A Study Of Three-dimensional Magnetotelluric Fast Forward Modelling

Magnetotellurics,a type of frequency domain electromagnetic sounding method,is used to make a study of subsurface medium by taking natural alternating electromagnetic waves as field source;with no need for artificial source,it is less restricted by topographical conditions so that it is convenient to operate in field at low cost.In addition,MT is sensitive to low resistivity responses but it can not be screened by high resistivity layers at the same time,therefore it is widely applied in the fields of regional geological surveys,mineral prospecting and deep geological structure studys,etc.It can give us an insight into the law of the electromagnetic field under various electrical structures by conducting magnetotelluric forward modelling.This thesis realized magnetotelluric 3D forward modeling through application of frequency-adaptive Edge-based Finite Element Method and calculating the electric field value of a specific kind of model rapidly by the quasi-linear integral equation method.Above all,on the basis of MAXWELL equations and boundary conditions of 3D Magnetotellurics,this thesis derived its equivalent variation equations by using Galerkin Method.After that,it took use of regular hexahedron to partition the computational domain and conducted elemental analyzing with vector interpolation primary functions.Finally we added all the units together into a huge and sparse coefficient matrix;and then stored and solved it.Then we found that when we partition grids in computational domain with regular hexahedron,the partition may not be precise enough in the domains with drastically changing electrical property so that field value within the hexahedron unit cannot be expressed by interpolation primary function of its twelve vector sides,which then leads to errors.Besides,since the boundary conditions of Magnetotelluric field can only be satisfied at infinity,inappropriate partition method may cause big errors in the results of calculation of numerical simulation.And then reasons and rules of errors under different frequencies are analyzed,Therefore,this thesis came up with basic principles of grid partition on basis of edge-based finite element method basing on regular hexahedron.And it thus improved the forward modeling process in the light of the principles and put forward the idea of frequency adaptivity.This research constantly adjusted grid partition method with the change of frequency so that computation speed was improved significantly in the premise of qualified calculation precision.Finally,this thesis conducted forward modeling and analyses on a series of geologic models.Then the calculation of coefficients matrix was speeded up through using of green's function space symmetry and reciprocal theory;so we achieved the rapid quasi-linear approximation method.The rapid quasi-linear approximation method was used to calculate the electric field value of a specific kind of model rapidly;then put forward disadvantages and suggestions of improvement in future studies.