Magnetotelluric method is one of the geoelectrical methods which imparts information about the electrical resistivity of the Earth’s crust and upper mantle. Electrical and electromagnetic methods do not conform well with the response of lumped circuit elements such as resistance, inductance and capacitance. Inhomogeneities and stratification in the subsurface have been found to give unexpected response to incident electromagnetic waves. The overall response of the subsurface to magnetotelluric signals encompasses relatively much larger depths and is found to change significantly. The term ‘apparent resistivity’ is generally used in electrical and electromagnetic methods, particularly in resistivity and magnetotelluric methods to deduce the subsurface resistivity arises primarily from the layered subsurface parameters, and at times is associated with characteristic oscillations and undulations.

 Magnetotelluric response in both frequency and time domains are used to express the observable data as apparent resistivity. The apparent resistivity basically is a weighted spatial average of nearby resistivity distribution. To deduce useful information about the geological structure, efforts have been made to explore few possible ways of presenting the Earth’s responses. The real, imaginary and absolute values of the surface impedance have recently been used to define apparent resistivity. These definitions provide additional information and characteristic features of the subsurface, which is otherwise not possible using classical definition alone. Similarly in time domain, the step and impulse responses of the Earth to magnetotelluric signals have been used in arriving at different apparent resistivity definitions. These definitions merely channel different ways of assigning different set of weights to the subsurface resistivity distribution. The apparent resistivity defined in different ways are found to provide subsurface resistivity distribution.

The apparent resistivity over various three layered Earth models (H, K, Q and A type) shows characteristic features of the layered parameters for different definitions of apparent resistivity. The distinctive behaviour of apparent resistivity curves in the broad band periods and delay times can be used as an appropriate definition for a particular H, K, Q and A type Earth models. The special features of apparent resistivity curves obtained using various definitions can be used as rules of thumb in the qualitative interpretation of magnetotelluric data in frequency and time domains.

For the prediction of subsurface resistivity distribution with the help of suitable and adequate mathematical function, it is essential to have the knowledge of functional characteristic over various layered models. Such functions are the characteristic of the changes in behaviour of apparent resistivity in frequency and time domains which are associated with changes in resistivity distribution of the layered Earth. This characterizes the ability of explaining the related phenomena that takes place at depths. The understanding of the changes in a model and corresponding changes in predictable data is important in developing a mathematical link. The Frechet derivative serves the connecting link for such changes and has been derived for various one-dimensional Earth models. Frechet derivatives provide immediate information about the geophysical environment of the subsurface which is useful in itself or in a second stage of inversion where in an acceptable resistivity model is deduced. In fact, resistivity often changes by many orders of magnitude, therefore, model perturbation and corresponding data perturbation are best represented on logarithmic scale. Frechet derivatives defined in this manner are known as ‘sensitivity functions’. Sensitivity functions have been studied in detail for various multi-layered and continuous Earth models with varying conductivity in both frequency and time domains. The sensitivity variations with depth show contribution of the resistivity structure at depths to the apparent resistivity at a particular period. It also gives s the direct estimation of the depth of investigations at a particular period. Moreover, the zones of localized maximum sensitivity in either domain are emphasized with ease. Such zones are found on or near the Earth surface in frequency domain and at depths below the Earth surface in case of time domain. The maximum sensitivity observed on or near the Earth surface can be attributed to the observed static shift in some of the regions. The behaviour of sensitivity functions shows that the static shift problem may not be present in time domain magnetotelluric measurement. The sensitivity functions using analytical expression are found to illustrate the problem of equivalence in magnetotelluric method.

The magnetotelluric data at various locations in the Indo-Gangetic basin have been recorded. Various magnetotelluric parameters at each location have been studied to deduce the resistivity structure of the Indo-Gangetic basin. It has been found that the high conducting top layer distorts the magnetotelluric data at longer periods. The influence of the high conducting sediments have been studied as a sensitivity on the Earth surface in the period range 1-4000 seconds. The conductance of this conductive sedimentary layer has been removed to avoid the screening effect to extract maximum information about the electrical resistivity of the deeper structure. The lower crustal conductivity zone is also found to be present in the Indo-Gangetic basin. The magnetotelluric data show the subsurface extension of the peninsular shield beneath the Indo-Gangetic basin.