Comparison of integral equation and physical scale modeling of the electromagnetic responses of models with large conductivity contrasts

Colin G. Farquharson, Ken Duckworth, and Douglas W. Oldenburg.

[2006, Geophysics, 71, G169-G177.]

ABSTRACT

A comparison is made between the results from two different approaches to modeling geophysical electromagnetic responses: a numerical approach based upon the electric-field integral equation and the physical scale modeling approach. The particular implementation of the integral-equation solution was developed recently, and the comparison presented here is essentially a test of this new formulation. The implementation approximates the region of anomalous conductivity by a mesh of uniform cuboidal cells and approximates the total electric field within a cell by a linear combination of bilinear edge-element basis functions. These basis functions give a representation of the electric field that is divergence free but not curl free within a cell, and whose tangential component is continuous between cells. The charge density (which arises from the discontinuity of the normal component of the electric field across interfaces between cells of different conductivities and between cells and the background) is incorporated in a similar manner to integral equation solutions to dc resistivity modeling. The scenarios considered for the comparison comprise a graphite cube of 6.3E+04 S/m conductivity and 14-cm length in free space and in brine (7.3 S/m conductivity). The transmitter and receiver were small horizontal loops; measurements and computations were made for various fixed transmitter-receiver separations and various heights of the transmitter-receiver pair for frequencies ranging from 1-400 kHz. The agreement between the numerical results from the integral-equation implementation and the measurements from the physical scale modeling was very good, contributing to the verification of this particular implementation of the integral-equation solution to electromagnetic modeling.


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Last update: 11 September 2006.
Colin Farquharson