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Strain estimation using ordinary Kriging interpolation

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Abstract

The ordinary kriging interpolation method is adopted to estimate the 2-D strain tensor elements. The results are then compared with those of the linear and spline interpolation methods. The ordinary kriging method is implemented on 12 GPS permanent stations in South California, collected during 2006 to 2012. By employing these time series, the coordinate changes in the UTM coordinate system can be obtained and the strain tensor elements at these 12 stations can be estimated by means of finite difference method. Interpolation of the strain tensor elements over the study area through these three methods (kriging, spline and linear) indicates that the ordinary kriging results, on average are 70% better than those of the spline and linear interpolation methods.

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... The analyses were performed using a combination of validated statistical information and reanalysis data (32-37 years) at temporal (hourly) and spatial resolutions (0.017-0.3°), depending on the availability of homogeneous data (Table 2.1). The Kriging method (Ghiasi and Nafisi, 2015) was employed to interpolate the data on a grid with 0.25° resolution. The evaluation criteria was based on reference operating thresholds for large wind turbines, WECs, site accessibility for logistics activities, offshore standards for technical requirements, and on statistics of offshore projects available in the literature (Table 2.2). ...
... The Kriging method (Ghiasi and Nafisi, 2015) was employed to interpolate the results on a homogeneous grid with a 0.10º resolution. ...
Thesis
Marine and coastal zones are currently under pressure due to an increasing demand for areas to develop different activities. This is the case of the renewable energy and aquaculture sectors, which are expanding offshore as a consequence of both energy and food demands for a growing world population and the possible surpassing of the carrying capacity of coastal and land-based systems. Therefore, the short to long-term progression of these marine sectors will require the adoption of integrated planning and management approaches, where competitive and synergistic interactions with the socio-ecological environment must be analyzed on an appropriate scale. However, marine renewable energy and offshore aquaculture sectors rely greatly on met-ocean and environmental conditions. Thus, the effects of climate change must be considered in the planning process of these activities. In this context, the general objective of this thesis was to develop and apply methodologies to recognize potential zones for the development of marine wind and wave energy production and offshore aquaculture, with the ultimate goal of promoting the sustainable development of these activities in the context of a marine spatial planning strategy. The major goal was developed through four different specific objectives: i) global assessment of renewable energy potential; ii) global assessment of opportunities for offshore aquaculture; iii) regional assessment of the co-location opportunities for renewable energy and aquaculture activities; iv) regional assessment of the possible effects of climate change on the renewable energy and aquaculture sectors. First, a global assessment of the potentialities and opportunities for the development of offshore marine renewable energy and aquaculture sectors was carried out. For this purpose, methodological approaches were developed and applied to identify potential zones for the exploitation of wind and wave energy and for the farming of marine fish species. For the first specific objective, a comprehensive analysis of the global potential of offshore resources was carried out considering the availability of energy resources, the structural survivability of energy conversion devices, logistics activities, and distances from consumer centers. The results allowed to recognize potential zones for the implementation of wind and wave energy activities in the short and mid-term, as well as zones for the combined exploitation of these activities. Regarding the wind energy sector, the zones identified as favorable for exploitation coincided with the offshore areas with the highest energy production in operation (e.g. the North Sea, the United States and China) and areas still under development (e.g. Greece, Japan and South Korea). On the other hand, zones that have not yet been exploited were also identified, opening opportunities for the wind and wave energy sector to grow, such as in the exclusive economic zone (EEZ) of Argentina, Chile, Colombia, Morocco and Peru. For aquaculture, the global assessment was based on the analysis of the biological conditions for the farming of seven fish species, met-ocean conditions to house offshore cages, and suitable conditions for operation and maintenance (O&M) activities (specific objective No. 2). Opportunities for the development of this industry were identified in unexploited zones, such as farming of meagre, gilthead seabream and European seabass to the west and east of South America. The potential zones identified also coincided with regions of remarkable aquaculture production for these species (e.g. Norway, Chile and the United Kingdom for the Atlantic salmon). The main potential zones identified for fish farming were concentrated in South America (South Pacific and South Atlantic oceans), Africa (Northern Atlantic Ocean), the Mediterranean, Japanese and Chinese seas, and Oceania. After the identification of potential zones for the exploitation of marine renewable energies and offshore aquaculture on a global scale, a more detailed study at a regional scale was carried out. This investigation sought to assess the offshore potential to develop these industries and to characterize the spatial synergies for the co-location of these three activities (specific objective No. 3). A multi-criteria approach based on independent probabilistic suitability and mapping analysis was applied to a case study in the Canary Archipelago for: i) wind