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Introduction

My Least-squares Joint Imaging of Multiples and Primaries (LSJIMP) algorithm Brown (2003b) separates pegleg multiples and primaries. LSJIMP computes separate images of the peglegs and primaries, and then uses the mutual consistency of the images to discriminate against unwanted noise types in each image. The images must be consistent in two respects: kinematics and amplitudes. A companion paper Brown (2003a) paper addresses the amplitude issue. In this paper, I address the kinematics. Kinematically, the events must be correctly positioned in time and flat with offset. To this end, I derive new time imaging operator, ``HEMNO'' (Heterogeneous Earth Multiple NMO Operator).

To correctly image primary or multiple reflections in a heterogeneous earth, migration reigns supreme, although its computational cost may be nontrivial over complex geology, in 3-D, or when a ``true amplitude'' image is required. My previously presented Brown (2002a) joint imaging technique used normal moveout (NMO), because of NMO's speed and its amplitude predictability, despite its inability to account for nonflat geology. HEMNO correctly accounts for moderate subsurface structure but retains the speed and amplitude advantages of NMO. I show that the 2-D and 3-D pegleg moveout equations for two dipping planes derived by Levin and Shah (1977) and Ross et al. (1999), respectively, reduce to HEMNO in the small dip angle limit.

When used in conjunction with LSJIMP, I show that HEMNO produces improved results on the moderately complex Mississippi Canyon 2-D multiples test dataset, relative to a flat-earth NMO operator. Nevertheless, the real value of HEMNO lies in 3-D. Guitton (2003) demonstrates that the ``Delft method'' Verschuur et al. (1992) (plus advanced multiple subtraction technology), almost perfectly separates surface-related multiples from 2-D data with complex 2-D structure. However, in real-world 3-D situations, acquisition and computational constraints diminish the method's applicability. I demonstrate that in a simple, yet realistic, 3-D synthetic example that HEMNO can accurately image pegleg multiples from a seabed that dips in both directions. In the future, HEMNO should prove a useful advance in 3-D multiple separation.


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Next: Traveltime Equation for Pegleg Up: Brown: Imaging operator for Previous: Brown: Imaging operator for
Stanford Exploration Project
7/8/2003