# Mathematical Model of MMR Inversion for a DISC Embedded in Overburden

## Abstract

In this paper, inverse problem with the use of optimization technique is proposed. Mathematical model of steady state magnetic field response is formulated. It is accomplished by using analytical method to solve boundary value problems in the wave number domain and then transforming back to the special domain. One dimensional geometric model of a two layered earth is considered. Probe sources of direct current are located perpendicularly in overburden. There is an ore body like a disc of radius  $c$ embedded in overburden. Magnetic field response is computed numerically to see their behavior against source-receiver spacing. The results show that, there are some relations between magnetic field responses and conductivity parameters or overburden thickness significantly as mentioned in some related works. Moreover, the magnetic field responses also depend on the size of disc as well. In our inversion process, conjugate gradient can be used to investigate radius of a disc embedded in overburden accurately.

## Article Details

How to Cite
1.
Yooyuanyong S. Mathematical Model of MMR Inversion for a DISC Embedded in Overburden. Prog Appl Sci Tech. [Internet]. 2020 Oct. 8 [cited 2024 Aug. 11];10(2):18-22. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/242162
Section
Mathematics and Applied Statistics

## References

Ali I, Kalla S. A generalized Hankel transform and its use for solving certain partial differential equation. J. Austral. Math. Soc. Ser.B. 1999;40: 105–17.

Chaladgarn T, Yooyuanyong S, Magnetometric Resistivity Sounding for a Conductive Bulge Earth. J. Appl. Math. Sci. 2016; 10(36):1775–82.

Chave A.D. Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics. 1983; 48:1671–86.

Edwords R.N. A downhole MMR technique for electrical sounding beneath a conductive surface layer. Geophysics. 1988;53(4):528–36.

Edwards R.N, Lee H, Nabighians M.N. On the theory of magnetometric resistivity (MMR) methods. Geophysics. 1978;43(6):1176–203.

Khonkhem Y, Yooyuanyong S. Finite Difference for Magnetic Field Response from a Two-Dimensional Conductive Ground. Appl. Math. Sci. 2016;10(3):137–50.

Siew P.F, Yooyuanyong S. The Electromagnetic Response of a Disk Beneath an Exponentially Varying Conductive Overburden. J. Austral. Math. Soc. Ser. B. 2000;41:1–28.

Sripanya W. Mathematical Modelling of Magnetic Field from Heterogeneous Media with a Homogeneous Overburden. Int. J. Pure Appl. Math. 2014;94(1):37–44.

Yooyuanyong S. Magneto Metric Resistivity sounding over Binomially Overburden Thickness. Int. J. Eng. Technol. 2018;7(4.28):699–702.

Yooyuanyong S, Sripanya W. Magnetic field of direct current in heterogeneous Ground. Songklanakarin J. Sci. Technol. 2007;29(2): 565–73.

Yooyuanyong S, Sripanya W. Mathematical Modelling of Magnetometric Resistivity Sounding Earth Structures. Thai J. Math. 2005;3(2):249–58.