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Stable Finite-Difference Methods for Elastic Wave Modeling with Characteristic Boundary Conditions

1
School of Geosciences and Info-Physics, Central South University, Changsha 410083, China
2
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(6), 1039; https://doi.org/10.3390/math8061039
Received: 14 June 2020 / Revised: 21 June 2020 / Accepted: 23 June 2020 / Published: 26 June 2020
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. View Full-Text
Keywords: elastic wave model; finite-different method; stability analysis; energy method; relaxation structure elastic wave model; finite-different method; stability analysis; energy method; relaxation structure
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Liu, J.; Yong, W.-A.; Liu, J.; Guo, Z. Stable Finite-Difference Methods for Elastic Wave Modeling with Characteristic Boundary Conditions. Mathematics 2020, 8, 1039.

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