and wave energy production potential; ii) structural requirements for energy devices and aquaculture cages; iii) limits for O&M activities; iv) feasibility to transport energy to the grid; and v) biological requirements for eight species of fish. Opportunities for the co-location of wind and aquaculture farms were identified in the southeastern portion of the islands, while opportunities for combining wind and wave energy were found mainly in the islands of Tenerife and Fuerteventura. Finally, to analyze the possible effects of climate change on these marine economies in Europe, the distribution of favorable conditions for the exploitation of wind energy, wave energy and aquaculture were analyzed considering two scenarios (specific objective No. 4). Wind and wave energy resources and environmental conditions for fish farming were evaluated based on a current scenario (reference climate) and another scenario towards the end of the 21st century (projected climate). The delta change method was considered for projections, using the General Circulation Models outputs (Representative Concentration Pathway 8.5) from the fifth phase of the Coupled Model Intercomparison Project. The results obtained showed that the observed climate changes will not have direct impacts on the geographical distribution of the potential zones for the energy industry (both wind and wave energy), that is, they do not seem to pose a real threat to this industry. For the aquaculture sector, a considerable change in environmental conditions was projected, requiring adaptation of this sector in relation to the geographical location of fish farms. Thus, strategic planning should be considered to reduce unfavorable conditions to areas with activities in operation and to maximize the opportunities generated by climate change. Therefore, the global analysis for marine renewable energy and offshore aquaculture provides guidelines to assist the development of these sectors, supporting the management of marine spaces. The identification of spatial synergies between these activities reflects the opportunities of combining different uses to promote a sustainable growth of the blue economy, reducing potential conflicts and optimizing the use of marine space. In addition, the assessment of potential zones for these activities, considering the possible effects of climate change, represents a useful stepping-stone for improving decision-making and assisting in the management of marine economies. In summary, the results of this thesis provide information and tools to assist in the integrated management and strategic planning of offshore wind energy, wave energy and aquaculture sectors, supporting specific strategies to optimize the use of space for sustainable exploitation of the marine environment, adaptive management in the face of climate change, and fostering the coexistence of uses to avoid conflicts and highlight synergies between these activities. Consequently, the contribution of this thesis is directly linked to the development of these emerging marine economies from a Blue Growth perspective.
... Since the weighting procedure depends on both the distance and statistical distribution of the samples, the variation function is adopted to estimate the weight by fitting a spatial model to the data and then defining the effectiveness of each point [12,13]. The variation function value at point x i is obtained by ...
... that needs to divide the data state that depended on some criterion for computing the transition probability. Assuming that the structural elements12 , ,..., ,..., |1 of each data point in the structural elements is expressed as the state division: ...
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... In other research by Derya Ozturk and Fatmagul Kilic [10] in 2016, geostatistical approaches have been employed in recent years to determine the geographical distribution of meteorological data, and the Ordinary Kriging method is currently the preferred choice in the literature. In this study [11], Ghiasi and Nafisi in 2016 said that the results of the strain tensor elements interpolation using these three techniques which are kriging, spline, and linear show that, on average, the results of Ordinary Kriging are 70% better than those of the spline and linear interpolation techniques. Some of the papers and researches above reveal that ...
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... Finally, map results are showing after a Kriging method interpolation (Ghiasi and Nafisi, 2016) on a homogeneous grid with 0.10 spatial resolution. ...
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... The analyses were performed using a combination of validated statistical information and reanalysis data (32-37 years) at temporal (hourly) and spatial resolutions (0.017-0.3°), depending on the availability of homogeneous data ( Table 1). The Kriging method [18] was employed to interpolate the data on a grid with 0.25°resolution. ...
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... Bos et al. [2008] found that simply filling the data gaps by linear interpolation and taking the first difference is much faster than the standard MLE method while being comparable in accuracy for trend estimates. Ghiasi and Nafisi [2016] used the ordinary kriging interpolation method to estimate the 2-D strain tensor elements. However, GPS coordinate time series are often disrupted by discontinuities (or offsets) caused by earthquakes and equipment changes. ...
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Knowledge of ore grades and ore reserves as well as error estimation of these values, is fundamental for mining engineers and mining geologists. Until now no appropriate scientific approach to those estimation problems has existed: geostatistics, the principles of which are summarized in this paper, constitutes a new science leading to such an approach. The author criticizes classical statistical methods still in use, and shows some of the main results given by geostatistics. Any ore deposit evaluation as well as proper decision of starting mining operations should be preceded by a geostatistical investigation which may avoid economic failures.
