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Tall buildings and flexible structures require a better characterization of long period ground motion spectra than the one provided by current seismic building codes. Motivated by that, a methodology is proposed and tested to improve recorded and synthetic ground motions which are consistent with the observed co-seismic displacement field obtained from interferometric synthetic aperture radar (InSAR) analysis of image data for the Tocopilla 2007 earthquake (Mw=7.7) in Northern Chile. A methodology is proposed to correct the observed motions such that, after double integration, they are coherent with the local value of the residual displacement. Synthetic records are generated by using a stochastic finite-fault model coupled with a long period pulse to capture the long period fling effect.It is observed that the proposed co-seismic correction yields records with more accurate long-period spectral components as compared with regular correction schemes such as acausal filtering. These signals provide an estimate for the velocity and displacement spectra, which are essential for tall-building design. Furthermore, hints are provided as to the shape of long-period spectra for seismic zones prone to large co-seismic displacements such as the Nazca-South American zone.

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... Thus, we do not aim to recover real displacements in this work and provide displacements traces for referential use only. Some works were able to match the observed residual InSAR displacements (e.g., Abell et al., 2011;Fortuño et al., 2014), but this is not feasible for an entire database at the moment. ...

Since the 1985 M 8.0 central Chile earthquake, national strong-motion seismic networks have recorded ten megathrust earthquakes with magnitudes greater than M 7.5 at the convergent margin, defined by the contact between the Nazca and South American plates. The analysis of these earthquake records have led to improved hazard analyses and design codes for conventional and seismically protected structures. Although strong-motion baseline correction is required for a meaningful interpretation of these records, correction methods have not been applied consistently in time. The inconsistencies between correction methods have been neglected in the practical use of these records in practice. Consequently, this work aims to provide a new strong-motion database for researchers and engineers, which has been processed by traceable and consistent data processing techniques. The record database comes from three uncorrected strong motion Chilean databases. All the records are corrected using a four-step novel methodology, which detects the P-wave arrival and introduces a baseline correction based on the reversible-jump Markov chain Monte Carlo method. The resulting strong motion database has more than 2000 events from 1985 to the date, and it is available to download at the Simulation Based Earthquake Risk and Resilience of Interdependent Systems and Networks (SIBER-RISK) project website.

... Some initial steps toward this analysis have been taken on previous research (e.g. Abell et al. 2011;Aguirre et al. 2017). Figure 2 shows a schematic representation that summarizes the methodology followed in this study. ...

This research performs a sensitivity analysis of response spectrum values for various physical earthquake parameters, which are used to generate synthetic seismograms consistent with the expected seismicity in north Chile. Sensitivity analyses are based on the earthquake scenario and slip distribution model of the 2014, Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 8.1 Pisagua earthquake, and seven other physically plausible interplate events for north Chile. A finite-fault rupture model, and slip distribution of the Pisagua earthquake, were obtained using inversion of InSAR and GPS data. Three other rupture models based on previous studies of interplate locking for north Chile and capable of generating Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 8.3–8.6 earthquakes with an estimated maximum slip of 9.2 m, were incorporated in the analyses. Also, four additional scenarios with moment magnitudes in the range Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 8.6–8.9 were generated by concatenating these physical scenarios into larger rupture areas within the north segment. Using these scenarios, synthetic ground motions were built at four observation sites: Pisagua, Iquique, Tocopilla, and Calama. Response sensitivity was studied for three key rupture parameters: mean rupture velocity, slip rise-time, and rupture directivity. Responses selected were peak ground displacement (PGD), spectral pseudo-velocities, Sv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_v$$\end{document}, and spectral displacements, Sd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_d$$\end{document}. First and second order variations of PGD, Sv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_v$$\end{document}, and Sd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_d$$\end{document} relative to the source parameters were computed and used together with a Taylor series expansion to propagate uncertainty into the responses as a function of vr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_r$$\end{document} and rise-time tr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_r$$\end{document}. To study the effect of rupture directivity, three different foci locations were considered for each scenario: north, south, and at the centroid of the slip model. Response PGD values show no clear trends with rupture velocity, vr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_r$$\end{document}; however, the variability increases as the system period increases. The effect of the slip rise-time is significant, and as tr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_r$$\end{document} increases, the spectral responses tend to decrease, suggesting that shorter slip rise-times lead to higher seismic demands in long period structures. The results obtained for the directivity analysis suggest that two factors control the expected waveforms and spectral responses: first, the direction of the rupture relative to the location of each site, and the hypocentral distance.

... EXSIM has been used to model major earthquakes in India (Nath et al. 2012; Chopra et al. 2010; Nath et al. 2009), China (Wang 2010; Wang and Xie 2009), Japan (Zhao and Xu 2012; Macias 2008), Italy (Ugurhan et al. 2012; Ameri et al. 2011; Castro et al. 2008), Turkey (Yalcinkaya et al. 2012; Ugurhan and Askan 2010), Cascadia subduction zone (Macias et al. 2008), California (Assatourians and Atkinson 2007), eastern North America (Atkinson and Boore 2006), Iran (Hamzehloo and Mahood 2012; Zafarani et al. 2012; Motazedian 2006), Portugal (Zonno et al. 2010), Mexico (Rodriguez-Perez et al. 2012), and Puerto Rico (Motazedian and Atkinson 2005b). The EXSIM program has also been used to develop time histories for engineering applications (Estevao and Oliveira 2012; Atkinson et al. 2011; Abell et al. 2011; Atkinson 2009). Other developments have been included in EXSIM, including the ability to model variable stress distribution along a fault (Assatourians and Atkinson 2007 ). ...

Stochastic finite-fault modeling is an important tool for simulating moderate to large earthquakes. It has proven to be useful in applications that require a reliable estimation of ground motions, mostly in the spectral frequency range of 1 to 10 Hz, which is the range of most interest to engineers. However, since there can be little resemblance between the low-frequency spectra of large and small earthquakes, this portion can be difficult to simulate using stochastic finite-fault techniques. This paper introduces two different methods to scale low-frequency spectra for stochastic finite-fault modeling. One method multiplies the subfault source spectrum by an empirical function. This function has three parameters to scale the low-frequency spectra: the level of scaling and the start and end frequencies of the taper. This empirical function adjusts the earthquake spectra only between the desired frequencies, conserving seismic moment in the simulated spectra. The other method is an empirical low-frequency coefficient that is added to the subfault corner frequency. This new parameter changes the ratio between high and low frequencies. For each simulation, the entire earthquake spectra is adjusted, which may result in the seismic moment not being conserved for a simulated earthquake. These low-frequency scaling methods were used to reproduce recorded earthquake spectra from several earthquakes recorded in the Pacific Earthquake Engineering Research Center (PEER) Next Generation Attenuation Models (NGA) database. There were two methods of determining the stochastic parameters of best fit for each earthquake: a general residual analysis and an earthquake-specific residual analysis. Both methods resulted in comparable values for stress drop and the low-frequency scaling parameters; however, the earthquake-specific residual analysis obtained a more accurate distribution of the averaged residuals.

