Extended least-squares inversion is superior to stack-based least-squares inversion for imaging the subsurface because it can better account for amplitude-variation-with-offset (AVO) effects as well as residual moveout (RMO) effects induced by erroneous velocity models. Surface-offset extensions have proven to be a robust alternative to angle gathers as well as subsurface extensions when applied to narrow-azimuth data acquisitions, especially when using erroneous velocity models. As such, least-squares reverse time migration (LSRTM) applied to surface-offset gathers (SOGs) obtains accurate surface-offset-dependent estimates of the reflectivity with better AVO behavior, while respecting the curvatures of the events in the gathers. Nevertheless, the computational expense incurred by SOG demigration generally renders this process unfeasible in many practical situations. We have exploited a compression scheme for SOGs that captures AVO and some RMO effects to improve efficiency of extended LSRTM. The decompression operator commutes with the demigration operator; therefore, gathers compressed in the model domain may be decompressed in the data domain. This obviates the need to demigrate all SOGs, requiring only the demigration of a few compressed gathers. We determine the accuracy of this compression in the model and data domains with a synthetic 2D data set. We then use our model-compression/data-decompression scheme to SOG-extended iterative LSRTM for two field data examples from offshore Brazil. These examples demonstrate that our compression can capture most AVO and some RMO information accurately, while greatly improving efficiency in many practical scenarios.

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