Three-dimensional Magnetotelluric Forward Modeling For Arbitrary Electrical Anisotropic Media And Practical Applications

Plenty of studies have shown that electrical anisotropy exists at different levels in the earth.In the upper crust,electrical anisotropy may result from preferred orientations of fracture porosity,or lithological layering,or oriented heterogeneity.In the lower crust,electrical anisotropy may result from preferred orientations of fluidized/melt-bearing or graphitized shear zones.In the upper mantle,adding to the prior causes which may act in pertinent scenarios,electrical anisotropy may also be caused by hydrous defects within shear-aligned olivine crystals.In marine settings,the orientation arrangement of mineral in sediments may cause intrinsic anisotropy;while the alternate occurrence of strata in different conductivities is regarded as macro-anisotropy.The isotropic inversion meets challenging as long as the electrical anisotropy exists in the underground media;meanwhile,it is necessary to further study the way to identify electrical anisotropy in subsurface structures with the observed data.Magnetotelluric sounding(MT)is a very effective method for measuring the electrical structures of crust,lithospheric mantle and asthenosphere.In recent years,considering anisotropy in MT has become a hot topic.Some 1D or 2D anisotropic inversion programs have been applied in the interpretation of observed MT data;there are reports on 3D anisotropic forward modeling continuously.However,it is still lacking special analysis of theoretical models and practical MT data based on 3D anisotropic media.In this study,we have realized 3D MT forward algorithm for arbitrary anisotropic media based on classic staggered-grid finite difference method.The stability and precision of the algorithm are tested with several synthetic models,after that,the codes are applied to the study of phase rolling out of quadrant(PROQ)effect in MT data and analyzing the existence of electrical anisotropy at the northern Qaidam Basin in the northern Tibetan Plateau.The main contents and research results are summarized as followings:(1)An overall review of the progress in anisotropy in MT research is presented.The development of anisotropy in MT study includes three main stages: the introduction of electrical anisotropy to MT in 1960~1970s,the slow development period and developing actively recent years.At present,it is still a focused issue to find a stable,rapid and compatible 3D forward algorithm.(2)With a brief introduction of the basic theories of MT,the 3D MT forward algorithm for arbitrary electrical anisotropic media has been accomplished.Basic equations: By operating the basic MT quasi stationary equations,we can obtain the electrical vector equation considering electrical anisotropy,and there can be in uniform form from 1D to 3D.Model subdivision and field definition: with a staggered grid finite difference method,the model space is discretized into rectangle blocks with electric fields placed on the edges of each block,and the magnetic fields normal to the faces of each block.Boundary conditions: The four sides of the 3D model are treated as 2D so to calculate the boundary values.The responses at sides parallel to y direction can be calculated by 2D anisotropic program directly.When we calculate the 2D responses at sides along x direction,both the initial fields and the model conductivities are rotated 90° clockwise around z axis;and the calculated fields should be rotated 90° counter-clockwise around z axis so to get the correct boundary values.Solutions of the FD equations: After approximating the electrical vector equation,a linear system for electric fields can be obtained.The linear system of equations is solved with a direct solver as PARDISO,and then the remaining magnetic field values can be computed by using electric field values.At the center of block face on earth's surface,the electric and magnetic field components are calculated by linear interpolation so to get the MT impedance responses.(3)Examination of the precision and stability of the forward program.Through comparing with the 1D anisotropic analytical,3D isotropic numerical and 2D anisotropic numerical results,our algorithm has been proved to be of high precision and stable.(4)Based on our forward program,we calculate the responses of synthetic anisotropic models to study the PROQ effect in MT.We classify the models generating PROQ effect into horizontal and upper-lower structures,and focus on the systematical study for anisotropic models with upper-lower structure.Based on the classic 2D anisotropic upper-lower structure,we construct corresponding 3D anisotropic upper-lower structures and analyze the influences of the scales and parameters of model on impedance phases.Some conclusion can be given as following: In all the models,the lower anomalous body is apparently larger than the upper one in scale or in a layer.If the upper anomalous body has a great difference in its horizontal length and can be treated as quasi two-dimensional structure,the model is easier to produce PROQ phenomenon.If the upper anomalous body shows similar length in both horizontal directions and can be considered as regular three-dimensional structure,it needs higher anisotropic ratio in anisotropic bodies to generate PROQ effect.Under the same conditions,increasing anisotropic ratio will be prone to PROQ;variations in anisotropic strike will influence the range of PROQ areas directly.We adopted and extended the approximately analytical analysis of PROQ in two-dimensional conditions,and further built an indicator function including the anisotropic conductivity,anisotropic strike,and host conductivity to interpret PROQ phenomenon in quasi two-dimensional or two-dimensional cases intuitively.(5)Based on the MT data acquired at the north Qaidam Basin of the northern Tibet,we make a research about the anisotropic characteristics in deep electrical structure of a MT profile crossing the north Qaidam Basin.The geological setting implies that the north Qaidam Basin is along an old suture where deep subduction of continent has occurred here.Previous seismic work indicates lithospheric anisotropy in neighboring area.The observed MT data show complex phase tensor skew values and phase splits at low frequencies.The electrical structure in the prior isotropic inversion results show macro-anisotropy at mid-lower crust in this area which may imply the existence of intrinsic electrical anisotropy.With the 3D anisotropic algorithm,the tests of parameter sensitivity for presuming anisotropic area have been implemented to obtain the initial macro-anisotropic parameters.Then,we perform trial-and-error modeling to find the suitable anisotropic angle.At last,we determine the anisotropic parameters equivalent to the isotropic structure of this area and verify the possible existence of electrical anisotropic structure at mid-lower crust if northern Qaidam Basin.