Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Internal wave characteristics in the eastern Arabian Sea during summer monsoon

The time series BT profiles and surface winds and atmospheric pressure, collected in the deep waters off Ratnagiri and Karwar during summer monsoon were utilized to document the characteristics of internal waves (IW). Low-frequency (≤2, cycle per day (cpd)) IW off Ratnagiri are found to propagate at 83 cm/s with wavelengths of 45 km and wave heights upto 40 m. These parameters for high-frequency (>2 cpd) IW off Karwar correspond to 99 cm/s, 3 km and 23 m. The IW off Karwar appear to leave the station at 70° (±10°) (measured from the horizontal). The data sets were further analysed to address the harmonic composition of the IW and identify the possible sources for the observed IW fields. Power spectra of the IW indicated energy peaks at inertial (0·6 cpd) and tidal (1 and 2 cpd) frequencies off Ratnagiri and in the high-frequency band of 0·5–2·0 cycles per hour off Karwar. The coherence between the IW and wind/tide is found to be good at several frequencies within the IW spectrum. This feature probably suggests tides as a source for the IW of tidal frequencies and winds and tides as a joint source for the IW at the remaining frequencies.     

Cuttability assessment of hard coal seams

Summary A number of field and laboratory tests have been carried out on more than 15 coal seams of compressive strengths ranging from 19 MPa to 44 MPa to evolve methods which would help in the selection of suitable coaling machines for hard coal seams. The effect of physico-mechanical properties on cuttability were studied in the laboratory for all these coal seams to identify the relevant parameters affecting the specific energy of coal cuttability. These data were subjected to regression analysis to find the best fit for estimation of laboratory specific energy of coal samples on the basis of simple laboratory and field tests for the strength parameters. Field studies were also conducted over a large number of active mechanized coal faces to study in situ cuttability along with the geo-mining conditions of the site. The field and the laboratory data so generated were correlated and an attempt is made to establish a relationship for estimating the field specific energy for a particular capacity of coaling machines by considering the geo-mining domain of the field in totality.     

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.     

Interpretation of vertical gravity and magnetic profiles

Summary Methods have been developed by quantitatively interpreting gravity and magnetic data in vertical bore-holes or shafts for geological bodies that can be approximated by spheres and cylinders. Master diagrams that can be directly used by the interpreter are provided.     

Diffuse X-ray background measurements in the energy range 2–18 keV

Rocket measurements, of the diffuse X-ray background in the energy range 2–18 keV, conducted from Thumba Equatorial Rocket Launching Station (TERLS), India, are presented. The estimates of the cosmic background are derived by the method which employs the Earth and its atmosphere as a shutter to intercept the celestial X-rays. The results are shown to be consistent with a power law photon spectrum.13.6 _–3.3 ^+4.3 E ^{–1.73±0.15} photons/cm²-sec-keV-ster the spectrum being much flatter than that observed at higher energies.     

Major Element, REE, and Other Trace Element Behavior in Amphibolite Weathering under Semiarid Conditions in Southern India

A body of komatiitic amphibolite, an enclave within the Archean high-grade orthogneisses in southern India, shows mild chemical weathering under semiarid conditions. Along fractures, chemical weathering has advanced (Chemical Index of Alteration &sqbl0;CIA&sqbr0;=53; CIA of fresh rock approximately 26) to the extent that secondary Mg-Fe-Al clay minerals have formed and the rock has turned brownish red, soft, and fine grained. The weathering process has resulted in the mobilization and redistribution of the so-called immobile elements Fe, Al, Ti, and REE effected by the nature of secondary mineral formation (talc vs. aluminous clay minerals) and also possibly by soil microbes. In the initial stages of secondary mineral formation, there is a small loss of Fe, Al, and REE (noticeably Eu). However, in the fracture zone as well as in the incipiently altered zone, there is significant REE enrichment, probably affected by a different precipitation mechanism. Mobilized REE may have come from a minor alteration of clinopyroxene.     

The behavior of natural and anthropogenic osmium in the Hudson River-Long Island Sound estuarine system

The extent to which riverine Os is trapped in a temperate estuary was the aim of this study. The behavior of Os through the Hudson River, East River and the Long Island Sound (LIS) system is addressed using both natural Os and anthropogenically mobilized Os. The Os concentration ([Os]) and isotopic composition (¹⁸⁷Os/¹⁸⁸Os) of the Mid-Atlantic Bight as inferred from the analysis of a water sample of 31‰ salinity (S) at Vineyard Sound, MA are 46 fM and 1.070, respectively. In comparison, the Hudson River at Newburgh, NY has [Os] = 68 fM and ¹⁸⁷Os/¹⁸⁸Os = 1.265. The Os concentration of the East River at the Whitestone Bridge is 51 fM and remains essentially constant proceeding eastward in the LIS despite the increase of salinity from 20‰ towards the higher value of the Mid-Atlantic Bight. The ¹⁸⁷Os/¹⁸⁸Os ratio of water at Whitestone Bridge is 0.945 and increases eastward through the Sound to 0.979 at 7 km and then to 1.019 at 39.6 km. The behavior of Os through LIS appears to be conservative at S > 20‰. On the basis of Os concentration and isotopic composition we infer that anthropogenic Os is being added to the East River through sewers with the likely isotopic ratio of ∼0.13 and that about 24% of riverine Os must be removed at S ? 20‰. There is a net transport of about 0.4-1 mole of anthropogenic Os per year from the East River into the LIS. The residence time of Os in the ocean at present must be about 39,000 years, unless an independent source of supply of Os can be identified.