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1.
Topographic effects due to irregular surface terrain may prevent accurate interpretation of magnetotelluric (MT) data. Three-dimensional (3-D) topographic effects have been investigated for a trapezoidal hill model using an edge finite-element method. The 3-D topography generates significant MT anomalies, and has both galvanic and inductive effects in any polarization. This paper presents two different correction algorithms, which are applied to the impedance tensor and to both electric and magnetic fields, respectively, to reduce topographic effects on MT data. The correction procedures using a homogeneous background resistivity derived from a simple averaging method effectively decrease distortions caused by surface topography, and improve the quality of subsurface interpretation. Nonlinear least-squares inversion of topography-corrected data successfully recovers most of structures including a conductive or resistive dyke.  相似文献   

2.
We present a semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous model consisting of eccentrically nested spheres. Several numerical methods for 2-D and 3-D viscoelastic relaxation modelling have been applied recently, including finite-element and spectral-finite-difference schemes. The present semi-analytical approach provides a model response against which more general numerical algorithms can be validated. The eccentrically nested sphere solution has been tested by comparing it with the analytical solutions for viscoelastic relaxation in a homogeneous sphere and in two concentrically nested spheres, and good agreement was obtained.  相似文献   

3.
Traveltime computation methods for strongly heterogeneous 3-D media developed during recent years are well suited for earthquake location. We present here a new method based on the traveltime algorithm of Podvin-Lecomte, related to the inverse problem formulation of Tarantola & Valette. The Podvin-Lecomte method, based on the Huygens principle, is very robust and allows arbitrary surface topography and station placement even for borehole instruments. First arrival traveltimes are computed for each of the recording stations using a fine 3-D velocity mesh (up to 106 cells on a workstation). The traveltime grid allows the use of the Tarantola & Valette formulation, which enables a full non-linear approach. The solution is given as a 3-D probability density function of hypocentre coordinates, which accounts for the arrival time measurements as well as a priori information for the location, the accuracy of both the arrival time readings and the computation of the theoretical traveltimes. This powerful method called 3DGRIDLOC gives the location of the induced seismicity of the gas field of Lacq (France) using 443 520 cells of a 3-D velocity mesh and the observations from nine recording stations, one of which is located at the bottom of a 3880 m deep borehole. Location of synthetic foci as well as more than 500 actual earthquakes shows the real advantages of this new method versus the classical HYPO71. A new insight into the induced seismicity is now possible: induced seismicity may occur as far away as 10 km from the gas reservoir and involve a much greater volume of rock than expected using earlier locations.  相似文献   

4.
To speed up the calculation of the field Jacobian for 2-D magnetoteliuric inversion using finite elements, the principle of electromagnetic reciprocity is applied. The governing relationship for the Jacobian of the field along strike is obtained by differentiating the Helmholtz equation with respect to the resistivity of each region in the finite-element mesh. The result is a similar Helmholtz equation for the Jacobian, with new sources distributed over all nodes within the parameter medium. However, according to the principle of electromagnetic reciprocity, the roles of sources and receivers are interchangeable. Utilizing reciprocity, the field values obtained from the original forward problem and for new unit sources imposed at the receivers are then utilized in the calculation of the Jacobian by simple multiplication and summation with finite-element terms at each rectangle in the mesh. For the auxiliary (across-strike) fields, the Jacobian terms are obtained by solving source vectors loaded with parabola coefficients used in the approximation to Maxwell's equations. Jacobian terms for the apparent resistivity ( p a), the impedance phase (φ) and the vertical magnetic field ( K zy) are then calculated utilizing the parallel- and auxiliary-field Jacobians. Comparison of Jacobian values obtained from reciprocity calculations and by differencing two forward solutions show that the reciprocity method is accurate and can be used to decrease the number of calculations required to obtain sensitivities by one to two orders of magnitude.  相似文献   

5.
Abstract

A vector-based geographical information system (GIS) is used to generate a variably-sized triangular element finite-element mesh from mappable features. Important digitally-mapped features are automatically linked to nodes in the finite-element model, ensuring an efficient, virtually error-free alternative to the tedious process of mesh design and data-input preparation by other methods. The procedure permits the user to work interactively with graphically-displayed hydrologic information about the study area allowing different mesh sizes to be used as needed, based on hydrologic complexity. The mesh-generaiion programs are stand-alone macros within the GIS that set up the basic data defining a finite-element mesh for many different finite-element model programs.  相似文献   

