Three Dimensional Magnetotelluric Numerical Modeling By Finite Difference Method

Magnetotelluric method(MT),as an important branch in the field of geophysical prospecting,with its unique advantages,is widely used in detection of underground medium.For decades,the research scopes of the MT are from one dimensional and two dimensional then to three dimensional and form ignoring the terrain to join terrain/marine,study structure is from isotropic to anisotropic.Actually,that is the process of geophysicists unceasingly to remove the ideal mathematical explanation and acquire the real information for underground medium.Searching the forward and inversion algorithm with high efficiency and precision and improving the standard of data interpretation are is the vital subject in the field of MT research.We use a finite difference method to model the three-dimentional algorithm of MT in this paper,and further enrich the theoretical knowledge in the field of MT.In this paper,we first research from the Maxwell equations of natural source,then acquire the three dimensional forward modeling by finite difference method(FD).In order to improve the precision of electromagnetic field,the total electric field is separated to background field and anomalous field.For gaining the background field,we derive the electromagnetic field analytic formulas in half-space medium and complex layered medium from the basic theory of electromagnetic field.We use the staggered grid finite difference method to disperse the study area and derive the formulas of magnetic field components and electric field components in every grid points.After that,we acquire the linear equations by matrix assembling.Eventually,we use the Biconjugate Gradients Stabilized Method(BICGSTAB)to solve linear equations which basing on incomplete Cholesky decomposition solver and gain the anomalous field.In order to verify the FD method's reliability and applicability in complex geologic structure,we compare it with analytical solution in half-space and layered medium and the total-field algorithm,then establishing four different models to analysis by the FM method.