Abstract

In this paper, a new stable finite-difference (FD) method for solving elastodynamic equations is presented and applied on the Biot and Biot/squirt (BISQ) models. This method is based on the operator splitting theory and makes use of the characteristic boundary conditions to confirm the overall stability which is demonstrated with the energy method. Through the stability analysis, it is showed that the stability conditions are more generous than that of the traditional algorithms. It allows us to use the larger time step τ in the procedures for the elastic wave field solutions. This context also provides and compares the computational results from the stable Biot and unstable BISQ models. The comparisons show that this FD method can apply a new numerical technique to detect the stability of the seismic wave propagation theories. The rigorous theoretical stability analysis with the energy method is presented and the stable/unstable performance with the numerical solutions is also revealed. The truncation errors and the detailed stability conditions of the FD methods with different characteristic boundary conditions have also been evaluated. Several applications of the constructed FD methods are presented. When the stable FD methods to the elastic wave models are applied, an initial stability test can be established. Further work is still necessary to improve the accuracy of the method.

Highlights

  • The propagation dynamics of seismic waves in fluid saturated porous media are of great importance for reservoir rock characterization and attract many geoscientists

  • We study the stability of scheme (6)/(7), and obtain the following theorem

  • The stable theories in mathematics are introduced into the solutions of the wave propagation theories in geology and try to reconsider the calculated results from the point of view of stability instead of accuracy

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Summary

Introduction

The propagation dynamics of seismic waves in fluid saturated porous media are of great importance for reservoir rock characterization and attract many geoscientists. The elastic waves travel through the underground material with attenuation and dispersion which is closely related to the heterogeneities of the porous continuum properties [1,2]. The Biot and squirt-flow mechanisms are believed to be the most important ones [6,9]. They have served as the rigorous and formal foundations to study acoustic wave propagation in saturated porous media. Numerous efforts are made to discuss the different form and numerical implementation of these two mechanisms [10]

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