虚谱法一阶应力—速度方程地震数值模拟

Pseudo spectral seismic simulation with one order stress-velocity equation

地震波场模拟是正确认识复杂条件下地震波传播机理、规律及波场特征的有效手段。交错网格高阶差分常用于一阶应力—速度声波方程数值模拟,但空间差分的固有特性使得数值频散难以避免。虚谱法利用模型空间的全部信息对波场函数进行傅氏变换,可得到精确的波场空间导数;由于它克服了对高频成分的限制,因而可实现全频带的地震波场模拟。将完美匹配层边界条件引入虚谱法数值模拟可更有效地消除边界反射,有利于更精确地模拟地震波的传播过程。数值算例表明,虚谱法一阶应力—速度声学方程模拟结果具有较高的时间分辨率,在同等模拟精度条件下则具有更高的计算效率。

Seismic wave field simulation is an effective method to correctly understand the spreading mechanism and the wave field characteristic for seismic wave in complex conditions.Staggered mesh high order difference is often used in one order stress-velocity acoustic equation seismic simulation,however the numerical dispersion caused by the algorithm can not be avoided.By using all information in model space and applying Fourier transformation to wave field function,accurate wave field space derivative is obtained in the Pseudo spectral method,as in this method the restriction to high frequency was overcame,the seismic wave field simulation with full frequency bandwidth was realized.With the use of perfected matched layers condition in Pseudo spectral seismic simulation,the reflection wave from artificial boundary can be eliminated efficiently,and the seismic wave penetrating process can be better and accurately simulated.In this paper the numerical test shows that simulation results with pseudo spectral method one order stress-velocity equation has good resolution in time domain and it has high calculating efficiency with the same simulation precision.