentral region is one of the three most seismic areas along the San Andreas fault in central California. It is characterized, however, by a relatively high incidence of large earthquakes in proportion to smaller shocks, compared to other active zones. The 1966 sequence occurred in an area where measured deformation across the fault for 1959-1965 shows a decrease from about 2 cm/year to the north to zero to the south of the area. Neither micro-earthquake nor normal seismic activity prior to the sequence gave indication of its coming. Seismicity before the sequence was confined to the north of the active zone, with some indication of convergence of foci toward the location of the initial shocks. The early aftershock distribution extended 20 km south of the main shock; cracking occurred to 33 km south of the main shock; and intense aftershock activity for the entire sequence extended 27 km south of the main shock. At least 95 per cent of the earthquakes, including the three largest, have P-wave radiation patterns consistent with right lateral transcurrent motion on the San Andreas fault. Earthquakes of the sequence fall very closely along the fault trace. About 75 per cent of the total strain release for the sequence can be accounted for by earthquakes in the main shock region, the principal shock (M = 5.5) contributing only 25 per cent of the total. The sequence is characterized by a high incidence of large aftershocks, an extensive area of aftershock activity, and average focal depths near 5 km-three properties apparently related, and distinguishing two types of sequence traits in central California.
Starting with geological data, this paper estimates the seismicity for applica-tions in seismic risk studies. The rate at which seismic moment is released can be estimated on a fault when the slip rate is known. It can also be estimated in a region of crustal convergence (without subduction) or divergence when the rate at which opposite sides of the zone are converging or the regional strain rate is known. Then, provided all of the deformation is released seismically, by assuming the relative frequency of different sizes of earthquakes, the absolute frequency of events can be obtained. The procedure is used to estimate seismicity in southern California. A review of geological literature has provided preliminary estimates of slip rates on many important faults. The estimates of the seismicity resulting from these slip rates are consistent with historical records of earthquake occurrences for southern California taken as a whole. For smaller regions or individual faults in southern California, the seismicity estimated from slip rates may differ from historical rates of seismicity by a factor of two or more. In the western basin and range region, the historical seismicity is also consistent with an estimate for the strain rate. Because of this agreement in larger regions, where many faults are involved, it is inferred that the geological data is also useful for studies of smaller regions, even though on this scale the model cannot be tested because of the too short historical record of earthquake occurrences.
The frequency of occurrence of earthquakes with different seismic moments is expressed in terms of the rate of slip on a fault and to the largest seismic moment likely to occur in the region. Beginning from the Gutenberg-Richter empirical expression relating the relative recurrence of events with different magnitudes and using another empirical relation between magnitude and seismic moment, the relative number of events with seismic moment greater than or equal to M0 is given by N(Mo) = aMo -B, fl can be determined from parameters in these empirical expressions. From average rates of slip on faults, this expression can be used to give the recurrence rates for events of different seismic moment: a --(1 -fl)Mo~fMo ~ax'-~ where Mo max is the maximum possible seismic moment in a region, and Mo ~ is the average rate of occurrence of the seismic moment. On a fault of area A, with shear modulus/L, and long-term average rate of slip ~, Mo ~ =/~A¢. A similar expression can be given for a for regions where deformation is distributed over a broad area without a major throughgoing fault. Using rates of convergence at island arcs determined from plate motions for the last 5 m.y., the calculated frequency of occurrence of earthquakes with large seismic moments agrees well with the historic record. At present, uncertainties in the requisite parameters and in assumptions on which the recurrence relation is based, however, make such an approach only marginally better than reliance on the historic record alone. With more data constraining fl, the largest possible seismic moments, the role of fault creep, and long-term rates of slip or defor-mation, however, this approach to seismic risk should be a more reliable predictor of recurrence rates than the existing historic record. As an example, the formulas are applied to the southeastern Caribbean.
This is a study of source characteristics of 13 earthquakes with magnitudes between 2.4 and 5.1 located near the San Andreas fault in central California. On the basis of hypocentral locations and fault-plane solutions the earthquakes separate into two source groups, one group clearly related to the throughgoing northwest-trending San Andreas fault zone and the other apparently associated with generally north-trending bifurcations such as the Calaveras fault. The basic data consist of broad-band recordings (0.03 to 10 Hz) of these earthquakes at two sites of the San Andreas Geophysical Observatory (SAGO). Epicentral distances range between 2 and 40 km, and maximum ground displacements from 4 to 4000 microns were recorded. The whole-record spectra computed from the seismograms lend themselves to source parameter studies in that they can be interpreted in terms of low-frequency level, corner frequency, and high-frequency slope. Synthetic seismograms have also been used to estimate source parameters in both the time domain and frequency domain, and the results compare favorably with those estimated directly from the spectra. The influences of tilts and non-linear response of the seismometer were considered in the interpretation of the low frequencies. Seismic source moments estimated from the low-frequency levels of the spectra show a linear dependence on magnitude with a slope slightly greater than 1. The geology at the recording site can contribute an uncertainty factor of at least 3 to the estimated moments. Observed corner frequencies are only weakly dependent on magnitude. Interpreted in terms of source dimension, these corner frequencies imply values of 1 to 2 km for the earthquakes of this study. The corner frequencies may also be interpreted in terms of the rise time of the source function, yielding values in the range 0.5 to 1.0 sec. The data indicate that the earthquakes of this study are all surprisingly similar in their fundamental source parameters, with only the seismic moment showing a strong dependence on magnitude.
