TTI介质Low-rank有限差分法高效正演模拟及逆时偏移

An efficient forward modeling with the low-rank finite-difference algorithm for complex TTI media and its application in reverse time migration

计算效率是制约各向异性逆时偏移实用化的关键因素,此外,伪横波假象、数值频散以及不稳定问题也是TTI介质qP波正演模拟及逆时偏移的固有难题。Low-rank波场延拓算法虽能解决上述三方面问题,但其运算速度受模型参数限制,计算效率较低。为此,本文基于混合网格有限差分思想,给出一种新的紧致差分模板,并借助Low-rank分解求取与模型匹配的自适应差分系数,进而实现一种针对TTI介质的Low-rank有限差分法高效正演模拟及逆时偏移成像策略。数值模型测试结果表明:本文方法既继承了有限差分法高效灵活的特点,又拥有Low-rank波场延拓方法准确计算纯qP波波场的优势,即在提高计算效率的同时避免了伪横波假象和数值不稳定,是一种兼顾成像精度与计算效率的各向异性逆时偏移实用方法。

The computation efficiency is the key factor to restrict the practicality of anisotropic reverse time migration.In addition,pseudo shear-wave artifacts, numerical dispersion,and instability are also inherent problems of TTI medium qP-wave forward modeling and reverse time migration.The low-rank wavefield extrapolation algorithm is basically free from pseudo shear-wave artifacts,numerical dispersion,and instability.However,this method is a time-consuming and inefficient because its computing speed is controlled by model parameters.To improve the computation efficiency,a new compact differential template is proposed based on the idea of mixed-grid finite-difference,and the adaptive difference coefficient matched with the model is obtained by means of low-rank decomposition.Then, a low-rank finite-difference forward modeling and reverse time migration for TTI media are imple-mented.Numerical tests show that the proposed scheme is an anisotropic reverse time migration practical approach which combines high imaging accuracy and high calculation efficiency.The proposed scheme possesses the flexibility and efficiency of finite-difference method and pure-qP-wave precise calculation of low-rank wavefield extrapolation algorithm.So it can remove the pseudo shearwave artifacts and numerical instability while improving the computation efficiency.