Prestack depth migration produces blurred images resultingfrom limited acquisition apertures, complexities in thevelocity model, and band-limited characteristics of seismicwaves. This distortion can be partially corrected using themodel-space least-squares migration/inversion approach,where a target-oriented wave-equation Hessian operator iscomputed explicitly and then inverse filtering is applied iterativelyto deblur or invert for the reflectivity. However, onedifficulty is the cost of computing the explicit Hessian operator,which requires storing a large number of Green’s functions,making it challenging for large-scale applications. Anew method to compute the Hessian operator for the waveequation-based least-squares migration/inversion problemmodifies the original explicit Hessian formula, enabling efficientcomputation of this operator. An advantage is that themethod eliminates disk storage of Green’s functions. Themodifications, however, also introduce undesired crosstalkartifacts. Two different phase-encoding schemes, planewave-phase encoding and random-phase encoding, suppressthe crosstalk. When the randomly phase-encoded Hessianoperator is applied to the Sigsbee2Asynthetic data set, an improvedsubsalt image with more balanced amplitudes isobtained.
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