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.

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.

This paper uses the boundary element methodto solve the problem of the effect of two-dimensional terrain with point current source on resistivity surveys. First, the 3-D boundary value problem of the electric field of a point source on 2-d terratin is converted in to a 2-D boundary value problem using a Fourer trans form. Then, the 2-D boundaryvalue poroblem is transformed into a boundary integral equation by means of Green's formula. The boundary element method is used to solve the integral equation. Finally, using an inverse Fourier inverse transform, we get the electric potential in 3-D space. Examples calculated for two terrain models show that the resultsform this method compare well with those from analytic andfinite elemont mothod. If the terrain has a clear strike, this method can be used for terrain corrections for resistivity surveys. An example of a terrain correction for electric sounding is given. This method can be run on a personal computer and takes a few minutes to correct a profile of data on an IBM AT-grade computer.

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.