Iterative Re-weighted Least Squares Gaussian Beam Migration and Velocity Inversion in the Image Domain based on Point Spread Functions

Amplitude-preserving migration is very important for reservoir characterization, which can faithfully provide information on the strength of the reflectors. However, conventional migration algorithms do not compensate for variable illumination effects and can hardly obtain true amplitudes of medium parameter. Least squares migration (LSM) is an effective method to address this issue. Unfortunately, there is a key problem with LSM methods: most LSM methods only consider illumination compensation but not consider the accuracy of migration velocity model. The accuracy of the migration velocity model directly affects the quality of migrated images. Moreover, changes in velocity are more indicative of reservoir properties than reflectivity. Therefore, it is necessary to incorporate velocity estimation into migration imaging to realize joint inversions. Based on these facts, we present an iterative re-weighted LSM method by approximating the local Hessian using point spread functions. Then, we related the LSM results to the scattering potential, simultaneously achieving velocity update with illumination compensation. Based on the gradually changing characteristics of rock properties, we adopted a sparse derivative constraint rather than requiring the result to be sparse. Consequently, this processing caused the results to contain broader bandwidths, giving the image a more continuous and textured appearance. Next, we evaluated the proposed method using the Marmousi2 model. The results had higher resolution and a more reliable amplitude than the initial migration images. Hence, we efficaciously completed the velocity model update, with our method achieving encouraging results under both relatively accurate migration velocity and highly smoothed migration velocity model tests.