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In this paper we present a global model (GSRM-1) of both horizontal velocities on the Earth's surface and horizontal strain rates for almost all deforming plate boundary zones. A model strain rate field is obtained jointly with a global velocity field in the process of solving for a global velocity gradient tensor field. In our model we perform a least-squares fit between model velocities and observed geodetic velocities, as well as between model strain rates and observed geological strain rates. Model velocities and strain rates are interpolated over a spherical Earth using bi-cubic Bessel splines. We include 3000 geodetic velocities from 50 different, mostly published, studies. Geological strain rates are obtained for central Asia only and they are inferred from Quaternary fault slip rates. For all areas where no geological information is included a priori constraints are placed on the style and direction (but not magnitude) of the model strain rate field. These constraints are taken from a seismic strain rate field inferred from (normalized) focal mechanisms of shallow earthquakes. We present a global solution of the second invariant of the model strain rate field as well as strain rate solutions for a few selected plate boundary zones. Generally, the strain rate tensor field is consistent with geological and seismological data. With the assumption of plate rigidity for all areas other than the plate boundary zones we also present relative angular velocities for most plate pairs. We find that in general there is a good agreement between the present-day plate motions we obtain and long-term plate motions, but a few significant differences exist. The rotation rates for the Indian, Arabian and Nubian plates relative to Eurasia are 30, 13 and 50 per cent slower than the NUVEL-1A estimate, respectively, and the rotation rate for the Nazca Plate relative to South America is 17 per cent slower. On the other hand, Caribbean-North America motion is 76 per cent faster than the NUVEL-1A estimate. While crustal blocks in the India-Eurasia collision zone move significantly and self-consistently with respect to bounding plates, only a very small motion is predicted between the Nubian and Somalian plates. By integrating plate boundary zone deformation with the traditional modelling of angular velocities of rigid plates we have obtained a model that has already been proven valuable in, for instance, redefining a no-net-rotation model of surface motions and by confirming a global correlation between seismicity rates and tectonic moment rates along subduction zones and within zones of continental deformation.
Article
We present a new geodetic velocity solution for Italy and the surrounding areas, obtained from an analysis of continuous and survey-mode Global Positioning System observations collected between 1991 and 2002. We have combined local, regional and global networks into a common reference frame velocity solution, providing a new detailed picture of the regional-scale defor-mation field in the central Mediterranean. Our velocity estimates are computed with respect to a new stable Eurasian reference frame, constraining the kinematics of the greater African– Eurasian plate boundary system in the study area. We provide strain-rate values for the main seismotectonic districts, which are in good agreement with the seismic deformation inferred from earthquake focal mechanisms. The southern Tyrrhenian area, Calabria, the Apennines, the southeastern Alps, the southern Dinarides and the Albanides display deformation rates at the order of 20–30 nanostrain yr −1 . The Corsica–Sardinia block moves according to Eurasian Plate motions, and there is no indication that the opening of the Tyrrhenian is still active. The Pelagian and Sicilian domains are separated by a northwest–southeast discontinuity, the Sicily Channel rifted area, and marginally significant relative motion between the Pelagian Plateau and the African Plate is also observed. The southern Tyrrhenian is affected by north–south compression and accommodates up to 50 per cent of the Africa–Eurasia relative plate motion, whereas the Calabrian Arc exhibits ∼2 mm yr −1 northwest–southeast extension. The observed deformation pattern suggests the presence of a major approximately north–south tectonic dis-continuity separating the Sicilian and Calabrian domains. An extensional boundary observed along peninsular Italy coincides with the distribution of seismogenic faults along the axis of the Apennines. This boundary separates a Tyrrhenian and an Adriatic domain with diverging velocities, orientated north–NNW-ward and northeastward, respectively. The Apennines are extending perpendicularly to the chain axis at rates of less than 3 mm yr −1 , and only in the outer northern Apennines indications of active shortening are observed. Insignificant deformation is observed in the western Po Plain and the western Alps, while the central and eastern Alps display north–south shortening. The eastern Adriatic domain is shortening perpendicular to the Dinaric front with strain rates increasing from north to south. The locus of collision between the Aegean/Balkan system and the Adriatic and Ionian domains is marked by the Kephalonia fault system, which accommodates up to 20±1 mm yr −1 of right-lateral motion. The defor-mation pattern observed in the peri-Adriatic domain is well described by a counter-clockwise rotation of the Adriatic microplate around a pole located in the western Alps.
