Showing papers in "Journal of Association of Exploration Geophysicists in 1996"

Localisation of the complex spectrum : The S transform

Abstract: The S transform, an extension to the ideas of the Gabor transform and the Wavelet transform, is based on a moving and scalable localising Gaussian window and is shown here to have characteristics that are superior to either of the transforms. The S transform is fully convertible both forward and inverse from the time domain to the 2-D frequency translation (time) domain and to the familiar Fourier frequency domain. Parallel to the translation (time) axis, the S transform collapses as the Fourier transform. The amplitude frequency-time spectrum and the phase frequency-time spectrum are both useful in defining local spectral characteristics. The superior properties of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis while the localising scalable Gaussian window dilates and translates. As a result, the phase spectrum is absolute in the sense that it is always referred to the origin of the time axis, the fixed reference point. The real and imaginary spectrum can be localised independently with a resolution in time corresponding to the period of the basis functions in question. Changes in the absolute phase ofa constituent frequency can be followed along the time axis and useful information can be extracted. An analysis of a sum of two oppositely progressing chirp signals provides a spectacular example of the power of the S transform. Other examples of the applications of the Stransform to synthetic as well as real data are provided.

Resistivity survey for describing the fresh water lenses of Agatti atoll, Lakshadweep, India.

Abstract: Fresh groundwater, the only natural source of water in the tiny coral atoll of Agatti, occurs in the form of lenses floating over sea water. Due to ignorance on the fragility of the aquifer and its water balance, the lenses are being subjected to over exploitation. At many locations, the fresh groundwater, as a result, turns brackish, a situation which is irreparable. Groundwater resource exploration was taken up in the island for planning its sustainable development and management by way of electrical resistivity surveys, profiling and sounding. The survey enabled delincating the spatial disposition of fresh water lenses and its lateral and vertical extent; two most important parameters necessary for evaluating the resource potential.

Complex demodulation and electromagnetic response function for geomagnetic field variations at 27-day and its harmonics

Abstract: To determine the upper mantle electrical conductivity distribution beyond the depths probed by Sq-periods, the daily mean geomagnetic field variations for the years 1975-1977, recorded through Indo-Russian chain of observatories is subjected to complex demodulation technique to isolate the space-time evolution of periodic field variations for 27-day and its harmonics. The data from this unique latitudinal distribution of 13 observatories has facilitated to best utilize and test statistically the implicit assumption on the representation of spatial characteristic of the field by spherical harmonic term P I 0 (cos θ). The isolated demodulates which satisfied the P 1 0 dependence are used to obtain the depth and conductivity of the substitute conductor for period bands of 25-32, 11-16 and 8-10 days, representative of 27-day and its harmonics. These results when combined with those obtained using Sq-periods help to visualize the mantle in the depth range of 50-1200 Km. as a stack of inhomogeneous layers with a clear suggestion of two layers of moderately high conductivity at 125 and 275 Km. and a sharp discontinuity in the depth range of 350-500 Km. The electrical conductivity and the depth of the conductosphere for the period band of 25-32 days are estimated to be 0.33 S/m and 1200 km. respectively. Both these estimates agree quite well with the values reported for southern Chinese and European regions, suggesting a laterally homogeneous electrical structure of the mantle at such great depths.

Estimation of structural geometry of Satpura conductivity anomaly through the Hilbert transformation of magnetovariational fields

Abstract: The magnetovariational data in horizontal and vertical field components recorded along a profile running across the SONATA and Satpura ranges are separated into its external and internal parts with an objective to decipher the configuration of anomalous currents associated with an elongated Satpura conductivity anomaly (SCA). The inferred distribution of anomalous internal currents approximate the SCA as an arcuate structure with its upper surface simulating asymmetric anticlinal geometry, in close agreement with the results of numerical modelling. In retrospective sense the results demonstrate that constraints provided by mapping the configuration of internal current distribution can be used as a guide on the choice of conductive structures to be investigated by modelling.

Conjugate gradient - An effective algorithm for seismic tomographic reconstruction

Abstract: Tomographic imaging is a technique which allows seismic waves to be used to gain information about the internal structure of masses, in a way conceptually similar to medical CAT scanning. In the present study we have emphasized the need of curved ray tomography in seismic exploration. To meet this end software has been developed for conjugate gradient method. The algorithm is quite robust which handles both straight and curved ray paths, accordingly two synthetic models have been generated and tested. The problem of initial guess of velocity values for the inversion program have been solved by using 'Back projection method'. The reconstructed images of different iterations for a particular model are then compared to determine the reliability and resolution of the tomograms.