3D high-resolution seismic inversion

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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.