The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3-D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.

Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4].

We extend classic Sommerfeld and Silver-Müller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If X= (x1,x2,x3)ϵℝ3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region ∣x3∣ > ∣∣x∣γ, for γϵ(1/4,1/2) and x large. For ∣x3∣ < ∣∣x∣∣γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

We propose a numerical procedure to extend to full aperture the acoustic far-field pattern (FFP) when measured in only few observation angles. The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion. The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms. We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.

This work pertains to numerical aspects of a finite element method based discontinuous functions. Our study focuses on the Interior Penalty Discontinuous Galerkin method (IPDGM) because of its high-level of flexibility for solving the full wave equation in heterogeneous media. We assess the performance of IPDGM through a comparison study with a spectral element method (SEM). We show that IPDGM is as accurate as SEM. In addition, we illustrate the efficiency of IPDGM when employed in a seismic imaging process by considering two-dimensional problems involving the Reverse Time Migration.

We propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden.

We present a new high order method in space and time for solving the wave equation, based on a new interpretation of the “Modified Equation” technique. Indeed, contrary to most of the works, we consider the time discretization before the space discretization. After the time discretization, an additional biharmonic operator appears, which can not be discretized by classical finite elements. We propose a new Discontinuous Galerkin method for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden.