3D复杂弹性介质多分量高斯束保幅偏移

Research on 3D elastic Gaussian beam true-amplitude migration and inversion is significant to covert object imaging and parameter estimation. However, Gaussian beam migration in complex elastic media suffers from problems about mode decomposition, wave propagation and true-amplitude imaging. Therefore, we propose corresponding approaches, including mode decomposition based on stress boundary condition, frequency-dependent complex eikonal equation, and elastic deconvolution imaging condition. As accurate mode decomposition need stress and displacement components on the exploring boundary, we will derive accurate decomposition and continuation formulas using boundary stress and displacement based on representation theorem, and develop the relationship from displacement to stress on a boundary by assuming only upgoing incident waves, to resolve unknown stress in normal three-component seismic data. For the problem of high frequency approximation of wave propagation, we propose complex eikonal equation to analyze finite frequency wave field. In order to enhance the applicability of the complex eikonal, we study the phenomena of two-way and multipath waves. As the polarizations of 3D elastic waves are complex, and the normal deconvolution imaging condition cannot be used in elastic migration, we derive deconvolution formulas for elastic media, and obtain accurate reflection coefficient imaging. The above problems are generated in different phases of elastic Gaussian beam migration, while they are all important for true amplitude migration and inversion.

3D弹性高斯束保幅偏移与反演对于地下隐蔽目标成像与参数评估具有重要研究意义。然而，当今高斯束偏移在3D复杂弹性介质中的应用面临波型分离、波场传播和保幅成像等多方面的问题。为此本项目提出相应的基于应力边界条件准确波型分离，频率相关的复程函方程，以及弹性波场反褶积成像研究方案。由于波型分离同时与探测边界的应力和位移有关，因此本项目基于表示定理推导准确波型分离和波场延拓表达式，并在上行入射假设下推导边界应力和位移关系式，解决常规三分量应力未知问题。对于波场传播面临的高频近似问题，本项目提出了频率相关的复程函方程及其求解算法，并研究双程波和多路径波场在复程函中分析。由于3D弹性波场偏振属性复杂，常规反褶积保幅成像不适用于弹性波场，为此本项目推导弹性波场反褶积成像条件，实现准确的多波反射系数保幅偏移。三个问题分属于弹性偏移成像的不同阶段，但均对保幅偏移与反演影响明显。

本项目以实现复杂弹性介质高斯束保幅偏移为目的，研究基于应力边界条件的多波耦合关系、频率相关的复程函方程、以及弹性波矢量场保幅成像条件，解决复杂弹性介质在波型分离、波场传播和保幅成像面临的问题。当前，本项目拟达到的多项预期成果均已实现。我们建立了基于应力边界条件的准确波型分离表达式并用于波场延拓，同时实现了海底和地表波速和密度反演，为波场分离提供准确参数设置；实现了基于Helmholtz方程数值解的复程函方程公式推导和数值计算，提取频率相关的射线路径、走时等信息；实现了适用于单炮保幅的反褶积成像，并发展了适用于多炮多参数反演的角度域广义Radon变换(AD-GRT)多参数反演理论。以上问题的有效解决为进一步发展高效、高精度、高分辨率、高灵活性的定量化多参数反演奠定了基础。