双平方根单程波动方程叠前τ偏移方法

DSR one-way wave equation prestack τ migration

本文将常规双平方根(DSR)单程波动方程从深度域变换到双程垂直走时(τ)域,由此推导出可从数学上实现“沉降观测”的单程波DSR传播算子.其递归波场延拓算法包含波数域针对常速背景的相移处理和空间域针对横向速度扰动的相位校正,可以应对上覆地层速度横向变化对构造成像的影响.结合零炮检距、零时间成像条件,提出了在τ域进行波场延拓与成像的DSR方程叠前偏移新方法.为了克服其全三维偏移算法在实际应用中可能面临的困难,本文采用稳相近似,在crossline常炮检距偏移理论基础上推导了实用的共方位角叠前τ偏移方法.数值试验表明,DSR方程叠前τ偏移在强横向非均匀介质中的成像精度与分辨率优于传统的时间域成像技术.

By transforming the classical double-square-root （DSR） one-way wave equation from the depth domain to the two-way vertical traveltime （τ） domain, we derive an one-way DSR wave propagator which can be applied to mathematically implement ＂sinking survey＂. Its algorithm to reeursively continue the source and receiver wavefields, which includes a wavenumber domain phase shift in a constant background medium followed by a phase correction in the space domain that accommodates lateral velocity variations, can tackle the effects of lateral velocity variations for imaging under complex overburdens. Combing with the zero-offset and zero-time imaging condition, we develop a DSR equation prestaek migration method that implements wavefield continuation and imaging in the τ space. To address the problems that full volume 3-D DSR equation migration could meet with in production application, we present a feasible common-azimuth prestack τ migration approach based on the theory of erossline common-offset migration. Numerical tests show that DSR equation prestaek τ migration provides a significant improvement over the traditional prestaek time migration technology in laterally varying media.