At least four events were recorded at El Centro in the first 25 sec, followed by nine events recorded in the next 5 min. Clear P, S, and surface waves were observed on the strong motion record. Although the main part of the earthquake energy was released during the first 15 sec, some of the later events as large as M equals 5. 8. It is concluded that a cumulative increase in amplitudes of building vibration resulting from the present sequence of shocks would be significant only for structures with relatively long natural period of vibration. Progressive weakening may lead to greater damage.
A technique is presented for determination of local magnitude, M_L, from strong-motion accelerograms. The accelerograph records are used as an acceleration input to the equation of motion of the Wood-Anderson torsion seismograph to produce a synthetic seismogram which is then read in the standard manner. When applied to 14 records from the San Fernando earthquake, the resulting M_L is 6.35, with a standard deviation of 0.26. This is in good agreement with the previously reported value of 6.3. The technique is also applied to other earthquakes in the western United States for which strong-motion records are available. An average value of M_L = 7.2 is obtained for the 1952 Kern County earthquake; this number is significantly smaller than the commonly used value of 7.7, which is more nearly a surface-wave magnitude.
The method presented broadens the base from which M_L can be found and allows M_L to be determined in large earthquakes for which no standard assessment of local magnitude is possible. In addition, in instances where a large number of accelerograms are available, reliable values of M_L can be determined by averaging.
A summary of accelerograms recovered from the Geological Survey's National Strong Motion Network during the period January 1 through April 30, 1979 is given. Also described is strong motion insturmentation in Imperial Valley, California. The seismicity of this region has been characterized by both earthquake swarms as well as mainshock-aftershock activity. Summaries of recent reports include information on earthquakes at Milford Sound, New Zealand; Santa Barbara, California; Bishop, California; St. Elias, Alaska; and Monte Negro, Yugoslavia. The availibility of strong-motion information data reports, digitalized data, and additional information pertinent to strong-motion programs is presented.
As has long been recognized in teleseismic studies, smooth rupture propa- gation significantly modifies the azimuthal variation in elastic wave radiation and introduces a dependence of peak motion on the ratio of rupture velocity to wave propagation velocity. Rupture propagation also has a first-order effect on the ground motions close to faults as calculated from models of coherent rupture. For engineering purposes, it is important to know whether the effect occurs only with coherent ruptures, or whether it is a more general phenomena of propagat- ing faults. This question was examined by both analytical and Monte Carlo studies of models of nonuniform ruptures. The principal models were defined by ruptures moving continuously in time along the fault with random variations in rupture velocity or in slip amplitude. These models were richer in high frequen- cies than the corresponding smooth ruptures. The randomness introduced a new corner into the spectrum at a frequency that is simply related to the coherence length of the random variations and to the azimuth between the fault and station. The lower frequency corner due to the overall rupture was pre- served. For the model with varying rupture velocity the azimuthal variation in spectral amplitude was enhanced over that for the smooth rupture. For the model with varying slip the azimuthal variation was the same as for a smooth rupture. These models showed directivity effects as strong or stronger than the corresponding smooth rupture, providing that the average rupture velocity was the same. Monte Carlo simulations with statistical models gave peak amplitudes with the same general dependence on rupture velocity as the peak amplitudes from smooth ruptures although in the mean the peak motions were enhanced in the incoherent model. An analytic expression was also derived for the mean spectrum of an extreme model in which rupture occurred in little patches distributed with complete randomness over the fault surface and in time. Even this model showed some effects of directivity. The results of our study are consistent with the interpretation that rupture propagation produces destructive interference in the radiated motion; incoherence reduces this interference and in general leads to higher peak motions and spectral levels.
A straightforward method for computing rates of slip from earthquakes in major fault zones is presented. The slip rate is calculated from the sum of moments for the earthquakes. Rates obtained are in approximate agreement with rates obtained from geodetic measurements or magnetic anomalies, provided that long time samples are considered and provided that adjustments are made in the vertical extent of the zone of earthquake generation. For some fault zones, particularly deep island arc shear zones, strain is perhaps being relieved by steady creep, whereas, in other fault zones, e.g., the San Andreas, strain is accumulating for a large earthquake. The zone of earthquake generation for oceanic transform faults may be as little as 5 km in vertical extent.
