Least Square Q-Kirchhoff Migration: Implementation and Application

Absorption effects caused by the anelastic nature of the earth lead to the attenuation of amplitude and distortion of phase of seismic waves. The so-called quality factor “Q” accounting for this absorption effect has to be included for correct imaging. The two main challenges in Q compensation are the ill-posed nature of the problem and the complex absorption patterns along ray paths in real geological structures. To tackle the instability caused by the ill-posed nature of the problem as well as maintain the correct compensation for high dipping structures, we propose least squares Q-Kirchhoff migration (LSQPSDM) in which absorption is incorporated into the Kirchhoff modelling operator and Q compensation is achieved naturally via inversion with proper sparse constraints. With better illumination and Q compensation, fault imaging is naturally enhanced and migration artefacts reduced through the proposed LSQPSDM. In contrast to standard least squares Kirchhoff migration, in our approach the inversion is approximated by inverse Hessian filtering to give a cost-effective solution. The proposed LSQPSDM approach has been applied to synthetic data for validation and a field dataset from NWS Australia. Better fault imaging and SNR are obtained compared to conventional Q migration.