共查询到20条相似文献，搜索用时 15 毫秒
1.
Zhang Jianfeng 《Geophysical Journal International》1999,139(1):171-182
A quadrangle-grid velocity–stress finite difference method, based on a first-order hyperbolic system that is equivalent to Biot's equations, is developed for the simulation of wave propagation in 2-D heterogeneous porous media. In this method the velocity components of the solid material and of the pore fluid relative to that of the solid, and the stress components of three solid stresses and one fluid pressure are defined at different nodes for a staggered non-rectangular grid. The scheme uses non-orthogonal grids, allowing surface topography and curved interfaces to be easily modelled in the numerical simulation of seismic responses of poroelastic reservoirs. The free-surface conditions of complex geometry are achieved by using integral equilibrium equations on the surface, and the source implementations are simple. The algorithm is an extension of the quadrangle-grid finite difference method used for elastic wave equations. 相似文献
2.
The dynamic coalescence of two mode II cracks on a planar fault is simulated here using the elastodynamic boundary integral equation method. We focus on the complexity of the resultant slip rate and seismic radiation in the crack coalescence model (CCM) and on the reconstruction of a single crack model (SCM) that can reproduce the CCM waveforms from heterogeneous source parameters rather than coalescence. Simulation results reveal that localized higher slip rates are generated by coalescence as a result of stress interaction between the approaching crack tips. The synthesized seismic radiation exhibits a distinct coalescence phase that has striking similarities to stopping phases in the radiation and propagation properties. The corresponding SCM yields a singular increase in the stress drop distribution, which is accompanied by a sudden decrease in it across the point of coalescence in the CCM. This implies that the generation of high-frequency radiation is more efficient from coalescence than from stopping, although both phenomena exhibit the same strong ω−2 -type displacement spectra. 相似文献
3.
A conservative staggered-grid finite difference method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth's deep interior. This solution in spherical geometry is derived from that originally presented by Mackie et al. (1994 ) for Cartesian geometry. The difference equations that we solve are second order in the magnetic field H , and are derived from the integral form of Maxwell's equations on a staggered grid in spherical coordinates. The resulting matrix system of equations is sparse, symmetric, real everywhere except along the diagonal and ill-conditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal sub-blocks of the coefficient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we compare our results against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model ( Kuvshinov & Pankratov 1994 ), and against a quasi-analytic solution for an azimuthally asymmetric configuration of eccentrically nested spheres ( Martinec 1998 ). 相似文献
4.
When interpreting electromagnetic fields observed at the Earth's surface in a realistic geophysical environment it is often necessary to pay special attention to the effects caused by inhomogeneities of the subsurface sedimentary and/or water layer and by inhomogeneities of the Earth's crust. The inhomogeneities of the Earth's crust are expected to be especially important when the electromagnetic field is generated by a source located in a magma chamber of a volcano. The simulation of such effects can be carried out using generalized thin-sheet models, which were independently introduced by Dmitriev (1969 ) and Ranganayaki & Madden (1980 ). In the first part of the paper, a system of integral equations is derived for the horizontal current that flows in the subsurface inhomogeneous conductive layer and for the vertical current crossing the inhomogeneous resistive layer representing the Earth's mantle. The terms relating to the finite thickness of the laterally inhomogeneous part of the model are retained in the equations. This only marginally complicates the equations, whilst allowing for a significant expansion of the approximation limits.
The system of integral equations is solved using the iterative dissipative method developed by the authors in the period from 1978 to 1988. The method can be applied to the simulation of the electromagnetic field in an arbitrary inhomogeneous medium that dissipates the electromagnetic energy. When considered on a finite numerical grid, the integral equations are reduced to a system of linear equations that possess the same contraction properties as the original equations. As a result, the rate at which the iterative-perturbation sequence converges to the solution remains independent of the numerical grid used for the calculations. In contrast to previous publications on the method, aspects of the algorithm implementation that guarantee its effectiveness and robustness are discussed here. 相似文献
The system of integral equations is solved using the iterative dissipative method developed by the authors in the period from 1978 to 1988. The method can be applied to the simulation of the electromagnetic field in an arbitrary inhomogeneous medium that dissipates the electromagnetic energy. When considered on a finite numerical grid, the integral equations are reduced to a system of linear equations that possess the same contraction properties as the original equations. As a result, the rate at which the iterative-perturbation sequence converges to the solution remains independent of the numerical grid used for the calculations. In contrast to previous publications on the method, aspects of the algorithm implementation that guarantee its effectiveness and robustness are discussed here. 相似文献
5.
