A finite‐element solution for the transient electromagnetic response of an arbitrary two‐dimensional resistivity distribution

Abstract

We present a numerical method for solving Maxwell’s equations in the case of an arbitrary two‐dimensional resistivity distribution excited by an infinite current line. The electric field is computed directly in the time domain. The computations are carried out in the lower half‐space only because exact boundary conditions are used on the free surface. The algorithm follows the finite‐element approach, which leads (after space discretization) to an equation system with a sparse matrix. Time stepping is done with an implicit time scheme. At each time step, the solution of the equation system is provided by the fast system ICCG(0). The resulting algorithm produces good results even when large resistivity contrasts are involved. We present a test of the algorithm’s performance in the case of a homogeneous earth. With a reasonable grid, the relative error with respect to the analytical solution does not exceed 1 percent, even 2 s after the source is turned off.

Diffusion of an electromagnetic pulse in a heterogeneous earth

“…In view of the above results and those obtained by Nabighian (1979), Oristaglio (1982), Oristaglio and Hohmann (1984), Nabighian and Oristaglio (1984), Adhidjaja et al (1985), Goldman et al (1986), and Adhidjaja and Hohmann (1988), etc., the process of subsurface diffusion of an electromagnetic pulse can be understood with the help of some simplified models. The diffusion phenomena in some models of increasing complexity are described below.…”

“…It is interesting to note that Goldman et al (1986), while solving the similar problem employing a finite-element scheme, arrive at a time step limit given by…”

Electromagnetic methods for exploration and monitoring of enhanced geothermal systems – A virtual experiment

“…At the surface an exact boundary condition has been implemented (Afanasjew et al, 2011(Afanasjew et al, , 2013Goldman et al, 1986). This allows to omit the discretization of the air halfspace, which results in a significant reduction of the number of degrees of freedom.…”

Time-domain inversion of GPR data containing attenuation due to conductive losses

“…Equations 3 and 4 are solved using the finite-element method ͑Goldman et al., 1986;Di and Wang, 1999͒, resulting in the following system of equations:…”