Excitation of thermoconvective waves in the continental lithosphere

For flows associated with small strains, the rheology of rocks is described by the linear integral (having a memory) law, which reduces to the Andrade law in the case of constant stress. A continental lithosphere with such a rheology is overstable. Thermoconvective waves that propagate through the lithosphere with minimal attenuation have a period of about 200  Myr and a wavelength of the order of 400  km. An initial temperature point-concentrated perturbation in the lithosphere excites amplitude-modulated thermoconvective waves (wave packets). When the initial perturbation occurs in a finite area, thermoconvective waves propagate outwards from this area, and thermoconvective oscillations (standing waves) are established inside the area. Thermoconvective waves induce oscillations of the Earth' surface, accompanied by sedimentation and erosion, and can be considered as a mechanism for the distribution of sediments on continental cratons.     

Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus

Plates are an integral part of the convection system in the fluid mantle, but plate boundaries are the product of brittle faulting and plate motions are strongly influenced by the existence of such faults. The conditions for plate tectonics are studied by considering brittle behaviour, using Byerlee's law to limit the maximum stress in the lithosphere, in a mantle convection model with temperature-dependent viscosity.
When the yield stress is high, convection is confined below a thick, stagnant lithosphere. At low yield stress, brittle deformation mobilizes the lithosphere which becomes a part of the overall circulation; surface deformation occurs in localized regions close to upwellings and downwellings in the system. At intermediate levels of the yield stress, there is a cycling between these two states: thick lithosphere episodically mobilizes and collapses into the interior before reforming.
The mobile-lid regime resembles convection of a fluid with temperature-dependent viscosity and the boundary-layer scalings are found to be analogous. This regime has a well defined Nusselt number–Rayleigh number relationship which is in good agreement with scaling theory. The surface velocity is nearly independent of the yield stress, indicating that the 'plate' motion is resisted by viscous stresses in the mantle.
Analysis suggests that mobilization of the Earth's lithosphere can occur if the friction coefficient in the lithosphere is less than 0.03–0.13—lower than laboratory values but consistent with seismic field studies. On Venus, the friction coefficient may be high as a result of the dry conditions, and brittle mobilization of the lithosphere would then be episodic and catastrophic.     

Comment on: 'Can horizontal P waves be trapped and resonate in a shallow sedimentary basin?' by F. J. Sácnhez-Sesma and F. LuzÓ

We show that most of the arguments in the above paper are either incorrect or irrelevant to the point the authors are trying to make. We show that their results have no bearing on the model proposed by our group, as they claim. They discuss the seismic response of a valley with a 2-D trapezoidal cross-section in a vertical plane, whereas we dealt with a closed basin with a 2-D cross-section but of arbitrary geometry and in the horizontal plane. Even more significantly, the width of the valley they use is much smaller than the wavelength of the horizontal P waves that can resonate, thereby precluding any possibility of them being trapped. Therefore, their arguments do not clarify the issue posed in the title of their article.     

Reply to comment by J. L. Mateos, O. Novaro, T. H. Seligman and J. Flores on 'Can horizontal P waves be trapped and resonate in a shallow sedimentary basin?'

Using a complete mathematical formulation, we show that the trapping of horizontal P waves in a very soft shallow alluvial layer is a minor effect. These waves do not have a stable way of propagation since in order to exist they require an incident wave and are therefore incapable of resonating in the lateral direction when confined in a basin of limited extent.     

Current channelling and three-dimensional effects detected from magnetotelluric data from a sedimentary basin in Sierras Pampeanas, Argentina

Aquifer-bearing intermontane sedimentary basins of the Sierras Pampeanas in the northwest of Argentina are in general very deep and narrow and contain economically important deposits of Tertiary sediments. This paper presents the results of a study to characterize the sedimentary basin bounded to the west by Sierra de Famatina and to the east by Sierra de Velasco, where an electromagnetic sensing technique, the magnetotelluric (MT) method, was applied. 12 MT sites were deployed along a 30  km E–W transect. Some of the data collected were used to derive a 2-D resistivity model of the basin. The model shows a subsurface trough with a thick (approximately 8  km) sedimentary sequence above it. Anomalous behaviour of the E–W electric-field component ( E _y ) was detected in the period range 1–100  s, where the amplitude of this component was below the instrumental noise level. The cause of this anomaly is not known, but it might be due to the presence of an embedded conducting body between 8 and 10  km, which would give rise to N–S current channelling.     

Eigendecomposition of the two-point correlation tensor for optimal characterization of mantle convection

The two-point correlation tensor provides complete information on mantle convection accurate up to second-order statistics. Unfortunately, the two-point spatial correlation tensor is in general a data-intensive quantity. In the case of mantle convection, a simplified representation of the two-point spatial correlation tensor can be obtained by using spherical symmetry. The two-point correlation can be expressed in terms of a planar correlation tensor, which reduces the correlation's dependence to only three independent variables: the radial locations of the two points and their angular separation. The eigendecomposition of the planar correlation tensor provides a rational methodology for further representing the second-order statistics contained within the two-point correlation in a compact manner. As an illustration, results on the planar correlation are presented for the thermal anomaly obtained from the tomographic model of Su, Woodward & Dziewonski (1994 ) and the corresponding velocity field obtained from a simple constant-viscosity convection model Zhang & Christensen 1993 ). The first 10 most energetic eigensolutions of the planar correlation, which constitute an almost three orders of magnitude reduction in the data, capture the two-point correlation to 97 per cent accuracy. Furthermore, the energetic eigenfunctions efficiently characterize the thermal and flow structures of the mantle. The signature of the transition zone is clearly evident in the most energetic temperature eigenfunction, which clearly shows a reversal of thermal fluctuations at a depth of around 830  km. In addition, a local peak in the thermal fluctuations can be observed around a depth of 600  km. In contrast, due to the simplicity of the convection model employed, the velocity eigenfunctions exhibit a simple cellular structure that extends over the entire depth of the mantle and do not exhibit transition-zone signatures.