Gravity interpretation of sedimentary basins with hyperbolic density contrast1

The variation in the density of sediments with depth in a sedimentary basin can be represented by a hyperbolic function. Gravity anomaly expressions for a 2D vertical prism and an asymmetric trapezium with a hyperbolic density distribution are derived in a closed form. These are used in inverting the gravity anomaly of a sedimentary basin with variable density. Firstly, the basin is viewed as a series of prisms juxtaposed with each other. The initial thickness of each prism is obtained from the gravity anomaly at its centre, based on the gravity anomaly of an infinite slab with a hyperbolic density contrast. These thicknesses are improved, based on the differences between the observed and the calculated anomalies. For an improved rate of convergence of the solution, these thicknesses may alternatively be refined using the well-known ridge regression technique. Secondly, the basin is approximated by an asymmetric trapezium and its anomalies are inverted for the parameters of the trapezium using the ridge regression. Since this approximation serves to oversimplify the floor of the basin, it must be used only when the sediment-basement interface has minor undulations. The results of a hypothetical case and two field cases (the San Jacinto Graben, California and the Godavari Graben, southern India) are presented. In both field cases, the interpreted depths are comparable with the real ones, proving the validity of the assumption of a hyperbolic density distribution of the sediments in the two basins considered.     

Assessment of the Present State and Future Fate of River Saraswati,India: Water Quality Indices and Forecast Models as Diagnostic and Management Tools

Water quality assessment is key to the conservation and management of rivers. River Saraswati, a distributary of the river Ganga, serves as a lifeline to many villages in the district Hooghly in West Bengal, India. As the river is gradually dying due to diverse man-made pollution, ten water quality parameters in two sampling spots (PR-1 and PR-2) in the river are monitored month-wise from March 2017 to February 2020,  and these are compared with those from a reference pond. The water quality index (WQI) is determined for the two riverine spots and the reference pond based on the Canadian Council of Ministers of Environment WQI (CCMEWQI) and weighted arithmetic WQI, respectively. In addition to actual observations, three different forecasting methods, exponential smoothing, autoregressive integrated moving average, and artificial neural network, are used to predict WQI for the next two years. This study indicates that free CO₂, dissolved oxygen, and turbidity are the key parameters to evaluate this river's anthropogenic stress and health. The actual and forecasted results reflect the precipitous degradation of CCMEWQI in PR-2. Therefore, the immediate intervention of all stakeholders is required to adopt an integrated and comprehensive river management plan to save the river from utter obliteration.     

Role of interannual equatorial forcing on the subsurface temperature dipole in the Bay of Bengal during IOD and ENSO events

Role of equatorial forcing on the thermocline variability in the Bay of Bengal (BoB) during positive and negative phases of the Indian Ocean Dipole (IOD) and El Niño Southern Oscillation (ENSO) was investigated using the Regional Ocean Modeling System (ROMS) simulations during 1988 to 2015. Two numerical experiments were carried out for (i) the Indian Ocean Model (IOM) with interannual open boundary conditions and (ii) the BoB Model (BoBM) with climatological boundary conditions. The first mode of Sea Surface Height Anomalies (SSHA) variability showed a west-east dipole nature in both IOM and altimetry observations around 11°N, which was absent in the BoBM. The vertical section of temperature along the same latitude showed a sharp subsurface temperature dipole with a core at ~ 100 m depth. The positive (negative) subsurface temperature anomalies were observed over the whole northeastern BoB during NIOD (PIOD) and LN (EN) composites due to stronger (weaker) second downwelling Kelvin Waves. During the negative phases of IOD and ENSO, the cyclonic eddy on the southwestern BoB strengthened due to intensified southward coastal current along the western BoB and local wind stress. The subsurface temperature dipole was at its peak during October–December (OND) with 1-month lag from IOD and was evident from the Argo observations and other reanalysis datasets as well. A new BoB dipole index (BDI) was defined as the normalized difference of 100-m temperature anomaly and found to be closely related to the frequency of cyclones and the surface chlorophyll-a concentration in the BoB.

     

Effect of dry sandiness parameter and initial stress on the scattering of plane SH wave

The present paper is incorporated into a mathematical model of transmission and reflection of shear waves through the initially stressed dry sandy medium sandwiched between two initially stressed distinct orthotropic half-spaces. The formulae of transmission and reflection coefficients have been deduced for the propagation of SH waves in the described model subjected to certain boundary conditions applying Snell’s law and Cramer’s method. These coefficients are observed as a function of wave number, phase velocity, initial stress, rigidity, and dry sandiness coefficients. The concepts of energy partition, phase shift, conservation of energy, critical angle, and slowness section are introduced. Graphical approach has been carried out to accomplish a relation between reflection/refraction coefficient, phase shift, and energy ratio with an angle of incidence and wave number on the propagation of shear wave. The study reveals that sandiness parameter, initial stress, and wave number have a cogent respond to the scattering of shear wave that has been illustrated graphically.     

Impact of pre-stress,inhomogeneity and porosity on the propagation of Love wave

This work presents a mathematical modelling of Love wave transference through a pre-stress influenced anisotropic medium with heterogeneity between a sandy medium and an initially stressed anisotropic porous medium. Variable separation method has been induced in order to derive the frequency relation. Using appropriate boundary conditions at two interfaces, the dispersion equation has been obtained in its closed form. Possible particular cases are considered, and the corresponding results are consonant with the classical cases. Numerical computations have been employed to demonstrate the role of inhomogeneity factors, initial stresses and porosity, and are depicted by means of graphs which substantiates that those parameters immensely affect the Love wave velocity. In mineral prospecting and exploring technique in earth, the method and the results of this problem may be applicable.     

Development of design flood hydrographs using probability density functions

Probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQ_P) and error of time to peak (ET_P) were computed. The best‐fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20‐, 50‐, 100‐ and 200‐year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20‐, 50‐, 100‐ and 200‐year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormal‐produced peak discharge was very close to the estimated design discharge in case of 20‐year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50‐, 100‐ and 200‐year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50‐, 100‐ and 200‐year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma. Copyright © 2009 John Wiley & Sons, Ltd.     

String membranes in higher dimensions

We shall study homogeneous and isotropic clouds formed of String membranes. These membranes are considered in extra dimensions of a higher dimensional Bianchi-I space-time. Some solutions are found for the field equations of the system.