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1.
Dionissios T. Hristopulos 《Stochastic Environmental Research and Risk Assessment (SERRA)》2015,29(3):739-754
Random fields based on energy functionals with local interactions possess flexible covariance functions, lead to computationally efficient algorithms for spatial data processing, and have important applications in Bayesian field theory. In this paper we address the calculation of covariance functions for a family of isotropic local-interaction random fields in two dimensions. We derive explicit expressions for non-differentiable Spartan covariance functions in \({\mathbb{R}}^2\) that are based on the modified Bessel function of the second kind. We also derive a family of infinitely differentiable, Bessel-Lommel covariance functions that exhibit a hole effect and are valid in \({\mathbb{R}}^{d}\), where d > 2. Finally, we define a generalized spectrum of correlation scales that can be applied to both differentiable and non-differentiable random fields in contrast with the smoothness microscale. 相似文献
2.
We developed a new approach for computing the changes in the length of day (LOD) due to earthquakes from both shear- and tensile-type faults. This approach was based on the point dislocation theory for a SNREI Earth, which was validated by comparing our results with the ones obtained by the normal mode method. We defined two numerical functions that vary with hypocenter depth. These functions allow us to compute the co-seismic change of the trace of the Earth's inertia tensor, and hence the co-seismic LOD change. For future applications, by adding a trace term, we corrected Lambeck's formulas (Lambeck, 1980), which are being commonly used for computing co-seismic LOD change. Finally, the new approach was used to compute the co-seismic LOD change from 1977 to 2011. The results show that the co-seismic trace and the co-seismic J2 changes contribute to the LOD change with the same magnitude (Gross and Chao, 2006). This means that, unlike other deformation mechanisms, the trace term cannot be neglected when modeling the co-seismic LOD change. The earthquakes from 1977 to 2011 decreased the LOD by about 12 μs, and the rate of decrease was enhanced after the 2004 Sumatra earthquake due to several large earthquakes. 相似文献
3.
Improving Regional Seismic Event Location in China 总被引：1，自引：0，他引：1
L.K. Steck A.A. Velasco A.H. CogbillL H.J. Patton 《Pure and Applied Geophysics》2001,158(1-2):211-240
—?In an effort to improve our ability to locate seismic events in China using only regional data, we have developed empirical propagation path corrections and applied such corrections using traditional location routines. Thus far, we have concentrated on corrections to observed P arrival times for crustal events using travel-time observations available from the USGS Earthquake Data Reports, the International Seismic Centre Bulletin, the preliminary International Data Center Reviewed Event Bulletin, and our own travel-time picks from regional data. Location ground truth for events used in this study ranges from 25?km for well-located teleseimic events, down to 2?km for nuclear explosions located using satellite imagery. We also use eight events for which depth is constrained using several waveform methods. We relocate events using the EvLoc algorithm from a region encompassing much of China (latitude 20°–55°N; longitude 65°–115°E). We observe that travel-time residuals exhibit a distance-dependent bias using IASPEI91 as our base model. To remedy this bias, we have developed a new 1-D model for China, which removes a significant portion of the distance bias. For individual stations having sufficient P-wave residual data, we produce a map of the regional travel-time residuals from all well-located teleseismic events. Residuals are used only if they are smaller than 10?s in absolute value and if the seismic event is located with accuracy better than 25?km. From the residual data, correction surfaces are constructed using modified Bayesian kriging. Modified Bayesian kriging offers us the advantage of providing well-behaved interpolants and their errors, but requires that we have adequate error estimates associated with the travel-time residuals from which they are constructed. For our P-wave residual error estimate, we use the sum of measurement and modeling errors, where measurement error is based on signal-to-noise ratios when available, and on the published catalog estimate otherwise. Our modeling error originates from the variance of travel-time residuals for our 1-D China model. We calculate propagation path correction surfaces for 74 stations in and around China, including six stations from the International Monitoring System. The statistical significance of each correction surface is evaluated using a cross-validation technique. We show relocation results for nuclear tests from the Balapan and Lop Nor test sites, and for earthquakes located using interferometric synthetic aperture radar. These examples show that the use of propagation path correction surfaces in regional relocations eliminates distance bias in the residual curves and significantly improves the accuracy and precision of seismic event locations. 相似文献
4.
