Inverse scattering internal multiple elimination: Leading‐order and higher‐order closed forms

Abstract

Internal multiples are multiply reflected events in the measured wavefield that have experienced all of their downward reflections below the free surface. The order of an internal multiple is defined to be the number of downward reflections it experiences, without reference to the location of the downward reflection. The objective of internal multiple elimination using only recorded data and information about the reference medium is achievable directly through the inverse scattering task specific subseries formalism. The first term in the inverse scattering subseries for first-order internal multiple elimination is an attenuator, which predicts the correct traveltime and an amplitude always less than the true internal multiples’ amplitude. The leading and higher-order terms in the elimination series correct the amplitude predicted by the attenuator moving the algorithm towards an eliminator. Leading-order as an eliminator means it eliminates a class of internal multiples and further attenuates the rest. Adding the leading-order terms in a closed form provides an algorithm that eliminates all internal multiples generated at the shallowest reflector. The generating reflector is the location where the downward reflection of a given firstorder internal multiple took place. The higher-order subseries and its closed form correct the attenuation due to information on the overburden of deeper generating reflectors. A prestack form of the algorithm, which can be extended to a multidimensional form, is given for the leading-order subseries and its closed form.