Numerical Accuracy And Efficiency Of 3D Magnetotelluric Modeling

The numerical simulation algorithms of three-dimensional magnetotelluric modeling include integral equation method(IE),finite element method(FE)and finite difference method(FD).IE method can provide very accurate result in simulating forward response of-simple geologic body,but it's still difficult to simulate the complex models.the algorithm using FE method requires large computer memory and long computation time,although it can provide accurate solutions for complex models with surface topography.FD method is a classical simulation algorithm earliest applied to geophysical field,and becomes the mainstream algorithms in modeling electromagnetic response in recent years due to much more efficient computation.The staggered-grid finite difference(SFD)method originally designed for solving Maxwell's equations in isotropic media by Yee(1966)becomes one of widely used 3-D MT modeling algorithms increasingly since the last century 90s,thanks to the rapid development of computational chips.Unlike most researchers focusing on boundary conditions,solver and preconditioner of SFD in simulating MT response,the difference in terms of numerical accuracy and computational efficiency of four finite-difference schemes which are combined by two staggered grid types and two forward equation formulations is compared in detail,and 3-D modeling SFD Fortran codes of four schemes are developed.One of staggered grid types is described by H fields sampled at midpoint along the edge of grid cell and E fields sampled at face center along the normal to face of cell,the other is is described by E fields sampled at midpoint along the cell edge and E fields sampled along the normal to cell face center.Two forward equation formulations are respectively H field formulation and E field formulation.All of four schemes apply Dirichlet condition to boundaries of computing domain,and use Bi-conjugate gradients stabilized method(BICGSTAB)preconditioned with incomplete LU decomposition(ILU)to solve equation system,and introduce divergence correction to iteration process in order to improve the convergence of relaxation.MT responses for models of half space,D bilayer earth,H trilayer earth,conductive prism and COMMEMI are computed using four finite-difference schemes to compare these algorithms'numerical accuracy on coarse mesh and fine mesh.These 1-D and 3-D numerical experiments'results show that numerical accuracy of SFD magnetotelluric modeling is related to staggered grid types rather than forward equation formulations.The solutions obtained from staggered grid type of H defined along cell edge always have higher accuracy than those obtained from other one no matter on coarse or fine mesh.Moreover,forward response from schemes defining H along cell edge is more sensitive to grid resolution.In addition,comparison of computation time of four difference schemes shows simulation efficiency is mainly influenced by forward equation formulations(H or E)rather than staggered grid types.And the computational speed of E formulation seems to be faster than H formulation.This thesis also discusses another comparison in terms of numerical accuracy of two definitions of resistivity at the E field sampling point which can be defined as the volume-weighted average value of resistivity of adjacent cells(used in this thesis),or the reciprocal of the volume-weighted average value of conductivity of adjacent cells.Layerd earth experiments show the staggered grid type of H defined along cell edge results to the same MT simulation responses using two kinds of average resistivity's definitions.When the definition refer to the average value of conductivity of adjacent cells,the staggered grid type of E defined at edge will obtain more accurate modeling results than the other.