Reiter et al. (1991) present an early example of imaging multiples directly using a prestack Kirchhoff scheme. Yu and Schuster (2001) describe a cross-correlation method for imaging multiples. Berkhout and Verschuur (1994) and Guitton (2002) apply shot-profile migration for multiples. The aforementioned approaches produce separate-but-complementary pseudo-primary and primary images, yet they either do not attempt to, or employ simplistic methods to integrate the information contained in the two images; either add Reiter et al. (1991) or multiply Yu and Schuster (2001) them together.

In this paper, I introduce a new methodology for jointly imaging primaries and multiples. In addition to a desire to correctly image the multiples, my approach is driven by three primary motivations:

- 1.
**Data Consistency**- The primary and pseudo-primary images both should be maximally consistent with the input data.- 2.
**Self-consistency**- The primary and pseudo-primary images should be consistent with one another, both kinematically and in terms of amplitudes.- 3.
**Noise Suppression**- In the primary image, all orders of multiples should be suppressed. In the pseudo-primary image created from, say first-order water-bottom multiples, contributions from primaries and secord-order or greater multiples should be suppressed.

In my approach, I use the simplest possible imaging operation, Normal Moveout (NMO). I derive an NMO equation for water-bottom multiple reflections, which maps these multiples to the same zero-offset traveltime as their associated primaries, creating a ``pseudo-primary'' section. To account for the amplitude differences between the primary and pseudo-primary sections, I assume constant seafloor AVO behavior and estimate a single water-bottom reflection coefficient from the data. To address the AVO differences between primary and pseudo-primary, I derive an expression - valid only for constant velocity - for the AVO of the pseudo-primary as a function of the AVO of the primary, and then enforce this constraint in the inversion via an offset- and time-dependent regularization term.

6/10/2002