Volume 108, Issue 2
June 1999, pages 69-116
pp 69-79 June 1999
For nearly two centuries, the partial differential equation of heat conduction has constituted the foundation for analyzing many physical systems, including those involving the flow of water in geologic media. Even as the differential equation continues to be a powerful tool for mathematical analysis in the earth sciences, it is useful to look at the groundwater flow process from other independent perspectives. The physical basis of the partial differential equation is the postulate of mass conservation. Alternatively, it is possible to understand groundwater movement in terms of energy and work because mechanical work has to be done in moving water against the resistance to flow offered by the solid material and to store water by opening up pore spaces. To this end, the behaviors of steady-state and transient groundwater systems are sought to be understood in terms of postulates concerning the state of a groundwater system, its tendency to optimally organize itself in response to impelling forces and its ability to store and release energy. This description of groundwater occurrence and flow, it is shown, is equivalent to the variational statement of the Laplace equation for the steady-state case and is similar to Gurtin’s (1964) variational principle for the transient case. The approach followed here has logical similarities with Hamilton’s principle for dynamical systems. Though the variational statement of the transient groundwater flow process is appealing in that it provides a rationale for deriving the parabolic equation, intriguing questions arise when one attempts to understand the physical significance of the variational statement. This work is motivated in part by a desire to develop a better understanding of the groundwater flow process from an intuitive base pertaining to discrete systems. Also, as we show an increasing preference to numerically solve groundwater flow problems on the basis of integro-differential equations, it is likely that the work presented here may contribute to improving such integral solution techniques.
pp 81-85 June 1999
Gravity and bathymetry data have been extensively used to infer the thermo-mechanical evolution of different segments of the oceanic lithosphere. It is now understood that magmatic fluid processes involved in the accretion of oceanic crust are spatially complex and episodic. The nature of these processes which are in general nonlinear, can be described using fractal analysis of marine geophysical data. Fractal analysis has been carried out for gravity and bathymetry profiles over the aseismic Chagos-Laccadive Ridge and the spreading Carlsberg Ridge. The Iterated Function Systems (IFS) have been used to generate synthetic profiles of known dimension (D) and these are compared with the observed profiles. The D for the data sets are in the range of 1–1.5. The D for gravity profiles is less than those of bathymetry and the D for gravity and bathymetry over spreading ridge is higher than the aseismic ridge. The low fractal dimension indicates that the processes generating them are of low dimensional dynamical systems.
pp 87-92 June 1999
Long-term conditional probabilities of occurrence of great earthquakes along the Himalaya plate boundary seismic zone have been estimated. The chance of occurrence of at least one great earthquake along this seismic zone over a period of 100 years (beginning the year 1999) is estimated to be about 0.89. The 100-year probability of such an earthquake occurring in the Kashmir seismic gap is about 0.27, in the central seismic gap about 0.52 and in the Assam gap about 0.21. The 25-year probabilities of their occurrence in these gaps are 0.07, 0.17, and 0.05 respectively. These probability estimates may be used profitably to assess the seismic hazard in the Himalaya and the adjoining Ganga plains.
pp 93-98 June 1999
In situ stress measurements by hydraulic fracturing were carried out in the 617 m deep borehole specially drilled in the epicentral zone of the 1993 Latur earthquake for the purpose of research. The stress measurements carried out at 592 m depth in this borehole are the deepest of all such measurements made so far in the Indian shield. The maximum and minimum principal horizontal stresses (SH max andSh min) have been derived from the hydrofracture data using the classical method. TheSH max andSh min are found to be 16.5 and 9.6 MPa at 373 m depth, and 25.0 and 14.1 MPa at 592 m depth, indicating that the vertical gradients ofShmax andShmin in the epicentral zone are 39 MPa/km and 21 MPa/km respectively. The principal horizontal stresses in the epicentral zone are comparable with those at Hyderabad and 30% higher than in most other comparable intra-continental regions. Analysis of the results indicate that the stresses in the focal region of the 1993 Latur earthquake have not undergone any significant change following its occurrence and this is in agreement with a similar inference drawn from the seismic data analysis. It appears that the Latur earthquake was caused due to rupturing of the overpressured fault segment at the base of the seismogenic zone.
pp 99-106 June 1999
The decrease of density contrast with depth in sedimentary basins is approximated by an exponential function. The anomaly equation, in frequency domain, of a prismatic model with an exponential density function is derived. The method has been extended to derive the Fourier transforms of the gravity anomalies of the sedimentary basin, wherein the basin is viewed as vertical prisms placed in juxtaposition. The gravity anomalies of the sedimentary basin are obtained by taking the inverse Fourier transforms. Filon’s method has been extended for calculating accurate inverse Fourier transforms. The accuracy of the method has been tested using a synthetic example. A combination of space and frequency domain methods have been developed for inversion of gravity anomalies over the sedimentary basin. The method has been applied to interpret one synthetic profile and one field profile over the Godavari basin. The method developed in this paper to calculate the inverse Fourier transforms yields continuous spectrum with accurate values. The maximum depth deduced from the gravity anomalies is of the same order as the depth encountered to the basement at the Aswaraopeta borewell.
pp 107-116 June 1999
A 54-m long core was raised from the bed of the Nal Sarovar, a large shallow lake located in the middle of the low-lying region linking the Gulfs of Kachchh and Khambhat, in western India. A three-layer sequence comprising: Zone-1 (top 3 m), predominantly silty-clay/clayey; Zone-2 (3–18 m), sandy; and Zone-3 (18–54 m), dominated by sticky silty-clay/clayey-silt with occasional thin sand layers and basalt fragments was identified. Smectite and illite are the dominant clay minerals with minor amounts of kaolinite and chlorite. Very high content of smectite (53–97%) in the clays of the lowermost zone (18–54 m) and the geomorphic features of the surrounding region suggested that the sediments were derived from the basaltic terrain of Saurashtra and/or via the Gulf of Khambhat. The clay content in the middle zone (3–18 m), dominantly sandy, is very low. Therefore, provenance for this zone was derived using heavy minerals in the sand fraction. The heavy mineral species in this zone suggested the mixed metamorphic and igneous terrain of Aravallis as the major source. The grain-size distribution of this zone closely matched with the sediments underlying the modern Sabarmati riverbed at Ahmedabad, suggesting fluvial depositional environment. Clays also dominate sediments of the topmost (0–3 m) zone with illite as the dominant (74–81%) specie followed by smectite suggesting derivation from the mixed metamorphic and igneous terrain of Aravallis.