Nomograms for determining the gravity attraction of a right rectangular prism

Summary A rectangular prism is one of the versatile models which is often used to approximate many geological features and also for calculation of topographic and isostatic effects. The analytical formula for the gravity attraction of a right rectangular prism contains 24 lengthy expressions which though compatible for use on an electronic computer, are rather prohibitive for hand computations.Some need has, therefore, been felt for designing a simple graphical device to enable a fairly quick estimate of the gravity effect of a rectangular block model, especially for small-scale jobs involving only a few computation points. In so far as is known to the author, no such graphical device has been made available to the geophysicists.The set of nomograms presented in this communication should fulfill this long felt need. With this aid now it is possible to compute in only a few minutes the gravity attraction of a finite rectangular prism at a point lying outside or on the prism surface.

---

Zusammenfassung Das Quader ist eines der Modelle, das häufig als Annäherung vieler geologischer Körper und bei der Berechnung topographischer und isostatischer Effekte angewandt wird. Die analytische Formel für die Schweresanziehung eines aufrechten Quaders enthält 24 lange Formeln, diezwar für elektronische Rechenautomat aber nicht für Berechnungen von Hand geeignet sind.Es bestand deshalb ein Bedarf für ein einfaches graphisches Mittel, welch eine rasche Abschätzung des Schwereseffektes eines Block-models ermöglichen kann, insbesondere für kleinere Aufgaben mit nur wenigen Berechnungspunkten. Dem Verfasser sind noch keine solche Diagramme bis jetzt bekannt.Die Nomogramme dieser Abhandlung sollten diesen Bedarf erfüllen; an Hand dieses Hilfsmittels sollte es möglich sein in wenigen Minuten die Schweresanziehung für jeden Punkt ausserhalb oder auf der Oberfläche eines begrenzten Quaders zu berechnen.

---

---

Paper presented at the 32nd E.A.E.G. Meeting in Edinburgh (May 1970).     

Assessment of diversity, distribution, conservation status and preparation of management plan for medicinal plants in the catchment area of parbati hydroelectric project stage — III in Northwestern Himalaya

The developmental activities, particularly the construction of hydroelectric projects are causing a great loss of biodiversity in the Indian Himalayan Region. The Himachal Pradesh, a part of IHR is well known for the development of hydroelectric projects. The Parbati H.E. Project is amongst the major projects of the State. The different stages of the project are all causing loss of biodiversity of the area. Stage III of the Parbati H.E. Project is a run of the river scheme on the Sainj River downstream of Power House of Parbati H.E. Project Stage II. The project shall utilize regulated discharge of Parbati H.E. Project Stage II and inflow of River Sainj for power generation, and has been contemplated as a peaking station operating in tandem with Stage II. The present study has been undertaken to see the impact of hydroelectric project on the biodiversity, particularly on medicinal plants. A total of 104 species of medicinal plants, belonging to different life forms, i.e., trees (23 spp.), shrubs (22 spp.), herbs (57 spp.) and ferns (2 spp.) were recorded. The species have been analyzed and studied for their distribution, classification, altitudinal zones, part (s) used, indigenous uses, nativity, endemism and rarity. DDifferent parts of these species, such as whole plants, roots (including rhizomes and tubers), leaves, flowers, fruits, seeds, stems, barks, spikes, nuts and insect galls are used by the inhabitants for curing various diseases and ailments. 30 species are native to the Himalayan region, 9 species native to the Himalayan region and adjacent countries also and 65 species are non-natives. 9 species are near endemics. Considering the whole Himalaya as a biogeographic unit (sensu lato), the near endemics are endemic to the Himalaya. Among these species, Zanthoxylum armatum is categorized as Endangered and Valeriana wallichii as Vulnerable. Hedychium spicatum, Rhus javanica, Berberis lycium, Thalictrum foliolossum, Salvia lanata, Rubia cordifolia and Bergenia ligulata may be considered as threatened species due to their over exploitation for trade. 90 species are propagated by seeds, 8 species by seeds and rhizomes/roots/tubers, 4 species by seeds and cuttings, and 2 species by sori. A management plan for the cultivation and conservation of the medicinal plants in the dam submergence area, and the commercially viable medicinal plants with high value in the catchment area is suggested.     

Wave velocities in a pre-stressed anisotropic elastic medium

Modified Christoffel equations are derived for three-dimensional wave propagation in a general anisotropic medium under initial stress. The three roots of a cubic equation define the phase velocities of three quasi-waves in the medium. Analytical expressions are used to calculate the directional derivatives of phase velocities. These derivatives are, further, used to calculate the group velocities and ray directions of the three quasi-waves in a pre-stressed anisotropic medium. Effect of initial stress on wave propagation is observed through the deviations in phase velocity, group velocity and ray direction for each of the quasi-waves. The variations of these deviations with the phase direction are plotted for a numerical model of general anisotropic medium with triclinic/ monoclinic/orthorhombic symmetry     

