Debiasing of seismic reflectivity inversion using basis pursuit de-noising algorithm

Abstract

Seismic reflectivity inversion using basis pursuit de-noising algorithm (BPDN) produces sparse solutions by applying l1-norm regularization. Due to the presence of the regularization term, there is always a deviation between the solution obtained by BPDN and the true one. A debiasing step of “adding back the residual” was introduced into seismic reflectivity inversion using BPDN to reduce the deviation, so that the accuracy of seismic reflectivity inversion using BPDN is improved. The debiasing step is carried out using a moderately large trade-off factor by iteratively performing the fast iterative soft thresholding algorithm (FISTA) to solve the objective function of BPDN with the input updated by adding back the residual to the initial input. The solution obtained by using FISTA with incorporation of the debiasing step of “adding back the residual” is a better approximation of the true solution than the result obtained by using FISTA a single time. In addition, the debiasing step of “adding back the residual” is not limited to the number of nonzero components in the solution and can be used in a low signal-to-noise ratio circumstance. A multichannel inversion method was adopted to recover the acoustic impedance from the inverted reflection coefficient, and it gained good results both in numerical and field examples.