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arXiv physics/0301050physics.geo-phphysics.comp-ph
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用矩阵指数法求解弹性介质中的地震波传播

Solving seismic wave propagation in elastic media using the matrix exponential approach

J. S. Kole

摘要:

本文提出了三种求解弹性固体中时变弹性动力学方程的数值算法。所有算法都是基于近似方程的解,其可以被写为矩阵指数。通过近似矩阵指数与产品的公式,一个无条件稳定的算法推导出,保持总的弹性能量密度。通过对特定时刻的切比雪夫多项式展开矩阵指数,构造了一个所谓的"一步“算法,该算法在时间积分方面非常精确。通过将传统的速度-应力时域有限差分算法(VS-FDTD)公式化为矩阵指数形式,可以通过一个小的修改消除时间上的交错性,并且可以容易地导出时间上的高阶算法。对两个不同的震波迹象,研究了算法的精度,并与传统VS-FDTD算法的结果进行了比较。

英文摘要:

Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By approximating the matrix exponential with a product formula, an unconditionally stable algorithm is derived that conserves the total elastic energy density. By expanding the matrix exponential in Chebyshev polynomials for a specific time instance, a so-called ``one-step'' algorithm is constructed that is very accurate with respect to the time integration. By formulating the conventional velocity-stress finite-difference time-domain algorithm (VS-FDTD) in matrix exponential form, the staggered-in-time nature can be removed by a small modification, and higher order in time algorithms can be easily derived. For two different seismic events the accuracy of the algorithms is studied and compared with the result obtained by using the conventional VS-FDTD algorithm.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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