复杂VTI介质频率域波动方程平均导数优化方法研究及应用

Vertical transversely isotropic(simplified by VTI) media as one of the most basic weak anisotropic medium, its research has the very important significance. Average-derivative optimal method(simplified by ADM) is a new thought of optimization for frequency domain finite difference algorithm. It can not only improve the computational accuracy, but also possess good flexibility which overcomes the limitations of the conventional method. Its application to frequency domain forward modeling for complex VTI media has showed a good application prospect which significantly improves the computational accuracy compared with the conventional algorithm. Based on the current work, we will continue to carry out an in-depth theoretical algorithms and applied research of frequency domain forward modeling and full waveform inversion(simplified by FWI) based on ADM for complex VTI media. Firstly we will do some work for further development and perfection of the available results for 2D forward modeling. Through the GPU high-performance computing research, we can improve the computational efficiency so as to make the algorithm more practical. Then we will carry out a feasibility study for 3D forward modeling. Based on the research of forward modeling, we will then study the 2D frequency domain FWI based on ADM for complex VTI media. We aim to develop the 2D frequency domain multi-scale FWI technique for complex VTI media by systematical research which can be applied to the actual production. It will achieve a good result of theoretical model test and can be used to process the marine towed streamer multichannel seismic data for actual application effect. Furthermore, the computing speed can be affordable for practical processing.

VTI介质作为最基本的一种弱各向异性介质，它的研究具有十分重要的意义。平均导数优化方法是频率域有限差分算法的一种新的优化思路，它不仅能有效提高计算精度，而且具有很好的灵活性，克服了常规方法的局限性。将其应用到复杂VTI介质频率域正演模拟中，相比常规算法明显提高了计算精度，已经体现出了良好的应用前景。在现有工作的基础上，继续深入开展基于平均导数优化方法的复杂VTI介质频率域正演和全波形反演的理论算法和应用研究。首先进一步发展和完善已经取得的二维正演成果，通过GPU高性能计算研究有效提高计算效率从而使算法更加实用化，并开展三维正演的可行性研究；然后在正演研究基础上开展二维VTI介质频率域平均导数优化方法全波形反演研究，拟通过系统研究得到一套可以适用于生产实际的二维复杂VTI介质频率域多尺度全波形反演技术，理论模型测试良好并可用于海洋拖缆多道实际地震资料处理，且计算速度达到可用于实际处理的程度。

垂直横向各向同性（VTI）介质作为最基本的一种弱各向异性介质，它的研究具有十分重要的意义。平均导数优化方法（ADM）是频率域有限差分算法的一种新的优化思路，它不仅能有效提高计算精度，而且具有很好的灵活性，克服了常规方法的局限性。将其应用到复杂VTI介质频率域正演模拟中，相比常规算法明显提高了计算精度，体现出了良好的应用前景。本项目开展基于平均导数优化方法的复杂VTI介质频率域正演和全波形反演（FWI）的理论算法和应用研究。首先进一步发展和完善已经取得的二维正演成果，通过GPU高性能计算技术开展研究明显提高了二维复杂VTI介质频率域正演算法的计算效率从而使算法更加实用化。然后将二维复杂VTI介质频率域正演算法扩展到了三维情形，开展三维正演算法的可行性研究，研究表明三维复杂VTI介质频率域正演算法所需要的内存存储量和计算量巨大，实际应用的难度较大，可行性不强，建议三维情形下还是应该采用时间域正演算法效率较高。为便于对比，还研究了二维和三维复杂VTI介质时间域正演算法。最后在正演研究基础上开展二维VTI介质频率域平均导数优化方法全波形反演研究，完成具体算法流程设计，进行了程序编写和数据测试，并从实际资料处理和应用的角度出发对实际地震资料全波形反演所需要的地震资料预处理、初始速度建模和震源子波提取等关键技术都开展了有益的研究。