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 waveequation-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, planewave-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.

Elastic least-squares reverse time migration

“…This cost increases linearly with the number of leastsquares iterations, but it can be reduced by the multisource migra- tion methodology (Tang, 2009;Dai and Schuster, 2009;Dai et al, 2011Dai et al, , 2012Huang and Schuster, 2012).…”

Migration-velocity analysis using image-space generalized wavefields

“…An eventual velocity update using this unbalanced amplitude gradient can originate a velocity model that violates the smoothness assumption implied by the Born approximation. Since these amplitude variations are not related to velocity inaccuracy, we should ideally attenuate them using some sort of illumination compensation scheme (Valenciano et al, 2009;Tang, 2009). Instead, to prevent these amplitude variations we apply a B-spline smoothing to the gradient, which consists of representing the gradient as B-spline basis functions, using the adjoint operator B , and transforming it back to the Cartesian space, using the forward operator B.…”

“…Recently, phase-encoded wavefields have also been applied to velocity estimation by waveform inversion (Vigh and Starr, 2008;Ben-Hadj-Ali et al, 2009;Krebs et al, 2009) and migration-velocity analysis using wavefield extrapolation (Shen and Symes, 2008;Guerra et al, 2009). Phase-encoded wavefields can also be used to decrease the cost of computing the Hessian operator in least-squares migration (Tang, 2009). …”

The possibilities of compressed-sensing-based Kirchhoff prestack migration

“…However, a major drawback of standard Kirchhoff migration is that it suffers from migration artifacts, which results in a blurred depiction of the true subsurface reflectivity distributions. This effect is primarily caused by the limited acquisition aperture, coarse source-receiver sampling, band-limited source wavelet, and low subsurface illumination (Nemeth et al, 1999;Tang, 2009).…”