Three-dimensional Controlled Source Electromagnetic Inversion Using Electric Field Data

Since the invention of controlled source audio-frequency magnetotelluric(CSAMT) at seventies and eighties of last century, it has became an important meansof electromagnetic exploration, it has been widely used by countries around the world.Nowadays,the research of one-dimensional, two-dimensional forward and inversionhas matured in the world, and the three-dimensional inversion also has greatprogress. There are many common algorithms, such as the forward finite differencemethod, finite element method and the integral equation method, inversion methods:conjugate gradient method, nonlinear conjugate gradient method, Newton method,quasi-Newton method. However, due to its very expensive amount of computationsand large memory there is a certain distance away from practical application.Therefore, this article on the basis of existing technologies expected, considering theinversion process how to select the initial model and frequency, by a large number ofnumerical simulations. It want to put forward a solution of controlled source ofpractical application that saving calculation and improving retrieval speed withoutsacrificing the inversion effect.First of all, we reference Commer’s idea, which decomposite the total electricfield excitation of finite-length lead source into the primary field and the secondaryfield that produced by three-dimensional l resistivity anomalies. The calculation ofprimary field using the virtual interface method, numerical calculation using the directintegration method. The calculation of secondary field uses a staggered grid finitedifference method. We use a limited memory (L-BFGS) method that one ofquasi-Newton methods for inversion. It doesn’t need to store large Hessian matrix orits inverse is its advantage. It only need to store m times of previously information ofiteration, thereby reducing the space occupied, improving computing speed. L-BFGSmethod global convergence under appropriate conditions.Then, two layers model is designed,calculate the response of this model. Thex-component of electric fields Exwith constant noises are put into inversion. Compareand analysis different results that inversion uses different the initial model andfrequency.Because the L-BFGS method is globally convergent under appropriateconditions, the initial model is a great impact for the inversion. In order to improvethe efficiency and accuracy of the inversion, we design a initial model through ainversion using coarse grid model and all frequencies. Then inversion use a fine gridsection and critical frequencies that calculate according to an exception to theinversion depth.Finally, this paper proposes the inversion scheme come from the theoretical model to verify inversion of actual data. The results of different sizes of mesh showthat the position of abnormal is almost same, but its abnormality appears to extendbecause the size of the mesh.Then design the initial model based on the results ofinversion. Select the frequency for inversion according to the actual need,combine thebest frequency with high-frequency, low-frequency.So it can control the up and downfalse anomalies appear.Compare and analysis the result that inversion use the bestfrequency combinations. Found that results is agree well with geological data andother geophysical methods, indicating the feasibility of the inversion scheme.Through inversion of theoretical models and real data,put forward the followingconclusions:1)Proposed a feasibility inversion scheme, design the initial model basedon the results of coarse grid full frequency, then obtained critical frequencies by thedepth of formula, adding high frequency and low frequency. This approach not onlysaves computing time, but also ensure the accuracy of the inversion.2)Whenresistivity of the initial model is lower than resistivity of the actual model,the results ismore difficult to fit.The resistivity of initial model is higher than the resistivity of theactual model is more close to the theoretical model.3)The number of frequenciesfor three-dimensional inversion is not all,it is important to obtain the key frequency bycalculating, adding high and low frequency control.So the result of inversion is moreaccurate.4)The inversion use electric field component Ex, in the x-direction control isbetter, extending the y direction.