A nomogram has been devised for situations, in which the source of a self-potential anomaly can be approximated by an obliquely polarized sphere or horizontal cylinder embedded in a homogeneous half space. The nomogram can be used for rapid determination of three parameters of the target: (1) depth to the centre, (2) angle between the axis of polarization and the horizontal, (3) shift of the point vertically above the centre of the body from zero potential value.The nomogram has been tested and the parameters determined for SP results obtained over ore bodies Weiss and Siileymankoy in the Ergani Copper district, Turkey. The curves computed for the estimated parameters match the field curves well.The earliest theoretical work on the self-potential (SP) method is that of Petrowsky (1928) who studied the potential distribution due to a hidden polarized sphere and showed that the potential on the surface varies as a cosine function. Heiland (1940) based his method of interpretation for a vertically polarized sphere on Petrowsky's theory of surface distribution of the potential. DeWitte (1948) developed a method of interpretation in which ore bodies were simulated by spheres. Yungul (1950) modified the Petrowsky's method and also suggested the removal of topographic and regional effects. Rao, Murthy and Reddy (1970) described a procedure for interpretation of self-potential anomalies for sphere, rod, and dipping sheet.In addition to the above works, which are directly related to the present paper, papers on SP interpretation were published by Roy and Chowdhury (1959), Meiser (1962), Paul (1965), Paul, Datta and Banerjee (1965 and Banerjee (1971). These authors outlined methods of interpretation for tabular bodies, arbitrary dipoles, inclined sheets, and vertical and inclined dipoles.

The resistivity interpretation problem involves the estimation of resistivity as a function of depth from the apparent resistivity values measured in the field as a function of electrode separation. This is commonly done either by curve matching using master curves or by more formal linearized inversion methods. The problems with linearized inversion schemes are fairly well known; they require that the starting model be close to the true solution. In this paper, we report the results from the application of a nonlinear global optimization method known as simulated annealing (SA) in the direct interpretation of resistivity sounding data. This method does not require a good starting model but is computationally more expensive. We used the heat bath algorithm of simulated annealing in which the mean square error (difference between observed and synthetic data) is used as the energy function that we attempt to minimize. Samples are drawn from the Gibbs probability distribution while the control parameter the temperature is slowly lowered, finally resulting in models that are very close to the globally optimal solutions. This method is also described in the framework of Bayesian statistics in which the Gibbs distribution is identified as the a posteriori probability density function in model space. Computation of the true posterior distribution requires computation of the energy function at each point in model space. However, a fairly good estimate of the most significant portion(s) of the function can be obtained from simulated annealing run in a reasonable computation time. This can be achieved by making several repeat runs of SA, each time starting with a new random number seed so that the most significant portion of the model space is adequately sampled. Once the posterior density function is known, many measures of dispersion can be made. In particular, we compute a mean model and the a posteriori covariance matrix. We have applied this method successfully to synthetic and field data. The resulting correlation covariance matrices indicate how the model parameters affect one another and are very useful in relating geology to the resulting resisitivity values.

An audiomagnetotelluric ͑AMT͒ study has been carried out in the Bakreswar Hot Spring ͑BHS͒ area of eastern India to locate the geothermal source in the vicinity of BHS. Phasetensor analysis of the AMT data shows that the region is broadly 2D. Rapid relaxation inversion ͑RRI͒ for both transverse-electric ͑TE͒ and transverse-magnetic ͑TM͒ modes has been carried out to obtain resistivity images of the subsurface. AMT results show that the north-south fault close to Bakreswar is a shallow feature, not deeper than 300 m, and thus cannot act as a heat source. The subsurface formation below the fault zone is highly resistive up to a great depth, indicating the absence of a heat source and geothermal reservoir in the vicinity of the BHS. AMT results indicate that the location of the geothermal reservoir is deep and lies beyond the profiles of measurement in the northwestern side of the Bakreswar Hot Spring.

Moho boundary, discovered about a century back, is well established on the basis of seismological studies. Electromagnetic studies using very low frequencies, however, have not been able to establish this boundary due to the presence of highly conducting continental lower crust. Magnetotelluric lithospheric study over the Eastern Indian Craton (3.3 Gyr) resolves the lower crust and upper mantle boundary due to the absence of highly conducting continental lower crust underneath the craton. From the present study it can be speculated that a dynamics other than the plate tectonics possibly existed up to the mid‐Archaean.