Application of DInSAR-GPS optimization for derivation of fine-scale surface motion maps of Southern California

A method based on random field theory and Gibbs-Markov random fields equivalency within Bayesian statistical framework is used to derive 3-D surface motion maps from sparse global positioning system (GPS) measurements and differential interferometric synthetic aperture radar (DInSAR) interferogram in the southern California region. The minimization of the Gibbs energy function is performed analytically, which is possible in the case when neighboring pixels are considered independent. The problem is well posed and the solution is unique and stable and not biased by the continuity condition. The technique produces a 3-D field containing estimates of surface motion on the spatial scale of the DInSAR image, over a given time period, complete with error estimates. Significant improvement in the accuracy of the vertical component and moderate improvement in the accuracy of the horizontal components of velocity are achieved in comparison with the GPS data alone. The method can be expanded to account for other available data sets, such as additional interferograms, lidar, or leveling data, in order to achieve even higher accuracy

Geostatistical analysis of an experimental stratigraphy

[1] A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln( K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln( K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/ floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process - dependent and problem-scale-dependent

Modeling Space-Time Data Using Stochastic Differential Equations

This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio

A geostatistical model based on Brownian motion to Krige regions in R2 with irregular boundaries and holes

Master's Project (M.S.) University of Alaska Fairbanks, 2019Kriging is a geostatistical interpolation method that produces predictions and prediction intervals. Classical kriging models use Euclidean (straight line) distance when modeling spatial autocorrelation. However, for estuaries, inlets, and bays, shortest-in-water distance may capture the system’s proximity dependencies better than Euclidean distance when boundary constraints are present. Shortest-in-water distance has been used to krige such regions (Little et al., 1997; Rathbun, 1998); however, the variance-covariance matrices used in these models have not been shown to be mathematically valid. In this project, a new kriging model is developed for irregularly shaped regions in R 2 . This model incorporates the notion of flow connected distance into a valid variance-covariance matrix through the use of a random walk on a lattice, process convolutions, and the non-stationary kriging equations. The model developed in this paper is compared to existing methods of spatial prediction over irregularly shaped regions using water quality data from Puget Sound

Various uses of statistical Tools for texture analysis

International audienc

The use of the mesh free methods (radial basis functions) in the modeling of radionuclide migration and moving boundary value problems

Recently, the mesh free methods (radial basis functions-RBFs) have emerged as a novel computing method in the scientific and engineering computing community. The numerical solution of partial differential equations (PDEs) has been usually obtained by finite difference methods (FDM), finite element methods (FEM) and boundary elements methods (BEM). These conventional numerical methods still have some drawbacks. For example, the construction of the mesh in two or more dimensions is a nontrivial problem. Solving PDEs using radial basis function (RBF) collocations is an attractive alternative to these traditional methods because no tedious mesh generation is required. We compare the mesh free method, which uses radial basis functions, with the traditional finite difference scheme and analytical solutions. We will present some examples of using RBFs in geostatistical analysis of radionuclide migration modeling. The advection-dispersion equation will be used in the Eulerian and Lagrangian forms. Stefan's or moving boundary value problems will also be presented. The position of the moving boundary will be simulated by the moving data centers method and level set method

Shear-Wave Velocities and Derivative Mapping For the Upper Mississippi Embayment

During the past two decades, University of Kentucky researchers have been acquiring seismic refraction/reflection data, as well as seismic downhole data, for characterizing the seismic velocity models of the soil/sediment overburden in the central United States. The dataset includes densely spaced measurements for urban microzonation studies and coarsely spaced measurements for regional assessments. The 519 measurements and their derivative products often were not in an organized electronic form, however, limiting their accessibility for use by other researchers. In order to make these data more accessible, this project constructed a database using the ArcGIS 9.1 software. The data have been formatted and integrated into a system serving a wider array of users. The seismic shear-wave velocity models collected at various locations are archived with corresponding x-, y-, and z-coordinate information. Flexibility has been included to allow input of additional data in the future (e.g., seismograms, strong ground-motion parameters and time histories, weak-motion waveform data, etc.). Using the completed database, maps of the region showing derivative dynamic site period (DSP) and weighted shear-wave velocity of the upper 30 m of soil (V30) were created using the ArcGIS 9.1 Geostatistical Analyst extension for examination of the distribution of pertinent dynamic properties for seismic hazard assessments. Both geostatistical and deterministic techniques were employed. Interpolation of V30 data yielded inaccurate predictions because of the high lateral variation in soil layer lithology in the Jackson Purchase Region. As a result of the relatively uniform distribution of depths to bedrock, the predictions of DSP values suggested a high degree of accuracy

Mapping long-period soil resonances in the Kathmandu basin using microtremors

This study reports the geostatistical analysis of a set of 40 single-station horizontal-to-vertical spectral ratio (HVSR) passive seismic survey data collected in the Kathmandu basin (Nepal). The Kathmandu basin is characterized by a heterogeneous sedimentary cover and by a complex geo-structural setting, inducing a high spatial variability of the bedrock depth. Due to the complex geological setting, the interpretation and analysis of soil resonance periods derived from the HVSR surveys is challenging, both from the perspective of bedrock depth estimation as well as of seismic-site effects characterization. To exploit the available information, the HVSR data are analyzed by means of a geostatistical approach. First, the spatial continuity structure of HVSR data is investigated and interpreted taking into consideration the geological setting and available stratigraphic and seismic information. Then, the exploitation of potential auxiliary variables, based on surface morphology and distance from outcropping bedrock, is evaluated. Finally, the mapping of HVSR resonance periods, together with the evaluation of interpolation uncertainty, is obtained by means of kriging with external drift interpolation. This work contributes to the characterization of local seismic response of the Kathmandu basin. The resulting map of soil resonance periods is compatible with the results of preceding studies and it is characterized by a high spatial variability, even in areas with a deep bedrock and long resonance periods