Inverse scattering series internal multiple attenuation is a promising method for predicting and attenuating internal multiples. Though the method has displayed great potential, it is not a routine step in the seismic processing workflow. Some of the issues with the method include small errors with the predicted amplitudes, which are corrected with an adaptive subtraction. After subtraction, the question often arises whether primary energy is being damaged in the removal of internal multiples. A new domain to carry out the adaptive subtraction is introduced here, which may mitigate this risk. This domain is a more natural space to create the filter as systematic amplitude errors due to the prediction algorithm can be corrected in this space. To further assist the amplitude mismatches, additional terms from the scattering series are incorporated, and the importance of how these terms are implemented is discussed. Combining this higher dimensional adaptive subtraction space with the higher order terms significantly improves the accuracy of the prediction.
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