基于 POD 有限元法的粘滞声波方程震源波场重构

叠前逆时偏移是地震勘探中一种流行的地下结构成像方法. 其成像条件需要同时刻的震源波场值与检波器波场值. 这在实际计算中就需要把正演模拟的所有时刻的震源波场数据全部存储下来,存储量需求大. 虽然震源波场重构技术可以降低对于波场数据的存储需求,但会引入额外的计算复杂度. 为解决这个问题,本文提出了POD有限元法,并将其应用于粘滞震源波场重构. 这里的本征正交分解方法( Proper Orthogonal Decomposition, POD)方法是一种降维方法,能够在降低数据量的同时提供足够的计算精度. 数值算例显示,该方法比传统的有限元方法更节省存储空间,能够加快重构速度.

POD finite element method for reconstruction of viscous acoustic wave equations

Prestack reverse time migration is a popular method for imaging underground structures in seismic exploration. Its imaging condition requires to gather data from the source wavefield and receiver wavefield samultaneously, which means that we have to store all source wavefield data at all times of the forward simulation and huge storage demand. The source wavefield reconstruction technologies can be used to solve this problem at the cost of introducing additional computational complexity. In this paper we introduce the POD finite element method and apply it to the reconstruction of viscous source wavefield, here the proper orthogonal decomposition (POD) method is used to reduce the storage demand by decreasing the dimensionality of data while keeping high enough accuracy. Numerical examples show that, compared with the traditional finite element methods, the POD finite element method can save more computer memory and speed up the reconstruction.