Spatial continuity measures for probabilistic and deterministic geostatistics

Geostatistics has traditionally used a probabilistic framework, one in which expected values or ensemble averages are of primary importance. The less familiar deterministic framework views geostatistical problems in terms of spatial integrals. This paper outlines the two frameworks and examines the issue of which spatial continuity measure, the covarianceC (h) or the variogram (h), is appropriate for each framework. AlthoughC (h) and (h) were defined originally in terms of spatial integrals, the convenience of probabilistic notation made the expected value definitions more common. These now classical expected value definitions entail a linear relationship betweenC (h) and (h); the spatial integral definitions do not. In a probabilistic framework, where available sample information is extrapolated to domains other than the one which was sampled, the expected value definitions are appropriate; furthermore, within a probabilistic framework, reasons exist for preferring the variogram to the covariance function. In a deterministic framework, where available sample information is interpolated within the same domain, the spatial integral definitions are appropriate and no reasons are known for preferring the variogram. A case study on a Wiener-Levy process demonstrates differences between the two frameworks and shows that, for most estimation problems, the deterministic viewpoint is more appropriate. Several case studies on real data sets reveal that the sample covariance function reflects the character of spatial continuity better than the sample variogram. From both theoretical and practical considerations, clearly for most geostatistical problems, direct estimation of the covariance is better than the traditional variogram approach.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.     

Hydroclimatic fluctuations of the Upper Narmada catchment and its association with break-monsoon days over India

In this paper, hydroclimatic fluctuations of the Upper Narmada catchment (upto Narmadasagar damsite) have been studied by examining the time series (1901–80) of (i) 1-to 10-day annual extreme rainfall; (ii) seasonal total rainfall between May and October; (iii) the precipitation concentration index (PCI); (iv) a modified version of PCI(MPCI); and (v) parameters of the periods contributing specified percentages of rainfall to annual total. Most of these parameters followed the normal distribution and did not show any significant long-term trend. However, some dominant long period oscillations have been noticed in extreme rainfall, seasonal rainfall, PCI and MPCI series. Influence of break-monsoon days over India during July and August on the rainfall activities of the Upper Narmada catchment has also been investigated and salient findings discussed.     

Physical and chemical response of zircons to deformation

An investigation of U-Pb isotopic systematics in zircons from mylonitized Henderson Gneiss (Sinha and Glover 1978) revealed that selected zircon fractions from the mylonite zone suffered total loss of radiogenic Pb at 460 m.y. To further investigate the relationship between Pb loss, U gain, and grain size reduction associated with increasing strain in the shear zone, we have characterized the chemistry and morphology of zircons in the mylonitic rocks, using both electron microprobe analysis and scanning electron microscopy.SEM photographs of the zircons indicate that strain-correlated fracturing and size reduction of the zircons accompanied Pb loss throughout the mylonite zone. Stresses imposed by the expansion of initially U-rich, -damaged portions of the crystal resulted in microfracturing of the more brittle crystalline material proximal to the U-rich zones. During mylonitization, fractures propagated preferentially along these zones allowing metamorphic fluids to penetrate the easily-leached, -damaged portions of the zircons. Removal of 75% of the radiogenic Pb from zircons in the least-deformed zone of the mylonites may have occurred via this mechanism.Irregular, porous zircon overgrowths are also evident from the SEM photographs. Overgrowths are strongly enriched in U, Y and P with respect to the relict, Henderson Gneiss-derived cores, and tend to increase in volume from the protomylonite to the blastomylonite. Thus, the development of overgrowths on the zircons accounts for the U gain observed by Sinha and Glover (1978), and indicates that the transport of high field strength cations (e.g., Zr⁴⁺, Hf⁴⁺, U⁴⁺, etc.) occurred during prograde mylonitization at 460 m.y.A retrograde shearing event at 273 m.y. caused no further disturbance in the U-Pb isotopic systematics of the zircons. Pb retention by zircons during the later episode may have been the result of 1) the participation of H₂O-rich, relatively noncorrosive fluids and/or 2) the lack of further fracturing and size reduction in a strain gradient of lower magnitude than the prograde event.     

Geology and geomorphology of Cumbum valley and Varushanadu hills,Madural district,Tamil Nadu through remote sensing

The Varushanad hills forms the eastern offshoot of the Western Ghats and the Cumbum valley divides the Varushnad hills from the Western Ghats. Investigations were carried out in about 1700 sq Km comprising the Cumbum valley and the Varushanad hills of the Western Ghats situated in Periakulam Srivalliputhur and Usilampatti taluks of Tamil Nadu on the geological and geomorphological aspects. Remote sensing techniques were used and limited field checks were made. Visual interpretation of aerial photographs on 1:60,000 scale was carried out for identifying the geomorphological features, drainage pattern and lithology. Digital analysis of the Landsat computer compatible tape (CCT) path-row 154–053 was also carried out to delineate major lithological variations. Major lineaments were also mapped from the Landsat imagery and false colour composite. The rock types of the Cumbum valley and the Varushanad hills are mainly charnockites, granite gneiss and pink granites which have been deformed by folds and faults. The various geomorphological units of the area are ridges, valleys, bazada zone and pediment zone of mountain complex. Resources evalution studies on the potential zone of ground water and possible construction materials were also discussed.     

