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.

本文提出一种反演非均匀的海山磁性的新方法——虚源法，海山的磁化强度由均匀和不均匀两部分组成。将均匀磁化强度J0看作位于无穷远处的虚磁源在海山中产生的场，非均匀磁化强度J'看作位于海山外部一组虚磁源在海山中产生的场和和。用电优化的方法使剩余异常取极小来反演J0和J'。模型研究表明，虚源法反演得到的均匀磁化强度J0与海山的主磁化方向很接近。

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.

倾度法电气探查にぉはゐ2次元地形の地形楠正法み境界要素法み用いて導出てた。倾度法电气探查にぉいては，信号源み水平方向の一样电场と考えるこがでをる。2次元境界值问题をケリンの定理な用いて分方程式に变换し，境界要素法に基づいて，地表面の电位な数值计算の可能を式ょして導いた。式の变形过程は，すぺて输文中に明记した。2次元地形をそっ比抵抗p0の均质大地の见挂比抵抗を上记の方法で计算してptopょする。测定さゎに见挂比抵抗pobaをptop/poでわったそのを地形補正见挂比抵抗pcorょ定义する。2次阮地形を有する均质大地内に比抵抗异常体をわいた场合の见挂比抵抗ょ，异常体の无い场合の见挂比抗を计算して，そわぞわpobsょptopょわき，上记の方法で地形補正した结果，地形の无い场合の见挂比抵抗ょ非常に近い见挂比抵抗が得ちわるこょを示した。ケーススタラィょして，安山岩质の母岩中に，金を伴ち高比抵抗の石英脈石が存在する地域の比抵抗探查ラータを用いて，本手法にょり地形補正を行った。補正后のラータに对してslop法にょり推定した埋设深度け12mでめった。试锥にょり确答ざぉた12.9mでめった。本手法けぺーソナルュンピュータで1～2秒の计算时间で简便に计算でさゐので，倾度法の地形補正法ょして极めて便利な方法あゐ。

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.

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.