地震波场数值模拟中的信号恢复问题

Signal restoration in numeral simulation of seismic wave field

(中国石油集团东方地球物理公司采集技术支持部，河北涿州072751)

Acquisition Technique Support Department, BGP, CNPC, Zhuozhou 072751, China

基于波动方程的数值模型正演模拟方法已经被广泛应用于地震数据采集、处理和解释的各个方面。为了选择最佳的网格尺寸以及以最小的计算量完整地恢复出信号，针对地震波场正演模拟中经常使用的Ricker子波，根据空间采样定理和地震波在不同速度介质中的传播规律，分析了有限差分算法中的假频和信号恢复问题，推导出模拟网格尺寸、模型地层的最小速度和能够恢复的子波主频之间的近似定量关系，并用数值算例验证了这一关系。

Forward modeling methods based on wave equation have been widely applied in seismic data acquisition, processing, and interpretation. In order to select optimal grid and good computation efficiency to recover the entire signal, aiming at the Ricker wavelet commonly used in forward modeling, we analyzed the alias and signal restoration problem in finite-difference method based on spatial sampling theorem and seismic wave traveling regulation in media with different velocity, to derive quantitative relationship among the modeling grid size, minimum velocity of model layer, and recovered main frequency of wavelet. At last we verified this relationship by a numerical example.