Three-Dimensional Transient Electromagnetic Forward Modeling In The Direct Time-Domain By Vector Finite Element

Currently, although transient electromagnetic method widely used in many fields, their interpretation, inversion level is not high, mainly staying in a one-dimensional phase. Forward is the basis of the inversion and data processing and interpretation, therefore, we need to study the three-dimensional transient electromagnetic forward modeling technology. Three-dimensional transient electromagnetic forward calculation method generally comprises FDTD, finite volume method, integral equation method and the finite element method. But studies using three-dimensional finite element method for transient electromagnetic field is rarely attempt, mainly because of the theory of finite element method complicated, and in the process of solving equations to be solved hundreds of thousands of bands, high hardware requirements and so on. However, the finite element method has other numerical methods do not have the characteristics such as accurate simulation of the geoelectric model complex structures, three-dimensional electromagnetic field simulation with the terrain and the like. Therefore, in order to study the propagation and response characteristics of transient electromagnetic field in a complex real geoelectric model, we need to study the finite element method to simulate the three-dimensional transient electromagnetic field.Three-dimensional finite element time domain transient electromagnetic forward modeling method generally includes two categories: one is the indirect method, to obtain the frequency domain electromagnetic field, and then transformed into the time domain; one is the direct method is to use the time difference format item discrete, and solved time-domain electromagnetic directly. The first method for solving frequency in the process of solving it affected the accuracy of the conversion of different time-frequency conversion process may correspond to different precision, and are subject to add source mode, it can’t forward a variety of different waveforms to calculate the full waveform. In this paper, the direct time domain vector finite element method was used to forward three-dimensional transient electromagnetic fields excited by loop source.From Maxwell’s equations met by time domain electromagnetic field we can directly export the double curl equations met by electric field, and then get the variation of electric field equations. Take backward difference to discrete the time item, after the element analysis for all units in the calculation area, and synthesize all units to get the stiffness matrix. The sparse matrix is stored by the CSR format. This work introduces the source current density into the double curl equations met by electric field. We use a trapezoidal waveform in the excitation source and taking the switch on-time, on-time and switch off-time into consideration. A loop source is added in modeling. In fact, this method makes the models arbitrarily complex in resistivity distribution. In the process of solving the equations, take the whole time zone segmentation process strategy, to take a unified iterative steps within the section to improve the computational efficiency. Then we use the direct time-domain vector finite element mothed to calculate and verify the uniform half-space model, shallow water undulating terrain model, typical layered model, lump model and surface-borehole model. In the end of this article points out some shortcomings and future direction of development.