Browsing by Author "Tarkeshwar Lal"

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Apparent resistivity over a three layer earth with an inhomogeneous interstratum
(Birkhäuser-Verlag, 1970) Tarkeshwar Lal
The theory of resistivity sounding on a three layer earth comprising an inhomogeneous interstratum has been presented. The electrical conductivity in the intermediate layer, embedded between two layers of uniform conductivity, is assumed to follow either generalised power law or exponential variation. A point source of current is placed on the surface. The electric potential functions on the ground surface have been obtained. The expressions for apparent resistivity over the above models for the Wenner and Schlumberger electrode configurations have been derived. © 1970 Birkhäuser Verlag.
Application of frequency analysis in two-dimensional gravity interpretation
(1972) B.N.P Agarwal; Tarkeshwar Lal
The processes of upward and downward continuation, and first and second vertical derivatives act as different types of filters on the gravity field (or any other field satisfying the Laplace equation). The theoretical frequency (amplitude) response characteristics of these filtering operations have been used to esolve a system of coefficient sets by means of which upward and downward continuation, and first and second vertical derivative values at various levels could be computed for two-dimensional geologic bodies. As the downward continuation process is very sensitive to the errors in observed data i.e., high frequencies (Dean, 1958), the smoothing of the data is very essential. A mathematical smoothing function has been incorporated in the downward continuation formula. The smoothing parameter could be chosen in such a way as to produce coefficient sets having response matching with those of the coefficient sets proposed in the literature. Thus an approximate equivalence of the effect of mathematical smoothing with the inherent smoothing introduced because of the numerical approximation (approximation error) in a particular method on the gravity data in frequency domain has been established. Amplitude response curves of the derived coefficient sets in comparison with some of the existing coefficient sets have also been presented. © 1972.
Coefficient sets for one dimensional gravity operations using filter theory
(Birkhäuser-Verlag, 1971) B.N.P. Agarwal; Tarkeshwar Lal
Analytical expressions for the weight coefficients of the upward and downward continuation, and first and second derivative and their downward continuation operations have been obtained from their corresponding theoretical amplitude response functions in cut off frequency region using filter theory. These expressions, along with the smoothing and shortening operators of Hanning and Hamming types have been utilized to calculate the coefficient sets for each operation. © 1971 Birkhäuser Verlag.
Electromagnetic response of an infinite cable over a layered inhomogeneous earth with exponential variation of conductivity
(1996) Nagendra P. Singh; Tarkeshwar Lal
The problem of calculating the electromagnetic (em) field response of an infinite cable over an inhomogeneous earth is formulated for a multi-layer earth model with one of the layers having exponential variation of conductivity with depth. Solutions for the field components are obtained for the three-layer earth models with the intermediate layer possessing above conductivity variation. Computations are performed for the the absolute-amplitude ratio values, for the quasi-static approximations pertaining to geophysical applications. Results showing the effects of variation of transition layer thickness and conductivity contrast between the top and bottom layers are presented as a function of normalised distance (actual distance divided by the skin-depth computed using top layer conductivity). Results depict characteristic em response over inhomogeneous earth models.
Love waves in an inhomogeneous interstratum
(Birkhäuser-Verlag, 1970) Tarkeshwar Lal
The propagation of Love waves in an inhomogeneous interstratum, whose rigidity and density follow generalized power law variation, lying between two homogeneous half-spaces has been considered. The characteristic frequency equations have been obtained. The computational results for some special cases are presented in the form of dispersion curves showing the variation of phase and group velocity of Love waves with wave number. © 1970 Birkhäuser Verlag.
Multi-system processing approach for resistivity profiling data to enhance the response of subsurface bodies
(Polska Akad Nauk, 2000) Nagendra Pratap Singh; Tarkeshwar Lal
A simple multi-system processing approach making use of the measurements of more than one measuring system is applied to the direct current resistivity profiling methods to study its effectiveness and applicability in enhancing the anomalous response of subsurface target bodies. The processing technique is applied to the two different sets of profiling measurements obtained over various three-dimensional (3-D) models. Procedure is applied firstly to the set of synthetic data obtained by Schlumberger and equatorial dipole-dipole configurations, and secondly to the set of data obtained by Wenner and two electrode configurations. The processed residual apparent resistivity variations are plotted and compared with those of the conventional single system, Schlumberger and Wenner apparent resistivity variations for the two data sets respectively. The results indicate that multi-system processed anomalies show more pronounced variation than those of conventionally processed single system anomalies for both sets of measurements. The enhancement in anomaly variation results in an improved detection of the subsurface target bodies. The results for synthetic models show the effectiveness of the multi-system processing in enhancing the anomalous response of the subsurface bodies in layered earth environment.; A simple multi-system processing approach making use of the measurements of more than one measuring system is applied to the direct current resistivity profiling methods to study its effectiveness and applicability in enhancing the anomalous response of subsurface target bodies. The processing technique is applied to the two different sets of profiling measurements obtained over various three-dimensional (3-D) models. Procedure is applied firstly to the set of synthetic data obtained by Schlumberger and equatorial dipole-dipole configurations, and secondly to the set of data obtained by Wenner and two electrode configurations. The processed residual apparent resistivity variations are plotted and compared with those of the conventional single system, Schlumberger and Wenner apparent resistivity variations for the two data sets respectively. The results indicate that multi-system processed anomalies show more pronounced variation than those of conventionally processed single system anomalies for both sets of measurements. The enhancement in anomaly variation results in an improved detection of the subsurface target bodies. The results for synthetic models show the effectiveness of the multi-system processing in enhancing the anomalous response of the subsurface bodies in layered earth environment.
Three criteria for the judgement of vertical continuation and derivative methods of geophysical interpretation: A discussion
(1970) B.N.P. Agarwal; Tarkeshwar Lal
[No abstract available]
Wave-Tilt Characteristics of EM Waves over a Two Layered Earth Model
(1984) Ramesh P. Singh; Tarkeshwar Lal; B.U.S. Kumar
Wave-tilt amplitudes and phase angle variation in the extended frequency range of 104-107 Hz have been presented for a two layer earth surface model. The effect of conductivity and dielectric constant variation of two layers on wave-tilt amplitude and phase angle have been computed. It is shown to vary with changing thickness of the upper layer. The potentiality of such curves in wave-tilt measurement of the subsurface layer has been discussed. © 1984, Society of Geomagnetism and Earth, Planetary and Space Sciences. All rights reserved.
Wavetilt Characteristics of EM Waves Over a Homogeneous Earth Model
(1980) Ramesh P. Singh; Tarkeshwar Lal
A theoretical analysis has been carried out to investigate the effect of resistivity, dielectric constant and angle of incidence on the amplitude and phase of the wavetilt over a homogeneous earth model over a range of frequency from very low frequency (VLF) to broadcast band (BCB). Numerical results for a wide range of above mentioned parameters are presented. Dependence of wavetilt on these factors has been discussed. Copyright © 1980 by The Institute of Electrical ind Electronics Engineers, Inc.