逆时偏移波场延拓中的几何扩散问题

THE GEOMETRY SPREADING OF WAVEFIELD EXTRAPOLATION FOR REVERSE TIME MIGRATION

从理论上分析逆时偏移波场延拓过程中的振幅变化有助于发展真振幅的逆时偏移方法,提高成像结果的精度和保真性。本文研究逆时偏移波场延拓中的几何扩散对振幅的影响,首先基于高频渐进理论,给出正向和逆时延拓波场的WKBJ近似表示;然后应用稳相原理,证明逆时偏移中逆向波场延拓能够补偿正向波场延拓中的几何扩散效应;最后通过数值算例验证理论推导的结果,分析逆时偏移自动补偿几何扩散后的成像振幅。该研究为真振幅逆时偏移方法研究提供理论基础。

Theoretical analysis about the amplitude of wavefield propagation for reverse time migration plays an important role in the development of true-amplitude migration methods and the improvement of the ac- curacy of imaging results. We analyze how the geometry spreading influence the amplitude of reverse time migration in this paper. Based on the high-frequency asymptotic theory, we express the forward and back- ward wavefield in its WKBJ approximate representations. Using stationary phase principle, we proved that the geometry spreading will be automatically compensated during the process of wavefield backward propa- gation for reverse time migration. The theoretical derivations are verified by numerical tests, and the re- sults from numerical experiments are consistent with the theoretical analysis. Our theoretical derivations provide a fundamental basis for developing true-amplitude reverse time migration algorithm.