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