Three‐dimensional electromagnetic modeling using finite difference equations: The magnetotelluric example

Abstract

We have developed a robust and efficient finite difference algorithm for computing the magnetotelluric response of general three‐dimensional (3‐D) models using the minimum residual relaxation method. The difference equations that we solve are second order in H and are derived from the integral forms of Maxwell's equations on a staggered grid. The boundary H field values are obtained from two‐dimensional transverse magnetic mode calculations for the vertical planes in the 3‐D model. An incomplete Cholesky decomposition of the diagonal subblocks of the coefficient matrix is used as a preconditioner, and corrections are made to the H fields every few iterations to ensure there are no H divergences in the solution. For a plane wave source field, this algorithm reduces the errors in the H field for simple 3‐D models to around the 0.01% level compared to their fully converged values in a modest number of iterations, taking only a few minutes of computation time on our desktop workstation. The E fields can then be determined from discretized versions of the curl of H equations.

An integrated magnetotelluric and aeromagnetic investigation of the Serra da Cangalha impact crater, Brazil

“…A 3D model was constructed using the Geotools model builder, and its forward responses were calculated using the code of Mackie et al (1994) that was recently modified by (Mackie and Booker, 2002;pers. comm.).…”

Paraguay‐Araguaia Belt Conductivity Anomaly: A fundamental tectonic boundary in South American Platform imaged by electromagnetic induction surveys

“…A qualitative investigation of conductivity structure was performed using the 3-D forward code of Mackie et al [1994]. A 3D model was created, covering a horizontal area of roughly 9.5 3 6.5 and with good vertical resolution in the crust.…”

3D Magnetotellurics for Mineral Exploration beneath Cover

“…Forward responses were calculated in 3D for 24 periods between 10 -4 and 10 2 s utilising the finite-difference code of Mackie et al (1994). Calculations were made for 141 model sites positioned in a square grid above the target.…”

“…A number of 3D inversion codes are available (Mackie et al 1994, Newman and Alumbaugh, 2000, Sasaki, 2004, Siripunvaraporn et al 2005a, and many model studies have been published (e.g. Siripunvaraporn et al 2005b, Han et al 2009).…”