添加正则化项的黏声逆时偏移成像方法研究

在实际地球介质中传播的地震波会产生衰减和频散现象,因此其更接近于黏弹性介质,在地震处理中补偿这些黏性影响是十分必要的。基于波动方程的叠前深度偏移中进行吸收衰减补偿更准确,也更有物理意义,直接求解双程波动方程的逆时偏移(RTM)能够成像大倾角复杂构造,具有诸多优势。然而当考虑吸收衰减补偿时通常会产生不稳定现象,大部分研究都是在逆时偏移的波场延拓中进行波数域的低通滤波来解决这个问题。本文采用广义标准线性固体的黏声波动方程进行吸收衰减补偿的Q--RTM方法,通过添加正则化项的方式来稳定延拓过程。添加正则化项本质上是低通滤波,滤波窗口是指数形式,在时空域有明确的形式,可以阻止发生高频不稳定。与直接滤波相比,正则化参数可以是空变的,因此比较适合剧烈变化的区域,我们还发现震源归一化互相关成像条件更适合Q--RTM方法。      

基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移

时间域常Q黏声波方程,由于含分数阶时间导数项,数值求解需要大量内存,计算效率低,不利于地震偏移的实施.通过一系列近似,可将该方程简化为介质频散效应和衰减效应解耦的分数阶拉普拉斯算子黏声波方程,数值求解内存需求少,计算效率高.本文采用交错网格有限差分逼近时间导数,改进的伪谱法计算空间导数,PML吸收边界去除边界反射,对该方程进行数值离散和地震正演模拟,开展地震数据的黏声介质逆时偏移,实现波场逆时延拓过程中同时完成频散校正和衰减补偿.改善深层构造的成像精度,数值结果表明,基于分数阶拉普拉斯算子解耦的黏声介质地震正演模拟与逆时偏移可大幅度提高地震模拟计算效率,偏移剖面明显优于常规声波偏移剖面,极大改善深层构造的成像品质.     

Implementation aspects of attenuation compensation in reverse‐time migration

Attenuation compensation in reverse‐time migration has been shown to improve the resolution of the seismic image. In this paper, three essential aspects of implementing attenuation compensation in reverse‐time migration are studied: the physical justification of attenuation compensation, the choice of imaging condition, and the choice of a low‐pass filter. The physical illustration of attenuation compensation supports the mathematical implementation by reversing the sign of the absorption operator and leaving the sign of the dispersion operator unchanged in the decoupled viscoacoustic wave equation. Further theoretical analysis shows that attenuation compensation in reverse‐time migration using the two imaging conditions (cross‐correlation and source‐normalized cross‐correlation) is able to effectively mitigate attenuation effects. In numerical experiments using a simple‐layered model, the source‐normalized cross‐correlation imaging condition may be preferable based on the criteria of amplitude corrections. The amplitude and phase recovery to some degree depend on the choice of a low‐pass filter. In an application to a realistic Marmousi model with added Q, high‐resolution seismic images with correct amplitude and kinematic phase are obtained by compensating for both absorption and dispersion effects. Compensating for absorption only can amplify the image amplitude but with a shifted phase.     

黏滞声波高斯束叠前深度偏移

高斯束偏移不仅具有接近于波动方程偏移的成像精度,而且保留了Kirchhoff 积分法高效、灵活的优点,可以对复杂介质准确成像。由于实际地下介质具有黏滞性,因此研究黏滞声波叠前深度偏移具有一定的现实意义。笔者采用高斯束偏移方法对地震数据进行吸收衰减补偿。首先给出共炮域高斯束叠前深度偏移原理;然后在此基础上推导补偿吸收衰减的表达式,校正品质因子Q引起的振幅衰减和相位畸变,实现基于吸收衰减补偿的高斯束叠前深度偏移;最后用两层模型和气云模型对偏移方法进行了测试。结果表明,在考虑地下介质的黏滞性时,黏滞声波高斯束叠前深度偏移比声波高斯束叠前深度偏移具有更高的成像分辨率。