Elastic wave propagation in an irregularly layered medium (original) (raw)
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Seismic response of irregularly stratified media using the indirect boundary element method
1995
The seismic response of irregularly elastic layered media is studied using the indirect boundary element method (IB EM) Excitation is given by incoming plane P and S waves and the free-field solution is obtained for a reference flat layered model by means of Thomson-Haskell's propagator method. Boundary conditions for the irregular configuration, are obtained from the analytical extension of the field in each layer and the underlaying half-space. In our approach, diffracted waves are constructed in terms of single layer boundary sources. In order to validate the technique, comparisons between our results and previous ones are given.
Journal of Computational Acoustics, 2008
A semi-analytic method based on the propagation matrix formulation of indirect boundary element method to compute response of elastic (and acoustic) waves in multi-layered media with irregular interfaces is presented. The method works recursively starting from the top-most free surface at which a stress-free boundary condition is applied, and the displacement-stress boundary conditions are then subsequently applied at each interface. The basic idea behind this method is the matrix formulation of the propagation matrix (PM) or more recently the reflectivity method as wide used in the geophysics community for the computation of synthetic seismograms in stratified media. The reflected and transmitted wave fields between arbitrary shapes of layers can be computed using the indirect boundary element (BEM) method. Like any standard BEM methods, the primary task of the BEM-based propagation matrix method (thereafter called PM-BEM) is the evaluation of element boundary integral of the Green's function, for which there are standard method that can be adapted. In addition, effective absorbing boundary conditions as used in the finite difference numerical method is adapted in our implementation to suppress the spurious arrivals from the artificial * 381 382 E. Liu et al.
Earthquake wave propagation in layered media by boundary integral methods
Soil Dynamics and Earthquake Engineering, 1991
The authors have previously presented work on the use of boundary methods to solve steadystate wave scattering problems in two-dimensional homogeneous systems and on the use of these solutions with Fourier transforms to solve problems of transient input waves. This paper extends that work to nonhomogeneous systems. The methodology is now applicable to profiles with various material parameters in media bounded by irregularly shaped interfaces subjected to transient or periodic incident waves of any form. The profiles which can be solved are layers of finite extent, layers of infinite extent, cavities, inclusions of different materials, lenses, cases of three media and three interfaces meeting at a single point, and any combination thereof. The paper presents the basic equations of wave propagation in a single medium, the extension of these equations to multiple media, and the methodology of correcting for the truncation of the numerical portions of a problem. Using these techniques, several simple geometries are solved and the solutions are compared to closed-form solutions when available. The comparisons are good and the value of correcting for the truncation is verified. The methodology is then applied to a test case of real data taken from real earthquake records, to wit: the response of the Santa Felicia earth dam to the San Fernando (1971) earthquake. The comparison is good in the time domain but in the frequency domain shows some inaccuracy at the higher frequencies. This loss of quality is attributed to the fact that a linear elastic system is not a good model for soil response. The final section is an initial attempt to examine the effects of some simple damping schemes. Great improvement is shown in the attempt to reproduce numerically the response of the Santa Felicia earth dam.
Soil Dynamics and Earthquake Engineering, 2011
In earthquake engineering and seismology it is of interest to know the surface motion at a given site due to the incoming and scattered seismic waves by surface geology. This can be formulated in terms of diffraction of elastic waves and then the indirect boundary element method (IBEM) for dynamic elasticity is used. It is based on the explicit construction of diffracted waves at the boundaries from which they radiate. This provides the analyst with insight on the physics of diffraction. The IBEM has been applied to study the amplification of elastic waves in irregular soil profiles. From the strong or weak satisfaction of boundary conditions and a simple analytical discretization scheme a linear system of equations for the boundary sources is obtained. Here, we explore the use of a weak discretization strategy with more collocation points than force densities. The least squares enforcement of boundary conditions leads to a system with reduced number of unknowns. This approach naturally allows one to use both coarser and finer boundary discretizations for smooth and rapidly varying profiles, respectively. A well studied semicircular canyon under incident P or SV in-plane waves is used to calibrate this method. Several benefits are obtained using mixed meshing that leads to the least squares condensation of the IBEM.