In this paper, we describe an efficient approach for quantifying uncertainty in two-phase flow applications due to perturbations of the permeability in a multiscale heterogeneous porous medium. The method is based on the application of the multiscale finite element method within the framework of Monte Carlo simulation and an efficient preprocessing construction of the multiscale basis functions. The quantities of interest for our applications are the Darcy velocity and breakthrough time and we quantify their uncertainty by constructing the respective cumulative distribution functions. For the Darcy velocity we use the multiscale finite element method, but due to lack of conservation, we apply the multiscale finite volume element method as an alternative for use with the two-phase flow problem. We provide a number of numerical examples to illustrate the performance of the method. 相似文献
5.
Nested covariance models, defined as linear combinations of basic covariance functions, are very popular in many branches of applied statistics, and in particular in geostatistics. A notorious limit of nested models is that the constants in the linear combination are bound to be nonnegative in order to preserve positive definiteness (admissibility). This paper studies nested models on d-dimensional spheres and spheres cross time. We show the exact interval of admissibility for the constants involved in the linear combinations. In particular, we show that at least one constant can be negative. One of the implications is that one can obtain a nested model attaining negative correlations. We provide characterization theorems for arbitrary linear combinations as well as for nonconvex combinations involving two covariance functions. We illustrate our findings through several examples involving nonconvex combinations of well-known parametric families of covariance functions. 相似文献
6.
The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity Keff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this ‘upscaling’ procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate Keff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function Keff (ψm) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent. 相似文献
7.
We compute site amplification functions for several sites in Mexico City using actual accelerograms recorded from 1985 to 2010 and we present field evidence of the change in the dominant period of a given site (Ts) as a consequence of ground subsidence produced by groundwater withdrawal. The changes in Ts are larger in the lake-bed zone where thicker clay deposits exist, although there are sites in the southwest part of the lake-bed zone where Ts has remained constant. With the information obtained from the site amplification functions and available geotechnical soundings we develop an empirical model to estimate the future value of Ts for several sites in Mexico City. Because the practical application of the model requires extrapolation we also present a method to compute the uncertainty of the model when it is used to forecast a future value of Ts at a given site. Our results suggest that significant changes in the dominant period at several sites in Mexico City can be expected in the future. 相似文献
8.
Wave-equation migration velocity analysis. I. Theory 总被引：2，自引：0，他引：2
We present a migration velocity analysis (MVA) method based on wavefield extrapolation. Similarly to conventional MVA, our method aims at iteratively improving the quality of the migrated image, as measured by the flatness of angle‐domain common‐image gathers (ADCIGs) over the aperture‐angle axis. However, instead of inverting the depth errors measured in ADCIGs using ray‐based tomography, we invert ‘image perturbations’ using a linearized wave‐equation operator. This operator relates perturbations of the migrated image to perturbations of the migration velocity. We use prestack Stolt residual migration to define the image perturbations that maximize the focusing and flatness of ADCIGs. Our linearized operator relates slowness perturbations to image perturbations, based on a truncation of the Born scattering series to the first‐order term. To avoid divergence of the inversion procedure when the velocity perturbations are too large for Born linearization of the wave equation, we do not invert directly the image perturbations obtained by residual migration, but a linearized version of the image perturbations. The linearized image perturbations are computed by a linearized prestack residual migration operator applied to the background image. We use numerical examples to illustrate how the backprojection of the linearized image perturbations, i.e. the gradient of our objective function, is well behaved, even in cases when backprojection of the original image perturbations would mislead the inversion and take it in the wrong direction. We demonstrate with simple synthetic examples that our method converges even when the initial velocity model is far from correct. In a companion paper, we illustrate the full potential of our method for estimating velocity anomalies under complex salt bodies. 相似文献
9.