When subjected to long‐period ground motions, many existing high‐rise buildings constructed on plains with soft, deep sediment layers experience severe lateral deflection, caused by the resonance between the long‐period natural frequency of the building and the long‐period ground motions, even if they are far from the epicenter. This was the case for a number of buildings in Tokyo, Nagoya, and Osaka affected by the ground motions produced by the 2011 off the Pacific coast of Tohoku earthquake in Japan. Oil‐dampers are commonly used to improve the seismic performance of existing high‐rise buildings subjected to long‐period ground motion. This paper proposes a simple but accurate analytical method of predicting the seismic performance of high‐rise buildings retrofitted with oil‐dampers installed inside and/or outside of the frames. The method extends the authors' previous one‐dimensional theory to a more general method that is applicable to buildings with internal and external oil‐dampers installed in an arbitrary story. The accuracy of the proposed method is demonstrated through numerical calculations using a model of a high‐rise building with and without internal and external oil‐dampers. The proposed method is effective in the preliminary stages of improving the seismic performance of high‐rise buildings.

Conventional acceleration records do not properly account for the observed coseismic ground displacements, thus leading to an inaccurate definition of the seismic demand needed for the design of flexible (long period) structures. Large coseismic displacements observed during the 27 February 2010 Maule earthquake suggest that this effect should be included in the design of flexible structures by modifying the design ground motions and spectra considered. Consequently, Green's functions are used herein to compute synthetic low-frequency seismograms that are consistent with the coseismic displacement field obtained from interferometry using synthetic aperture radar (SAR) images. In this case, the coseismic displacement field was determined by interfering twenty SAR images of the Advanced Land Observation Satellite (ALOS)/PALSAR satellite taken between 12 October 2007 and 28 May 2010. These images cover the region affected by the 2010 M-w 8.8 Maule earthquake. Synthetic broadband seismograms are built by superimposing the low-pass filtered synthetic low-frequency seismograms with high-frequency strong-motion data. The broadband seismograms generated are then consistent with the coseismic displacement field and the high-frequency content of the earthquake. A sensitivity analysis is performed using three different fault and slip parameters, the rupture velocity, the corner frequency, and the slip rise time. Results show that the optimal corner frequency of the low-pass filter f(c) = 1/T-c, leads to a trade-off between acceleration and displacement accuracy. Furthermore, spectral response for long periods, say T >= 8 s, is relatively insensitive to the value of T-c, whereas shorter periods are strongly dependent on both the slip rise time and T-c. In general, larger displacements consistent with coseismic data are obtained using this technique instead of digitally processing the acceleration ground-motion records.

We present a methodology for generating broadband (0 -10 Hz) ground motion time histories for moderate and larger crustal earthquakes. Our hybrid technique combines a stochastic approach at high frequencies with a deterministic approach at low frequencies. The broadband response is obtained by summing the separate responses in the time domain using matched filters centered at 1 Hz. We use a kinematic description of fault rupture, incorporating spatial heterogeneity in slip, rupture velocity and rise time by discretizing an extended finite-fault into a number of smaller subfaults. The stochastic approach sums the response for each subfault assuming a random phase, an omega-squared source spectrum and generic ray-path Green's functions. Gross impedance effects are incorporated using quarter wavelength theory to bring the response to a reference baserock velocity level. The deterministic approach sums the response for many point sources distributed across each subfault. Wave propagation at frequencies below 1 Hz is modeled using a 3D viscoelastic finite difference algorithm with the minimum shear wave velocity set between 600 and 1000 m/s, depending on the scope and complexity of the velocity structure. To account for site-specific geologic conditions, short-and mid-period empirical amplification factors provided by Borcherdt [1] are used to develop frequency-dependent non-linear site response functions. The amplification functions are applied to the stochastic and deterministic responses separately since these may have different (computational) reference site velocities. We note that although the amplification factors are strictly defined for response spectra, we have applied them to the Fourier amplitude spectra of our simulated time histories. This process appears to be justified because the amplification functions vary slowly with frequency and the method produces favorable comparisons with observations. We demonstrate the applicability of the technique by modeling the broadband strong ground motion recordings from the 1989 Loma Prieta and 1994 Northridge earthquakes.

The specific barrier model, proposed and developed by Papageorgiou and Aki (1983a,b; 1985) provides the most complete, yet parsimonious, self-consistent description of the faulting process. It applies both in the "near-fault" and in the "far-field" region, thus allowing for consistent ground-motion simulations over the entire frequency range and for all distances of engineering interest. The model has been implemented in the stochastic method and calibrated with extended databases of response spectral amplitudes from earthquakes of intraplate regions (mainly eastern North America events), interplate regions, and regions of tectonic extension (Spudich et al., 1999, database). The ensemble average value of a key parameter of the specific barrier model, the local stress drop ΔσL, is ∼161 bars for interplate earthquakes, ∼114 bars for extensional regime earthquakes, and ∼180 bars for intraplate earthquakes. The high-frequency source spectral levels of interplate and extensional regime earthquakes deviate significantly from self-similar scaling. The deviation is most likely caused by the "effective" source area and/or irregularities in the rupture kinematics. We account for their overall effects through a high-frequency source complexity factor, ζ, in the source spectrum of the specific barrier model. As a result, inter- and intraplate source spectra show similar high-frequency levels at moderate magnitudes but intraplate earthquakes have higher spectral levels at the larger magnitudes. The interplate soil residuals show clear signs of nonlinear site response, whereas only slight signs of such nonlinearity are observed for the extensional dataset. The regional models calibrated in this study are in reasonably good agreement with other regional attenuation relationships and provide a reliable and physically realistic, yet computationally efficient, way to model strong ground motions with implications for seismic hazard and risk analysis.

Retrieving displacement from seismic acceleration records is often difficult because unknown small baseline offsets in the acceleration time series will contaminate the doubly integrated record with large quadratic errors. One-hertz Global Positioning System (GPS) position estimates and collocated seismic data are available from the 2003 M-W 8 Tokachi-Oki (Hokkaido) earthquake. After a process of correcting for possible misorientation of the seismic sensors, an inversion method is used to simultaneously solve for ground displacement with both data sets as input constraints. This inversion method takes into account the presence of unknown offsets in the acceleration record, and the relatively large uncertainties in the estimated 1-Hz GPS positions. In this study, 117 channels of seismic data were analyzed. Only 5% of the time does the static displacement retrieved from traditional baseline correction processing without GPS information agree with the absolute displacement measured with 1-Hz GPS to within the errors of the GPS data. In solving simultaneously for constrained displacements that agree with both the seismic and GPS data sets, an optimal solution was found that included only one- or two-step functions in the acceleration records. Potential explanations for the offsets are analyzed in terms of tilt of the sensor or electronic noise. For nine stations, clear misorientations of the seismic sensors of more than 20 deg from the reported orientation were found. For this size event, the 30-sec sampled GPS solutions were also a sufficient constraint for establishing the offset errors and recovering reliable displacements. The results significantly extend the frequency band over which accelerometer data are reliable for source inversion studies.