Wave-induced nearshore circulation along the Calangute-Candolim beach,Goa, west coast of India

The wave-induced nearshore circulation model suggested by Noda has been modified and applied for three small segments along the coast of Goa. The present model incorporates the prevailing bottom topography and considers its variation along with the radiation stress as the driving force for the circulation. We find that the flow pattern is strongly dependent on bottom topography. While normal incidence of waves results in a cellular pattern of flow, meandering flows prevail for oblique incidence along the coast. The shoreward flows are always located over shoals while the rip currents prevail over channels. The onshore/offshore flows show magnitudes as high as 3·1 m/s, while those alongshore reach a maximum of 1·1 m/s. When compared with field observations these values are slightly higher.     

Strontium isotopic and selected trace element variations between two Aleutian volcanic centers (Adak and Atka): implications for the development of arc volcanic plumbing systems

Major and trace element concentrations and initial ⁸⁷Sr/⁸⁶Sr ratios of lavas from the Aleutian volcanic centers of Adak and Atka have been used to study the evolution of their respective lithospheric plumbing systems. The centers are within 150 km of one another and show similar overall silica ranges (47–67%), but Adak (40 km³) is smaller than Atka (200 km³). Adak's lavas are chemically and isotopically heterogeneous (⁸⁷Sr/⁸⁶Sr:0.70285–0.70330) and two units contain lithospheric xenoliths. The lavas of the much larger Atka, on the other hand, have much less variability in major and trace elements as well as ⁸⁷Sr/⁸⁶Sr (0.70320–0.70345). We suggest that these characteristics are a measure of the relative maturity and cleanliness of the lithospheric plumbing systems that supply magma to these centers. Because Aleutian volcanic centers often remain fixed for relatively long periods of time (5 m.y.), once established, magmatic passageways are repeatedly used. Young plumbing systems are relatively cool and contain large amounts of wallrock contaminant, and ascending magmas undergo contamination as well as concurrent crystallization and fractionation. With time, however, heat and mass transfer between ascending magmas and wallrock produce thermal and chemical boundary layers that insulate subsequent magmas. In effect, the plumbing system matures. The chemical heterogeneity displayed by young, dirty systems (like Adak) reflects not only the magma source but also the wallrock encountered during ascent and possibly the effects of extensive crystal fractionation. Thus, it is the petrologic data of mature, clean systems, like Atka, that yield the most direct and unambiguous information on the ultimate origin of the lavas and their near surface evolution.     

Evaluation of reservoir temperatures and local utilization of geothermal waters of the Konkan Coast, India

Geochemical studies on fifteen geothermal manifestations (38–70°C) from the Konkan coast geothermal province of India have been used to evaluate the reservoir temperatures. Activity studies of the minerals and the waters present in the reservoirs suggest that the thermal waters are in equilibrium with montmorillonite, kaolinite and quartz at about 100°C. Reservoir temperatures of these geothermal systems as estimated by geochemical thermometers, are 88 to 128°C, and thus too low for economic electricity production.     

Sunspots and physics of magnetic flux tubes overstability and Kelvin-Helmholtz instability in a magnetic field

We have studied the dynamical properties of convective overstability and Kelvin-Helmholtz instability in a vertical magnetic field with a downdraft. The Kelvin-Helmholtz instability and overstability produce the upward downward propagating Alfvén waves depending upon the magnitudes of the kinematic viscosity coefficient (eddy viscosity) ν, and thermometric conductivity κ. It is found that the instability may be driven by the density stratification and the effect of the eddy viscosity is to make the system stable. We discuss also the interaction of the overstability inx<0 and the downdraft inx>0, and the overstability at a vertical boundary of the field.     

Equivalent width of molecular lines in stars

We have calculated the expected equivalent widths of the individual rotational lines of the Lyman band of H₂ and (A-X) band of CO and SiO for Main Sequence stars. The results indicate that the lines of H₂ should be observable in absorption up toT _e9000 K. The lines of CO are found to be much weaker than those of H₂ lines. A discussion of these results is presented.     

Detection of marine aerosols with IRS P4-Ocean Colour Monitor

The atmospheric correction bands 7 and 8 (765nm and 865nm respectively) of the Indian Remote Sensing Satellite IRS P4-0CM (Ocean Colour Monitor) can be used for deriving aerosol optical depth (AOD) over the oceans. A retrieval algorithm has been developed which computes the AOD using band 7 data by treating the ocean surface as a dark background after removing the Rayleigh path radiance in the sensor-detected radiances. This algorithm has been used to detect marine aerosol distributions at different coastal and offshore locations around India. A comparison between OCM derived AOD and the NOAA operational AOD shows a correlation ∼0.92 while that between OCM derived AOD and the ground-based sun photometer measurements near the coast of Trivandrum shows a correlation of ∼0.90.