Least-squares joint imaging of multiples and primaries

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 inversion method, Least-Squares Joint Imaging of Multiples and Primaries (LSJIMP), 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 like shear wave conversions. We present a particular LSJIMP implementation which 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 normal moveout (NMO). Our operator’s kinematic component is an extension of the NMO equation which independently images “split” peglegs in a moderately heterogeneous Earth. Its amplitude component corrects multiples for their differences in angle-dependent reflection strength