This paper describes refinements to the hybrid broadband ground-motion simulation methodology of Graves and Pitarka (2004), which combines a deterministic approach at low frequencies (f < 1 Hz) with a semistochastic approach at high frequencies (f > 1 Hz). In our approach, fault rupture is represented kinematically and incorporates spatial heterogeneity in slip, rupture speed, and rise time. The prescribed slip distribution is constrained to follow an inverse wavenumber-squared fall-off and the average rupture speed is set at 80% of the local shear-wave velocity, which is then adjusted such that the rupture propagates faster in regions of high slip and slower in regions of low slip. We use a Kostrov-like slip-rate function having a rise time proportional to the square root of slip, with the average rise time across the entire fault constrained empirically. Recent observations from large surface rupturing earthquakes indicate a reduction of rupture propagation speed and lengthening of rise time in the near surface, which we model by applying a 70% reduction of the rupture speed and increasing the rise time by a factor of 2 in a zone extending from the surface to a depth of 5 km. We demonstrate the fidelity of the technique by modeling the strong-motion recordings from the Imperial Valley, Loma Prieta, Landers, and Northridge earthquakes.

We use Interferometric Synthetic Aperture Radar (InSAR) data to derive continuous maps for three orthogonal components of the co-seismic surface displacement field due to the 1999 Mw7.1 Hector Mine earthquake in southern California. Vertical and horizontal displacements are both predominantly antisymmetric with respect to the fault plane, consistent with predictions of linear elastic models of deformation for a strike-slip fault. Some deviations from symmetry apparent in the surface displacement data may result from complexity in the fault geometry.

We use a combination of satellite radar and GPS data to estimate the slip distribution of the 1999 Mw 7.1 Hector Mine Earthquake, a right-lateral strikeslip earthquake that occurred on a northwest–southeast striking fault in
the southern California Mojave Desert. The data include synthetic aperture radar interferograms (InSAR) from both ascending
and descending orbits, radar amplitude image offset fields (SARIO) for both ascending and descending azimuth directions, and
campaign GPS observations from 55 stations provided by Agnew et al. (2002). We model the fault with nine segments derived from the field-mapped fault rupture, the SARIO data, and aftershock locations.
We first estimate the dip of each fault segment, as well as a single constant strike-slip component across each segment, resulting
in an average dip of 83° to the northeast and slip of up to 5.6 m. Then, we fix the optimal fault segment dip, discretize
the fault segments into 1.5 km × 1.5 km patches, and solve for the variable slip distribution using a nonnegative least-squares
method that includes an appropriate degree of smoothing. Our preferred solution has both right-lateral strike-slip and reverse
faulting. The estimated geodetic moment is 5.93 × 1019 N m (Mw 7.1), similar to seismological estimates, indicating that there are insignificant interseismic and postseismic deformation
signals in the data. We find strike-slip displacements of up to 6.0 m and reverse faulting of up to 1.6 m, with the maximum
slip located just northwest of the epicenter. Most of the slip is concentrated northwest and south of the epicenter; little
slip is found on the northeastern branch of the fault. The SARIO data and our modeling indicate that the amount and extent
of surface fault rupture were underestimated in the field.

A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms representing deformations in an infinite medium, a term related to surface deformation and that is multiplied by the depth of observation point. Several practical suggestions to avoid mathematical singularities and computational instabilities are also presented. The expressions derived here represent power- ful tools both for the observational and theoretical analyses of static field changes associated with earthquake and volcanic phenomena.

We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.

The coseismic deformation due to the 1992 Mw7.3 Landers earthquake, southern California, is investigated using synthetic aperture radar (SAR) and Global Positioning System (GPS) measurements. The ERS-1 satellite data from the ascending and descending orbits are used to generate contiguous maps of three orthogonal components (east, north, up) of the coseismic surface displacement field. The coseismic displacement field exhibits symmetries with respect to the rupture plane that are suggestive of a linear relationship between stress and strain in the crust. Interferometric synthetic aperture radar (InSAR) data show small-scale deformation on nearby faults of the Eastern California Shear Zone. Some of these faults (in particular, the Calico, Rodman, and Pinto Mountain faults) were also subsequently strained by the 1999 Mw7.1 Hector Mine earthquake. I test the hypothesis that the anomalous fault strain represents essentially an elastic response of kilometer-scale compliant fault zones to stressing by nearby earthquakes [Fialko et al., 2002]. The coseismic stress perturbations due to the Landers earthquake are computed using a slip model derived from inversions of the InSAR and GPS data. Calculations are performed for both homogeneous and transversely isotropic half-space models. The compliant zone model that best explains the deformation on the Calico and Pinto Mountain faults due to the Hector Mine earthquake successfully predicts the coseismic displacements on these faults induced by the Landers earthquake. Deformation on the Calico and Pinto Mountain faults implies about a factor of 2 reduction in the effective shear modulus within the ∼2 km wide fault zones. The depth extent of the low-rigidity zones is poorly constrained but is likely in excess of a few kilometers. The same type of structure is able to explain high gradients in the radar line of sight displacements observed on other faults adjacent to the Landers rupture. In particular, the Lenwood fault north of the Soggy Lake has likely experienced a few centimeters of left-lateral motion across

Westdahl volcano, located at the west end of Unimak Island in the central Aleutian volcanic arc, Alaska, is a broad shield that produced moderate-sized eruptions in 1964, 1978–79, and 1991–92. Satellite radar interferometry detected about 17 cm of volcano-wide inflation from September 1993 to October 1998. Multiple independent interferograms reveal that the deformation rate has not been steady; more inflation occurred from 1993 to 1995 than from 1995 to 1998. Numerical modeling indicates that a source located about 9 km beneath the center of the volcano inflated by about 0.05 km³ from 1993 to 1998. On the basis of the timing and volume of recent eruptions at Westdahl and the fact that it has been inflating for more than 5 years, the next eruption can be expected within the next several years.

The slip distribution of the Mw 7.7 Tocopilla earthquake was obtained from the joint inversion of teleseismic and strong-motion data. Rupture occurred as underthrusting at the base of the seismically coupled plate interface, mainly between 35 and 50 km depth. From the hypocenter, located below the coast 25 km south of the town of Tocopilla, the rupture propagated 50 km northward and 100 km southward. Overall, the slip distribution was dominated by two slip patches, one near the hypo- center and the other 70 km to the south where slip reached its maximum value (3 m). An additional branch of moderate slip propagated at shallower depth toward the west near the northern tip of the Mejillones peninsula. Rupture velocity remained close to 2:8 km=sec, with a total rupture duration of 45 sec. The first 2 weeks of aftershocks located with a local seismic network display a strong correlation with the slip distri- bution. The 2007 rupture ended below the Mejillones peninsula, where the 1995 An- tofagasta rupture also ended (Ruegg et al., 1996; Delouis et al., 1997; Pritchard et al., 2006). This corroborates the role of barrier played by this structure. The downdip end of the seismically coupled zone at 50 km depth, evidenced by previous studies for the 1995 event, is also confirmed. The 2007 Tocopilla earthquake contributed only mod- erately to the rupturing of the great northern Chile seismic gap, which still has the capacity for generating a much larger underthrusting event.

