A. Manglik

Rheology of Indian continental crust and upper mantle

A rheological model of the Indian shield has been constructed using the thermal structure derived from available surface heat flow and heat generation data and the flow properties of characteristic minerals and rocks like quartz, diabase and olivine which respectively represent the upper crust, lower crust and upper mantle. Lateral variations in the thicknesses of the brittle and ductile crust and of the brittle upper mantle have thus been obtained for different tectonic environments. Implications of these results to interpretation of the seismic structure of the Indian shield have been pointed out.

Identification of radiogenic heat source distribution in the crust: A variational approach

Radiogenic heat sources present in the continental crust contribute significantly to the total surface heat flow and temperature distribution in the crust. Various models for the depth distribution of radiogenic sources have been proposed. Among these models the exponential model has been shown to be an optimal, smooth model through the variational approach applied to the heat conduction equation. In the present work, a two-layered model of the crust is considered and heat transport by advection is included in the upper layer. The heat transport in the lower layer is by conduction only. Application of variational principle determines the nature of the radiogenic source distribution in both the layers. The results thus obtained indicate a radiogenic source distribution which is more complex than a simple exponential model.

Rheological thickness and strength of the Indian continental lithosphere

The estimates of rheological thickness and total lithospheric strength for the Indian continental lithosphere have been obtained based on the representative rheological properties of upper crust, lower crust and upper mantle, and some of the available heat flow and heat generation data. The rheological thickness, computed at different locations in the Indian shield, shows lateral variation ranging from 79km in the southern part to 65 km in the northern part for a strain rate of 10-14 s-1. The total strength of the continental lithosphere is of the order of 1013 Nm-1 for the same value of strain rate and decreases northward. The computations carried out for a range of strain rates show an increase in the rheological thickness and strength of the lithosphere with increasing strain rate. These results would be important in understanding the flexural response of the Indian continental lithosphere to surface and subsurface loading, and response to tectonic forces acting on it.

Shear wave velocity structure of the upper mantle under the NW Indian Ocean

Abstract Shear wave velocity structure of the NW Indian ocean is analysed by using fundamental mode Rayleigh wave dispersion data of 67 events occurred during 1990–98 at the central Indian Ridge and Carlsberg Ridge and recorded at Hyderabad Geoscope station (HYB). These events provide a dense coverage of the NW Indian ocean and Chagos-Laccadive Ridge (CLR) in the back-azimuthal range of 192–253° with respect to HYB. The dispersion curves, corrected for continental and young ocean paths, indicate large variations in the shear wave velocity structure of the region. The group velocities along the CLR path support a typical aseismic ridge-type structure. However, the central region bounded between the Central Indian Ridge and India in the back-azimuth of 206–234° indicates a decrease in the group velocity by 0.1 km/s. Inversion of these data sets indicates presence of aseismic-ridge type lithospheric structure for CLR, a thin lithosphere and high velocity block in the depth range of 125–200 km for the central region, and a continental-type lithospheric structure for the northern-most part of the Indian ocean. It is inferred that the dynamic state of the upper mantle in this region has been significantly perturbed during the recent geological past.

Rheological stratification of the Indian continental lithosphere : Role of diffusion creep

Dynamic recrystallization and reduction in grain-size at large strains, e.g. in shear zones, leads to rheological weakening of the lithosphere and facilitates intense ductile deformation. In the present work, we include this effect into the rheological models of the Indian continental lithosphere to analyse its role in modifying the rheological structure and strength of the Indian lithosphere. The results computed by using quartz and felspar rheologies for the upper and lower crust, respectively, and grain-size dependent olivine rheology for the upper mantle, indicate an increase in the ductility of the mantle lithosphere.

