声波介质中基于D-bar方法的地震逆散射反演成像研究

Most of current mainstream methods for seismic inverse scattering inversion are approximate methods based on forward scattering model, and the theoretical basis for seismic inverse scattering is not very secure. It is necessary to investigate new strategy to break through the limitation of the traditional seismic inversion theory of inverse scattering . In this study, we will consider the inverse scattering problem in acoustics, investigate direct nonlinear intrinsic inversion imaging theory based on D-bar method via mathematically auxiliary tools and their properties and relationships (e.g., complex geometrical optics solutions, nonlinear scattering transform, boundary integral operators), and expect to better understand the problem. This study tentatively explores a new method in seismic direct inversion imaging, and will provide a firm foundation for describing complex reservoir characterization quantitatively.

目前大多数成熟的地震逆散射反演方法都是建立在正散射模型基础上的近似反演方法，真正意义上的地震逆散射反演理论基础还不是很牢固。为了突破传统地震逆散射反演方法的局限性，有必要探讨新的反演策略。本申请项目从声波逆散射问题出发，利用复几何光学解、非线性散射变换、边界积分算子等辅助工具的性质和联系，探索基于D-bar方法的直接非线性反演成像理论，以期在声波逆散射问题上得到更好的认识。本项目尝试性探索地震直接反演成像新方法，将为复杂储层的定量描述打下牢固的理论基础。

目前大多数成熟的地震逆散射反演方法都是建立在正散射模型基础上的近似反演方法，真正意义上的地震逆散射反演理论基础还不是很牢固。为了突破传统地震逆散射反演方法的局限性，有必要探讨新的反演策略。在该项目中，我们从声波逆散射问题出发，借鉴电磁散射的D-bar反演技术，构建了Faddeev复几何光学解，定义了散射变换，建立了波场与散射位势的D-bar方程，为进一步探索基于地震数据的D-bar直接非线性反演理论奠定基础。