A hybrid deterministic-stochastic method (DSM) is developed to cal-culate synthetic time series of ground accelerations radiated from an extended source. The main goal of the proposed methodology is to include in the classical point-source stochastic method (PSSM) the effects of the rupture propagation on a finite fault. This purpose is achieved through two important modifications of the PSSM technique. First, the envelope does not have a predetermined functional form; rather, it is calculated deterministically following the isochron formulation with a kinematic rupture model. Second, we have generalized the various parameters of the point-source ground motion spectrum to account for the extended fault: corner frequency, distance from the fault, and radiation pattern are evaluated through the kinematic modeling. The guiding principal in all these modifications has been to develop a robust methodology capable of capturing the complexity of near-source ground mo-tion even when input information about earthquake source, propagation medium, and site characteristics are of a very schematic nature. We show that the synthetic envelope contains the required information on the rupture process on extended fault, such as directivity effects and azimuthal variations depending on the source-to-receiver geometry. The method's capability is demon-strated by modeling strong ground motions of the 1992 M w 7.3 Landers, California, earthquake and comparing them with the recorded accelerograms, which are clearly affected by directivity effects. The proposed technique reproduces the main charac-teristics of strong-motion recordings, and can be implemented using only a limited number of parameters to describe the source (dimension and geometry), the propa-gation medium (wave velocities and layers), and the site effects (transfer function). These characteristics are important for a methodology aimed to simulate ground-shaking scenarios for which a more complete description of the faulting process is not available.

Residual displacements for large earthquakes can sometimes be deter-mined from recordings on modern digital instruments, but baseline offsets of un-known origin make it difficult in many cases to do so. To recover the residual dis-placement, we suggest tailoring a correction scheme by studying the character of the velocity obtained by integration of zeroth-order-corrected acceleration and then see-ing if the residual displacements are stable when the various parameters in the par-ticular correction scheme are varied. For many seismological and engineering pur-poses, however, the residual displacements are of lesser importance than ground motions at periods less than about 20 sec. These ground motions are often recoverable with simple baseline correction and low-cut filtering. In this largely empirical study, we illustrate the consequences of various correction schemes, drawing primarily from digital recordings of the 1999 Hector Mine, California, earthquake. We show that with simple processing the displacement waveforms for this event are very similar for stations separated by as much as 20 km. We also show that a strong pulse on the transverse component was radiated from the Hector Mine earthquake and propagated with little distortion to distances exceeding 170 km; this pulse leads to large response spectral amplitudes around 10 sec.

Three-dimensional finite-difference (3D-FD) simulations of earthquake wave propagations in the Yanhuai area were performed for the 1720 Shacheng earthquake (Ms 7.0) using a stochastic finite-fault model, running on a parallel supercomputer Hitachi-SR8000 (http://www.lrz-muenchen.de). A stochastic finite-fault model was implemented into the 3D-FD program. The basic idea of the stochastic finite-fault model is that the fault plane can be subdivided into several subfaults (or elements, sources). Radiation from a large earthquake is the sum of contributions from all subfaults with proper time delays, each of which acts as a small independent double-couple point source. Heterogeneity of the fault rupture process was modeled by randomizing the location of initial rupture (hypocenter), slip vectors (slip, rake), and rise-times of subfaults in this study. A 3D velocity model of the Yanhuai area was constructed based on studies that analyzed available geological and geophysical information. A grid increment of 75 m in three directions was used in the 3D-FD simulation, which made it possible to capture the short period information with a resolution as low as 0.5 s in sediment regions. The uncertainties of simulated results caused by the stochastic finite-fault model were studied with a homogeneous 3D model. We found that the effects of the randomness of source on simulated ground motions are only limited in near-fault-region including the surface exposure of the fault and its vicinities, which occupies about 5% of the whole study area. This article presents an integrated approach for simulating the strong ground motions for engineering purpose using the 3D-FD method. Such simulations would be useful for hazard mapping, land using planning, insurance rate assessment, particularly in planning, preparedness, and coordinating emergency response, which must be based on realistic situations induced by concrete (historic or scenario) earthquakes.

We use interferometric synthetic aperture radar, GPS, and teleseismic data to constrain the relative location of coseismic slip from 11 earthquakes on the subduction interface in northern Chile (23°–25°S) between the years 1993 and 2000. We invert body wave waveforms and geodetic data both jointly and separately for the four largest earthquakes during this time period (1993 M_w 6.8; 1995 M_w 8.1; 1996 M_w 6.7; 1998 M_w 7.1). While the location of slip in the teleseismic-only, geodetic-only, and joint slip inversions is similar for the small earthquakes, there are differences for the 1995 M_w 8.1 event, probably related to nonuniqueness of models that fit the teleseismic data. There is a consistent mislocation of the Harvard centroid moment tensor locations of many of the 6 < M_w < 8 earthquakes by 30–50 km toward the trench. For all models, the teleseismic data are better able to resolve fine details of the earthquake slip distribution. The 1995 earthquake did not rupture to the maximum depth of the seismogenic zone (as defined by the other earthquakes). In addition to the above events, we use only teleseismic data to determine the rupture characteristics of four other M_w > 6 earthquakes, as well as three M_w > 7 events from the 1980s. All of these earthquakes appear to rupture different portions of the fault interface and do not rerupture a limited number of asperities.

We present a map of the coseimic displacement field resulting from the Landers, California, June 28, 1992, earthquake derived using data acquired from an orbiting high-resolution radar system. We achieve results more accurate than previous space studies and similar in accuracy to those obtained by conventional field survey techniques. Data from the ERS 1 synthetic aperture radar instrument acquired in April, July, and August 1992 are used to generate a high-resolution, wide area map of the displacements. The data represent the motion in the direction of the radar line of sight to centimeter level precision of each 30-m resolution element in a 113 km by 90 km image. Our coseismic displacement contour map gives a lobed pattern consistent with theoretical models of the displacement field from the earthquake. Fine structure observed as displacement tiling in regions several kilometers from the fault appears to be the result of local surface fracturing. Comparison of these data with Global Positioning System and electronic distance measurement survey data yield a correlation of 0.96; thus the radar measurements are a means to extend the point measurements acquired by traditional techniques to an area map format. The technique we use is (1) more automatic, (2) more precise, and (3) better validated than previous similar applications of differential radar interferometry. Since we require only remotely sensed satellite data with no additioanl requirements for ancillary information. the technique is well suited for global seismic monitoring and analysis.

The Yellowstone caldera, in the western United States, formed approximately 640,000 years ago when an explosive eruption ejected approximately 1,000 km3 of material. It is the youngest of a series of large calderas that formed during sequential cataclysmic eruptions that began approximately 16 million years ago in eastern Oregon and northern Nevada. The Yellowstone caldera was largely buried by rhyolite lava flows during eruptions that occurred from approximately 150,000 to approximately 70,000 years ago. Since the last eruption, Yellowstone has remained restless, with high seismicity, continuing uplift/subsidence episodes with movements of approximately 70 cm historically to several metres since the Pleistocene epoch, and intense hydrothermal activity. Here we present observations of a new mode of surface deformation in Yellowstone, based on radar interferometry observations from the European Space Agency ERS-2 satellite. We infer that the observed pattern of uplift and subsidence results from variations in the movement of molten basalt into and out of the Yellowstone volcanic system.