Integrating migration velocity analysis and full waveform inversion can help reduce the high non‐linearity of the classic full waveform inversion objective function. The combination of inverting for the long and short wavelength components of the velocity model using a dual objective function that is sensitive to both components is still very expensive and have produced mixed results. We develop an approach that includes both components integrated to complement each other. We specifically utilize the image to generate reflections in our synthetic data only when the velocity model is not capable of producing such reflections. As a result, we get the migration velocity analysis working when we need it, and we mitigate its influence when the velocity model produces accurate reflections (possibly first for the low frequencies). This is achieved using a novel objective function that includes both objectives. Applications to a layered model and the Marmousi model demonstrate the main features of the approach. 相似文献
10.
A few extensively studied downhole seismic arrays are commonly used in detailed site response studies. Thus, there is a critical need to increase the number of sites that are used to compare soil constitutive models. Toward this end, we develop a classification scheme for downhole arrays that identifies stations where common wave propagation assumptions are valid. For stations where the one-dimensional (1D) assumption does not hold, we identify different levels of complexity that must be accounted for, which is a function of the inter-event variability and the similarity between the empirical and one-dimensional theoretical transfer functions. The classification is based on 100 seismic arrays in Japan that have recorded surface accelerations in excess of 0.3g, 69 of which exhibit low inter-event variability. The response at 16 of these sites resembles the one-dimensional response, while the others deviate from one-dimensional behavior, indicating that the one-dimensional assumption is not acceptable in most cases. We check our interpretation of the taxonomy with field investigations at two stations. The field observations show large lateral variations of the velocity profile across distances of hundreds of meters at the station where we expect the one-dimensional assumption does not hold. 相似文献
11.
We propose a mathematical representation to qualitatively describe the spatio-temporal slip evolution during earthquake rupture
in an efficient and easy-to-use manner for numerical simulations of strong ground motion. It is based on three basis functions
and associated expansion coefficients. It is an extension of the approach of Ide and Takeo, (J Geophys Res, 102:27379–27391, 1997). We compare our approach and theirs using simple kinematic source models to illustrate differences
between the two approaches, and show that our approach more accurately represents the spatio-temporal slip evolution. We also
propose a technique based on our representation for extracting a spatio-temporal slip velocity function from a kinematic source
model obtained by the conventional source inversion. We then demonstrate the feasibility of our procedure with application
to an inverted source model of the 26 March 1997 Northwestern Kagoshima, Japan, earthquake (M
W6.1). In the simulations for actual earthquakes, source models obtained from kinematic source inversions are commonly employed.
Our scheme could be used as an interpolation method of slip time functions from relatively coarse finite-source models obtained
by conventional kinematic source inversions. 相似文献
12.
《Advances in water resources》2005,28(9):964-974
Water flow in partially saturated heterogeneous porous formations is modelled by regarding the hydraulic parameters as stationary random space functions (RSFs). As a consequence, the flow variables are also RSFs, and we aim to develop a procedure to derive the effective hydraulic conductivity (EHC). The methodology relies on a perturbation approach which regards the variances of the hydraulic parameters as small quantities. By using the Gardner’s [Gardner WR. Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table. Soil Sci 1958;85:228–32] two-parameters (Ks, α) model for the local unsaturated conductivity, we obtain the EHC for any dimensionality d of the flow domain, and arbitrary correlation functions of the input RSFs. Unlike previous studies [e.g. Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 1. Statistically isotropic media. Water Resour Res 1985;21;447–56, Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 2. Statistically anisotropic media with variable α. Water Resour Res 1985:21:457–64], the EHC is represented here as product between the local scale conductivity valid for a domain of mean parameters, and a correction function κ1 which depends on the medium heterogeneity structure and the mean pressure head.Generally, the correction function κ1 is expressed by d-fold quadrature. These quadratures are further reduced after adopting specific (i.e. exponential and Gaussian) structure for the (cross) correlation functions involved in the computation of κ1. We have also focused on some particular formation structures which are relevant for the applications, and permit simplification of the computational aspect, as well.We investigate effects of the heterogeneity formation properties as well as the mean head on the structure of κ1. Overall, results suggest that, given the formation statistics, the impact of the heterogeneity upon κ1 is enhanced as the medium becomes drier. This is particularly so when the variability of the fluctuation of Y = ln Ks is small compared with that of ζ = ln α. Conversely, when the heterogeneity of Y is prevalent upon that of ζ, κ1 is influenced solely by the anisotropic structure of the formation unless the horizontal correlation scales are much greater than the vertical ones. 相似文献
13.
