Joint Inversion Of CSEM And Seismic Data Based On Cross-gradient

The controlled-source electromagnetic(CSEM)data and seismic data contain information complementary to each other,so joint inversion of CSEM and seismic data could produce more reliable imaging of the subsurface.It is common that the 3D CSEM and 3D seismic surveys(maybe multiple 2D seismic lines in some exploration areas)exist in onshore or offshore survey areas for oil and gas exploration.Thus,it is very necessary to how to improve recovered resistivity and velocity models through joint inversion of 3D CSEM and seismic data.This paper develops an approach to joint inversion of 3D CSEM and seismic data based on cross-gradient operator.The method formulates a simultaneous objective function,which is minimized via nonlinear conjugate gradient(NLCG)algorithm.In addition,based on adjacent data misfits in the iterative inversion process,an adaptive regularization is designed to adjust model regularization parameter.In order to address the problem of the traditional cross-gradient-based joint inversion and enhance the computational efficiency and stability of inversion process,the following three methods will be included into the iteration process of joint inversion:(1)Adaptive correction method: rock physics relationships and cross-gradient operator are typically used to link resistivity with velocity in joint EM-seismic inversion.Compared to rock physics relationships,cross-gradient operator,serving for similar model structure,utilizes only the information on physical properties change and does not need specific rock physics relationships explicitly.Therefore cross-gradient operator could be applied in complex geologic situations under which the lithology varies rapidly and several rock physics relationships exist.However,when the spatial distribution of resistivity and velocity of a geologic body is different,it is difficult for existing cross-gradient operator to adjust the boundaries of resistivity and velocity for similar model structure.To this end,an adaptive correction method,based on both k-means and regression analysis,is proposed here and is applied to correct the model with relatively low level of confidence through use of the model with relatively high level of confidence in the iteration process.(2)Multi-level electromagnetic frequency and multi-level grid method: the electromagnetic fields of CSEM survey in the frequency domain are uncoupled,so the long wavelength of recovered resistivity model could be obtained by inverting the relatively low frequency CSEM data and the short wavelength of recovered resistivity model could be obtained by inverting the relatively high frequency CSEM data.Considering the match of different scale model,this paper adopts both multi-level electromagnetic frequency and multi-level grid method,that is,joint inversion of seismic data and different frequency range of CSEM data is performed with different scale grid.This could improve the inversion results,alleviate the dependence on initial models for gradient-descent-based NLCG algorithm to some extent,and enhance the computational efficiency at the same time.(3)Weighted cross-gradient method: due to the relatively reliable recovery of velocity in the cells near the seismic profile,a relatively large weighting factor is assigned to those cells.Thus the resistivity and velocity in the cells near the seismic profile have a stronger coupling,resulting in the improved imaging of the resistivity in those cells.The test of synthetic models shows that the proposed method can recover the resistivity and velocity models closer to the true models.Lastly,an application on 3D MT and seismic data acquired in some exploration area is carried out and yields the resistivity and velocity models which are in good agreement with the available geological knowledge,showing the utility of the method.