Benford’s Distribution in Extrasolar World: Do the Exoplanets Follow Benford’s Distribution?

In many real life situations, it is observed that the first digits (i.e., 1,2,…,9) of a numerical data-set, which is expressed using decimal system, do not follow a uniform distribution. In fact, the probability of occurrence of these digits decreases in an almost exponential fashion starting from 30.1 % for 1 to 4.6 % for 9. Specifically, smaller numbers are favoured by nature in accordance with a logarithmic distribution law, which is referred to as Benford’s law. The existence and applicability of this empirical law have been extensively studied by physicists, accountants, computer scientists, mathematicians, statisticians, etc., and it has been observed that a large number of data-sets related to diverse problems follow this distribution. However, except two recent works related to astronomy, applicability of Benford’s law has not been tested for extrasolar objects. Motivated by this fact, this paper investigates the existence of Benford’s distribution in the extrasolar world using Kepler data for exoplanets. The quantitative investigations have revealed the presence of Benford’s distribution in various physical properties of these exoplanets. Further, some specific comments have been made on the possible generalizations of the obtained results, its potential applications in analysing the data-set of candidate exoplanets.     

Hydro-uvarovite from Mantle Peridotites of Naga Hills Ophiolite:A Mineral Tracer for Neo-Tethyan Mantle Wedge Metasomatism

Hydrous Cr-bearing uvarovite garnets are rare in natural occurrences and belong to the ugrandite series and exist in binary solid solutions with grossular and andradite garnets.Here,we report the occurrence of hydrous uvarovite garnet having Cr2O3 upto 19.66 wt％and CaO of 32.12-35.14 wt％in the serpentinized mantle peridotites of Naga Hills Ophiolite(NHO),India.They occur in association with low-Cr diopsides.They are enriched in LILE(Ba,Sr),LREEs,with fractionating LREE-MREE[avg.(La/Sm)N=2.16]with flat MREE/HREE patterns[avg.(Sm/Yb)N=0.95].Raman spectra indicate the presence of hydroxyl(OH-)peaks from 3500 to 3700 cm-1.Relative abundances in fluid mobile elements and their close association with clinopyroxenes are suggestive of the formation of uvarovite garnets through low temperature metasomatic alteration of low-Cr diopsides by hydrothermal slab fluids.The high LREE concentration and absence of Eu anomaly in the garnet further attest to alkaline nature of the transporting slab dehydrated fluid rather the involvement of low-pH solution.The chemical characteristics of the hydroxyl bearing uvarovite hosted by the mantle peridotite of NHO deviate from the classical features of uvarovite garnet,and their origin is attributed to the fluid-induced metasomatism of the sub arc mantle wedge in a suprasubduction zone regime.     

ON THE SIGNIFICANCE OF AMPLITUDE STUDIES IN SHALLOW REFRACTION SEISMICS*

An analysis of amplitudes of refraction records of some shallow refraction profiles shot primarily for detailing the near-surface structure in a granitic terrain has yielded information on refractor properties: reduced amplitudes are plotted on amplitude-distance graphs. The negative power n to which distance should be raised to represent (elastic) amplitude decay with respect to distance due to spreading of the critically refracted wave involved is examined. Computed values of this “spreading index”n are close to n = 2 as predicted by the theory. With this value of n, amplitude data are processed to determine residual attenuation attributable to elastic absorption in the bedrock. A graphical approach for this purpose from comparison of amplitude-distance graphs with the plots of amplitude decay due to spreading which is applicable to flat and horizontal refractor situations is suggested. Assuming residual attenuation to represent absorption in the granite bedrock, the computed coefficients of absorption, which vary from 0.5 to 3.90 km^?1 for a frequency of 50 Hz, are obtained. From amplitude graphs of reversed profiles it is shown that the amplitude differences plot bears a relation to lateral velocity changes in the refractor. From comparison of practical amplitude decay graphs with those computed for different subsurface models, it appears possible to detect fractured rock occurrences in the refractor.