We have developed an inversion formuialion for velocity and attenuation structure using seismic attributes, including envelope amplitude, instantaneous frequency and arrival times of selected seismic phases. We refer to this approach as AFT inversion for amplitude, (instantaneous) frequency and time. Complex trace analysis is used to extract the different seismic attributes. The instantaneous frequency data are converted to t * using a matching procedure that approximately removes the effects of the source spectra. To invert for structure, ray-perturbation methods are used to compute the sensitivity of the seismic attributes to variations in the model. An iterative inversion procedure is then performed from smooth to less smooth models that progressively incorporates the shorter-wavelength components of the model. To illustrate the method, seismic attributes are extracted from seismic-refraction data of the Ouachita PASSCAL experiment and used to invert for shallow crustal velocity and attenuation structure. Although amplitude data are sensitive to model roughness, the inverted velocity and attenuation models were required by the data to maintain a relatively smooth character. The amplitude and t * data were needed, along with the traveltimes, at each step of the inversion in order to fit all the seismic attributes at the final iteration. 相似文献
6.
C. H. Chapman 《Geophysical Journal International》1981,66(2):445-453
Summary. The Radon transform or slant stack is becoming a widely used technique for analysing high-quality reflection and refraction data. The transform normally used is applicable to data from a line source in a plane model, that is, one Cartesian coordinate. The theoretical basis for the Radon transform pair for one Cartesian coordinate has appeared in the seismological literature. For a point source in plane or spherical geometry, or a line source in cylindrical geometry only the Radon transform for the direct problem (computation of synthetic seismograms) has been published. To analyse data an approximate inverse transform has been used. In this research note, the exact forms of the generalized Radon transform pairs are completed for a point source in plane or spherical geometry, and for a line source in cylindrical geometry. The differences will be important if the waveforms are being interpreted, and are most significant for near-vertical reflections—the type of data most commonly slant stacked. 相似文献
7.
Summary. The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time.
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves. 相似文献
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves. 相似文献
8.
Volcano seismology often deals with rather shallow seismic sources and seismic stations deployed in their near field. The complex stratigraphy on volcanoes and near‐field source effects have a strong impact on the seismic wavefield, complicating the interpretation techniques that are usually employed in earthquake seismology. In addition, as most volcanoes have a pronounced topography, the interference of the seismic wavefield with the stress‐free surface results in severe waveform perturbations that affect seismic interpretation methods. In this study we deal predominantly with the surface effects, but take into account the impact of a typical volcano stratigraphy as well as near‐field source effects. We derive a correction term for plane seismic waves and a plane‐free surface such that for smooth topographies the effect of the free surface can be totally removed. Seismo‐volcanic sources radiate energy in a broad frequency range with a correspondingly wide range of different Fresnel zones. A 2‐D boundary element method is employed to study how the size of the Fresnel zone is dependent on source depth, dominant wavelength and topography in order to estimate the limits of the plane wave approximation. This approximation remains valid if the dominant wavelength does not exceed twice the source depth. Further aspects of this study concern particle motion analysis to locate point sources and the influence of the stratigraphy on particle motions. Furthermore, the deployment strategy of seismic instruments on volcanoes, as well as the direct interpretation of the broad‐band waveforms in terms of pressure fluctuations in the volcanic plumbing system, are discussed. 相似文献
9.
Summary. The one-dimensional acoustic wave equation has been transformed to two coupled first-order equations whose inverse solution is obtained through application of the Gopinath and Sondhi integral equation. A scattering solution of the Schrödinger wave equation for an explosive source leads us to express the kernel of the Gopinath–Sondhi integral equation in terms of a seismic reflection response. A numerical solution of the integral equation obtained by a trapezoidal rule yields a continuous impedance profile whose derivative has step-like discontinuities. The method is illustrated with computer model studies. 相似文献
10.
S. N. Bhattacharya 《Geophysical Journal International》1976,47(3):411-444
Summary. Amplitude spectra of Rayleigh and Love waves in a layered non-gravitating spherical earth have been obtained using as a source, displacement and stress discontinuities. In each layer elastic parameters and density follow specified functions of radial distance and the solutions of the equations of motion are obtained in terms of exponential functions. The Thomson—Haskell method is extended to this case. The problem reduces to simple calculations as in a plane-layered medium. Numerical results of phase and group velocities up to periods of 300 s in various earth models when compared with earlier results (obtained by numerical integration) show that the present method can be used with sufficient accuracy. The differences in phase velocity, group velocity and amplitude (also surface ellipticity in the case of Rayleigh waves) between spherical- and flat-earth models have been investigated in the range 20–300–s period and expressed in polynomials in the period. 相似文献
11.