14.
— Average envelope shapes (mean square amplitude time histories) of small earthquakes represent a convenient basis for the construction of semi-empirical stochastic “Green's functions,” needed for prediction of future strong ground motion. At the same time, they provide crucial evidence for verification of the theories of scattering of high-frequency seismic waves in the lithosphere. To determine such shapes in the Kamchatka region we use the records of near (R = 50–200 km) shallow earthquakes located around the broadband station PET. On these records, we select the S-wave group and determine its root-mean-square duration T rms, separately for each of the five octave frequency bands. We determine the empirical T rms vs. distance dependence and find it to be very close to a linear one. At the reference distance R = 100 km, average T rms decreases from 5.4 se c for the 0.75 Hz band to 3.9 sec for the 12 Hz band. To analyze average envelopes, we assume that the functional form of the envelope shape function is independent of distance, and stretch each of the observed envelopes along the time axis so as to reduce it to a fixed distance. Through averaging of these envelopes we obtain characteristic envelope shape functions. We qualitatively analyze these shapes and find that around the peak they are close to the shapes expected for a medium with power-law inhomogeneity spectrum, with the spectral exponent 3.5–4. From onset-to-peak delay times we derive the values of transport mean free path and of scattering Q for a set of distances. 相似文献
15.
Mathieu Ribatet Eric Sauquet Jean-Michel Grésillon Taha B. M. J. Ouarda 《Stochastic Environmental Research and Risk Assessment (SERRA)》2007,21(4):327-339
Flood frequency analysis is usually based on the fitting of an extreme value distribution to the local streamflow series.
However, when the local data series is short, frequency analysis results become unreliable. Regional frequency analysis is
a convenient way to reduce the estimation uncertainty. In this work, we propose a regional Bayesian model for short record
length sites. This model is less restrictive than the index flood model while preserving the formalism of “homogeneous regions”.
The performance of the proposed model is assessed on a set of gauging stations in France. The accuracy of quantile estimates
as a function of the degree of homogeneity of the pooling group is also analysed. The results indicate that the regional Bayesian
model outperforms the index flood model and local estimators. Furthermore, it seems that working with relatively large and
homogeneous regions may lead to more accurate results than working with smaller and highly homogeneous regions. 相似文献
16.
In this study, we adopt an improved Bayesian approach based on free-knot B-spline bases to study the spatial and temporal distribution of the b-value. Synthetic tests show that the improved Bayesian approach has a superior performance compared to the Bayesian approach as well as the widely used maximum likelihood estimation (MLE) method in fitting the real variation of b-values. We then apply the improved Bayesian approach to North China and find that the b-value has a clear relevance to seismicity. Temporal changes of b-values are also investigated in two specific areas of North China. We interpret sharp decreases in the b-values as useful messages in earthquake hazard analysis. 相似文献
17.
