Unstructured grids are capable of faithfully representing real-life geologic models and topography with relatively few mesh cells. We have developed a finite-volume solution to the 3D time-domain electromagnetic forward modeling problems using unstructured Delaunay-Voronoï dual meshes. We consider the Helmholtz equation for the electric field and a combination of the Helmholtz equation and the conservation of charge equation for the magnetic vector (A) and electric scalar ($\varphi$) potentials. The $\mathbf{A}-\varphi$ formulation requires initial values for A that can be obtained by solving the magnetostatic problem. We use backward Euler time stepping to advance the electric field and the potentials in the time domain. When using the potential method, the electric and magnetic fields are calculated from $\mathbf{A}-\varphi$ solutions. To obtain consistent potential solutions at different time steps, we enforce the Coulomb gauge condition, using implicit and explicit methods. We validate the proposed method with a simple 3D conductive block model and with a comparison with other numerical methods. By using $\mathbf{A}-\varphi$ potentials, it is possible to decompose the electric field into galvanic and inductive parts, which is helpful in understanding the physics behind the behavior of the electromagnetic fields in the ground. We use vector plots to visualize the decomposed electric fields for horizontal and vertical thin conductor models with inductive loop sources. This allows the interplay between inductive and galvanic parts as the electric field and current density develop with time to be visualized.

中文翻译：

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非结构化网格上利用电势的地球物理电磁数据的3D有限体积时域建模

非结构化网格能够以相对较少的网格单元忠实地表示现实生活中的地质模型和地形。我们使用非结构化Delaunay-Voronoï对偶网格为3D时域电磁正向建模问题开发了有限体积的解决方案。我们考虑电场的Helmholtz方程，并考虑了Helmholtz方程与磁矢量（A）和电标量（$\varphi$）潜力。的$\mathbf{一种}-\varphi$配方要求A的初始值可以通过解决静磁问题获得。我们使用后向欧拉时间步进来推进时域中的电场和电势。使用电位法时，电场和磁场的计算公式为$\mathbf{一种}-\varphi$解决方案。为了在不同的时间步长获得一致的潜在解决方案，我们使用隐式和显式方法强制执行库仑规范条件。我们使用简单的3D导电块模型并与其他数值方法进行比较来验证所提出的方法。通过使用$\mathbf{一种}-\varphi$电位，有可能将电场分解成电流和感应部分，这有助于理解地下电磁场的行为背后的物理原理。我们使用向量图来可视化带有感应环路源的水平和垂直薄导体模型的分解电场。当电场和电流密度随时间发展时，这将允许感应部分和电流部分之间的相互作用可视化。