基于互相关目标函数的远震资料弹性波全波形反演及其应用

Teleseismic data-based imaging methods are important tools to survey the structures of the Earth's interior. Conventional traveltime-based tomography method only uses the kinematics information included in seismic data, while wave-equation-based full waveform inversion method simultaneously makes full use of both kinematics and dynamics information which can obtain velocity models with high resolution. Although conventional L2-norm-based full waveform inversion tries to directly match the amplitude between the observed data and simulated data, it is imperfect especially for real data. In view of this, we intend to develop elastic full waveform inversion based on cross-correlation objective function by relaxing on the amplitude matching and using phase constraint, which is more practical and robust compared with the conventional L2-norm-based full waveform inversion. As triangular spectral element method (TSEM) has some advantages, such as meshing flexibility, high computational accuracy and efficiency, we combine it with the efficient propagator matrix method to develop a hybrid teleseismic wavefield modeling method. After that, we intend to develop the elastic full waveform inversion for teleseismic data by constructing the cross-correlation objective function and deduce its sensitive kernels based on adjoint-state equation, which can improve the resolution of velocity structures significantly. Finally, we try to apply this method to the teleseismic data from Qinling-Dabashan orogen to obtain the fine structures of the crust and upper mantle, which provides deep structural constraints on the dynamics of the basin-mountain coupling.

基于远震资料的地震波成像是地球内部结构探测的重要手段。与传统的走时层析成像方法仅利用运动学信息相比，基于波动方程的全波形反演方法能充分利用地震波的运动学和动力学信息，获得更高分辨率的成像结果。针对传统的基于L2范数目标函数全波形反演在实际资料中振幅匹配不理想的问题，本研究拟发展基于互相关目标函数的时间域弹性波全波形反演方法，通过松弛振幅匹配强调相位约束，发展一种更加实用和稳健的反演成像方法。鉴于在大尺度地震波场数值模拟中，谱元法在剖分灵活性、计算精度和计算效率的综合优势，拟发展三角网格谱元法与高效的传输矩阵法相结合的混合远震波场数值模拟方法。建立时间域弹性波全波形反演的互相关目标函数，利用伴随状态方程推导反演敏感核，开展远震资料的时间域弹性波全波形反演成像方法研究，提高速度结构图像的分辨率，并尝试应用于秦岭-大巴山造山带地区，获得精细的壳幔结构，为该区的盆山耦合动力学演化提供深部结构约束。

本项目围绕地震波传播与成像方法开展了系统性研究工作，取得了如下主要成果：.（1）发展了高阶高精度三角网格谱元法地震波场数值模拟，相比于传统方法，将三角网格谱元法的计算精度提高一个数量级，并将自适应网格剖分与基于OpenACC的并行算法相结合，提出了自适应三角网格谱元并行算法，将计算速度提高~20倍；.（2）构建了归一化零延迟互相关目标函数，利用互相关目标函数松弛振幅匹配强调相位约束对振幅差异不敏感的特性，发展了稳健的波形反演方法，从而有效地克服了数据中的非高斯噪声，相比于传统方法，能够获得高信噪比的速度模型；.（3）实现了震源时间函数反演，通过给定已知初始震源时间函数，进行单次额外的波场正演进行震源时间函数反演，从而解决震源时间函数反演估计不准确带来的反演结果失真问题；.（4）开展了谱元法震源波场重建工作，针对谱元法在伴随反演中震源波场重建的巨大存储问题，充分利用其拉普拉斯算子的单元全局性，发展了一种仅需存储单层边界节点波场值的低存储且精确重建方法，节省一个数量级的存储；.（5）发展了FK方法与自适应三角网格谱元法相结合的混合远震波场数值模拟方法，并实现了远震资料的归一化零延迟互相关目标函数波形反演，该方法能显著提高计算效率；.（6）开展了新方法在实际结构成像中的应用研究，在胶辽地区的远震资料中均取得了良好的效果，获得了清晰的地壳速度结构和界面形态，并发现该地区中地壳存在显著的低速层。