We derive a set of non-hypersingular boundary integral equations, both elastodynamic and elastostatic, for the analysis of arbitrarily shaped 2-D anti-plane and in-plane cracks located in an infinite homogeneous isotropic medium, rendered in a unified nomenclature for all cases. The hypersingularities that appear in the usual formulations for the dynamic cases, existent both at the source point and at the wavefront, are removed by way of a regularization technique based on integration by parts. The equations for the in-plane cases are presented in terms of a local Cartesian coordinate system, one of the axes of which is always held locally tangential to the crack trace. The expressions for the elastic field at any point on the model plane are also given.
Our formulations are shown to yield accurate numerical results, as long as appropriate stabilization measures are taken in the numerical scheme. The numerical applicability of our method to non-planar crack problems is illustrated by simulations of dynamic growth of a hackly crack which has small off-plane side-branches. The results imply that the branching of a crack brings about a significant decrease in the crack-tip stress concentration level and consequently may play an essential role in the arrest of earthquake rupturing. 相似文献
Our formulations are shown to yield accurate numerical results, as long as appropriate stabilization measures are taken in the numerical scheme. The numerical applicability of our method to non-planar crack problems is illustrated by simulations of dynamic growth of a hackly crack which has small off-plane side-branches. The results imply that the branching of a crack brings about a significant decrease in the crack-tip stress concentration level and consequently may play an essential role in the arrest of earthquake rupturing. 相似文献
12.
Summary. The long wavelength radiation patterns of P - and S -waves are determined for an elastic prestressed earth model. The prestress is treated as a perturbation of an isotropic medium. Non-zero first-order corrections are found to the eigenvalues and eigenvectors of the deviatoric seismic moment tensor. The radiation pattern given by a purely tangential dislocation is equivalent to a double couple contaminated by a dipolar term linear in the perturbation. 相似文献
13.
Simulation of the spontaneous growth of a dynamic crack without constraints on the crack tip path 总被引：2，自引：0，他引：2
The spontaneous growth of a dynamic in-plane shear crack is simulated using a newly developed method of analysis in which no a priori constraint is required for the crack tip path, unlike in other classical studies. We formulate the problem in terms of boundary integral equations; the hypersingularities of the integration kernels are removed by taking the finite parts. Our analysis shows that dynamic crack growth is spontaneously arrested soon after the bending of the crack tips, even in a uniformly stressed medium with homogeneously distributed fracture strengths. This shows that the dynamics of crack growth has a significant effect on forming the non-planar crack shape, and consequently plays an essential role in the arrest of earthquake rupturing. 相似文献
14.
Genti Toyokuni Hiroshi Takenaka Masaki Kanao Douglas A. Wiens Andrew Nyblade 《Polar Science》2012,6(2):155-164
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
15.
Bernard Valette 《Geophysical Journal International》1986,85(1):179-208
Summary. In this paper we examine the influence of the state of stress in the equilibrium configuration of the Earth (i.e. the pre-stress) upon its adiabatic perturbations. The equations governing these perturbations to the first order (Woodhouse & Dahlen; Dahlen) are re-derived using a Lagrangian approach. Different expressions of the sesquilinear form associated to the elastic-gravitational operator are given. One of these provides a way to extend to hydrostatically pre-stressed solids the criterion of local stability given by Friedman & Schutz for uniformly rotating fluids. Then the propagation in the Earth of seismic wavefronts is considered. It is shown that the nature of these different wavefronts is entirely determined by the quadratic coefficients of the development of the specific internal energy variation, corresponding to isentropic evolution, with respect to the Lagrangian finite deformation tensor. Expressions for the velocities of the various waves are given as functions of incidence angle and pre-stress for orthotropic elastic material. In the particular case where the elastic parameters depend only on one coordinate of a curvilinear system and the axis of orthotropy of the material coincides with the corresponding natural base vector, the elastodynamic equations are reduced to a simple system for a displacement stress vector, using surface operators. In particular for spherical geometry, equations are obtained which generalize to orthotropic pre-stress those given by Alterman et al. and Takeuchi & Saito. 相似文献
16.
