A new method is presented in this paper for modeling the 3-D terrain effect that, in turn, can be approximately removed by applying a terrain correction to resistivity surveys. First, the 3-D electrical boundary value problem is transformed into an integral equation problem by use of Green's theorem. Then the boundary element method is used to solve the integral equation. The ground surface and the boundary of the anomalous body are divided into triangular elements. Linear variation of quantities is assumed within each element and a Gaussian quadrature formula is used to calculate the integral. In this way. the integral equation is converted into a set of linear equations. The potential field value on the ground surface is obtained by solving the linear equation system with Gaussian elimination.

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.

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.

Using the boundary element method, thenumerical modeling problem of three-dimensional terrain effect on magnetotelluric (MT) field is solved. This modeling technique can be run on PC in the case of adopting special net divison. The result of modeling test for 2-D terrain hy this modeling technique isbasically coincident with that by 2-D modeling technique, but there is a great difference between the results of 3-D and 2-D modeling for 3-D terrain.

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.