Three-Dimensional Transient Electromagnetic Numerical Simulation Using FDFD Based on Octree Grids

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 finitedifference 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. INDEX TERMS Finite-difference frequency-domain (FDFD), frequency-time transformation, numerical simulation, octree grids, transient electromagnetic method (TEM).

Assessment of the Application Fields of One- And Three-Dimensional Approaches to Tem Data Interpretation on the Example of Geological Conditions in the South of the Siberian Craton

“…Тем самым, области, где одномерный подбор не работает, на комплексной геоэлектрической модели обозначаются как зоны осложненной интерпретации, прогноз геоэлектрического строения которых невозможен или, в лучшем варианте, приблизителен. В описанном случае, для учета влияния неоднородности, используется математическое трехмерное моделирование электромагнитных данных [Luan at al., 2019]. Механизм моделирования, основанный на методе конечных элементов, позволяет учитывать при расчете прямой задачи боковое влияние неоднородных объектов путем аппроксимации анамалиеобразующего тела и слоев вмещающей среды набором простых геометрических объектов с подобными геоэлектрическими характеристиками [Тригубович, Персова, Соловейчик, 2009].…”

A novel FDFD method for electromagnetic simulation based on adaptive grids

“…This not only ensures simulation accuracy, but also avoids excessive memory consumption. In recent years, researchers have proposed subgridding method that have used various different grid forms, such as quadtree/octree grids [9][10] , nonuniform grids [11] , non-graded tree-based grids [12] and nine grids [13][14][15][16] . However, for fine grid distribution, it is often manually set and cannot fully achieve adaptation.…”

Transient Electromagnetic Voltage Imaging of Dense UXO-Like Targets Based on Improved Mathematical Morphology

“…According to the "smoke ring" effect, a typical non-linear equation is solved to obtain the target apparent resistivity and depth, and the layered geological model is built to carry out the forward and inverse analysis [11][12][13]. Based on Yee grids, the finite-difference frequency-domain (FDFD) method is proposed to avoid calculation of large linear equations [14]. However, it is very difficult to achieve the accurate resistivities and depths of the shallow and small targets by solving the nonlinear equation and inverse computation.…”