First-order internal multiples are a source of coherent noise in seismic images because they do not satisfy the single-scattering assumption fundamental to most seismic processing. There are a number of techniques to estimate internal multiples in data; in many cases, these algorithms leave some residual multiple energy in the data. This energy produces artifacts in the image, and the location of these artifacts is unknown because the multiples were estimated in the data before the image was formed. To avoid this problem, we propose a method by which the artifacts caused by internal multiples are estimated directly in the image. We use ideas from the generalized Bremmer series and the Lippmann-Schwinger scattering series to create a forward-scattering series to model multiples and an inverse-scattering series to describethe impact these multiples have on the common-image gather and the image. We present an algorithm that implements the third term of this series, responsible for the formation of first-order in-ternal multiples. The algorithm works as part of a wave-equation migration; the multiple estimation is made at each depth using a technique related to one used to estimate surface-related multi-ples. This method requires knowledge of the velocity model to the depth of the shallowest reflector involved in the generation of the multiple of interest. This information allows us to estimate internal multiples without assumptions inherent to other methods. In particular, we account for the formation of caustics. Results of the techniques on synthetic data illustrate the kinematic accuracy of predicted multiples, and results on field data illustrate the potential of estimating artifacts caused by internal multiples in the image rather than in the data.

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