This paper presents the results of a blind experiment that is performed using two pairs of dihedral reflectors. The aim of the experiment was to demonstrate that interferometric synthetic aperture radar (InSAR) measurements can indeed allow a displacement time series estimation with submillimeter accuracy (both in horizontal and vertical directions), provided that the data are properly processed and the impact of in situ as well as atmospheric effects is minimized. One pair of dihedral reflectors was moved a few millimeters between SAR acquisitions, in the vertical and east-west (EW) directions, and the ground truth was compared with the InSAR data. The experiment was designed to allow a multiplatform and multigeometry analysis, i.e., each reflector was carefully pointed in order to be visible in both Envisat and Radarsat acquisitions. Moreover, two pairs of reflectors were used to allow the combination of data gathered along ascending and descending orbits. The standard deviation of the error is 0.75 mm in the vertical direction and 0.58 mm in the horizontal (EW) direction. GPS data were also collected during this experiment in order to cross-check the SAR results

Synthetic aperture radar interferometry is an imaging technique
for measuring the topography of a surface, its changes over time, and
other changes in the detailed characteristic of the surface. By
exploiting the phase of the coherent radar signal, interferometry has
transformed radar remote sensing from a largely interpretive science to
a quantitative tool, with applications in cartography, geodesy, land
cover characterization, and natural hazards. This paper reviews the
techniques of interferometry, systems and limitations, and applications
in a rapidly growing area of science and engineering

. We propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indefinite) quadratic function, for which a local minimizer subject to bounds is required, and is particularily suitable for the large-scale problem. Our new method exhibits strong convergence properties, global and quadratic convergence, and appears to have significant practical potential. Strictly feasible points are generated. Experimental results on moderately large and sparse problems support the claim of practicality for large-scale problems. 1 Research partially supported by the Applied Mathematical Sciences Research Program (KC04 -02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG0286ER25013. A000, and by the Computational Mathematics Program of the National Science Foundation under grant DMS-8706133, and by the Cornell Theory Cen...

A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

Displacements derived from many of the accelerogram recordings of the 1999 Chi-Chi, Taiwan, earthquake show drifts when only a simple baseline derived from the pre-event portion of the record is removed from the records. The appearance of the velocity and displacement records suggests that changes in the zero level of the acceleration are responsible for these drifts. The source of the shifts in zero level are unknown, but in at least one case it is almost certainly due to tilting of the ground. This article illustrates the effect on the ground velocity, ground displacement, and response spectra of several schemes for accounting for these baseline shifts. A wide range of final displacements can be obtained for various choices of baseline correction, and comparison with nearby GPS stations (none of which are colocated with the accelerograph stations) do not help in choosing the appropriate baseline correction. The results suggest that final displacements estimated from the records should be used with caution. The most important conclusion for earthquake engineering purposes, however, is that the response spectra for periods less than about 20 see are usually unaffected by the baseline correction. Although limited to the analysis of only a small number of recordings, the results may have more general significance both for the many other recordings of this earthquake and for data that will be obtained in the future from similar high-quality accelerograph networks now being installed or soon to be installed in many parts of the world.

A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. Several practical suggestions to avoid mathematical singularities and computational instabilities are presented. -from Author

Residual displacements for large earthquakes can sometimes be determined from recordings on modern digital instruments, but baseline offsets of unknown origin make it difficult in many cases to do so. To recover the residual displacement, we suggest tailoring a correction scheme by studying the character of the velocity obtained by integration of zeroth-order-corrected acceleration and then seeing if the residual displacements are stable when the various parameters in the particular correction scheme are varied. For many seismological and engineering purposes, however, the residual displacements are of lesser importance than ground motions at periods less than about 20 sec. These ground motions are often recoverable with simple baseline correction and low-cut filtering. In this largely empirical study, we illustrate the consequences of various correction schemes, drawing primarily from digital recordings of the 1999 Hector Mine, California, earthquake. We show that with simple processing the displacement waveforms for this event are very similar for stations separated by as much as 20 km. We also show that a strong pulse on the transverse component was radiated from the Hector Mine earthquake and propagated with little distortion to distances exceeding 170 km; this pulse leads to large response spectral amplitudes around 10 sec.

INTRODUCTION
Ground motions from earthquakes are created by ruptures on tectonic faults. The causative faults can be considered point sources at distances large compared to the fault dimensions. At closer distances, the finite-fault effects become important. These effects are primarily related to the finite speed of rupture propagation, which causes certain parts of the fault to radiate energy much earlier than do other parts; the delayed waves then interfere, creating significant directivity effects. The duration and amplitude of ground motion become dependent on the angle of observation.
Finite-source modeling has been an important part of ground-motion prediction near the epicenters of large earthquakes (Hartzell, 1978; Irikura, 1983; Joyner and Boore, 1986; Heaton and Hartzell, 1989; Somerville et al., 1991; Hutchings, 1994; Tumarkin and Archuleta, 1994; Zeng et al. , 1994). In the approach adopted in most studies, the fault plane is discretized into elements, each element is treated as a small...

Acceleration spectra from nine earthquakes and up to 11 stations per earthquake are inverted to find the source spectra, the site response, and the quality factor Q of S waves. This method is applied to moderate earthquakes (4.0<M<7.0) digitally recorded on an accelerograph array installed since 1985 above the subduction zone of Guerrero, Mexico. Results obtained using a two-step inversion and a complete parametric approach are not significantly different. When the source spectra are interpreted in terms of Brune's model, the stress drops obtained are less than 20 bars for the four larger events analyzed. The site functions obtained indicate that although all the stations used are on rock, the effect of the near surface geology caused important amplifications at some stations. -from Authors

We analyse radar interferometric and GPS observations of the displacement field from the 1995 July 30 Mw= 8.1 Antofagasta, Chile, earthquake and invert for the distribution of slip along the co-seismic fault plane. Using a fixed fault geometry, we compare the use of singular-value decomposition and constrained linear inversion to invert for the slip distribution and find that the latter approach is better resolved and more physically reasonable. Separate inversions using only GPS data, only InSAR data from descending orbits, and InSAR data from both ascending and descending orbits without the GPS data illustrate the complimentary nature of GPS and the presently available InSAR data. The GPS data resolve slip near GPS benchmarks well, while the InSAR provides greater spatial sampling. The combination of ascending and descending InSAR data contributes greatly to the ability of InSAR to resolve the slip model, thereby emphasizing the need to acquire this data for future earthquakes. The rake, distribution of slip and seismic moment of our preferred model are generally consistent with previous seismic and geodetic inversions, although significant differences do exist. GPS data projected in the radar line-of-sight (LOS) and corresponding InSAR pixels have a root mean square (rms) difference of about 3 cm. Comparison of our predictions of vertical displacement and observed uplift from corraline algae have an rms of 10 cm. Our inversion and previous results reveal that the location of slip might be influenced by the 1987 Mw= 7.5 event. Our analysis further reveals that the 1995 slip distribution was affected by a 1988 Mw= 7.2 event, and might have influenced a 1998 Mw= 7.0 earthquake that occurred downdip of the 1995 rupture. Our slip inversion reveals a potential change in mechanism in the southern portion of the rupture, consistent with seismic results. Predictions of the satellite LOS displacement from a seismic inversion and a joint seismic/GPS inversion do not compare favourably with the InSAR observations.

