A reflection/transmission matrix formulation for seismoacoustic scattering by an irregular fluid--solid interface

Abstract

The seismoacoustic scattering due to an irregular fluid-solid interface (i.e. the ocean bottom) must be considered when modelling seismic wave propagation in oceanic regions. In this paper, we present an accurate method to treat this problem. The method is an extension of the reflection/transmission matrix approach that was developed to model scattering due to an irregular interface between two elastic solids. This approach uses the discrete wavenumber representation of the wavefield and the Rayleigh ansatz; the wavefield is decomposed into a set of plane waves, and we assume that the scattered wavefield due to an incident plane wave can be expanded in terms of only the waves moving away from the interface. The plane waves at both sides of the interface are then connected to each other based on this hypothesis and proper boundary conditions. The elements of the reflection/transmission matrices describe these connection coefficients.As the fluid-solid interface, the direct application of the above method is difficult because the tangential displacement at the interface is not necessarily continuous. To avoid this problem, we use pressure as the variable inside the fluid layer. The reflection/transmission matrices between the pressure wave (i.e. the acoustic wave) and the elastic waves are then developed by using the standard boundary conditions at the fluid-solid interface (i.e. normal stress continuity, zero tangential stress, and normal displacement continuity) and the Rayleigh ansatz.To demonstrate the validity and feasibility of our method, we compare the results of our method with those of other methods. First, we examine the reflection of plane elastic waves by a periodic sinusoidal interface for a single frequency. The interface profile is characterized by its periodicity or wavelength (D) and peak to trough height (h). The behaviour of the reflection calculated by our method shows almost complete agreement with that calculated by a boundary element method (BEM) up to a relatively steep interface whose height to wavelength ratio (h/D) is 0.5.Second, we calculate the synthetic time domain waveforms for a plane vertically incident P wave into basin-like fluid layers. We compare the waveforms calculated by the present method with those calculated by the finite difference method (FDM). In general, the waveforms calculated by the two methods match well. A quantitative study shows that the degree of agreement indicated by the RMS residuals between the waveforms of the two methods becomes better when we use a smaller grid interval in the FDM calculation. For the models treated here, the cases of 30 grid-points per wavelength results in RMS residuals less than about 10-15 per cent. This grid interval is smaller than that usually applied (more than 5-10 grid-points per wavelength). Since, in general, the accuracy of the FDM calculation becomes better as the grid interval decreases, these results indicate the validity of the present method.

An Efficient Approach for Seismoacoustic Scattering Simulation Based on Boundary Element Method

“…To overcome the problem, the reflection/transmission matrices for the fluid-solid irregular interface [20] were developed based on the discrete wavenumber representation of the wave field, i.e. the Aki-Larner method [25].…”

“…However, the traditional BEM requires a tremendous increase in memory capacity and computational time when it's used to model the wave propagation in multilayered media. Motivated by the work in [19][20], we develop a method based on the combination of the traditional BEM and a global matrix propagator to simulate the seismoacoustic scattering due to an irregular fluid-solid interface. This method takes the advantage of the global matrix propagator to suppress the tremendous increase in computational resources required for simulating wave propagation in multilayered media, but also retains the merits of the boundary element method.…”

“…(20) Here the subscript s in the Fs vector just indicates the source layer index. One more step needed to solve the above equations is to substitute i  s1 and s1 separately into Eqs.…”

“…This kind of problem is related to a wide range of seismic research conducted at or close to oceanic regions or gulf areas [20], such as deep ocean acoustic experiments, ocean bottom seismic observations, or the interpretation of the effects of water layer on the observed surface wave traveling through gulf areas. Many metropolitan cities all over the world are located at or close to seaside, so it is important to take into account the effect of the sea water when conducting the earthquake resistant design for high-rise buildings in such big gulf cities.…”

Shear waves at a corrugated interface between two dissimilar fiber-reinforced elastic half-spaces

“…Rayleigh used this method, in his paper "On the dynamical theory of grating" [1907], and later, researchers in various fields applied his method to explain reflection and transmission phenomena of waves from irregular boundary surfaces. Using different techniques, many problems of reflection and refraction of elastic waves from irregular boundary surfaces have appeared in the open literature, such as [Abubakar 1962;Asano 1960;1961;1966;Dunkin and Eringen 1962;Tomar and Saini 1997;Okamoto and Takenaka 1999;Tomar et al 2002;Gupta 1987;Kumar et al 2003;Tomar and Kaur 2003;Kaur and Tomar 2004;Kaur et al 2005].…”