TEM Response of a Large Loop Source over a Homogeneous Earth Model: A Generalized Expression for Arbitrary Source-Receiver Offsets

Abstract

In the present research, an attempt is made to derive the generalized expressions for the transient electromagnetic response of a large loop source over the surface of a homogeneous earth model for arbitrary receiver positions inside or outside the source loop. Expressions are derived for the impulse as well as step excitations of the source loop. As a cross check for validity of expressions, the step response expression is obtained from the impulse response expression and vice versa. Computations are performed for the TEM response over a homogeneous earth model for source-receiver offset (r = 0) pertinent to the central loop configuration and the results are compared with the published results for the central loop TEM responses. The results are in well coincidence with each other and thus provide the check for the authenticity of the expressions. To exemplify the nature of TEM response at various source receiver offsets, results are presented for the TEM response at source receiver offsets r = 0, r = a/2, r = a and r = 2a, 6a, 12a pertaining to the central loop, in-loop, on-loop and offset loop configurations, respectively. The results depict their characteristic variations. At receiver positions inside the loop source, both the impulse as well as step responses are of same sign, whereas at the receiver positions outside the loop source, both the curves exhibit a change of sign that shifts towards the later times with increase in the offset distances. The change of sign in impulse response occurs at a relatively later time than that in the step response. This is the initial presentation of TEM response expressions for the large loop source over a homogeneous earth model for arbitrary receiver position inside and/ or outside the loop source except for the case of receiver at the center of the loop and at the coincident loop point. This research would be of immense use in the development and use of the large loop TEM method in its various configurations and thus would enhance the applicability and cost effectiveness of the large loop source TEM method.