波动方程全波形速度反演数值方法研究

项目名称： 波动方程全波形速度反演数值方法研究

项目编号： No.11471328

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 张文生

作者单位： 中国科学院数学与系统科学研究院

项目金额： 60万元

中文摘要： 本项目针对复杂构造模型，在正演模拟的基础上，研究声波动方程和弹性波方程的全波形速度反演方法。首先研究声波方程和弹性波方程新型高效的时间域和频率域的波场模拟方法，包括规则网格上的有限差分法、非规则网格上的交错间断有限元法和谱有限体积法等数值方法，以及相应方法的稳定性和收敛性理论分析；然后针对复杂构造模型，研究稳健的全波形反演方法，包括：建立基于不同频段波场的逐次反演算法，提出新的波形反演的正则化参数选择策略，比较和综合应用多种优化正则化技术如信赖域法、高斯牛顿法、变尺度BFGS法等；最后，基于研究的方法和算法，对复杂构造模型及实际资料进行数值计算，实现大规模并行反演，从而研究出一种新的稳健的适应复杂构造模型的声波方程和弹性波方程的全波形速度反演方法。由于波动方程可以描述复杂介质波的传播，其全波形速度反演结果非常适合于复杂油气藏的描述，因此该研究对油气藏的勘探开发有重要理论意义和应用价值。

中文关键词： 波动方程；全波形反演；复杂构造；数值方法；不适定问题

英文摘要： 。 In this project, concentrating on the models with complex structures, we will study full-waveform inversion methods for the acoustic and elastic wave euqations on the basis of the forward simulation. Firstly, we will study the new and high effective numerical methods for the acoustic and elastic wave equations in the time and frequency domains. They include the finite-difference method computed on regular grids, and the methods computed on unstructured meshes such as the staggered discontinuous Galerkin method and the spectral finite volume method and so on. The theoretical analysis of convergence and stability for corresponding methods is also included. Secondely, focusing on the complicate structure models, we will study the robust full-waveform inversion methods. Among of them, we will construct a novel successive inversion alorithm based on the multi-frequency band data, propose new strategies for choosing regularization parameters which are suitable for waveform inversion, compare and adopt comprehensively various iterative regularization optimiazation algorithms such as the trust region algorithm, the Gauss-Newton method and the varibale metric method and so on. Finally, based on the methods and algorithms research, we will investigate numerical computations for complicate structure models and field data and then carry out large-scale parallel inversion. Therefore we will study out a novel and robust full-waveform inversion technique for the acoustic and elastic wave equations. Moreover, the technique is suitable for inversing the complicate structural models. The wave equations can describe wave propagation in the complex media and the velocity results by full-waveform inversion results are very suitable for describing complex oil and gas reservoir, thus this project has very important theoretical significance and application values in exploration and development for oil and gas reservoir.

英文关键词： wave equation;full-waveform inversion;complex structure;numerical method;ill-posed problem