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叠前逆时偏移是对地下介质进行精确成像的方法之一。由于实际地下介质具有粘滞性,研究粘滞声波叠前逆时偏移具有一定的现实意义。逆时偏移的步骤之一是求解波动方程,对地震波场进行正向和反向外推,因此,精确、高效地求解波动方程对逆时偏移的成像效果和计算效率具有重要影响。本文中,我们利用基于优化时空域频散关系的高阶有限差分方法求解粘滞声波方程。频散分析和数值模拟的结果证明了优化时空域有限差分方法具有较高的精度,可以很好地压制数值频散。利用混合吸收边界条件处理边界反射,然后利用震源归一化互相关成像条件进行成像,并利用拉普拉斯滤波方法去除低频噪音。数值模型的测试结果显示,在考虑地下介质的粘滞性时,粘滞声波方程逆时偏移比声波方程逆时偏移具有更高的成像分辨率。另外,在进行波场外推的时候,采用自适应变长度的有限差分算子计算空间导数,在不影响求解精度的情况下,有效地提高了计算效率。
Pre-stack reverse-time migration is one of the most accurate methods for imaging subterranean media. Because of the viscosity of the actual underground medium, it is of practical significance to study the prestack reverse-time migration of viscous acoustic wave. One of the steps of inverse time migration is to solve the wave equation and forward and reverse seismic wavefield extrapolation. Therefore, to accurately and efficiently solve the wave equation has an important influence on the imaging effect and computational efficiency of inverse time migration. In this paper, we use the higher-order finite-difference method based on the optimization of the dispersion relation in time-space to solve the viscous acoustic equation. The results of dispersion analysis and numerical simulation show that the proposed method has better accuracy and can suppress the numerical dispersion well. Boundary reflection is processed using mixed absorption boundary conditions and then imaged using source normalized cross-correlation imaging conditions and Laplacian filtering is used to remove low-frequency noise. The numerical results show that when considering the viscosity of underground media, the viscoelastic wave equation has a higher imaging resolution than the inverse time-offset of acoustic equation. In addition, when carrying out wave field extrapolation, using the finite difference operator with adaptive variable length to calculate the spatial derivative, the computational efficiency is effectively improved without affecting the accuracy of the solution.