Target-oriented wave-equation least-squares migration/inversion with phase-encoded Hessian

Abstract

Prestack depth migration produces blurred images resulting from limited acquisition apertures, complexities in the velocity model, and band-limited characteristics of seismic waves. This distortion can be partially corrected using the model-space least-squares migration/inversion approach, where a target-oriented wave-equation Hessian operator is computed explicitly and then inverse filtering is applied iteratively to deblur or invert for the reflectivity. However, one difficulty 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. A new method to compute the Hessian operator for the wave-equation-based least-squares migration/inversion problem modifies the original explicit Hessian formula, enabling efficient computation of this operator. An advantage is that the method eliminates disk storage of Green’s functions. The modifications, however, also introduce undesired crosstalk artifacts. Two different phase-encoding schemes, plane-wave-phase encoding and random-phase encoding, suppress the crosstalk. When the randomly phase-encoded Hessian operator is applied to the Sigsbee2A synthetic data set, an improved subsalt image with more balanced amplitudes is obtained.