Elastic Impedance Reconstruction Using Compound First- and Second-Order Total Variation Regularization

This study introduces a novel compound regularization technique for Elastic Impedance (EI) inversion that combines Total Variation (TV1) and Total Variation of the second-order (TV2) regularizations. This method leverages the Split-Bregman algorithm to effectively address the staircase effect, a common limitation of using TV1 regularization alone. The proposed approach enforces smoothness (TV1) and improved edge preservation (TV2) in the reconstructed EI models, leading to more accurate representations. The efficacy of this method is demonstrated by applying it to two geologically relevant elastic models: the Marmousi model (complex but synthetic) and seismic field data from the Gulf of Mexico. Numerical tests were conducted using realistic noise levels, and the results confirmed the proposed method’s ability to reconstruct detailed and accurate EI models for both models, highlighting its generalizability to diverse geological scenarios. Unlike the simpler TV1 and TV2 regularizations, our combined approach adeptly handles complex models featuring both smooth and abrupt transitions, though its performance can vary across different geological scenarios. This method provides a promising framework for improved EI reconstruction in diverse geological settings.