Intraplate stresses along a section of the Kavali-Udipi DSS profile in the south Indian shield induced by density heterogeneities and topography

Abstract Occurrence of intraplate seismicity has been attributed to several causes. The perturbation in the local stress regime, either due to local strength weakening of rock mass or surface and subsurface loading, is considered as a plausible mechanism of intraplate earthquake occurrences. The present work is aimed at analysing the state of stress in a part of south Indian shield induced by existing topography and undulations in the subsurface interfaces. The stresses are computed along a section of well studied Kavali-Udipi profile. The general nature of the stresses is compressive in the upper lithosphere except for a small region of extensional regime at both the ends of the profile. The magnitude of these stresses in comparison to the plate tectonic stresses shows that it also forms a significant component of the prevailing stresses in the region. The computed results also show a lateral variation in the stresses along the profile section. Thus, the role of stresses due to density heterogeneities and topography should be taken into consideration in explaining the microseismicity of the region.

Application of the Fourier method to the numerical solution of moving boundary problem in heat conduction

An algorithm for the solution of a nonlinear problem of phase boundary movement and evolution of temperature distribution due to the perturbation in the basal heat flux has been discussed. The reduction of the problem to a system of nonlinear ordinary differential equations with the help of a Fourier series method leads to a stiff system. This stiffness is taken care of by the use of a modified Euler’s method. Various cases of basal heat flow variation have been considered to show the performance and stability of the technique for such a nonlinear system. The first case of step-wise function is taken to analyse the performance of the technique, and the study has been extended to other general cases of linear increase, periodic variation, and box and triangular function type variations in the heat flux. In the step-wise case the phase boundary attains a constant position rapidly if the supplied heat flux is sufficiently large. The effect of periodicity in the heat flow is clearly depicted in the phase boundary movement, where the phase boundary oscillates about the mean position at large times. The absence of any constant level in the case of linear increase in heat flux is due to a very large value of heat flux. In the cases of box car and triangular heat flux the boundary starts moving downward after the cessation of excess heat flux but does not immediately return to its original preperturbation state, instead approaches it at large times. This technique may be applied to more general cases of heat flow variation.

A moving boundary solution for solidification of lava lake and magma intrusion in the presence of time-varying contact temperature

During the solidification of a lava lake heat is released convectively from the top surface as well as conductively into the country rock from the base, leading to non-uniform solidification. The upper solidified layer grows at a faster rate than the lower solidified layer. Similarly, solidification of magma intrusion within the crust is also non-uniform due to the presence of thermal gradient in the crust. Available analytical solution for solidification of a melt layer assumes only symmetric cooling about the centre of the layer. In the present work a moving boundary solution for thermal evolution and non-uniform solidification of a melt layer incorporating time-varying contact temperature conditions at both of its boundaries is developed. The solution is obtained by using the Fourier spectral approach in the space domain and a modified finite difference scheme in the time domain, and is validated with available analytical solutions for simple cases and a semi-analytical solution for the case involving temperature gradient in the country rock. This solution can be used to analyse solidification of lava lakes and magma intrusions experiencing time-dependent temperature variation at their contacts with the country rock.

Parameterized Mantle Convection Analysis for Crustal Processes

Thermal convection is considered as the main heat transport mechanism in the mantle that brings heat from earth’s interior to the base of the lithosphere. Many large-scale geological and tectonic processes such as initiation of plate tectonics and its persistence throughout the geological history, formation and stability of cratons, generation of komatiites in Archaean, etc. are controlled by heat. These processes and the presence of radioactive elements support the view that the early earth would have been at a much higher temperature compared to the present state indicating that the mantle convection would have been more vigorous during the early Archaean. Therefore, reconstruction of evolution of average mantle temperature and the geotherm of the convecting mantle through the geological history is important for the understanding of the geological processes. This chapter deals with simplified treatment of mantle convection, so called parameterized model of thermal convection. From the energy balance for the mantle, an equation for the average temperature is derived using Nusselt and Rayleigh number relationship and temperature dependent viscosity. Solution of this nonlinear equation, given evolution of core heat flux and decay of radioactive elements, yields the cooling history of average mantle temperature. Implications of the mantle cooling history on the generation of komatiites, initiation of plate tectonics and craton stability are discussed.