Direct current electric potential computation in an inhomogeneous and arbitrarily anisotropic layered earth^l

Abstract

We consider the calculation of the electrical field quantities, electric potential and the vertical component of the total volume density of electric current, in a horizontally layered, piecewise homogeneous and arbitrarily anisotropic earth due to a system of direct current point sources. By applying Fourier transformation with respect to the horizontal space coordinates to the static field equations, the field quantities are obtained as the solutions of the system of transform-domain differential equations in the vertical (depth) coordinates. A recurrence scheme has been given to compute the tranform-domain field quantities at any depth. The corresponding space-domain quantities are then obtained by inverse Fast Fourier Transformation (FFT). A complete computer program has been developed for computing the electric potentials at any depth of the layered earth, which is composed of an arbitrary number of anisotropic layers with arbitrary conductivity tensors. By considering the point sources at different depths from the surface, equipotential contours on the surface of arbitrarily anisotropic layered earth models are given.

Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN

“…Forward modeling is a way of simulating ERT data for any given 1D, 2D, or 3D electrical conductivity models of the earth. For 1D conductivity models, the electrical potentials generated by an induced point current source can be obtained by using analytical or semi-analytical methods (Das, 1995;Pervago et al, 2006). However, for multi-dimensional heterogeneous conductivity models with complex geometries, one must use numerical methods to compute the electrical potential.…”

Electric field modeling in arbitrary anisotropic layered media using the set of Fast Hankel Transformations of integer orders

“…Applying the 2D FT, Le Masne and Vasseur (1981) computed the electromagnetic field of sources at the surface of a homogeneous conducting half space with a horizontal anisotropy axis. The scheme for the numerical computation of the electric potential from a point source in a layered earth with arbitrary anisotropy was developed by Das (1995) and extended by Li (1996) on the case of arbitrary sources. The 2D FT approach was used in Li and Pedersen (1991) for determining the electromagnetic response of a horizontal electric dipole on the surface of an azimuthally anisotropic half space.…”

Analytical solution for the electric potential in arbitrary anisotropic layered media applying the set of Hankel transforms of integer order

“…By applying 2D FTs, Le Masne and Vasseur (1981) computed the electromagnetic field of sources on the surface of a homogeneous conductive half‐space with a horizontal anisotropy axis. The scheme for the numerical computation of the electric potential from a point source in a layered earth with arbitrary anisotropy was developed by Das (1995) and extended by Li (1996) for the case of arbitrary sources. The 2D FT approach was used by Li and Pedersen (1991) to determine the electromagnetic response of a horizontal electric dipole on the surface of an azimuthally anisotropic medium.…”