3D high-resolution seismic inversion

该项目涉及地震成像，目的是大幅提高这种图像的分辨率和可靠性。目前的地震成像技术主要是作为20世纪中叶首次出现的概念范例的改进而发展起来的，例如射线追踪和双曲旅行时曲面。最近，逆散射方法已经证明，还可以做更多的事情。在我个人的工作中，我已经证明了现代数学概念，如Gabor变换和伪微分算子，可以在分辨率和图像精度方面产生实质性的改善。这项拟议的研究将在这些成功的基础上，扩展最近开发的非平稳Gabor反卷积和深度偏移方法，使其具有新的能力。Gabor反褶积在优化地震子波的同时，校正了地震数据的地球衰减效应。这一过程将通过限制估计空间上一致的衰减模型的方法、纳入来自可用井眼的更多信息以及通过改进对地震子波相位的理解来改进。我最近开发的深度成像方法，FOCI方法和Gabor成像方法，将扩展到3D，并针对数值性能进行优化。在这两种情况下，3D扩展都涉及到重大的研究挑战，但回报可能会很大，因为两者都被证明提供了异常高的分辨率。这两种方法都将作为成像速度分析和迭代反演方法的可能引擎进行研究。此外，还将研究非标准波类型的成像，如模式转换反射和多次波。最后，从数学采样理论的角度分析了三维地震勘探的基本设计。已经证明，实际测量永远不能满足适当的无混叠采样的要求，因此它旨在寻求采集几何，即源和接收器的布置，以及将不可避免的混叠的后果降至最低的成像算法。

This project addresses seismic imaging with the goal of substantial improvements in the resolution and the reliability of such images. Present seismic imaging technology has developed mostly as refinements of conceptual paradigms that first emerged in the middle of the 20th century, such as raytracing and hyperbolic traveltime surfaces. More recently, inverse scattering approaches have proven that much more can be done. In my personal work, I have shown that modern mathematical concepts, such as Gabor transforms and pseudodifferential operators, can result in substantial improvements both in resolution and image accuracy. This proposed research will build upon these successes by extending recently developed nonstationary Gabor deconvolution and depth migration methods with new capabilities. Gabor deconvolution corrects seismic data for earth attenuation effects while simultaneously optimizing the seismic wavelet. This process will be improved by constraining the method to estimate a spatially consistent attenuation model, by incorporating more information from available boreholes, and by an improved understanding of seismic wavelet phase. My recently developed depth imaging methods, the FOCI method and the Gabor Imaging method, will be extended to 3D and optimized for numerical performance. In both cases, the 3D extension involves significant research challenges but the rewards could be large since both have been shown to give exceptionally high resolution. Both methods will be studied as possible engines for imaging velocity analysis and for iterative inversion methods. Also, the imaging of nonstandard wave types, such as mode-converted reflections and multiples, will be pursued. Finally, the basic design of 3D seismic surveys will be analyzed from the perspective of mathematical sampling theory. It has been shown that practical surveys can never meet the requirements of proper unaliased sampling and so it is intended to seek acquisition geometries, i.e. the placement of sources and receivers, and imaging algorithms, that will minimize the consequences of unavoidable aliasing.