6.
This study introduces a new Triangulated Irregular Network(TIN) compression method and a progressive visualization technique using Delaunay triangulation. The compression strategy is based on the assumption that most triangulated 2.5-dimensional terrains are very similar to their Delaunay triangulation. Therefore, the compression algorithm only needs to maintain a few edges that are not included in the Delaunay edges. An efficient encoding method is presented for the set of edges by using vertex reordering and a general bracketing method. In experiments, the compression method examined several sets of TIN data with various resolutions, which were generated by five typical terrain simplification algorithms. By exploiting the results, the connecting structures of common terrain data are compressed to 0.17 bits per vertex on average, which is superior to the results of previous methods. The results are shown by a progressive visualization method for web-based GIS.  相似文献   

7.
Applying the infinite Prandtl number approximation, a semi-analytical solution for computing 2-D axisymmetric viscous Stokes flow in a model consisting of two eccentrically nested spheres of different viscosities is derived. Since numerical codes based on spectral or finite techniques for modelling mantle flow in a spherical geometry in the presence of lateral viscosity variation are becoming more and more popular, reliable examples for testing and validating such codes are extremely useful. The eccentrically nested sphere solution was used to test a numerical algorithm based on a mixed spherical-harmonic finite-element formulation of the Stokes problem, and good agreement was obtained.  相似文献   

8.
When full 3-D modelling is too costly or cumbersome, computations of 3-D elastic wave propagation in laterally heterogeneous, multilayered 2-D geological structures may enhance considerably our ability to predict strong ground motion for seismological and engineering purposes. Towards this goal, we extend the method based on the combination of the thin-layer finite-element and boundary-element methods (TLFE-BEM) and calculate windowend f - k spectra of the 3-D wavefield. The windowed f - k spectra are spatially localized spectra from which the local properties of the wavefield can be extracted. The TLFE-BEM is particularly suited for calculating the complete wavefield where surface waves are dominant in multilayered media. The computations are performed in the frequency domain, providing the f - k spectra directly. From the results for the 3-D wavefield excited by a point source in a 2-D multilayered, sloped structure, it can be said that the phase velocity of the fundamental-mode Rayleigh wave in a laterally heterogeneous multilayered medium, estimated from the windowed f - k spectra, varies with the location of the point source. For the model calculated in this article, the phase velocity varies between the value for the flat layered structure of the thick-layer side and that for the structure just under the centre of the window. The exact subsurface structure just under the centre of an array in a laterally heterogeneous medium cannot be obtained if we use the f - k spectral analysis assuming a flat layered structure.  相似文献   

9.
We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are considered: (i) the spherical analogue of the one-dimensional (1-D) periodogram, (ii) the maximum-likelihood method and (iii) a spherical analogue of the 1-D multitaper method. The periodogram exhibits strong spectral leakage, especially for small regions of area   A ≪ 4π  , and is generally unsuitable for spherical spectral analysis applications, just as it is in 1-D. The maximum-likelihood method is particularly useful in the case of nearly-whole-sphere coverage,   A ≈ 4π  , and has been widely used in cosmology to estimate the spectrum of the cosmic microwave background radiation from spacecraft observations. The spherical multitaper method affords easy control over the fundamental trade-off between spectral resolution and variance, and is easily implemented regardless of the region size, requiring neither non-linear iteration nor large-scale matrix inversion. As a result, the method is ideally suited for most applications in geophysics, geodesy or planetary science, where the objective is to obtain a spatially localized estimate of the spectrum of a signal from noisy data within a pre-selected and typically small region.  相似文献   

10.
We present a spectral-finite-element approach to the 2-D forward problem for electromagnetic induction in a spherical earth. It represents an alternative to a variety of numerical methods for 2-D global electromagnetic modelling introduced recently (e.g. the perturbation expansion approach, the finite difference scheme). It may be used to estimate the effect of a possible axisymmetric structure of electrical conductivity of the mantle on surface observations, or it may serve as a tool for testing methods and codes for 3-D global electromagnetic modelling. The ultimate goal of these electromagnetic studies is to learn about the Earth's 3-D electrical structure.
Since the spectral-finite-element approach comes from the variational formulation, we formulate the 2-D electromagnetic induction problem in a variational sense. The boundary data used in this formulation consist of the horizontal components of the total magnetic intensity measured on the Earth's surface. In this the variational approach differs from other methods, which usually use spherical harmonic coefficients of external magnetic sources as input data. We verify the assumptions of the Lax-Milgram theorem and show that the variational solution exists and is unique. The spectral-finite-element approach then means that the problem is parametrized by spherical harmonics in the angular direction, whereas finite elements span the radial direction. The solution is searched for by the Galerkin method, which leads to the solving of a system of linear algebraic equations. The method and code have been tested for Everett & Schultz's (1995) model of two eccentrically nested spheres, and good agreement has been obtained.  相似文献   

