Abstract
The transient electromagnetic method (TEM) has been widely used as a geophysical exploration method in recent years. When Maxwell's equations are discretized in the time domain by the direct solution method, the initial field is used as a substitute for the source, so the electromagnetic response of a shallow three-dimensional anomalous body cannot be calculated. Maxwell's equations in the frequency domain are simple in form, and the current source can be directly added without calculating the initial field. However, large linear equations must be calculated. The coefficient matrix is large, and the calculation speed is slow, which limits their application. Based on Yee grids, this paper combines octree grids with the finite-difference frequency-domain (FDFD) method. Ensuring a sufficiently large computational area, octree grids are used to refine the area of anomalous bodies, while coarse grids are still used to reduce the total number of grids and improve the efficiency. In the numerical simulation, the vacancy positions are set to zero to solve the data storage problem of the coarse grids and fine grids. The binary paraboloid interpolation method is used to solve the electromagnetic field component transfer problem at the intersection of the coarse grid and fine grid. Finally, the electromagnetic response curve in the time domain is obtained by a frequency-time transformation. By comparing the calculation results of typical models, the correctness of the FDFD method based on octree grids is verified. By comparing the computational time of complex anomalous bodies for Yee grids and octree grids, it can be concluded that the efficiency of the FDFD method based on octree grids is improved to a certain extent.
Highlights
The transient electromagnetic method (TEM) is a detection method based on the principle of electromagnetic induction, which can be used to detect the resistivity of underground nonmagnetic materials
The number of grids in the finite-difference frequencydomain (FDFD) method is the key factor in the computational time
More grids are needed to calculate the electromagnetic response of a complex anomalous body, and the computational time is longer
Summary
The transient electromagnetic method (TEM) is a detection method based on the principle of electromagnetic induction, which can be used to detect the resistivity of underground nonmagnetic materials. H. Luan et al.: Three-Dimensional Transient Electromagnetic Numerical Simulation Using FDFD Based on Octree Grids the FDTD algorithms mostly calculate the initial field and the iterated field separately. In geophysics, based on Yee grids, Hedlin [13] used the FDFD method for magnetotelluric numerical simulation He analyzed the influence of grid spacing on the calculation error and deduced the corresponding error expression. For the FDFD method, because the responses of each frequency point are obtained by solving the linear equations directly, it is difficult to calculate the refined region separately by the subgridding technique. Haber and Heldmann [23] deduced the integral form of Maxwell’s equations with the finite volume method based on octree grids and used the flux conservation method to connect the components in different grids. Comparing the computational time of the FDFD method based on Yee grids with that based on octree grids, the rationality of the application of the octree grids to the FDFD method is analyzed
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