EFFECTS OF DATA ERRORS AND ACCURACY IN SECOND DERIVATIVE COMPUTATION BY RATIONAL APPROXIMATION*

The effects of systematic (constant) and random errors in the observed data have been investigated analytically for rational approximation method of computing second derivative involving a summation of the products of the averages of the gravity field with the corresponding weight coefficients, both in numerator as well as in denominator. A theoretical gravity anomaly over three spheres has been analyzed to demonstrate the high accuracy in the approximation. Since the sums of the weight coefficients in numerator and denominator are zero and one respectively, the regional gravity anomaly, even though approximated by a constant value over the entire area under computation, can produce substantially large error in the calculated derivative value. This is happening because of the contribution of the regional field in the denominator. Thus, inspite of the high accuracy in rational approximation, the method has limited application to field cases where a combined gravity field consisting of regional and residual anomalies is usually used. Master curves are presented for the constant and random errors by which a rough estimate of the percentage of error in second derivative computation can be made provided one has some idea of the magnitudes of the regional field and random error.     

HIGH-FREQUENCY SHALLOW SEISMIC REFLECTION MAPPING IN TIN MINING*

Field results of shallow seismic reflections obtained with a propane-oxygen detonator (POD) are presented. The survey site was in a tin-mining area of the Kinta Valley in Malaysia. The shallow and irregular limestone bedrock is overlain by alluvial “tailing” and virgin sediments. Sizes of such mining areas can range from about 320 ± 320 m² to 900 ± 900 m². The survey was intended to delineate the topography of the bedrock, which is of vital importance in tin ore exploration and exploitation. The equipment included single- and 12-channel signal enhancement seismographs, the POD, a hammer and thumper. The inexpensive and portable POD generates directional waves of reproducible form, variable energy of high frequency, and only a few surface waves at short offsets. Reflections at around 200 Hz were obtained from the shallow bedrock at about 25 m as well as from very shallow lithological interfaces. The interpretation of seismograms is supported by drill-hole lithological sections and synthetic seismograms. The data illustrate the successful use of shallow reflections for mapping irregular bedrock. Reflection seismics can provide better horizontal and vertical details than the refraction method. Further improvements based on the data-processing flexibility of new signal enhancement seismographs and synthetic seismograms are suggested.     

A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses: I. Known pdf

Abstract

Two probability density functions (pdf), popular in hydrological analyses, namely the log-Gumbel (LG) and log-logistic (LL), are discussed with respect to (a) their applicability to hydrological data and (b) the drawbacks resulting from their mathematical properties. This paper—the first in a two-part series—examines a classical problem in which the considered pdf is assumed to be the true distribution. The most significant drawback is the existence of the statistical moments of LG and LL for a very limited range of parameters. For these parameters, a very rapid increase of the skewness coefficient, as a function of the coefficient of variation, is observed (especially for the log-Gumbel distribution), which is seldom observed in the hydrological data. These probability distributions can be applied with confidence only to extreme situations. For other cases, there is an important disagreement between empirical data and theoretical distributions in their tails, which is very important for the characterization of the distribution asymmetry. The limited range of shape parameters in both distributions makes the analyses (such as the method of moments), that make use of the interpretation of moments, inconvenient. It is also shown that the often-used L-moments are not sufficient for the characterization of the location, scale and shape parameters of pdfs, particularly in the case where attention is paid to the tail part of probability distributions. The maximum likelihood method guarantees an asymptotic convergence of the estimators beyond the domain of the existence of the first two moments (or L-moments), but it is not sensitive enough to the upper tails shape.     

Grain-size distribution,morphoscopy and elemental chemistry of suspended sediments of Pindari Glacier,Kumaon Himalaya,India

Abstract

Suspended sediment concentrations in the meltwater of Pindari Glacier were determined at regular intervals in four ablation seasons. The late ablation periods (September 1994 and October 1995) were characterized by a reduced level of sediment concentration, while the sampling periods of early ablation (May 1994 and July 1995) showed very high concentrations of suspended sediment in the meltwater. Grain size distribution shows the dominance of medium and coarse silt fractions of the mean size of the suspended sediments between 4.35 and 5.82 ø. Clay size constitutes about 7% of the total size population. The majority of the samples are poorly sorted, symmetrically to finely skewed and mesokurtic in nature. The grain shows texture of mechanical and chemical origin, in which mechanical texture is predominant on most of the grains. It was observed that the grains were mostly subangular to subrounded in shape with variable size ranges. Bulk sediment chemistry consists mostly (>70%) of the five elements, Si, Al, K, Fe and Mg. Iron (Fe) and Mn are dominant heavy metals and sediments show the elemental abundance in the order of Fe > Mn > Zn > Cu > Ni > Pb. The Chemical Index of Alteration (CIA) of suspended sediments (57) is relatively higher than in the case of average unweathered upper continental crust (~50) indicating a higher degree of weathering due to glacier grinding and crushing action. Quartz is the most dominant mineral, followed by mica, illite, feldspar and kaolinite.     

Simulation of infiltration from porous clay pipe in subsurface irrigation

Abstract

Advances in the traditional method of subsurface porous clay pipe irrigation rely on knowledge of the distribution of water in the soil. Knowing the relationships among the hydraulic and physical parameters in the system is important for both the design and management of the system. To simulate the infiltration from the porous clay pipe and predict the wetted zone geometry in the soil, a computer model is developed herein. Laboratory experiments were conducted on soil samples representing two different soil textures in a specially designed bin to understand the flow phenomenon and to validate the developed model. In a given soil texture, the installation depth of the pipe and the volume of water applied in the soil are the major factors affecting the wetted zone. The relationships among various parameters, namely lateral spacing, installation depth, irrigation run time, hydraulic conductivity of the body of the pipe, and hydraulic head in the system, were established using the developed model.     

Cambrian trace fossils and worm like impressions from the Tal Group, Gopi-Chand-Ka Mahal section, Mussoorie syncline, Lesser Himalaya

Cambrian trace fossils and worm like impressions are described herein from the three stratigraphic units of Tal Group of rocks exposed along the track from Maldeota to Dhaulagiri in Gopi-Chand-Ka Mahal sec-tion, Mussoorie syncline. The upper 10 m thick sand-stone succession (Arenaceous Member) of Deo-Ka- Tibba Formation (lower Tal Group) contains high den-sity and low diversity Skolithos pipe rock. The Sko-lithos pipe rock in sandstone succession of Arenaceous Member (Deo-Ka-Tibba Formation) indicates shallow marine condition under sand shifting environment of deposition. Higher in the succession, in calcareous Member (Deo-Ka-Tibba Formation), Cruziana ichno-facies occurs in association with Monomorphichnus, Planolites and Paleophycus.