The boundary-element method is used to model the 2D terrain effect on the magnetotelluric (MT) field. Firstly, the boundary-value problem of a 2D magnetotelluric field is transfored into an integral equation problem by using Green's theorem. Then the boundary-element method is used to solve the integral equation andto obt ain the MT field and its normal derivative on the terrain. From these values, the apparent resistivity can be calculated. Compared with the finite-element method, the boundary-element method is simpler in element division and the initital data preparation. The configuration of a terrain dividedby the boundary-element method is more consistenr with the practical terrain. the method proposed in this paper can be run on a microcomputer, so that it can be used in the field.

Anew boundary element method (BEM) is presented for 2-D dc resistivity modeling with a point source. When compared with previously published techniques, the new method has two main features: (1)The normal derivative of potential has been eliminated from the integral equation. The formulation of the present method is simpler and requires less memory and time than the previous published methods. (2) Multiple subsurface inhomogeneous bodies can be modeled.For a simple testing model, the maximum relative error of reciprocity test is 0.24% and the average relative error is 0.05%. For the same model, the maximum relative difference between the BEM solution and the finite-element method solution is 1.14% and the average relative difference is 0.73%. For a field geoelectrical profile, the responses of the constructed model agree with the observed data quite well.

An optimizationmethod is used to select the wavenumbers k for the inverse Fourier transform in 2.5D electrical modelling. The model tests show that with the wavenumbers k selected in this way the inverse Fourier transform performs with satisfactory accuracy.

The problem of 2-D terrain corrections for pointsource electric resistivity data is considered. The total electric potential is divided into normal and anomalous terms. An integral equation is derived for the Fourier transform of the anomalous potential and is solved using a boundary element method. An inverse Fourier transform is applied to recover the anomalous potential along a "longitudinal" profile passing through the point source and oriented perpendicular to the vertical plane containing the 2-D terrain variations. The sum of the normal and anomalous potentials are then used to calculate an apparent resistivity. A sample calculation demonstrates that the longitudinal apparent resistivity calculated in this manner is less sensitive to terrain variations than the traditional "transverse" apparent resistivity that is computed from potential measurements made parallel to the vertical plane containing the 2-D terrain variations.

A 3D potential on a 3D topography is approximately regarded as a potential on an imaginary horizontal plane. Afast Fourier transform (FFT) is applied to calculate the outward normal derivative of the potential on the horizontal plane. An approximation can be made such that the calculated derivative is used as the outward normal derivative of the potentialon the3Dtopographic surface. Based on the potential and the approximated normal derivative on the topography, Green's formula is used to obtain the potential at an arbitrary point above the topography. When the potential at a flat level above the topography is obtained, an FFT is used again to determine the potential at other levels above the source of the potential. A model test shows that the results from this method compare well with analytic solutions. The method has high computation speed and can be used for continuation of 3D potential fields for large data sets, e.g., aeromagnetic data.