The seismic moment (M0) of an earthquake is a more consistent and more physical measure of source strength than magnitude (M) or strain release (see pdf for formula), and this measure of source strength is determined for 47 of the larger earthquakes occurring in the Southern California region since 1857. Most of the seismic moments are obtained by conventional seismological means, but a relationship between M0 and the areal distribution of Intensity VI (AVI) is developed and scaled to estimate M0 when intensity data are available but instrumental data are not. This relationship is log M0 = 1.97 log AVI - 2.55. For the region as a whole, earthquakes at the threshold of M0 ≥ 1025, ≥1026, and ≥1027 dyne-cm have occurred once every 3, 8, and 25 yr, respectively. The spatial occurrence of the five largest earthquakes (M0 ≥ 1 × 1027 dyne-cm) is not limited to a particular geologic province, mode of tectonic accommodation, or geographic locality. It is unlikely that this data set can reliably predict long-term spatial and temporal patterns of the M0 ≥ 1025 dyne-cm seismicity of the Southern California region.
Recent measurements of Qbeta-1 of S waves in the lithosphere for frequency range from 0.02 to 25 Hz show a remarkable frequency dependence and systematic variation from place to place depending on the current tectonic activity. In order to test the hypothesis that the attenuation of S waves may be caused by the loss of energy by scattering due to heterogeneity, the amplitudes of S and coda waves were measured simultaneously for 900 local earthquakes in the central Japan for various frequency bands. The data were interpreted using the S to S single-scattering theory for coda waves, which is now supported by the observed agreement between Q of coda and Qbeta, and also by the observed identical local site effect on coda and S waves. The result shows that the loss of energy from S waves required to explain coda amplitudes agrees with the attenuation of S waves within the uncertainty of measurements. This conclusion is supported by several recent studies on Q of coda, Q of Lg, Abeta, and coda excitation by other workers.
Measurements of peak ground velocity v and acceleration a for earthquakes and mine tremors, with local magnitudes ranging from -0.8 to 6.4, have been analyzed in terms of a model of inhomogeneous faulting. The fault model involves the failure of a circular 'asperity' of radius ri surrounded by a previously faulted annular region of outer radius r0. The failure of the asperity results in seismic radiation with a characteristic frequency proportional to 1/r0 followed by lower-frequency radiation, proportional to 1/r1, as static equilibrium is regained over the larger region. For r0/ri>>1 both v and a are associated primarily with the failure of the asperity but also depend on the large-scale source parameters. Specifically, v = (betaDeltataur0/muR)(0.10r0/ri+ 0.15), and a = (Deltatau/rhoR)[0.30(r0/ri)2+0.45], where beta is the shear wave velocity, Deltatau is the overall stress drop, mu is the modulus of rigidity, and rho is density. The terms involving r0/ri correspond to the high-frequency radiation associated with the failure of the asperity, and the other terms indicate the peak parameters due to the broad-scale readjustment. Observations of peak ground motion for events with seismic moments ranging from 5×1016 dyn cm indicate that r0/ri is normally in the range of 1-10 and appears to be independent of earthquake size. The inhomogeneous fault model also yields convenient expressions for the small-scale displacement and stress drop of the asperity failure as well as for the level of regional stress available to cause slip.
The nearly conincident forms of the relations between seismic moment Mo and the magnitudes ML, Ms, and Mw imply a moment magnitude scale M=2/3 log Mo-10.7 which is uniformly valid for 3
Synthetic seisomograms constructed by addition of surface-wave modes in a layered half-space are compared to Cagniard-de Hoop calculations of Heaton and Helmberger (1977, 1978) and to ground displacement recordings near El Centro, California to examine the applicability of modal superposition as a means of simulating ground motion of possible engineering interest. Modal solutions of flat earth problems are desirable because of the modest cost involved and the versatility of the method in simulating extended sources and anelastic damping. P-SV and SH motions can be computed with almost equal ease. The comparisons show that in sedimentary structures surface waves can dominate ground displacement motion at epicentral distances of only a few source depths. Superposition of the higher modes often approximates quite well impulsive arrivals with analogies to refracted and reflected rays. Ground displacement recordings of El Centro from the 1968 Borrego Moun- tain earthquake are modeled using a multi-layered geological structure and a source model based on independent studies. The gross character of the records appears to be insensitive to the details of the source. Both point sources and propagating sources with horizontal dimensions larger than half the epicentral distance give'reasonable fits to the observed transverse motion. This insensitiv- ity appears to be due to a complex interaction between rupture propagation and the surface-wave dispersion. By using the integrated El Centro accelerogram, which may have more reliable amplitude information than the Carder displace- ment record used in other studies, the moment is estimated to be 12 x 102s dyne-cm. This is similar to values found from studies of teleseismic data.
Strong-motion data from earthquakes of western North America are examined to provide the basis for estimating peak acceleration, velocity, and displacement as a function of distance for three magnitude classes, 5.0 to 5.7, 6.0 to 6.4, and 7.1 to 7.6. Analysis of a subset of the data from the San Fernando earthquake shows that small but statistically significant differences exist between peak values of horizontal acceleration, velocity, and displacement recorded on soil at the base of small structures and values recorded at the base of large structures. The peak acceleration tends to be less and the peak velocity and displacement to be greater at the base of large structures than at the base of small structures. In the distance range used in the regression analysis (15 to 100 km), the values of peak horizontal acceleration recorded at soil sites in the San Fernando earthquake are not significantly different from the values recorded at rock sites, but values of peak horizontal velocity and displacement are significantly greater at sol