Pre-stack sparse envelope seismic inversion method adopting the L0-L2 norm regularization

Abstract

The essence of pre-stack inversion is the model inversion, but challenges hinder its accuracy in obtaining precise initial models, particularly in marine environments or regions with limited well-log data. To enhance stability and accuracy in pre-stack seismic inversion in these areas, we propose an elastic parameter estimation approach utilizing sparse envelope inversion with L0- L2 norm regularization. Our method combines signal sparse representation and modulation theories to derive a new formula for sparse envelope extraction at lower frequencies. By applying L2 norm regularization to the sparse envelope, we obtain parameter inversion results with smoothed trends, augmenting low wave-number information for improved model constraints. Additionally, taking the envelope inversion results obtained by the L2 norm as the model constraint, the sparsest inversion results with obvious block-like characteristics are obtained by regularizing the inversion equation with the L0 norm. Notably, our method effectively suppresses wavelet side-lobes, resulting in stable and accurate inversions without the need for initial low-frequency models based on well-logs, as required in traditional methods. We present a synthetic example to illustrate the feasibility and stability of our proposed approach, and further demonstrate its practicality in reservoir parameter estimation through a field case study of gas exploration.