Toshiro Tanimoto 《Geophysical Journal International》1998,134(1):199-206
The state of stress within a bending spherical shell has some special features that are caused by sphericity. While most lithospheres are more like spherical shells than flat plates, our ideas of the state of stress have been dominated by flat-plate models. As a consequence, we might be missing some important aspects of the state of stress within subducting lithospheres. In order to examine this problem, we analyse spherical-shell bending problems from basic equations. We present two approaches to solve spherical-shell bending problems: one by the variational approach, which is suitable for global-scale problems, and the other by the asymptotic equation, which is valid to first order in h/R , where h is the thickness of the lithosphere and R is its curvature radius (i.e. under the assumption of small curvature). The form of the equation for displacement shows that wavelengths of deformation are determined by the spherical (elastic) effect and the gravitational buoyancy effect, for which only the latter effect is included in the usual flat-plate formulations. In the case of the Earth, the buoyancy force is dominant and, consequently, spherical effects are suppressed to a large extent; this explains why flat-plate models have been successful for Earth's lithospheric problems. On the other hand, the state of stress shows interesting spherical effects: while bending (fibre) stress along the subduction zone is always important, bending stress along the trench-strike direction can also be important, in particular when the subduction zone arc is small. Numerical results also indicate that compressive normal stress along the trench-strike direction is important when a subduction zone arc is large. These two stresses, the bending stress and the compressive normal stress, both along the trench-strike direction, may have important implications for intraplate earthquakes at subduction zones. 相似文献
17.
Our objectives are as follows. First, we wish to develop a methodology to recover the long-term component of deformation from any set of distributed, time-averaged geodetic strain measurements that were subject to seismic disturbance, given a catalogue of local seismicity that occurred during the measurement period. Second, using seismic and geodetic data sets that span approximately 100 years, we apply this technique in the western Aegean to assess the role of local seismicity in regional deformation. The methodology is developed using a model for crustal deformation constructed from a long-term, smooth regional strain field combined with instantaneous, local perturbations from upper-crustal earthquakes approximated by static elastic dislocations. By inverting geodetic displacements for the smooth field while simultaneously floating influential but uncertain earthquake source parameters, an estimate of the regional component of deformation that is approximately independent of the seismicity can be made. In the western Aegean we find that the horizontal component of regional deformation can be described with minor inaccuracy by a quadratic relative displacement field. The principal horizontal extensional axes calculated from the regionally smooth displacement field agree in orientation with the T-axes of earthquakes in the region. These observations indicate that the instantaneous elastic strain of the 10 km thick seismogenic layer is driven by a stress field that is smooth on the scale of the geodetic network as a whole, 200-300 km. 相似文献
18.
Characteristics of near-surface electrokinetic coupling 总被引：2，自引：0，他引：2
David Beamish 《Geophysical Journal International》1999,137(1):231-242
Naturally occurring electric potentials at the Earth's surface are traditionally studied using self-potential geophysics. Recent theoretical and experimental work has reinvestigated the manner in which the measurement can be made dynamically using a pressure source. The methodology, often referred to as seismoelectric, relies on electrokinetic coupling at interfaces in the streaming potential coefficient. The ultimate aim of the developing methodologies lies in the detection of zones of high fluid mobility (permeability) and fluid geochemical contrasts within the subsurface. As yet there are no standard methods of recording and interpretation: the technique remains experimental. Field measurements are made using a seismic source and by recording electric voltage across arrays of surface dipoles. This study presents observational characteristics of electrokinetic coupling based on experiments carried out in a wide range of environments. Theory concerning the coupled elastic and electromagnetic wave equations in a saturated porous medium is discussed. It is predicted that coupling will produce electromagnetic radiation patterns from vertical electric dipoles generated at interfaces. Surface- and body-wave coupling mechanisms should provide different time–distance patterns. Vertical electric dipole radiation sources are modelled and their spatial characteristics presented. A variety of experimental configurations have been used, and geometries that exploit phase asymmetry to enhance the separation of signal and noise are emphasized. The main experimental results presented are detailed observations in the immediate vicinity of the source. Simultaneous arrivals across arrays of surface dipoles are not common. The majority of such experiments have indicated that shot-symmetric voltages which display low-velocity moveout are the dominant received waveforms. 相似文献
19.
20.
G. Quiroga-Goode R. Padilla-Hernández S. Jiménez-Hernández 《Geophysical Journal International》2007,170(3):1227-1242
It is quantified the properties of seismic waves in fully saturated homogeneous porous media within the framework of Sahay's modified and reformulated poroelastic theory. The computational results comprise amplitude attenuation, velocity dispersion and seismic waveforms. They show that the behaviour of all four waves modelled as a function of offset, frequency, porosity, fluid viscosity and source bandwidth depicts realistic dissipation within the sonic–ultrasonic band. Therefore, it appears that there is no need to include material heterogeneity to model attenuation. By inference it is concluded that the fluid viscosity effects may be enhanced by dynamic porosity. 相似文献