Modelling for Science, for a better future - some recent outcomes
Propagation of torsional surface waves in a double porous layer lying over a Gibson half space
by Sushant Shekhar and Imtiyaz A Parvez
The present study deals with the behavior of torsional surface waves when they propagate through an inhomogeneous fluid saturated porous double layers over a dry sandy inhomogeneous Gibson half space. The inhomogeneities of the porous layers are taken as quadratic and exponential variation with depth in the density, elastic moduli and initial stress. In the half space it varies linearly in the elastic moduli and initial stress. For simplicity of the problem, we have used the separation of variable technique. The dispersion equation has been derived with boundary conditions and solved by an iterative method (Newton Raphson method). We have also converted our dynamical equations into non-dimensional form. It has been observed from the numerical validation of the proposed model that the presence of the initial stress and inhomogeneity of both media affect significantly the phase velocity of torsional surface waves. The effect of initial stress, inhomogeneity parameters, depth ratio, sandy parameter, Biot׳s gravity parameter and porosity of the layer on the dimensionless phase velocity of the torsional surface waves are demonstrated graphically with respect to the non-dimensional wave number kH1 (where k is the wave number and H1 is the thickness of the second porous layer).
Propagation of Torsional surface waves in an inhomogeneous anisotropic fluid saturated porous layered half space under initial stress with varying properties
by Sushant Shekhar and Imtiyaz A Parvez
We study the behavior of torsional surface waves when they propagate through inhomogeneous fluid saturated porous layer over a homogeneous porous half space. The layer has three types of inhomogeneity, viz; linear, quadratic and exponential, varies with depth as rigidity, density and initial stress. We assume both media under compressive initial stresses and the analysis is based on the Biot’s theory. The effect of inhomogeneity of the layer in the propagation of torsional surface waves have been studied. The dispersion equations are derived for each case and solved by an iterative method (Newton–Raphson method). It is observed from the numerical calculation that the presence of initial stress and inhomogeneity of the medium affect significantly to the phase velocity of torsional surface waves. Also, propagation of torsional surface waves depend upon the medium in which they propagate as torsional surface waves propagate fastly in presence of elastic half space in comparison to porous half space.
Wave propagation across the imperfectly bonded interface between cracked elastic solid and porous solid saturated with two immiscible viscous fluids
by Sushant Shekhar and Imtiyaz A. Parvez
The present study is aimed at understanding the effect of a vertically aligned crack, present in the elastic half space on the propagation of attenuated waves. These waves are incident at a point on the interface between the porous half space and the cracked elastic half space. The analysis is based on Snell’s law for reflection and refraction of an incident wave at the interface. A loose bonding at the interface between the porous half space and the cracked elastic half space has been considered and represented here as the tangential slip. The proposed model is solved for the propagation of harmonic plane waves. The final equations are in the form of Christoffel equations from which we find four reflected waves (three longitudinal body waves and one transverse body wave) and two refracted waves (one longitudinal body wave and one transverse body wave). The expression of reflection–refraction coefficients and energy share of each reflected and refracted waves for a given incident wave is obtained in closed form and computed numerically in the present study. Numerical examples are considered for the partition of the incident energy in which we have studied the effect of aspect ratio, crack density and loose bonding parameter.
- Prediction of Indian rainfall during the summer monsoon season on the basis of links with equatorial Pacific and Indian Ocean climate indices
- Robust signals of future projections of Indian summer monsoon rainfall by IPCC AR5 climate models: Role of seasonal cycle and interannual variability
- Dichotomy in mode propagation of coseismic ionospheric disturbance: Observations from April 11, 2012 Indian Ocean earthquake
- Seismic hazard and risk assessment based on the unified scaling law for earthquakes
- Comparing statistically downscaled simulations of Indian monsoon at different spatial resolutions