Observations of deformation from 1992 to 1997 in the southern Coso Range using satellite radar interferometry show deformation rates of up to 35 mm yr-1 in an area ~10 km by 15 km. The deformation is most likely the result of subsidence in an area around the Coso geothermal field. The deformation signal has a short-wavelength component, related to production in the field, and a long-wavelength component, deforming at a constant rate, that may represent a source of deformation deeper than the geothermal reservoir. We have modeled the long-wavelength component of deformation and inferred a deformation source at ~4 km depth. The source depth is near the brittle-ductile transition depth (inferred from seismicity) and ~1.5 km above the top of the rhyolite magma body that was a source for the most recent volcanic eruption in the Coso volcanic field [Manley and Bacon, 2000]. From this evidence and results of other studies in the Coso Range, we interpret the source to be a leaking deep reservoir of magmatic fluids derived from a crystallizing rhyolite magma body.

A simple, yet effective, analytical model is proposed for the representation of near-field strong ground motions. The model
adequately describes the impulsive character of near-fault ground motions both qualitatively and quantitatively. In addition,
it can be used to analytically reproduce empirical observations that are based on available near-source records. The input
parameters of the model have an unambiguous physical meaning. The proposed analytical model has been calibrated using a large
number of actual near-field ground-motion records. It successfully simulates the entire set of available near-fault displacement,
velocity, and (in many cases) acceleration time histories, as well as the corresponding deformation, velocity, and acceleration
response spectra. Furthermore, a very simplified methodology for generating realistic synthetic ground motions that are adequate
for engineering analysis and design is outlined and applied. Finally, it should be noted that the analytical model (along
with the scaling laws of its parameters) proposed in the present work has the potential to facilitate the study of the elastic
and inelastic response of conventional, nonconventional (e.g., base-isolated), and special structures (e.g., suspension bridges,
fluid-storage tanks) subjected to near-source seismic excitations as a function of the model input parameters and thus, ultimately,
as a function of earthquake size.

The stochastic finite-fault ground-motion modeling technique is modified to simulate the effects of a variable-stress parameter on the fault. The radiated source spectrum of each subsource that comprises the fault plane is multiplied by a correction spectrum that leaves the low-frequency portion of the spectrum intact and multiplies the high-frequency end of the spectrum by a constant proportional to the stress parameter of each subfault raised to the power of 2/3; this scaling behavior follows from the Brune source model. The modification causes the response spectra and time series of simulated traces to be sensitive to the stress parameter distribution on the fault surface. The approach is implemented using an inversion tool that effectively inverts observed response spectral data to derive the stress parameter distribution on the fault surface. It applies the Levenberg-Marquardt nonlinear inversion method to minimize differences of average (log) response spectra ordinates at high frequencies between observations and simulations at all stations. We perform a number of experiments to study the effects of fault-dip angle, iterations per station, initial guess of the stress distribution, and station distribution on the capabilities of the inversion tool. We also evaluate the ability of the inversion tool to resolve the relative stress parameters of multiple asperities. Application of the inversion tool to the data of the M 6 2004 Parkfield earthquake indicates that an asperity with a high stress parameter is located in the southeast end of the fault, at a depth greater than 4 km; another asperity is located in the center of the fault, but with a lower stress parameter. This distribution is in agreement with results by other researchers.

The high-frequency seismic field near the epicenter of a large earthquake is modeled by subdividing the fault plane into subelements and summing their contributions at the observation point. Each element is treated as a point source with an ω2 spectral shape, where ω is the angular frequency. Ground-motion contributions from the subsources are calculated using a stochastic model. Attenuation is based on simple geometric spreading in a whole space, coupled with regional anelastic attenuation (Q operator).
The form of the ωn spectrum with natural n follows from point shear-dislocation theory with an appropriately chosen slip time function. The seismic moment and corner frequency are the two parameters defining the point-source spectrum and must be linked to the subfault size to make the method complete. Two coefficients, Δσ and K, provide this link. Assigning a moment to a subfault of specified size introduces the stress parameter, Δσ. The relationship between corner frequency (dislocation growth rate) and fault size is established through the coefficient K, which is inherently nonunique. These two parameters control the number of subsources and the amplitudes of high-frequency radiation, respectively. Derivation of the model from shear-dislocation theory reveals the unavoidable uncertainty in assigning ωn spectrum to faults with finite size. This uncertainty can only be reduced through empirical validation.
The method is verified by simulating data recorded on rock sites near epicenters of the M8.0 1985 Michoacan (Mexico), the M8.0 1985 Valparaíso (Chile), and the M5.8 1988 Saguenay (Québec) earthquakes. Each of these events is among the largest for which strong-motion records are available, in their respective tectonic environments. The simulations for the first two earthquakes are compared to the more detailed modeling of Somerville et al. (1991), which employs an empirical source function and represents the effects of crustal structure using the theoretical impulse response. Both methods predict the observations accurately on average. The precision of the methods is also approximately equal; the predicted acceleration amplitudes in our model are generally within 15% of observations. An unexpected result of this study is that a single value of a parameter K provides a good fit to the data at high frequencies for all three earthquakes, despite their different tectonic environments. This suggests a simplicity in the modeling of source processes that was unanticipated.

Displacements derived from many of the accelerogram recordings of the 1999 Chi-Chi, Taiwan, earthquake show drifts when only a simple baseline de- rived from the pre-event portion of the record is removed from the records. The appearance of the velocity and displacement records suggests that changes in the zero level of the acceleration are responsible for these drifts. The source of the shifts in zero level are unknown, but in at least one case it is almost certainly due to tilting of the ground. This article illustrates the effect on the ground velocity, ground dis- placement, and response spectra of several schemes for accounting for these baseline shifts. A wide range of final displacements can be obtained for various choices of baseline correction, and comparison with nearby GPS stations (none of which are colocated with the accelerograph stations) do not help in choosing the appropriate baseline correction. The results suggest that final displacements estimated from the records should be used with caution. The most important conclusion for earthquake engineering purposes, however, is that the response spectra for periods less than about 20 sec are usually unaffected by the baseline correction. Although limited to the analysis of only a small number of recordings, the results may have more general significance both for the many other recordings of this earthquake and for data that will be obtained in the future from similar high-quality accelerograph networks now being installed or soon to be installed in many parts of the world.

In the absence of sufficient data in the very near source, predictions of the intensity and variability of ground motions from future large earthquakes depend strongly on our ability to develop realistic models of the earthquake source. In this article we simulate near-fault strong ground motion using dynamic source models. We use a boundary integral method to simulate dynamic rupture of earthquakes by specifying dynamic source parameters (fracture energy and stress drop) as spatial random fields. We choose these quantities such that they are consistent with the statistical properties of slip heterogeneity found in finite-source models of past earth- quakes. From these rupture models we compute theoretical strong-motion seismo- grams up to a frequency of 2 Hz for several realizations of a scenario strike-slip Mw 7.0 earthquake and compare empirical response spectra, spectra obtained from our dynamic models, and spectra determined from corresponding kinematic simulations. We find that spatial and temporal variations in slip, slip rise time, and rupture prop- agation consistent with dynamic rupture models exert a strong influence on near- source ground motion. Our results lead to a feasible approach to specify the vari- ability in the rupture time distribution in kinematic models through a generalization of Andrews' (1976) result relating rupture speed to apparent fracture energy, stress drop, and crack length to 3D dynamic models. This suggests that a simplified rep- resentation of dynamic rupture may be obtained to approximate the effects of dy- namic rupture without having to do full dynamic simulations.

