Three-Dimensional Joint Inversion of EM and Acoustic Data Based on Contrast Source Inversion

In this article, we study a 3-D joint inversion algorithm for acoustic and electromagnetic data. This algorithm is based on the contrast source inversion method, which aims to reconstruct acoustic and electromagnetic parameters by updating two contrasts and two contrast sources alternately. The contrast is defined as the relative difference between the parameter, such as permittivity, of the object and the background, while the contrast source is expressed as the function of the contrast and the total field to partially linearize the problem. Besides, two multiplicative regularization terms are employed to alleviate the ill-posedness. Because the physical parameters in electromagnetics and acoustics share the same structure, we use the gradient of the contrast in acoustics and electromagnetics to constrain each other to achieve the enhanced structural similarity between inverted models. Then, by minimizing the predefined cost function using the conjugate gradient method, those acoustic and electromagnetic parameters, such as compressibility, attenuation, permittivity, and conductivity, can be reconstructed. Two numerical examples are given to compare the results of separate inversion and joint inversion.