Hybrid Simulation of Seismic Wave Propagation in Laterally Inhomogeneous Media
The main aim of this work is to develop, validate and applied in simulation study an efficient hybrid approach to study 2D seismic wave propagation in local multilayered geological region rested on inhomogeneous in depth half-space with a seismic source. Plane strain state is considered. The vertically varying of the soil properties in the half space is modelled by a set of horizontal flat isotropic, elastic and homogeneous layers. The finite local region is with nonparallel layers and with a free surface relief. The hybrid computational tool is based on the analytical wave number integration method (WNIM) and the numerical boundary integral equation method (BIEM). The WNIM is applied considering the bedrock model to compute the input signals for the laterally varying part where the signals are obtained by BIEM at a set of sites. The numerical simulation results reveal that the hybrid method is able to demonstrate the sensitivity of the obtained synthetic signals to the seismic source properties, to the heterogeneous character of the wave path and to the relief peculiarities of the local stratified geological deposit.
Two-Dimensional Seismic Wave Modeling and Inversion by the Boundary Element Method
GeoCongress 2012, 2012
Surface wave methods (SWM) are widely used for the geophysical characterization of geological bodies and tectonic structures in both Earth Sciences and Engineering. SWMs exploit the dispersive nature of Rayleigh waves to indirectly estimate shear wave velocity profiles from surface wave measurements, but they are limited to parallel-layered geometries. To overcome such limitations, we exploit the Boundary Element Method (BEM) to define a new class of geometric inversion models that allows to go directly from raw measurements to estimating the shape of laterally varying soil interfaces. The proposed approach enables a robust identification of the subsurface geometry and it aims at filling the gap between the standard simplistic parallel-layered-based SWM and the more complex three-dimensional Full Wave Inversion (FWI) based on Finite Element Methods. Numerical tests on synthetic data unveil the effectiveness of the inverse algorithm and its applicability to wave measurements. An application to field data is finally presented.
Mathematical modeling of seismic wave propagation in layered media
An analytically based computer model for transient pulse propagation in a layered elastic half-space is developed. The model involves an explicit integral representation derived in terms of an elastodynamic Green's matrix for the half-space. The model is intended to simulate waves from a distant impulsive source. Certain resonance phenomena associated with the specific structure of the dispersion curves for the layered medium are discussed. These results may be helpful for seismic protection and earthquake resistant construction.
Soil Dynamics and Earthquake Engineering, 2015
In this review paper, we concentrate on the use of boundary integral equation (BIE) based methods for the numerical modeling of elastic wave motion in naturally occurring media. The main reason for using BIE is the presence of the free surface of the earth, whereby large categories of problems involve continua with a small surface to volume ratio. Given that under most circumstances, BIE require surface discretization only, substantial savings can be realized in terms of the size of the mesh resulting from the discretization procedure as compared to domain-type numerical methods. We note that this is not necessarily the case with man-made materials that have finite boundaries. Thus, although the emphasis here is on wave motion in geological media, this review is potentially of interest to researchers working in other scientific fields such as material science. Most of the material referenced in this reviews drawn from research work conducted in the last fifteen years, i.e., since the year 2000, but for reasons of completeness reference is made to seminal papers and books dating since the early 1970s. Furthermore, we include here methods other than the BIE-based ones, in order to better explain all the constituent parts of hybrid methods. These have become quite popular in recent years because they seem to combine the best features of surface-only discretization techniques with those of domain type approaches such as finite elements and finite differences. The result is a more rounded approach to the subject of elastic wave motion, which is the underlying foundation of all problems that have to do with time-dependent phenomena in solids.
3D elastic wave propagation modelling in the presence of 2D fluid-filled thin inclusions
Engineering Analysis with Boundary Elements, 2006
In this paper, the traction boundary element method (TBEM) and the boundary element method (BEM), formulated in the frequency domain, are combined so as to evaluate the 3D scattered wave field generated by 2D fluid-filled thin inclusions. This model overcomes the thin-body difficulty posed when the classical BEM is applied. The inclusion may exhibit arbitrary geometry and orientation, and may have null thickness. The singular and hypersingular integrals that appear during the model's implementation are computed analytically, which overcomes one of the drawbacks of this formulation. Different source types such as plane, cylindrical and spherical sources, may excite the medium. The results provided by the proposed model are verified against responses provided by analytical models derived for a cylindrical circular fluid-filled borehole. The performance of the proposed model is illustrated by solving the cases of a flat fluid-filled fracture with small thickness and a fluid-filled Sshaped inclusion, modelled with both small and null thickness, all of which are buried in an unbounded elastic medium. Time and frequency responses are presented when spherical pulses with a Ricker wavelet time evolution strikes the cracked medium. To avoid the aliasing phenomena in the time domain, complex frequencies are used. The effect of these complex frequencies is removed by rescaling the time responses obtained by first applying an inverse Fourier transformation to the frequency domain computations. The numerical results are analysed and a selection of snapshots from different computer animations is given. This makes it possible to understand the time evolution of the wave propagation around and through the fluid-filled inclusion.