Circuit Theory Approach with Fractional Calculus to describe Half-Space Geophysical Analysisfor Transient Electro-Magnetic Method
© Sh. Das, Sh. Bhattacharya, R.T. Keshwani, S. Sundar Rajan
In this paper, a new approach is described by circuit theory approach, for the transient electromagnetic method (TEM), which is employed for conductivity depth imaging and other geophysical exploration studies. The method in TEM is to excite the surface of earth by an impulse magnetic moment and receive and record the pulse character. The detailed solution to electromagnetic set of equations by Schelkunoff's potential formulation and decomposition of the EM-fields into modes, gives the diffusion patterns of E- and H-field inside the homogeneous or layered earth, as propagation of 'smoke-rings'. These detailed physical studies do help in formulating the field pattern behavior, flux diffusion speeds and profiles. The behavior or observation is at the input terminal of the circuit i.e. homogeneous or layered earth. The received voltage profiles do depict the nature of the half space and compares about the apparent conductivities of the exploration site. This treatment enables electrical engineers to visualize, and conceptualize the nature of signals obtained and give comparative idea about the apparent conductivity. The detailed derivation regarding this approach gives idea of fractional calculus, and representation of the earth half space (a semi infinite) system as half derivative between volt-ampere relations. The solutions to these fractional differential equations give the power law curves of current and received voltage at the terminal point to an impulse excitation, the same is too observed in actual experiments. Attempt is made here to explain the circuit behavior due to multiple reflections at the layered half space boundaries giving the non linear curves in log-log plots of the receive voltage profiles. Research in this direction will enable to make new inversion layer packages to describe conductivity depth imaging of the layered earth, in TEM exploration systems.
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