We obtained an exact solution in terms of the discharge potential for a constant-strength line-sink that satisfies the modified Helmholtz equation for groundwater flow, for example for semi-confined flow and transient flow. The solution is obtained by integrating the potential for a point sink (well) along a straight line element. The potential for the point-sink is the modified Bessel function of the second kind and zero order K0. Since K0 cannot be integrated directly (in closed form) along a line-element, earlier solutions for a line-sink have been obtained by integrating polynomial approximations to K0. These approximations, however, are only valid up to a certain distance from the well and consequently impose a limit on the length of the line-sink. In this paper we integrate an exact series representation for K0 that is valid at any distance from the well, thus allowing integration along line-elements of any length, at least in theory. Numerical difficulties arise when evaluating our expressions at large distances from the line-sink, but these are shown to be of little consequence in practice. We made use of Wirtinger calculus to facilitate integration and also to allow us to arrive at exact expressions for the integrated flux over a poly-line and the total leakage over a domain. These properties are essential when using the solution in the context of the Analytic Element Method (AEM). We demonstrate our solution for the case of semi-confined flow (with leakage) and for the case of transient flow in the context of the Laplace Transform Analytic Element Method (LT-AEM). 相似文献
18.
Seismic hazard and risk in the Beijing?CTianjin?CTangshan, China, area were estimated from 500-year intensity observations. First, we digitized the intensity observations (maps) using ArcGIS with a cell size of 0.1?×?0.1°. Second, we performed a statistical analysis on the digitized intensity data, determined an average b value (0.39), and derived the intensity?Cfrequency relationship (hazard curve) for each cell. Finally, based on a Poisson model for earthquake occurrence, we calculated seismic risk in terms of a probability of I????7, 8, or 9 in 50?years. We also calculated the corresponding 10 percent probability of exceedance of these intensities in 50?years. The advantages of assessing seismic hazard and risk from intensity records are that (1) fewer assumptions (i.e., earthquake source and ground motion attenuation) are made, and (2) site-effect is included. Our study shows that the area has high seismic hazard and risk. Our study also suggests that current design peak ground acceleration or intensity for the area may not be adequate. 相似文献
19.
Hwa-Lung Yu Shang-Chen Ku Alexander Kolovos 《Stochastic Environmental Research and Risk Assessment (SERRA)》2016,30(2):665-679
In recent years, there has been a fast growing interest in the space–time data processing capacity of Geographic Information Systems (GIS). In this paper we present a new GIS-based tool for advanced geostatistical analysis of space–time data; it combines stochastic analysis, prediction, and GIS visualization technology. The proposed toolbox is based on the Bayesian Maximum Entropy theory that formulates its approach under a mature knowledge synthesis framework. We exhibit the toolbox features and use it for particulate matter spatiotemporal mapping in Taipei, in a proof-of-concept study where the serious preferential sampling issue is present. The proposed toolbox enables tight coupling of advanced spatiotemporal analysis functions with a GIS environment, i.e. QGIS. As a result, our contribution leads to a more seamless interaction between spatiotemporal analysis tools and GIS built-in functions; and utterly enhances the functionality of GIS software as a comprehensive knowledge processing and dissemination platform. 相似文献
20.
Convection in the Earth’s core is usually studied in the Boussinesq approximation in which the compressibility of the liquid is ignored. The density of the Earth’s core varies from ICB to CMB by approximately 20%. The question of whether we need to take this variation into account in core convection and dynamo models is examined. We show that it is in the thermodynamic equations that differences between compressible and Boussinesq models become most apparent. The heat flux conducted down the adiabat is much smaller near the inner core boundary than it is near the core-mantle boundary. In consequence, the heat flux carried by convection is much larger nearer the inner core boundary than it is near the core-mantle boundary. This effect will have an important influence on dynamo models. Boussinesq models also assume implicitly that the rate of working of the gravitational and buoyancy forces, as well as the Ohmic and viscous dissipation, are small compared to the heat flux through the core. These terms are not negligible in the Earth’s core heat budget, and neglecting them makes it difficult to get a thermodynamically consistent picture of core convection. We show that the usual anelastic equations simplify considerably if the anelastic liquid approximation, valid if αT?1, where α is the coefficient of expansion and T a typical core temperature, is used. The resulting set of equations are not significantly more difficult to solve numerically than the usual Boussinesq equations. The relationship of our anelastic liquid equations to the Boussinesq equations is also examined. 相似文献