3D finite-volume time-domain modeling of geophysical electromagnetic data on unstructured grids using potentials

Abstract

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 ([Formula: see text]) potentials. The [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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.