On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems

Sanna Mönkölä

doi:10.1155/2016/9431583

Abstract

This study concentrates on transient multiphysical wave problems for simulating seismic waves. The presented models cover the coupling between elastic wave equations in solid structures and acoustic wave equations in fluids. We focus especially on the accuracy and efficiency of the numerical solution based on higher-order discretizations. The spatial discretization is performed by the spectral element method. For time discretization we compare three different schemes. The efficiency of the higher-order time discretization schemes depends on several factors which we discuss by presenting numerical experiments with the fourth-order Runge-Kutta and the fourth-order Adams-Bashforth time-stepping. We generate a synthetic seismogram and demonstrate its function by a numerical simulation.

Highlights

Several formulations exist for modeling the seismic vibrations as interaction between acoustic and elastic waves
We demonstrate how the efficiency of the method can be improved by using the fourth-order Runge-Kutta scheme instead of the central finite difference time discretization
We considered the spectral element space discretization for time-dependent equations considering acoustic and elastic wave propagation and their interaction

Summary

Introduction

Several formulations exist for modeling the seismic vibrations as interaction between acoustic and elastic waves. The method has been applied for acoustic wave equations to provide the fourthorder accuracy, with the finite difference space discretization by Dablain [24] and with the spectral element space discretization by Cohen and Joly [25] This approach does not fit to a case, in which an absorbing boundary condition is used for truncating the computational domain, unless velocity-stress or velocity-displacement formulation is used [26]. Since there were no research results considering the accuracy and efficiency of the numerical simulation of fluid and solid waves, in which the fourth-order Runge-Kutta (RK) time discretization is combined with higher-order space discretization, we have applied it for acoustic [31] and elastic [32] waves.

Numerical Models

Numerical Examples

Conclusions