Static Effect in Magnetotelluric Responses: An Implication from the EM Integral Equation

Yoonho Song

doi:10.7582/GGE.2024.27.3.181

All Issue

2024 Vol.27, Issue 3 Preview Page

Tutorial

Static Effect in Magnetotelluric Responses: An Implication from the EM Integral Equation MT 탐사 반응에서 정적효과: 적분방정식을 통한 고찰

31 August 2024. pp. 181-195

PDF XML

Abstract

This tutorial explains that the static effect in the magnetotelluric (MT) survey is a physical phenomenon caused by charges accumulated on the boundaries of subsurface inhomogeneities. To facilitate understanding of the physical phenomenon, differences between static induction and charge accumulation on the boundary are explained and analyzed with help of schematic illustrations. Subsequently, from the electromagnetic (EM) integral equation formulation, it is clearly shown that the secondary electric field due to charges accumulated on the interface in the presence of the primary field appears as the static effect. Therefore, except in the cases of the layered earth or a two-dimensional earth with transverse magnetic (TM) mode excitation, the static effect always exists in MT responses and further, it is not ‘static’ but rather frequency dependent.

Despite the fact that the static effect is a secondary electric field due to inhomogeneity, inevitable under-sampling in the frequency and spatial domains prevent the effect from being handled properly in numerical inversion. Therefore, considering the practical aspects of the MT survey, which cannot be a continuous measurement covering the entire survey area over a wide frequency band, a three-dimensional (3-D) inversion incorporating the static shift as a constraint with the Gaussian distribution is introduced. To enhance understanding of the integral equation EM modeling, the formulation of the 3-D integral equation and mathematical analyses of the Green tensor and scattering current are described in detail in the Appendix.

Keywords

magnetotelluric (MT) response

static effect

electromagnetic (EM)

integral equation

charge accumulation

이 해설 논문에서는 자기지전류(magnetotelluric; MT) 탐사에서의 정적효과가 지하 불균질체의 경계면에서 축적되는 전하 축적에 의해 발생하는 물리적 현상임을 설명하였다. 먼저 정적효과를 일으키는 물리적 현상에 대한 이해를 위해 정전유도와 경계면에서의 전하 축적의 차이에 대해 모식도를 이용해 설명하고 분석하였다. 그리고 적분방정식을 통해 지하에 있는 불균질체에 1차 전기장이 가해졌을 때, 전기전도도 경계면에서의 전하 축적에 의한 2차 전기장이 정적효과로 나타남을 명확히 하였다. 따라서 MT 탐사에서 1차원 층서구조나 2차원 TM (transverse magnetic) 모드의 경우를 제외하고 정적효과는 항상 존재하고 또한 그 용어와는 달리 ‘정적’이 아닌 주파수 의존적임을 보였다.

정적효과가 지하 불균질체에 의한 2차장임에도 MT 탐사의 역산에서 수식적으로 해결되지 않고 심부 구조의 해석에 장애 요인으로 작용하는 이유는 현장 탐사에서 피할 수 없는 ‘주파수 및 공간 영역에서의 과소 샘플링’이기 때문이다. 따라서 광대역 주파수와 전체 탐사 대상 면적에서의 연속 측정이 아닌 실제 MT 탐사를 고려할 때, 3차원 역산시에 정적효과를 전체 탐사 영역에서 정규분포를 갖는 변수로 가정하고 이를 역산의 제약 조건으로 포함하는 시도에 대해 알아보았다. 적분방정식 전자탐사 모델링의 이해를 돕기 위해 3차원 적분방정식의 유도, Green 텐서 및 산란전류의 수학적 분석을 부록에 자세히 서술하였다.

키워드

자기지전류(MT)탐사

정적효과

전자탐사

적분방정식

전하축적

References

Hohmann, G. W., 1987, Numerical modeling for electromagnetic methods of geophysics, in Nabighian, M. N., Ed., Electromagnetic Methods in Applied Geophysics - Theory, Vol. 1, Soc. Expl. Geophys., 312-363.

10.1190/1.9781560802631.ch5

Jang, H., Song, Y., and Nam, M.-J., 2024, Analysis of static shift and its correction in magnetotelluric surveys, Geophys. and Geophys. Explor., 27, 129-143 (in Korean with English abstract).

Kaufman, A. A., 1992, Geophysical field theory and method, Part A - Gravitational, electric, and magnetic fields, Academic Press, Inc., 581p.

Kwon, H.-S., Song, Y., Yi, M.-J., Chung, H.-J., and Kim, K.-S., 2006, Case histories of electrical resistivity and controlled-source magnetotelluric surveys for the site investigation of tunnel construction, J. Env. Eng. Geophys., 11, 237-248.

10.2113/JEEG11.4.237

Lee, T. J., Kim, M. S., Park, I. H., Song, Y., Nam, M. J., Song, S. Y., and Yun, K.-H., 2019, Geoelectrical structure of Ulleung island, Korea, Interpretation of three-dimensional magnetotelluric data, Expl. Geophys., 50, 481-489.

10.1080/08123985.2019.1634192

Lee, T. J., Nam, M.-J., Lee, S. K., Song, Y., and Uchida, T., 2009, The Jeju dataset: Three-dimensional interpretation of MT data from mid-mountain area of Jeju island, Korea, J. Appl. Geophys., 68, 171-181.

10.1016/j.jappgeo.2008.11.006

Lee, T. J., Song, Y., and Uchida, T., 2005, Two- and three-dimensional interpretation of magnetotelluric data from Pohang geothermal site, J. Kor. Soc. Geosystem Eng., 42, 297-307 (in Korean with English abstract).

Sasaki, Y., 2004, Three-dimensional inversion of static-shifted magnetotelluric data, Earth, Planet and Space, 56, 239-248.

10.1186/BF03353406

Song, Y., Kim, H. H., and Lee, K. H., 2002, An integral equation representation of wide-band electromagnetic scattering by thin sheets, Geophysics, 67, 746-754.

10.1190/1.1484517

Tai, C.-T., 1994, Dyadic Green functions in electromagnetic theory, 2nd Ed., IEEE Press, 343p.

Torres-Verdin, C., 1991, Continuous profiling of magnetotelluric fields, Ph.D. thesis, University of California, Berkeley.

10.2172/10106102

Torres-Verdin, C. and Bostick, F. X. Jr., 1992, Principles of spatial surface electric field filtering in magnetotellurics: Electromagnetic array profiling (EMAP), Geophysics, 57, 503-622.

10.1190/1.1443273

Vozoff, K., 1991, The magnetotelluric method, in Nabighian, M. N., Ed., Electromagnetic Methods in Applied Geophysics, Vol. 2, Application, Part B, Soc. Expl. Geophys., 641-711.

10.1190/1.9781560802686.ch8

Weidelt, P., 1981, Report on dipole induction by a thin plate in a conductive halfspace with an overburden, Fed. Inst. EarthSci. And Math. Report 89727.

Information

Publisher :Korean Society of Earth and Exploration Geophysicists
Publisher(Ko) :한국지구물리물리탐사학회
Journal Title :Geophysics and Geophysical Exploration
Journal Title(Ko) :지구물리와 물리탐사
Volume : 27
No :3
Pages :181-195
Received Date : 2024-05-16
Revised Date : 2024-06-27
Accepted Date : 2024-08-01
DOI :https://doi.org/10.7582/GGE.2024.27.3.181

Geophysics and Geophysical Exploration ISSN:1229-1064(Print) 2384-051X(Online) 지구물리와 물리탐사

All Issue