Fast finite-difference time-domain modeling for marine-subsurface electromagnetic problems

Abstract

In the low-frequency limit, the displacement currents in the Maxwell equations can be neglected. However, for numerical simulations, a small displacement current should be present to achieve numerical stability. This requirement leads to a large range of propagation velocities with high velocities for the high frequencies and low velocities for the low frequencies. As a consequence, the number of time steps may become large. I show that it is possible to transform mathematically the original physical problem to one that has propagation velocities with less frequency dependence. Hence, the number of time steps necessary for a signal to travel a certain distance with the lowest velocity is significantly reduced. A typical example shows a reduction in computational time by a factor of 40. A comparison of the solutions from plane-layered modeling in the frequency and wavenumber domain and the proposed method shows good agreement between the two. The proposed method can also be used for other systems of diffusive equations.

Fast Forward Modeling of Electromagnetic Induction Using Correspondence Principle

“…Previous studies (Oristaglio and Hohmann 1984;Wang and Hohmann 1993) observed that the computation time can be reduced by introducing a small wave-like contribution in the solution by the DuFort-Frankel method. Maaø (2007) proposes a transformation method that reduces CPU time by a factor of 40 compared to a fixed time-step DuFort-Frankel-based scheme. Maaø's approach (2007) is closely related to the finite difference time domain (FDTD) method introduced by Lee et al (1989) and more formally discussed by de Hoop (1996) as a correspondence principle for time-domain electromagnetic wave and diffusion fields.…”

The impact of 3D tilted resistivity anisotropy on marine CSEM measurements

“…An FD scheme can be solved using different iterative solvers; however, the SLDM solver allows fast simultaneous computation of wide-band frequency results at the computing cost of a single frequency run. Unlike most other researchers using the standard Yee FD scheme to model EM fields in the earth (Yee, 1966;Druskin and Knizhnerman, 1994;Mulder, 2006;Maaø, 2007), we use the Lebedev staggered FD grid approach that enables efficient treatment of the arbitrary dipping anisotropy of the electric conductivity. Such a grid gives the ability to determine different components of the electric field (E x , E y , E z ) and the electric current density ( J x , J y , J z ) at the same spatial nodes (Figure 1).…”

Simulation of Electromagnetic Diffusion in Anisotropic Media

“…Further research is necessary to verify if the present algorithm can be used with an electricmagnetic formulation of Maxwell's equations, where derivatives of the material properties are avoided [9,36]. A promising approach can be to solve a fictitious hyperbolic representation of the electromagnetic equations [20,22].…”

“…This model introduces a high permittivity as in the case of Wang and Hohmann [32]. Maaø [20] further reduced the computer time solving the equations in the high-frequency range by using a complexfrequency Fourier transform to filter high-frequency wave-like signals.…”

“…Maaø [20] performed 3-D simulations with a FD method by using a mathematical transformation similar to the Kelvin-Voigt viscoelastic model. This model introduces a high permittivity as in the case of Wang and Hohmann [32].…”