Study On Three-dimension Numerical Simulation Of CSAMT Based On Aggregation-based Algebraic Multigrid Method

Controlled-source audio-frequency magnetotellurics(CSAMT), one of the significant methods of geophysical prospecting, has been widely applied to many fields such as mineral exploration and geological survey. Nevertheless, it is of great challenge to truly outline the complicated geologic bodies with 1D and 2D inversion technologies, making the practicability of 3D CSAMT inversion technique extremely urgent, and seeking an efficient and stable forward simulation method is one of the key factors to promote the practicability process of 3D CSAMT inversion. Thus we carry out the study of 3D numerical simulation of CSAMT based on aggregation-based algebraic multigrid method.In this paper, we firstly start from Maxwell equations that CSAMT satisfies, and divide the total field into primary field and secondary field. For convenience, we apply electromagnetic boundary conditions and Fourier transformation to derive the electromagnetic formulas induced by finite long electric dipole, and realize the fast computation by fast Hankel transformation, then adopt staged-grid finite difference to derive the relationship between electric and magnetic components, and finally eliminate the magnetic components via transformation to convert the secondary filed computation of3 D CSAMT numerical simulation into the solution of linear equations systems only with respect to electric components. In order to improve CSAMT numerical simulation speed of iteration solution, the aggregation-based algebraic multigrid method which with high-speed convergence was introduced, and we have had an emphasis on studying the algorithm realization aggregation-coarsening process and solving process of this proposed method.Furthermore, in allusion to the large sparse system of linear equations of CSAMT with respect to finite difference simulation, we adopt the way that taking AGMG as preconditioner for the generalized minimum residual method(GCR) to realize the system of linear equations solution and the development 3D CSAMT forward modeling software.With that, we use a typical two-dimensional LAPLACE equation numericalcalculation to compare the superiority of those proposed algorithms and reach the conclusion that AGMG-GCR is both of strong stability of GCR algorithm, and of a linear fast attenuation and iterations keep unchanged with mesh dissection increasing compared with the traditional Krylov subspace iteration method(BCGSTAB, CG, BCG, GCR,DQGMRES, ILU-GCR), and then verify the accuracy and applicability of codes by a horizontal layered model, on the basis of which, we conduct the numerical simulation of several typical geoelectric models(low resistance model, high resistance model and composite model) then conclude and summarize three-dimensional response characteristics of 3D CSAMT to provide reference for field data acquisition and interpretation.