Joint Inversion Method Based On Electromagnetic Wave And Acoustic Wave

Efficient two-dimensional(2-D)full-waveform forward and joint inverse scattering solvers about electromagnetic and acoustics are presented in this paper.The combined field volume integral equation(CF VIE)is formulated in homogeneous and layered medium.Different from the previous work,the mixed-order basis function is adopted in the discretization of the 2-D CFVIE.The contrasts of permittivity and per-meability in EM wave equation are considered simultaneously by CFVIE method.Both the contrasts of velocity and mass density in acoustic wave equation are solved by CFVIE method.All the forward solvers are solved iteratively by stabilized bi-conjugate gradient(BCGS)and accelerated by the fast Fourier transform(FFT).Meanwhile,the permittivity and permeability in EM,and the velocity and mass density in acoustics are simultaneously reconstructed with multi-frequency data in the inver-sion through the variational Born iteration method(VBIM),which is enhanced with a self-adaptive regularization factor and applied to the multi-frequency data.In the joint in-version based on the structural constraints,the cross-gradient function is incorporated into the cost function of the separate inversion to enforce the structure similarity between electric conductivity and acoustic velocity.We use VBIM and two different iteration strategies to minimize the cost function and reconstruct the contrasts.Several typical models in geophysical applications are used to validate our joint inversion method,and the numerical simulation results show that the joint inversion can improve the inversion results significantly when compared with those from the separate inversion and have a good ability of anti-noise.In the joint inversion based on the petrophysical links,by using the petrophysical equations about the porosity and saturation and applying the chain rule,we fuse the EM and seismic data,and construct the joint petrophysical inversion equations,which can be solved by VBIM.Furthermore,in order to enhance the effects of reconstructed results of the joint petrophysical inversion,we enforce the structural similarity constraint between the porosity and water saturation,and add the cross-gradient function to the joint petro-physical inversion cost function.Two typical geophysical models based on the remote sensing measurement are used to validate the proposed methods.One is the cross-well model,and the other is the marine surface exploration model.The advantage of the joint inversion compared with the separate inversion is evaluated based on the resolution and the data misfits of the reconstructed profiles as well as the anti-noise ability.