11.
New techniques for improving both the computational and imaging performance of the three-dimensional (3-D) electromagnetic inverse problem are presented. A non-linear conjugate gradient algorithm is the framework of the inversion scheme. Full wave equation modelling for controlled sources is utilized for data simulation along with an efficient gradient computation approach for the model update. Improving the modelling efficiency of the 3-D finite difference (FD) method involves the separation of the potentially large modelling mesh, defining the set of model parameters, from the computational FD meshes used for field simulation. Grid spacings and thus overall grid sizes can be reduced and optimized according to source frequencies and source–receiver offsets of a given input data set. Further computational efficiency is obtained by combining different levels of parallelization. While the parallel scheme allows for an arbitrarily large number of parallel tasks, the relative amount of message passing is kept constant. Image enhancement is achieved by model parameter transformation functions, which enforce bounded conductivity parameters and thus prevent parameter overshoots. Further, a remedy for treating distorted data within the inversion process is presented. Data distortions simulated here include positioning errors and a highly conductive overburden, hiding the desired target signal. The methods are demonstrated using both synthetic and field data.  相似文献   

12.
We have been developing an accurate and efficient numerical scheme, which uses the finite-difference method (FDM) in spherical coordinates, for the computation of global seismic wave propagation through laterally heterogeneous realistic Earth models. In the field of global seismology, traditional axisymmetric modeling has been used widely as an efficient approach since it can solve the 3-D elastodynamic equation in spherical coordinates on a 2-D cross-section of the Earth, assuming structures to be invariant with respect to the axis through the seismic source. However, it has the severe disadvantages that asymmetric structures about the axis cannot be incorporated and the source mechanisms with arbitrary shear dislocation have not been attempted for a long time. Our scheme is based on the framework of axisymmetric modeling but has been extended to treat asymmetric structures, arbitrary moment-tensor point sources, anelastic attenuation, and the Earth center which is a singularity of wave equations in spherical coordinates. All these types of schemes which solve 3-D wavefields on a 2-D model cross-section are classified as 2.5-D modeling, so we have named our scheme the spherical 2.5-D FDM. In this study, we compare synthetic seismograms calculated using our FDM scheme with three-component observed long-period seismograms including data from stations newly installed in Antarctica in conjunction with the International Polar Year (IPY) 2007–2008. Seismic data from inland Antarctica are expected to reveal images of the Earth's deep interior with enhanced resolution because of the high signal-to-noise ratio and wide extent of this region, in addition to the rarity of sampling paths along the rotation axis of the Earth. We calculate synthetic seismograms through the preliminary reference earth model (PREM) including attenuation using a moment-tensor point source for the November 9, 2009 Fiji earthquake. Our results show quite good agreement between synthetic and observed seismograms, which indicates the accuracy of observations in the Antarctica, as well as the feasibility of the spherical 2.5-D modeling scheme.  相似文献   

13.
Today's numerical methods like the Spectral Element Method (SEM) allow accurate simulation of the whole seismic field in complex 3-D geological media. However, the accuracy of such a method requires physical discontinuities to be matched by mesh interfaces. In many realistic earth models, the design of such a mesh is difficult and quite ineffective in terms of numerical cost. In this paper, we address a limited aspect of this problem: an earth model with a thin shallow layer below the free surface in which the elastic and density properties are different from the rest of the medium and in which rapid vertical variations are allowed. We only consider here smooth lateral variations of the thickness and elastic properties of the shallow layer. In the limit of a shallow layer thickness very small compared to the smallest wavelength of the wavefield, by resorting to a second order matching asymptotic approximation, the thin layer can be replaced by a vertically smooth effective medium without discontinuities together with a specific Dirichlet to Neumann (DtN) surface boundary condition. Such a formulation allows to accurately take into account complex thin shallow structures within the SEM without the classical mesh design and time step constraints. Corrections at receivers and source—when the source is located within the thin shallow layer—have been also derived. Accuracy and efficiency of this formulation are assessed on academic tests. The stability and limitations of this formulation are also discussed.  相似文献   

14.
I present a 2-D numerical-modelling algorithm based on a first-order velocity-stress hyperbolic system and a non-rectangular-grid finite-difference operator. In this method the velocity and stress are defined at different nodes for a staggered grid. The scheme uses non-orthogonal grids, thereby surface topography and curved interfaces can be easily modelled in the seismic-wave-propagation stimulation. The free-surface conditions of complex geometry are achieved by using integral equilibrium equations on the surface, and the stability of the free-surface conditions is improved by introducing local filter modification. The method incorporates desirable qualities of the finite-element method and the staggered-grid finite-difference scheme, which is of high accuracy and low computational cost.  相似文献   

