The Study Of Large Scale Magnetotelluric Modelling And The Effect Of The Cartesian Approximation

It has been almost 70 years for the development of magnetotelluric(MT),it is a geophysical exploration method that utilizing natural alternating electromagnetic fields to detect the inner electric structure of Earth.Magnetotelluric is widely used in many fields due to its low cost,easy-taking and sensitive to the high conductance.The theory of magnetotelluric is impeccable and a complete processing flow from data acquisition to three-dimensional interpretation has been established.Traditionally,magnetotellurics(MT)rests on an assumption that plane wave incidents vertically into flat Earth.With more and more magnetotellurics data coming in and the expansion of research area,Cartesian approximation and plane wave assumption may no longer suitable for the large-scale modeling due to the inevitable Earth curve.Based on such background,this thesis proposes 3D magnetotelluric modeling algorithm in spherical coordinates system.Starting from the Maxwell's equations in the frequency domain,the linear equations for solving the electric fields are derived by using the staggered grid finite difference method.Depending on the framework of modular software ModEM,the spherical modeling code was developed.The correctness and effectiveness of the spherical code were tested by one-dimensional conductivity model and three-dimensional conductivity model respectively.Before discussing the influence of Earth curvature on Cartesian simulation,this thesis elaborates a method of mutual conversion between sphere model and Cartesian model.It mainly includes two steps,one is projection of numerical grid and the another is model conductivity interpolation,among which map projection dominates.Five representative projection methods—cylinder equidistance,cylindrical equal area,Lambert conformal conic,UTM and azimuth equal area—are used for model transformation.The third chapter of this thesis uses the static and default numerical grids to transform the model,which fully shows the characteristics and suitable usage of different map projection methods,which is of great help to understand the essence of model transformation.In order to study the influence of Earth curvature,the thesis uses the conductivity model of the western United States to calculate the surface response values of the sphere model and the Cartesian model respectively,then compares their data for one same period.The results show that the spatial distribution of apparent resistivity difference is related to the adopted map projection method,and it is also affected by the lateral change of the conductivity of the model.In the region where the conductivity is abrupt,such as the boundary,the apparent resistivity difference will be more obvious.In the same way,bilinear interpolation with smoothing is more effective in model transformation than nearest neighbor interpolation.Contrastive experiments prove that the curvature of the earth has a non-negligible influence on the three-dimensional model.For the western model of the United States,the influence of curvature can be minimized by using cylindrical equidistant and equal-area projections.Less noticed than the map projection and interpolation methods,the meridian convergence angle is often neglected.This thesis introduces the definition of the meridian convergence angle,and derives the expression of the convergence angle of different map projections.The impedance calculated from the Cartesian model is corrected.The corrected response value gets closer to the result calculated directly in the spherical coordinate system.The magnitude of the convergence angle is related to the distance from the central longitude.The farther the distance is,the larger the angle is,and the corresponding correction effect is more powerful.In the field of large-scale electromagnetic simulation,the source effect has always been one of the research hotspots.The electric fields are represented by poloidaltoroidal decomposition,then solved based on spherical harmonic and Bessel function to construct the source model that can replace plane wave.The change of the source has a significant influence on the electric fields of the forward calculation.The distribution of the difference has a great correlation with the source structure and conductivity.The influence on the short period data is greater than that of the long period.High conductors in the model are more sensitive to changes in the source.Taking all the lessons we have learnt,this thesis,in the end,quantitatively evaluates the western United States and the continental United States model to determine whether they can still be processed and interpreted using the Cartesian coordinate system.If the difference in apparent resistivity is greater than the 5% error floor of the real data,the Cartesian approximation is no longer applicable.Statistical results on the measured MT sites show that the Cartesian coordinate system can still be used in the western United States,while the larger continental model needs to be calculated and interpreted in the spherical coordinate system.