Chapter introduces the LSJIMP method. The chapter is divided into three sections. In section I motivate the LSJIMP inverse problem in general. Generally, as the non-regularized LSJIMP inverse problem is underdetermined, it suffers from non-uniqueness. I describe three model regularization operators which ``steer'' the LSJIMP minimization toward an optimally crosstalk-free solution which still fits the data. In Section , I go on to outline my particular implementation of LSJIMP. In section , I show how, in a laterally-homogeneous earth, to create prestack time-domain images of pegleg multiples that are directly comparable, both in terms of kinematics and amplitudes, to the image of the primaries. In a heterogeneous earth, peglegs ``split'' into multiple arrivals. To account for this phenomenon, in section I introduce the HEMNO (Heterogeneous Earth NMO Operator), which can independently image each leg of split peglegs in a moderately heterogeneous earth. HEMNO images with a vertical stretch, sacrificing accuracy in a complex earth for the efficiency required to make iterative solutions to the LSJIMP inverse problem computationally tractable.
In Chapter I apply my implementation of LSJIMP to a 2-D seismic line, donated by WesternGeco, and acquired in the deepwater Mississippi Canyon region of the Gulf of Mexico. The data exhibit strong surface-related multiples from a variety of multiple generators, and prove challenging for all existing methods to attenuate. LSJIMP demonstrates the ability to cleanly separate multiples and primaries, even in regions with moderate geologic complexity.
In Chapter I outline the extension of the LSJIMP method to 3-D data. To minimize acquisition costs, most 3-D marine data are sampled quite sparsely along the crossline source axis, and this sparsity severely hampers some multiple attenuation methods which otherwise excel in 2-D. Because HEMNO images multiples with a vertical stretch, my implementation of LSJIMP is more immune from the crossline sparsity issue.
In Chapter I apply my implementation of LSJIMP to a real 3-D dataset from the Green Canyon region of the Gulf of Mexico. The data were acquired by CGG and contain surface-related multiples, although they are not as strong as those seen in the 2-D Mississippi Canyon data. However, the reflectors in the study area contain fairly strong crossline dips, which challenge many multiple suppression algorithms when the crossline geometry is sparse. Again, my implementation of LSJIMP cleanly separates multiples from primaries. Additionally, this data example showcases LSJIMP's ability to act as an interpolation operator. Due to fast ship speed, the inline offset resolution of common midpoint gathers is coarse. I demonstrate how LSJIMP uses the multiples to simultaneously separate modes, interpolate missing traces, and improve amplitude analysis. A comparison of LSJIMP with least-squares Hyperbolic Radon demultiple illustrates that LSJIMP is an effective and computationally tractable option for 3-D prestack multiple separation.