Geophysical expression of natural recharge in different geological terrains

Behavior of the Dar-Zarrouk parameters--longitudinal unit conductance, transverse unit resistance, longitudinal resistivity, and transverse resistivity--has been compared with the behavior of the natural recharge in two geological terrains. Contour patterns of the geophysical parameters and those of natural recharge have been analyzed and a qualitative relation in their behavior was recognized. Graphical comparison of the geophysical and hydrogeological parameters clearly illustrates a qualitative relationship between the two parameters. Use of such qualitative relation in the field of ground water exploration and management studies is explained. A modest beginning is attempted to arrive at a quantitative relation between natural recharge and Dar-Zarrouk parameters.     

Thermoelastic stresses in an infinitely extended aelotropic thin plate due to a sudden heating of the boundary of a circular hole in it

Summary Methods of transform calculus are used to determine the temperature and stresses in an infinitely extended aelotropic plate with a time dependent temperature distribution suddenly applied on the inner boundary of a circular hole in it.     

Ground water recharge techniques for the Deccan Trap Aquifer formations

The Deccan Trap terrain covers an area of about 200,000 sq. miles in Peninsular India. The geomorphological features of the terrain provide fewer number of sites for the surface storage of water, like dams, tanks etc. Hence most of the farm-lands of this terrain have to depend upon rains and ground water in trap rocks for their irrigation needs. The Trap rocks are not only poor producers of water but also have lesser water holding capacities when compared to the sand and gravel beds. The latter problem is further accentuated by their near horizontal dips and steeply eroded hill stopes. Wherever lateral truncation of the Trap flows due to crosion occur, ground water from these flows seeps out through the sides of their slopes into the gullies, streams and rivers, due to reduction in the length of path of movement of ground waters. The flows get drained so fast, that by summer, water tables recede faster and go deeper, thereby wells become useless for irrigation purposes. Thus, vast areas of the Trap terrain remain barren during summer months and are exposed to wind erosion. The rate at which the water levels of wells starts falling down along with the variations in quantity and distribution of rain fall make irrigation a problem even during winter months, especially for the high yielding varieties of crops. In order to solve this problem, water levels of wells have been measured prior to the construction of contour bunds in Nariaoli Mechanised farm near Nariaoli village, Sagar district, as an experimental measure, for which detailed soil and ground surveys were made. On the basis of soil characteristics of the land, the contour bunds are located in such a manner that the pools formed behind them acted as recharge areas. In addition, check dams across the nallahs are constructed such that some of the reservoirs, situated in the influent parts of the stream courses acted as recharge basins, while those situated in the effluent parts of the streams served to check the free flow of ground water into the streams. On this principle pratically all the villages around Sagar have been bunded, though not all the streams check-dammed. Sets of water table maps were prepared, once before the onset of rains and the second time immediately after the rains. As a result of these recharge methods, each dug well is now capable of irrigating eight to sixteen times more acreage during winter and two to four times more acreage during summer than what each well was capable of before. Streams, that were ephemeral, have become seasonal, and seasonal streams have become nearly perennial. The authors, therefore, conclude that vast areas of low ground farm-lands of the Trap terrains can be provided with adequate irrigation facilities even during summer months with the help of soil and water conservation practices. This may go a long way to meet the demands for food by the ever growing population of India, as the major part of Deccan Trap terrain involved is endowed with rich soils.     

Nonlinear pseudo-radial oscillation of a rotating magnetic star

The nonlinear pseudo-radial mode of oscillation of a rotating magnetic star is studied. It is shown that for a general rotational field, the coupling between magnetic field and rotation tends to reduce the average rotational energy parameterT. This result in a lowering of the maximum pulsation amplitudeq _max, which depends on strength of rotation and magnetic field. The configuration tends, therefore, to a new equilibrium state at lower value ofq _max. The analytic solution of the pulsation equation for the case ofy=5/3 in the presence of rotation and magnetic field has also been derived in the Appendix.     

Exact solution of a basic equation in finite atmosphere by the method of Laplace transform and linear singular operators

A finite atmosphere having distribution of intensity at both surfaces with definite form of scattering function and source function is considered here. The basic integro-differential equation for the intensity distribution at any optical depth is subjected to the finite Laplace transform to have linear integral equations for the surface quantities under interest. These linear integral equations are transformed into linear singular integral equations by use of the Plemelj's formulae. The solution of these linear singular integral equations are obtained in terms of theX-Y equations of Chandrasekhar by use of the theory of linear singular operators which is applied in Das (1978a).     

Determination of the polynomial moments of the seismic moment rate density distribution with positivity constraints

We present a new formulation of the inverse problem of determining the temporal and spatial power moments of the seismic moment rate density distribution, in which its positivity is enforced through a set of linear conditions. To test and demonstrate the method, we apply it to artificial data for the great 1994 deep Bolivian earthquake. We use two different kinds of faulting models to generate the artificial data. One is the Haskell-type of faulting model. The other consists of a collection of a few isolated points releasing moment on a fault, as was proposed in recent studies of this earthquake. The positions of 13 teleseismic stations for which P - and SH -wave data are actually available for this earthquake are used. The numerical experiments illustrate the importance of the positivity constraints without which incorrect solutions are obtained. We also show that the Green functions associated with the problem must be approximated with a low approximation error to obtain reliable solutions. This is achieved by using a more uniform approximation than Taylor's series. We also find that it is necessary to use relatively long-period data first to obtain the low- (0th and 1st) degree moments. Using the insight obtained into the size and duration of the process from the first-degree moments, we can decrease the integration region, substitute these low-degree moments into the problem and use higher-frequency data to find the higher-power moments, so as to obtain more reliable estimates of the spatial and temporal source dimensions. At the higher frequencies, it is necessary to divide the region in which we approximate the Green functions into small pieces and approximate the Green functions separately in each piece to achieve a low approximation error. A derivation showing that the mixed spatio-temporal moments of second degree represent the average speeds of the centroids in the corresponding direction is given.