Morgan Parker Brown

# Least-squares joint imaging of multiples and primaries

## Abstract

Current exploration geophysics practice still regards multiple reflections as noise, although multiples often contain considerable information about the earth's angle-dependent reflectivity that primary reflections do not. To exploit this information, multiples and primaries must be combined in a domain in which they are comparable, such as in the prestack image domain. However, unless the multiples and primaries have been pre-separated from the data, crosstalk leakage between multiple and primary images will significantly degrade any gains in the signal fidelity, geologic interpretability, and signal-to-noise ratio of the combined image. Moreover, by dividing the joint imaging process into individual separation and combination steps, each of which may produce biased results, it is difficult to ensure that the combined image honors the recorded data in any quantitative sense.

In this thesis, I present a global linear least-squares algorithm which simultaneously separates multiples from primaries and combines their information. The algorithm, denoted LSJIMP (Least-squares Joint Imaging of Multiples and Primaries), takes as input reflection seismic data with multiples, and outputs a set of images, each of which ideally contains energy only from the primaries or from one type of pegleg multiple. The novelty of the method lies in the three model regularization operators which both discriminate between crosstalk and signal and extend information between multiple and primary images. The LSJIMP method represents generalizations both of prestack algorithms which separate multiples and primaries and those which compensate for incomplete illumination. To better accomplish both goals, the method exploits another, hitherto ignored, source of redundancy in the data - that between primaries and multiples.

While many different types of multiple imaging operators are well-suited for use with the LSJIMP method, in this thesis I utilize an efficient prestack time imaging strategy for multiples which sacrifices accuracy in a complex earth for computational speed and convenience. I derive a variant of the normal moveout (NMO) equation for multiples, called HEMNO, which can image split'' pegleg multiples which arise from a moderately heterogeneous earth. I also derive a series of prestack amplitude compensation operators which when combined with HEMNO, transform pegleg multiples into events are directly comparable - kinematically and in terms of amplitudes - to the primary reflection.

I test my implementation of LSJIMP on two real datasets from the deepwater Gulf of Mexico. The first, a 2-D line in the Mississippi Canyon region, exhibits a variety of strong surface-related pegleg multiples - generated by shallow reflectors and by a tabular salt body - which strongly inhibit interpretation. The second dataset, consisting of portions of two sail lines extracted from a 3-D dataset acquired in the Green Canyon region, contains surface-related multiples which stacking mostly suppresses, but which nontheless inhibit prestack amplitude analysis. In both cases, LSJIMP excellently and non-destructively separates primaries from multiples, and moreover, reliably reconstructs missing traces and illumination gaps.