Crosshole EM 2.5D Modeling by the Extended Born Approximation

확장된 Born 근사에 의한 시추공간 전자탐사 2.5차원 모델링

  • Cho, In-Ky (Dept. of Geophysics, Kangwon National University) ;
  • Suh, Jung-Hee (Sch. of Urban, Civil & Geosystem Eng., Seoul National University)
  • 조인기 (강원대학교 자연과학대학 지구물리학과) ;
  • 서정희 (서울대학교 지구환경시스템공학부)
  • Published : 1998.08.01


The Born approximation is widely used for solving the complex scattering problems in electromagnetics. Approximating total internal electric field by the background field is reasonable for small material contrasts as long as scatterer is not too large and the frequency is not too high. However in many geophysical applications, moderate and high conductivity contrasts cause both real and imaginary part of internal electric field to differ greatly from background. In the extended Born approximation, which can improve the accuracy of Born approximation dramatically, the total electric field in the integral over the scattering volume is approximated by the background electric field projected to a depolarization tensor. The finite difference and elements methods are usually used in EM scattering problems with a 2D model and a 3D source, due to their capability for simulating complex subsurface conductivity distributions. The price paid for a 3D source is that many wavenumber domain solutions and their inverse Fourier transform must be computed. In these differential equation methods, all the area including homogeneous region should be discretized, which increases the number of nodes and matrix size. Therefore, the differential equation methods need a lot of computing time and large memory. In this study, EM modeling program for a 2D model and a 3D source is developed, which is based on the extended Born approximation. The solution is very fast and stable. Using the program, crosshole EM responses with a vertical magnetic dipole source are obtained and the results are compared with those of 3D integral equation solutions. The agreement between the integral equation solution and extended Born approximation is remarkable within the entire frequency range, but degrades with the increase of conductivity contrast between anomalous body and background medium. The extended Born approximation is accurate in the case conductivity contrast is lower than 1:10. Therefore, the location and conductivity of the anomalous body can be estimated effectively by the extended Born approximation although the quantitative estimate of conductivity is difficult for the case conductivity contrast is too high.