International Journal of Geophysics

Volume 2018, Article ID 9891548, 7 pages

https://doi.org/10.1155/2018/9891548

## TEM Response of a Large Loop Source over the Multilayer Earth Models

Department of Geophysics, Faculty of Science, Banaras Hindu University, Varanasi 221005, India

Correspondence should be addressed to N. P. Singh; ni.oc.oohay@uhbpnhgnis

Received 8 March 2018; Accepted 11 April 2018; Published 8 May 2018

Academic Editor: Rudolf A. Treumann

Copyright © 2018 A. K. Tiwari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The general expression of TEM response of large loop source over the layered earth models is not available in the literature for arbitrary source-receiver positions, except for the case of central loop and coincident loop configurations over the homogeneous earth model. In the present study, an attempt is made to present the TEM response of a large loop source over the layered earth model for arbitrary receiver positions. The frequency domain responses of large loop source over the layer earth model for arbitrary receiver positions are converted into the impulse (time derivative of magnetic field) TEM response using Fourier cosine or sine transform. These impulse TEM responses in turn are converted into voltage responses for arbitrary receiver positions, namely, central loop, arbitrary in-loop, and offset-loop TEM responses over the layered earth models. For checking the accuracy of the method, results are compared with the results obtained using analytical expression over a homogeneous earth model. The complete matching of both of the results suggests that the present computational technique is capable of computing TEM response of large loop source over the homogeneous earth model with high accuracy. Thereafter, the technique is applied for computation of TEM response of a large loop source over the layered earth (2-layer, 3-layer, and 4-layer) models for the central loop, in-loop, and offset-loop configurations and the results are presented in voltage decay form. The results depict their characteristic variations. These results would be useful for modeling and inversion of large loop TEM data over the layer earth models for all the possible configurations resulting from a large loop source.

#### 1. Introduction

A large horizontal loop on or above the earth is one of the most widely used sources in TEM and airborne TEM (ATEM) methods. Using a large loop source, one can measure at the center of the loop, at any arbitrary point inside the loop, coincident loop, and at arbitrary offset-loop points. A number of studies on methods of computation of TEM response and modeling can be found in the literature [1–13]. All these studies are based on considering transmitter as a large circular loop and receiver either at the center of the loop and/or coincident with the loop, over the simple layer/homogenous earth models, and majority of them are based on the computation of TEM responses from their frequency responses only for the central and/or coincident loop configurations, because of the computational intricacies associated with the frequency domain response computation of large loop TEM source for arbitrary receiver positions (except for central and coincident loop configurations) over the layer earth models which involve product of two Basel functions that make the integral unstable and nonconvergent. Singh and Mogi [14, 15] for the first time presented a new computational method for computation of EM responses of large loop source over the layer earth models for arbitrary receiver positions. Thereafter, a number of researches appeared in the literature [16–24]. Thus, there was scarcity of EM modeling due to large loop sources over the layer earth models even in frequency domain, which resulted in a lack of studies in TEM response of large loop sources over the layer earth models for arbitrary receiver positions, except for the case of central loop and coincident loop configurations that were too over the homogeneous half-space because of nonavailability of analytical expression for arbitrary receiver positions, and sophisticated computational methods for computing the frequency domain responses from which TEM responses are usually derived. Moreover, during the process of converting the frequency domain EM response into time domain, even a small error of less than 1% in frequency response can produce a considerable difference in time domain EM response of large loop source over the layered earth models for all the configurations. Therefore, with the view of overcoming this drawback and filling the gap in the existing literature for TEM response of large loop sources, in this study, an attempt is made to present a reliable method for computation of TEM response of a large loop source over the layer earth models for any arbitrary receiver positions using the frequency response computation method described in [14, 15]. The computed TEM voltage response is compared with the available TEM responses over the homogeneous earth model for checking the accuracy and reliability of the method.

#### 2. Theoretical Background

The plan view of large loop TEM method with central loop, in-loop, and offset-loop configurations over a layer earth is shown in Figure 1. The large loop presents a source loop and the small loop at the center of the source loop () represents receiver position corresponding to the central loop configuration. Similarly, the large loop presents a source loop and small loop at arbitrary position inside the source loop () represents receiver position corresponding to the in-loop configuration and small loop at arbitrary point outside the source loop () represents receiver position corresponding to arbitrary offset-loop configuration.