Least-squares joint imaging of multiples and primaries

Abstract

Multiple reflections contain subsurface reflectivity information which often complements that found in primary reflections. Previous attempts to combine the additional information by summing prestack images of the primaries and multiples have generally failed because of crosstalk leakage between the images. We present a general linear least-squares joint imaging of multiples-and primaries (LSJIMP) inversion method to simultaneously suppress crosstalk noise and combine pegleg multiples and primaries in a prestack sense. In general, LSJIMP is compatible with a wide variety of prestack imaging methods and can be extended to jointly image primaries and other embedded wave modes such as shear-wave conversions. We present a particular LSJIMP implementation that utilizes an efficient linear operator to model and image pegleg multiples in a true relative-amplitude sense. Applied to a given type of pegleg multiple in the data, our imaging operator produces an image directly comparable to primaries after NMO. Our operator's kinematic component is an extension of the NMO equation that independently images split peglegs in a moderately heterogeneous earth. Its amplitude component corrects multiples for their differences in angle-dependent reflection strength and illumination, relative to a primary. We test our LSJIMP implementation on 2D and 3D prestack field data examples and show that the method cleanly separates primaries and multiples and also uses joint information in the events to interpolate the signal in acquisition gaps.