Joint Inversion Of Wave Impedance And Resistivity Based On Cross-Gradient

The inversion results of a single geophysical method can only reflect one or several physical parameters of the underground structure and are easy to generate multiple solutions Therefore,it is necessary to develop joint inversion between different geophysical methods.Seismic exploration reflects the information of density and velocity changes of underground structures.Wave impedance inversion has good effect on the delamination and positioning of anomalous bodies,while DC resistivity method can reflect the electrical parameters of underground structures.But due to the impact of volume effect,the boundary division of the abnormal body is not accurate.In this paper,the seismic impedance data is applied to the inversion of DC electrical data by using the cross gradient function,and the joint inversion based on structural constraints is realized.This method relies only on the structural change rules of two physical properties,and does not depend on the specific relation expression between different physical parameters,and avoids the problem of merging the different physical parameters of the two dimensions into the same formula.Firstly,the two-dimensional finite element forward and inverse process of the resistivity method was deduced.In the model mesh generation,the structured grid is combined with unstructured grid,and the normalized potential is used to calculate the apparent resistivity and the Jacobian matrix,skipping the process of converting the conversion potential to the real potential by using the inverse Fourier cosine transform in conventional computation.Without losing the accuracy of inversion results,it reduces computation difficulty and improves computation speed.Then,the basic principle of wave impedance inversion is explained,and calculated by STRATA.The basic principle of cross gradient function is expounded,and the central difference quotient is used to discretize it,and the basic properties of cross gradient function are obtained.The two dimensional joint inversion target function of wave impedance and resistivity method under the constraint of cross gradient function is derived.The Lagrange multiplier method is used to solve the objective function,and the inversion calculation is realized by programming.Finally,the theoretical model trials for the consistency and inconsistency of the two physical property parameters were performed.The results show that when the joint inversion is performed,the boundary division of the abnormal body is more accurate and clearer,the geometric shape is closer to the real model,the resolving power of multiple abnormal bodies is greatly improved,the value of the physical property parameter is closer to the actual value,and the speed and stability of the iteration are further improved.When the wave impedance model and the resistivity model structure are not consistent,the joint inversion algorithm based on the cross gradient function constraint has strong constraint on the region with the same structure,but there is no obvious adverse effect on the area with different physical change structure,and it is not easy to introduce the external error.Through numerical simulation,the validity and reliability of the joint inversion algorithm based on the cross-gradient function constraint are well illustrated.The multi-solution of inversion results can be greatly reduced,and the calculation of physical parameters can be more accurate.