Article
The seismicity of southern California results from stresses that arise from the relative motion of the Pacific and North American Plates being accommodated along the San Andreas Fault (SAF) system and the Eastern California Shear Zone (ECSZ). Here we calculate how the stress field in southern California has evolved over the past two centuries due to interseismic loading, as inferred from current GPS observations of surface velocities, from redistributions of static stress induced by large (M w ≥ 6.5) earthquakes since the 1812 Wrightwood quake, and postseismic viscoelastic relaxation associated with these events that serves to transfer coseismic stresses from the deep, warm, lower crust and upper mantle to the overlying seismogenic upper crust. We calculate Coulomb stress changes on vertical strike-slip faults striking parallel to the SAF and at the hypocenters on the rupture planes of all M w ≥ 6 events over the past two centuries. Our results suggest that the 1857 M w = 8.2 Fort Tejon earthquake, by far the largest event to have occurred in the region over the past two centuries, had a profound influence on the state of stress in Southern California during the 19th century, inducing significant stress increases to the north (Parkfield region and adjoining creeping SAF) and south (southern SAF and San Jacinto fault), and stress relief across the southern ECSZ. These stress changes were then greatly magnified by postseismic relaxation through the early part of the 20th century. Slow interseismic build-up of stress further loads all major strike-slip faults and works to reload the areas of the ECSZ where stress was relieved by the 1857 quake. Our calculations suggest that only 56% of hypocenters were pushed closer to failure by preceding coseismic stress changes, suggesting that the occurrence of large earthquakes is not strongly determined by coseismic Coulomb stress changes. This percentage rises to 70% when postseismic stress changes are also considered. Our calculations demonstrate the importance of postseismic viscoelastic relaxation in the redistribution of stress following large earthquakes. We find, however, that postseismic processes associated with events more than about a decade old are near completion and thus do not significantly influence the regional velocity field presently observed in southern California.
Article
While emphasizing new insights from the last decade of research, Tectonic Geomorphology reviews the fundamentals of the subject which include the nature of ...
Chapter
First published in 1982, Don Turcotte and Jerry Schubert's Geodynamics became a classic textbook for several generations of students of geophysics and geology. The authors bring this text completely up-to-date in this second edition. Important additions include a chapter on chemical geodynamics, an updated coverage of comparative planetology based on recent planetary missions, and a variety of other new topics. Geodynamics provides the fundamentals necessary for an understanding of the workings of the solid earth, describing the mechanics of earthquakes, volcanic eruptions, and mountain building in the context of the role of mantle convection and plate tectonics. Observations such as the earth's gravity field, surface heat flow, distribution of earthquakes, surface stresses and strains, and distribution of elements are discussed.
Article
In this study we rigorously combine 18 old campaign GPS data sets from Greece covering the period 1994–2000. Although the majority of these old datasets have been analyzed and reported previously, it has not been possible to combine them into a single velocity field and apply strain analysis. Here a uniform, final coordinate solution is given by reprocessing 43 global, long-running International GNSS Service (IGS) sites together with 280 local sites. The 221 daily SINEX files are then combined in a least squares approach and the geodetic horizontal velocity field in ITRF2000 and Europe-fixed reference frame is derived. Two methods are used to compute the geodetic strain rates: (i) discrete estimates within contiguous polygons, and (ii) a continuous curvature surface fitted to the velocity field. The seismic hazard potential can be determined by comparing the geodetic and seismic strain rates. The published 300 year earthquake catalogue best describes the major active tectonic features at the scale of geodetic strain determination. The geodetic strain appears larger than the seismic strain for the majority of the region, suggesting that accumulated strain has not yet been released by earthquakes. The geodetic field is consistent with the detailed constraints implied by the observed orientations of faulting as these are given in the 300-year catalogue. We have shown that with the GPS dataset used in this work and following this processing scheme reasonable results can be obtained comparable with more recent studies, CGPS data and by recent earthquake activity.
Article
An analysis of a deformation process in dynamic models is presented, where time is considered as the essential part. A rigorous adjustment model of unregularly spanned observations in space and time is proposed for the estimation of point velocities and strain rate parameters. The problem of the reference frame definition and choices of deformation models are discussed. Finally an application is given in order to illustrate the method, using real data from GPS observations at the geodynamically unstable area of the Ionian Sea.
Article
An algorithm and the corresponding computer program for solution of the scattered data interpolation problem is described. Given points (xk, yk, fk), k = 1,…,N a locally defined function F(x, y) which has the property F(xk, yk) = fk, k = 1,…,N is constructed. The algorithm is based on a weighted sum of locally defined thin plate splines, and yields an interpolation function which is differentiable. The program is available from the author.
Article
A text detailing critical aspects of geographic information systems for land resources assessment. Nine chapters cover themes on: 1. Overview of GIS components - computer mapping, data bases, future directions. 2. Data structures for thematic maps, including files, spatial data definitions, vector and raster structures, database facilities. 3. Digital elevation models. 4. Data input, verification, storage and output. 5. Methods of spatial data analysis and modelling, ranging from basic map overlay, to natural language processing. 6. Data quality, errors, and the nature of spatial data on maps. 7. Classification techniques - multivariate, and using expert systems. 8. Spatial interpolation methods. 9. Selecting a GIS. Each chapter has a list of references, and two appendices give a glossary of terms, and a list of selected information sources.-after Author
Investigation of strain analysis method validity in geodynamics displacements using GNSS data
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