# Mathematical Model of Transient Electromagnetic Response from Heterogeneous Ground Structure

## Abstract

In this paper, we study the earth’s surface layers using time-domain electromagnetic field by constructing 2 mathematical models. In the first model, the ground is considered uniformly and having constant conductivity profile, denoted by a positive constant σ0 . The second model, we divide the ground surface into 2 laterally uniform layers. The conductivity of overburden increases with depth, given by σ0 e-b(z-d), 0 ≤z ≤ d, where b is a positive constant, and d is the thickness of overburden. The conductivity of host medium, z ≥ d, is a constant σ0 . By solving the models using mathematical techniques, the electric fields response from the ground surface are simulated and plotted to show their behaviors which decay rapidly depending on the conductivity of ground structure.

## Article Details

How to Cite
Yooyuanyong, S. (2013). Mathematical Model of Transient Electromagnetic Response from Heterogeneous Ground Structure. Science, Engineering and Health Studies, 1(1), 45–51. Retrieved from https://li01.tci-thaijo.org/index.php/sehs/article/view/7112
Section
Research Articles

## References

Banerjee, B., Sengupta, B. J. and Pal, B. P. (1980). Apparent resistivity of a multilayered earth with a layer having exponential conductivity, Geophysical Prospecting, 28: 435-452.

Hohmann, G. W. and Raiche, A. P. (1988). Inversion of Controlled-Source Electromagnetic Data, Electromagnetic methods in applied geophysics Vol. 1: 469-503 (ed. Nabighian, M. N.) SEG.

Ignetik, R., Thio, Y. C. and Westfold, K. C. (1985). The transient EM response of a permeable and conducting half-space, Geophysical. Journal Royal Astronomical. Society, 81: 623-639.

Jeffrey, A. (1995). Handbook of Mathematical Formulas and integrals, Academic Press.

Kim, H. S. and Lee, K. (1996). Response of a multilayered earth with layers having exponentially varying resistivities, Geophysics, 61: 180-191.

Lee, T. J. and Ignetik, R. (1994). Transient electromagnetic response of a half-space with exponential conductivity profile and its applications to salinity mapping, Exploration Geophysics, 25: 150-164.

Morrison, H. F., Phillips, R. J. and O'Brien, D. P. (1969). Quantitative interpretation of transient electromagnetic fields over a layered half-space, Geophysics Prospecting, 21: 1-20.

Siew, P. F. and Yooyuanyong, S. (2000). The electromagnetic response of a disk beneath an exponentially varying conductive overburden, The Journal of the Australian Mathematical Society, B 41(E): E1-E28.

Wunsch, A. D. (1994). Complex Variables with Applications, Addison-Wesley Publishing Company, 2nd edition.

Yooyuanyong, S. (1999). Inversion by EM sounding for a disk embedded in a conducting hatf-space, Songklanakarin Journal of Science and Techmology, 21(2): 197-205.

Yooyuanyong, S. (2000). Electromagnetic response over a varying conductive ground, Songklanakarin Journal of Science and Technology, 22(4): 457-466.