3D Numerical Simulation For Transient Electromagnetic Field Excited By Large Source Loop Based On Vector Finite Element Method

Large source loop transient electromagnetic method is one of common electromagnetic methods. Once transmitting loop laid later, several receivers can measure simultaneously within the central area of the transmitting loop. The method's advantages are high efficiency and large exploration depth. However, the level of data processing and inversion stays in one-dimensional stage. The forward is the basis for inversion and data processing, so it is necessary to conduct research forward firstly. To reflect the real propagation of transient electromagnetic field, correct terrain on the impact of transient electromagnetic fields, improve the interpretation of transient electromagnetic data processing level, improve the application of transient electromagnetic effects, we use the vector finite element method for simulating3D transient electromagnetic field excited by large source loop. The main contents are as follows:(1) We deduced transient electromagnetic field expressions excited by large source loop. According to the electric field excited by vertical magnetic dipole in frequency domain, the electric field excited by large source loop could be got using loop area integral for magnetic moment. Using differential expressions between0and1orders Bessel function and spatial location cooridinates, the electric field expressions were transformed from area integral to line integral. Using Gaver-Stehfest algorithm, the electric field excited by large source loop in time domain was converted from in frequency domain. Based on Faraday law of electromagnetic induction, impulse responses of magnetic induction were deduced from electric field strength step responses, and then we could obtain EMF.1D transient electromagnetic field excited by large source loop is mainly used for defining all-time apparent resistivity, validating vector finite element method numerical solutions and calculating background electromagnetic field for forward. (2) We determined the optimal number of coefficients and the application scope of Gaver-Stehfest algorithm. Researching the coefficient's optimal number and the application scope of Gaver-Stehfest algorithm is to improve the accuracy of EMF, in particular at late times. Because the Gaver-Stehfest algorithm requires double precision calculation, the accuracy is closely related with the computer word length. We test Gaver-Stehfest algorithm in32-bit Windows operating systems. We found the optimal number of coefficients is14. If the value needs to be calculated is less than5×10-13V, Gaver-Stehfest algorithm doesn't validate.(3) We simulated3D transient electromagnetic field excited by large source loop using vector finite element method. By Laplace transform, Maxwell's equations were transformed from time domain to Laplace domain, and then Helmholtz equations for electromagnetic field were deduced. We made electric field Helmholtz equation as governing equation, and derived the corresponding system of vector finite element method equations using the Galerkin method. For solving the governing equation using vector finite element, we divided the computing domain into homogenous brick elements, and used Whitney type vector basis functions. To solve linear system of equations, we used Bicgstab method with a SSOR preconditioner. After obtaining the electric field values by vector finite element method, we used Gaver-Stehfest algorithm to transform these values to the time domain, and obtained the magnetic field impulse response through Faraday law of electromagnetic induction. By comparing quasi-analytic solutions of layered model and integral equation method and FDTD solutions of low resistiviy block, we verified vector finite element method solutions. Finally, we simulated transient electromagnetic field of different models, such as upright low resitivity sheet model.(4) The all-time apparent resistivity including measuring point position information is obtained. Firstly, we take late time apparent resistivity of transient electromagnetic method as the priori information for VFSA. Then, utilizing VFSA to fit theoretical EMF and measured EMF obtains the all-time apparent resistivity of the measuring points in rectangular transmitting loop. At last, we applied this algorithm to carve out of the boundaries of clastic rocks and basalt at Narenbalige in Inner Mongolia Autonomous Region.