Robust frequency-domain acoustic waveform inversion using a measurement of smooth radical function derived from compressive sensing

Abstract

A smooth radical function derived from compressive sensing is introduced, aiming to measure the misfit in frequency-domain acoustic waveform inversion. The purpose of employing this function is to improve inverse accuracy and reliability. With a novel approximation of L1 norm, the objective function constructed by this measurement can exhibit favorable robustness throughout the inverse iteration. By exploiting the smoothness property, the misfit can be minimized through a cost-effective approach of taking derivatives. The inverse framework of the smooth radical function is derived which indicates comparable computing complexity per iterative step to L2 case, theoretically. The experiential data with outliers are employed for inversion and compared with the traditional optimization-based L1 norm and L2 norm. The obtained results are consistent with theoretical analysis and demonstrate the superiority of the proposed measurement.