15.
We present two equivalent algorithms for iterative linearized waveform inversion for 3-D Earth structure with respect to an arbitrary 3-D starting model; one is a matrix formulation, and the second is a wavefield formulation. Both algorithms require the computation of accurate synthetic seismograms, but neither requires that any particular method be used to compute the synthetics. The matrix formulation is equivalent to our previously published algorithm (Hara, Tsuboi & Geller 1991), but requires less than 10 per cent of the CPU time of the previous algorithm. The wavefield algorithm is equivalent to that of Tarantola (1986) and Mora (1987), but appears to be substantially more efficient.  相似文献   

16.
Summary. The reflectivity method for complete SH seismograms has been extended to two-dimensionally layered structures. The Aki-Larner technique is generalized to solve the integral equations for 2-D boundary conditions, and propagator matrices are enlarged to express a total SH wavefield. Synthetic seismograms in a soft basin are calculated for an incident plane-wave. They compare favourably with the results of the finite-element and finite-difference methods even in the later portion where asymptotic ray and beam theories break down. Synthetic seismograms due to a line force and a point dislocation are also presented.  相似文献   

17.
二维Delaunay三角网的任意点删除算法研究   总被引：1，自引：0，他引：1  
针对目前基于影响域多边形剖分的点删除算法缺陷,提出一种二维Delaunay三角网点删除算法。首先利用具有拓扑关系的三角网搜索影响多边形,并以三角形矢量面积为工具三角剖分影响域多边形,最后通过镶嵌优化后的剖分三角网完成点的删除,且满足Delaunay法则。通过测试证明了算法的可靠性和高效性。  相似文献   

18.
Seismic imaging of the laterally varying D" region beneath the Cocos Plate   总被引：1，自引：0，他引：1  
We use an axisymmetric, spherical Earth finite difference algorithm to model SH -wave propagation through cross-sections of laterally varying lower mantle models beneath the Cocos Plate derived from recent data analyses. Synthetic seismograms with dominant periods as short as 4 s are computed for several models: (1) a D" reflector 264 km above the core–mantle boundary with laterally varying S -wave velocity increases of 0.9–2.6 per cent, based on localized structures from a 1-D double-array stacking method; (2) an undulating D" reflector with large topography and uniform velocity increase obtained using a 3-D migration method and (3) cross-sections through the 3-D mantle S -wave velocity tomography model TXBW. We apply double-array stacking to assess model predictions of data. Of the models explored, the S -wave tomography model TXBW displays the best overall agreement with data. The undulating reflector produces a double Scd arrival that may be useful in future studies for distinguishing between D" volumetric heterogeneity and D" discontinuity topography. Synthetics for the laterally varying models show waveform variability not observed in 1-D model predictions. It is challenging to predict 3-D structure based on localized 1-D models when lateral structural variations are on the order of a few wavelengths of the energy used, particularly for the grazing geometry of our data. Iterative approaches of computing synthetic seismograms and adjusting model characteristics by considering path integral effects are necessary to accurately model fine-scale D" structure.  相似文献   

19.
Long-period geomagnetic data can resolve large-scale 3-D mantle electrical conductivity heterogeneities which are indicators of physiochemical variations found in the Earth's dynamic mantle. A prerequisite for mapping such heterogeneity is the ability to model accurately electromagnetic induction in a heterogeneous sphere. A previously developed finite element method solution to the geomagnetic induction problem is validated against an analytic solution for a fully 3-D geometry: an off-axis spherical inclusion embedded in a uniform sphere. Geomagnetic induction is then modelled in a uniform spherical mantle overlain by a realistic distribution of oceanic and continental conductances. Our results indicate that the contrast in electrical conductivity between oceans and continents is not primarily responsible for the observed geographic variability of long-period geomagnetic data. In the absence of persistent high-wavenumber magnetospheric disturbances, this argues strongly for the existence of large-scale, high-contrast electrical conductivity heterogeneities in the mid-mantle. Lastly, for several periods the geomagnetic anomaly associated with a mid-mantle spherical inclusion is calculated. A high-contrast inclusion can be readily detected beneath the outer shell of oceans and continents. A comparison between observed and computed c responses suggests that the mid-mantle contains more than one order of magnitude of lateral variability in electrical conductivity, while the upper mantle contains at least two orders of magnitude of lateral variability in electrical conductivity.  相似文献   

20.
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