Ground-motion models based on the Brune point-source approximation have an underlying ω2 spectrum, with a single corner frequency. These models over-predict observed spectral amplitudes at low to intermediate frequencies (∼0.1 to 2 Hz), for earthquakes with moment magnitudes M of 4 or greater. The empirical spectra of moderate to large events tend to sag at these frequencies, relative to the level suggested by the Brune point-source model.
A model that accounts for the finite extent of the fault plane correctly describes the observed spectral shapes. The model represents seismic radiation as a sum of contributions from several subfaults. Each subfault may be represented as a point source, and each subevent has an ω2 spectrum. When contributions to ground motion at an observation point are summed over all subfaults, the resulting spectral shape has two corner frequencies and more closely matches observed spectra. The more realistic spectral shape obtained through finite-fault modeling reflects the underlying reality that the radiation from real faults is formed by ruptures of their smaller parts, whose corner frequencies are higher than those implied by the full fault dimension. The two corners appear naturally as a result of subevent summation.
We use the stochastic finite-fault methodology to simulate the recorded ground-motion data from all significant earthquakes in eastern North America (ENA). These data include eight events of M > 4 recorded on modern digital instruments (regional seismographs and strong-motion instruments), and three historical events of M 5.8 to 7.3 recorded on analog instruments. The goodness of fit of synthetics to the data is defined as simulation bias, which is indicated by the difference between the logarithms of the observed and the simulated spectrum, averaged over all recordings of an earthquake. The finite-fault simulations provide an unbiased fit to the observational database over a broad frequency range (0.1 to 50 Hz), for all events.
A surprising conclusion of these simulations is that the subfault size that best fits the observed spectral shape increases linearly with moment magnitude, in an apparently deterministic manner. This strongly suggests that the subfault size can be unambiguously defined by the magnitude of the simulated earthquake. In this case, the radiation-strength factor(s), which is proportional to the square root of the high-frequency Fourier acceleration level, remains the only free parameter of the model. Its value is related to the maximum slip velocity on the fault. The strength factors for all modeled ENA events are within the range of 1.0 to 1.6, with the exception of the Saguenay mainshock (s = 2.2). This suggests a remarkable uniformity in earthquake slip processes.

In finite-fault modeling of earthquake ground motions, a large fault is divided into N subfaults, where each subfault is considered as a small point source. The ground motions contributed by each subfault can be calculated by the stochastic point-source method and then summed at the observation point, with a proper time delay, to obtain the ground motion from the entire fault. A new variation of this approach is introduced based on a "dynamic corner frequency." In this model, the corner frequency is a function of time, and the rupture history controls the frequency content of the simulated time series of each subfault. The rupture begins with a high corner frequency and progresses to lower corner frequencies as the ruptured area grows. Limiting the number of active subfaults in the calculation of dynamic corner frequency can control the amplitude of lower frequencies. Our dynamic corner frequency approach has several advantages over previous formulations of the stochastic finite-fault method, including conservation of radiated energy at high frequencies regardless of subfault size, application to a broader mag-nitude range, and control of the relative amplitude of higher versus lower frequencies. The model parameters of the new approach are calibrated by finding the best overall fit to a ground-motion database from 27 well-recorded earthquakes in California. The lowest average residuals are obtained for a dynamic corner frequency model with a stress drop of 60 bars and with 25% of the fault actively slipping at any time in the rupture. As an additional tool to allow the stochastic modeling to generate the impulsive long-period velocity pulses that can be caused by forward directivity of the source, the analytical approach proposed by Mavroeidis and Papageorgiou (2003) has been included in our program. This novel mathematical model of near-fault ground mo-tions is based on a few additional input parameters that have an unambiguous physi-cal meaning; the method has been shown by Mavroeidis and Papageorgiou to sim-ulate the entire set of available near-fault displacement and velocity records, as well as the corresponding deformation, velocity, and acceleration response spectra. The inclusion of this analytical model of long-period pulses substantially increases the power of the stochastic finite-fault simulation method to model broadband time his-tories over a wide range of distances, magnitudes, and frequencies.

Performance-based seismic design (PBSD) can be considered as the coupling of expected levels of ground motion with desired levels of structural performance, with the objective of achieving greater control over earthquake-induced losses. Eurocode 8 (EC8) already envisages two design levels of motion, for no collapse and damage limitation performance targets, anchored to recommended return periods of 475 and 95 years, respectively. For PBSD the earthquake actions need to be presented in ways that are appropriate to the estimation of inelastic displacements, since these provide an effective control on damage at different limit states. The adequacy of current earthquake actions in EC8 are reviewed from this perspective and areas requiring additional development are identified. The implications of these representations of the seismic loads, in terms of mapping and zonation, are discussed. The current practice of defining the loading levels on the basis of the pre-selected return periods is challenged, and ideas are discussed for calibrating the loading-performance levels for design on the basis of quantitative earthquake loss estimation. Copyright © 2005 John Wiley & Sons, Ltd.

The effect of the long-period filter cut-off, Tc, on elastic spectral displacements is investigated using a strong ground-motion database from Europe and the Middle East. The relation between the filter and oscillator responses is considered to observe the influence of Tc for both analogue and digital records, and the variations with site classification, magnitude, filter order and viscous damping. Robust statistics are derived using the re-processed European data to generalize the effects of the long-period filter cut-off on maximum oscillator deformation demands as a function of these seismological and structural features. Statistics with a 95% confidence interval are derived to suggest usable period ranges for spectral displacement computations as a function of Tc. The results indicate that the maximum period at which spectral displacements can be confidently calculated depend strongly on the site class, magnitude and filter order. The period range where reliable long-period information can be extracted from digital accelerograms is twice that of analogue records. Copyright © 2006 John Wiley & Sons, Ltd.

-- A simple and powerful method for simulating ground motions is to combine parametric or functional descriptions of the ground motion's amplitude spectrum with a random phase spectrum modified such that the motion is distributed over a duration related to the earthquake magnitude and to the distance from the source. This method of simulating ground motions often goes by the name "the stochastic method." It is particularly useful for simulating the higher-frequency ground motions of most interest to engineers (generally, f>0.1 Hz), and it is widely used to predict ground motions for regions of the world in which recordings of motion from potentially damaging earthquakes are not available. This simple method has been successful in matching a variety of ground-motion measures for earthquakes with seismic moments spanning more than 12 orders of magnitude and in diverse tectonic environments. One of the essential characteristics of the method is that it distills what is known about the various factors affecting ground motions (source, path, and site) into simple functional forms. This provides a means by which the results of the rigorous studies reported in other papers in this volume can be incorporated into practical predictions of ground motion.

