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This paper is concerned with the numerical modeling of elastic wave propagation in layered media. It considers two isotropic homogeneous elastic solids in perfect contact. The interface is parallel to the free surface. Two finite difference methods are developed. The usefulness of the methods are investigated for long time simulations and the accuracy of the results are compared with the response from an approximate model.

Numerical methods for computing the three-dimensional pressure field in a flat fluid channel bounded either by a rigid boundary, an elastic semi-infinite medium or by a layer of sediment, subjected to incoherent line sources are presented. After verification Greens functions are incorporated in a Boundary Element Method (BEM) code that simulates the pressure variation inside the fluid channel in the vicinity of a rigid or elastic inclusion, avoiding the discretization of the fluid and solid channel interfaces. After the verification of the solution, the models developed are then used to simulate the pressure variation within the fluid channel in the presence of infinitely long rigid and elastic inclusions of differing sizes, when the channel is struck by a spatially-sinusoidal harmonic pressure line load. The results are then compared with those obtained when the channel floor is assumed to be rigid. Time domain results are given by means of inverse Fourier transforms, to help understand how the mechanical properties of the channel floor may affect the variation of the pressure field within the channel.

A stable matrix method is presented for studying acoustic wave propagation in thick periodically layered anisotropic media at high frequencies. The method enables Floquet waves to be determined reliably based on the solutions to a generalized eigenproblem involving scattering matrix. The method thus overcomes the numerical difficulty in the standard eigenproblem involving cell transfer matrix, which occurs when the unit cell is thick or the frequency is high. With its numerical stability and reliability, the method is useful for analysis of periodic media with wide range of thickness at high frequencies.

This work deals with the extension of the partition of unity finite element method (PUFEM) "(Comput. Meth. Appl. Mech. Eng.139 (1996) pp. 289–314; Int. J. Numer. Math. Eng.40 (1997) 727–758)" to solve wave problems involving propagation, transmission and reflection in layered elastic media. The proposed method consists of applying the plane wave basis decomposition to the elastic wave equation in each layer of the elastic medium and then enforce necessary continuity conditions at the interfaces through the use of Lagrange multipliers. The accuracy and effectiveness of the proposed technique is determined by comparing results for selected problems with known analytical solutions. Complementary results dealing with the modeling of pure Rayleigh waves are also presented where the PUFEM model incorporates information about the pressure and shear waves rather than the Rayleigh wave itself.

The fast scattering and inverse scattering algorithms for acoustic wave propagation and scattering in a layered medium with buried objects are an important research topic, especially for large-scale geophysical applications and for target detection. There have been increasing efforts in the development of practical, accurate, and efficient means of imaging subsurface target anomalies. In this work, the acoustic scattering problem in layered media is formulated as a volume integral equation and is solved by the stabilized bi-conjugate gradient fast Fourier transform (BCGS-FFT) method. By splitting the layered medium Green’s function interacting with the induced source into a convolution and a correlation, the acoustic fields can be calculated efficiently by the FFT algorithm. This allows both the forward solution and inverse solution to be computed with only $O(NlogN)$ computation time per iteration, where $N$ is the number of degrees of freedom. The inverse scattering is solved using a simultaneous multiple frequency contrast source inversion (CSI). The stable convergence of this inversion process makes the multiple frequency simultaneous CSI reconstruction practical for large acoustic problems. Some representative examples are shown to demonstrate the effectiveness of the forward and inverse solvers for acoustic applications.

The paper is devoted to the propagation of electromagnetic waves in continuously and planarly inhomogeneous media. Transversely-polarized waves are investigated. The wave solution is sought in the form of a generalized plane wave. The approach is based on a Volterra integral equation that arises from a direct integration of a first-order system of differential equations. In connection with the reflection-transmission process, the wave solution is obtained as a power-series of the angular frequency.