A methodology to determine thermal conductivity of soils from flux measurement

Determination of thermal properties of soils (viz., thermal resistivity, thermal conductivity, thermal diffusivity and heat capacity), which primarily influence heat migration through the soil mass, is essential in situations where geomaterials are relentlessly subjected to higher temperatures and temperature variations. These properties of the soil mainly depend upon its type, mineralogy, particle size and gradational characteristics, density and water content. In this context, earlier researchers have determined thermal conductivity of soils by employing a thermal probe (a line heat source), which works on the principle of transient method (TM) of heat conduction. However, this methodology cannot be employed for establishing the heat flow (read thermal regime) through the soil. Hence, development of an alternate technique, which facilitates quantification of temporal and spatial variation of the heat flux and temperature in the soil mass, becomes essential. With this in mind, a methodology to determine thermal conductivity of soils by employing the concept of thermal flux measurement (TFM) has been developed and its details are presented in this paper. Results obtained from the TM and TFM have also been critically evaluated for the sake of validation and generating more confidence in the proposed methodology.     

An upland soil erosion model derived from the basic principles

Starting from the basic erosion principles, an upland soil erosion model to predict soil loss by overland flow from individual storms on forested hillslopes can be derived in the form where Q_s is total soil loss for a storm event, n is roughness coefficient, x is down slope distance, K_f is soil erodibility factor, S is slope, α is slope exponent and Q is runoff. Values of n and α are to be determined for different environments and are 0·58 and 2·1 for a mixed pine forest ecosystem. A significant correlation (r = 0·933, n = 96) fits between the observed and predicted values using this expression, and the model fitting is good.     

Study of total electron content variations over equatorial and low latitude ionosphere during extreme solar minimum

In recent years with the advancement in satellite based navigational applications, study of Total Electron Content (TEC) has gained significant importance. It is well known that due to dynamical behaviour of equatorial and low latitude ionosphere, the levels of ionization is relatively high herein. The sustained decrease in solar extreme ultraviolet radiations during the current minimum is greater than any in recent history. This gives us the opportunity to study the observations of global positioning system total electron content (GPS-TEC) dual frequency signals from the GPS satellites continuously recorded at Trivandrum (an equatorial station) and Delhi (a low latitude station) during the extremely low solar activity period from January 2007 to June 2009. This study illustrates the diurnal, seasonal and annual variations of TEC during the extended solar minimum period. This study also investigates the behaviour of daytime ionosphere around spring and autumn equinoxes at low solar activity period. The results clearly reveal the presence of equinoctial asymmetry which is more pronounced at equatorial station Trivandrum. The diurnal variation of TEC shows a short-lived day minimum which occurs between 0500 to 0600 LT at both the stations. Delhi TEC values show its steep increase and reach at its peak value between 1200 and 1400 LT, while at the equator the peak is broad and occurs around 1600 LT. Further, the daily maximum TEC ranges from about 5 to 40 TEC units at Trivandrum and about 10 to 40 TEC units at Delhi, which correspond to range delay variations of about 1 to 8 m at the GPS L1 frequency of 1.575 GHz. The Maximum values of TEC were observed during spring equinox rather than autumn equinox, showing presence of semi annual variation at both the locations. The minimum values of TEC were observed during the summer solstice at Trivandrum indicating the presence of winter anomaly at equatorial region while Delhi TEC values were minimum during winter solstice showing absence of winter anomaly. Also the TEC values at both the locations have been decreasing since 2007 onwards exhibit good positive correlation with solar activity.     

Tilted Bianchi Type I Models with Heat Conduction Filled with Disordered Radiations of Perfect Fluid in General Relativity

In this paper, we have investigated some tilted Bianchi Type I models with heat conduction filled with disordered radiation of perfect fluid. To get a determinate solution, we have assumed a condition A =(BC) ⁿ between metric potentials. Alternatively we have discussed the case A=(BC) ^1/3 for which tilted nature of the model is preserved. The various and geometrical features with singularities in the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two-dimensional non-linear inversion of VLF-R data using simulated annealing

The VLF-R (very low frequency-resistivity) data, i.e. the apparent resistivity ( ρ _a ) and phase ( φ ) data, were inverted individually and jointly using the VFSA (very fast simulated annealing) global inversion approach. Global inversion results for synthetic data without and with various amounts of random and normally distributed Gaussian noise reveal that the inversion of neither the ρ _a nor φ data alone yields the true parameters of the structures. However, the joint inversion of the ρ _a and φ data yields very good estimates of the model parameters. Five models, representing typical subsurface structures in the shield areas, are studied here. Various models achieved after 10 VFSA runs were used to compute the mean model and the corresponding covariance and correlation matrices, which were used to estimate the uncertainties in the mean model parameters and correlations between the model parameters. We observe that these correlations follow the physics associated with the problem. VLF-R field data due to a nearly vertical contact structure and a very thick dyke-like structure were also inverted to demonstrate the efficacy of the approach in the delineation of the parameters of 2-D structures.     

Nubra-Gartang Superlineament,Ladakh -some geological observations and their implications

Geological observations along the Leh-Panamic traverse, which includes the northwestern portion of the Nubra-Gartang Superlineament, are being reported. Nubra-Shyok Thrust and the Tirit-Khalsar Fault are two imporant structural features in the area, the latter having a linear trend over regional extent is clearly picked up in the LANDSAT imagery.