A long-standing goal of subduction zone earthquake studies is to determine whether or not there are physical processes that control seismogenesis and the along-strike segmentation of the megathrust. Studies of individual earthquakes and global compilations of earthquakes find favorable comparison between coseismic interplate slip distributions and several different long-lived forearc characteristics, such as bathymetry, coastline morphology, crustal structure, and interplate frictional properties, but no single explanation seems to govern the location and slip distribution of all earthquakes. One possible reason for the lack of a unifying explanation is that the inferred earthquake parameters, most importantly the slip distribution, calculated in some areas were inaccurate, blurring correlation between earthquake and physical parameters. In this paper, we seek to test this possibility by comparing accurate slip distributions constrained by multiple datasets along several segments of a single subduction zone with the various physical properties that have been proposed to control or correlate with seismogenesis. We examine the rupture area and slip distribution of 6 recent and historical large (Mw > 7) earthquakes on the Peru–northern Chile subduction zone. This analysis includes a new slip distribution of the 14 November 2007 Mw = 7.7 earthquake offshore Tocopilla, Chile constrained by teleseismic body wave and InSAR data. In studying the 6 events, we find that no single mechanism can explain the location or extent of rupture of all earthquakes, but analysis of the forearc gravity field and its gradients shows correlation with many of the observed slip patterns, as suggested by previous studies. Additionally, large-scale morphological features including the Nazca Ridge, Arica Bend, Mejillones Peninsula, and transverse crustal fault systems serve as boundaries between distinct earthquake segments.

Recordings from strong-motion accelerographs are of fundamental importance in earthquake engineering, forming the basis for all characterizations of ground shaking employed for seismic design. The recordings, particularly those from analog instruments, invariably contain noise that can mask and distort the ground-motion signal at both high and low frequencies. For any application of recorded accelerograms in engineering seismology or earthquake engineering, it is important to identify the presence of this noise in the digitized time-history and its influence on the parameters that are to be derived from the records. If the parameters of interest are affected by noise then appropriate processing needs to be applied to the records, although it must be accepted from the outset that it is generally not possible to recover the actual ground motion over a wide range of frequencies. There are many schemes available for processing strong-motion data and it is important to be aware of the merits and pitfalls associated with each option. Equally important is to appreciate the effects of the procedures on the records in order to avoid errors in the interpretation and use of the results. Options for processing strong-motion accelerograms are presented, discussed and evaluated from the perspective of engineering application.

On 14 November 2007, a subduction thrust earthquake, magnitude Mw = 7.8, occurred in the coastal region of northern Chile, causing substantial damage to the city of Tocopilla. We investigate the source fault of the earthquake, slip distribution and fault interaction by integrating aftershock locations, satellite interferometry data and stress model simulations. Aftershock measurements allow us to locate the area and geometry of the rupture plane in the coastal region between the cities of Tocopilla and Antofagasta. Combining two satellite viewing geometries, acquired in Envisat's Wide Swath and Image modes, we observe decimetre-scale coseismic deformation. The maximum line-of-sight displacement is found to be about 40 cm, located at the Mejillones Peninsula. Slip inversions using elastic half-space models with geometry constrained by aftershocks suggest rupturing of an area of ∼ 160 km by ∼50 km along the Nazca–South America convergent margin between latitudes 22°S and 23.5°S. The main slip is concentrated on two asperities, the largest being located in the southern part of the rupture area at a depth of approximately 30–50 km with a magnitude of about 2.5 m. Because aftershock distribution may also suggest a region of shallow crustal deformation activity located offshore, we investigate whether the 2007 Tocopilla earthquake also involved shallow crustal fault slip offshore. Although we find that the latter assumption is supported by Coulomb stress modelling and geologic inferences, our geodetic and seismic data provide insufficient constraints to resolve the exact geometry and kinematics of dislocation on this structure.

We combine interferometric synthetic aperture radar
(InSAR) and teleseismic body waves to study the largest
earthquake (Mw 8.1) in a sequence of events on the
subduction megathrust near Pisco, Peru. Our analysis
includes some of the first InSAR data from the ALOS
satellite and wide swath data from the Envisat satellite. The
teleseismic data indicate the slip maximum occurred 60–
90 seconds after the mainshock started. The InSAR data
constrain the main slip patch to be about 70 km from the
hypocenter, suggesting an extremely low rupture velocity
(<1.5 km/s) or long slip rise time. No large earthquake has
occurred in the 2007 rupture area since at least 1746 and
possibly 1687, suggesting significant aseismic deformation
in the area. The slip deficit apparently cannot be filled with
rapid after-slip. In addition, the area where the Nazca Ridge
is subducting appears to be either a seismic gap or a
persistent area of aseismic slip.

The Pisco earthquake (Mw 8.0; 2007 August 15) occurred offshore of Peru's southern coast at the subduction interface between the Nazca and South American plates. It ruptured a previously identified seismic gap along the Peruvian margin. We use Wide Swath InSAR observations acquired by the Envisat satellite in descending and ascending orbits to constrain coseismic slip distribution of this subduction earthquake. The data show movement of the coastal regions by as much as 85 cm in the line-of-sight of the satellite. Distributed-slip model indicates that the coseismic slip reaches values of about 5.5 m at a depth of ∼18–20 km. The slip is confined to less than 40 km depth, with most of the moment release located on the shallow parts of the interface above 30 km depth. The region with maximum coseismic slip in the InSAR model is located offshore, close to the seismic moment centroid location. The geodetic estimate of seismic moment is 1.23 × 1021 Nm (Mw 8.06), consistent with seismic estimates. The slip model inferred from the InSAR observations suggests that the Pisco earthquake ruptured only a portion of the seismic gap zone in Peru between 13.5° S and 14.5° S, hence there is still a significant seismic gap to the south of the 2007 event that has not experienced a large earthquake since at least 1687.

Interferometric synthetic aperture radar (InSAR) techniques are today applied in many areas of remote sensing, ranging from digital elevation model (DEM) generation to surface motion mapping and InSAR tomography. To enhance the understanding of the InSAR mapping process and to test new algorithms, accurate tools for the simulation of the topographic InSAR phase are necessary. Whereas the equations for the interferometric phase of a given DEM are well known, the actual implementation is tedious. Furthermore, a straightforward implementation would take far more computation time than all the other InSAR processing steps put together. This paper presents a novel algorithm for the efficient simulation of the InSAR phase, taking into account the special problems in mountainous terrain. Simulation results are compared to and illustrated with real data from the European Remote Sensing satellite (ERS-1/2) tandem mission and the Shuttle Radar Topography Mission (SRTM). Accuracy estimates for the phase simulation are given for different terrain types. The algorithm is described in enough detail that it can be implemented as a general-purpose tool for the accurate simulation of interferograms with virtually unlimited size, taking no more processing time than other InSAR processing steps. The algorithm in the presented form is used operationally within the interferometry software GENESIS to support the processing of SRTM/X-SAR data at the German Aerospace Center (DLR).

Testing mechanisms of subduction zone segmentation and seismogenesis with slip distributions from recent andean earthquakes1–2):15–33 13 Please cite this article as: Abell JA, et al. Enhancement of long period components of recorded and synthetic ground motions using InSAR

- J Loveless
- M Pritchard
- Kukowski

Loveless J, Pritchard M, Kukowski N. Testing mechanisms of subduction zone segmentation and seismogenesis with slip distributions from recent andean earthquakes. Tectonophysics 2010;495(1–2):15–33. J.A. Abell et al. / Soil Dynamics and Earthquake Engineering ] (]]]]) ]]]–]]] 13 Please cite this article as: Abell JA, et al. Enhancement of long period components of recorded and synthetic ground motions using InSAR. Soil Dyn Earthquake Eng (2011), doi:10.1016/j.soildyn.2011.01.005