Yuri Y. Podladchikov

Diapiric ascent of magmas through power law crust and mantle

There has never been a convincing explanation of the way in which diapirs of molten granite can effectively rise through mantle and crust. We argue here that this is mainly because the country rocks have previously been assumed to be Newtonian, and we show that granitoid diapirs rising through thermally graded power law crust may indeed rise to shallow crustal levels while still molten. The ascent velocity of diapirs is calculated through an equation with the form of the Hadamard-Rybczynski equation for the rise of spheres through Newtonian ambient fluids. This well-known equation is corrected by factors dependent on the power law exponent n of the ambient fluid and the viscosity contrast between the drop and the ambient fluid. These correction factors were derived from results reported in the fluid mechanical and chemical engineering literature for the ascent of Newtonian drops through power law fluids. The equation allows calculation of the ascent rates of diapirs by direct application of rheological parameters of rocks. The velocity equation is numerically integrated for the ascent of diapirs through a lithosphere in which the temperature increases with depth. The depth of solidification of the diapir is systematically studied as a function of the geothermal gradient, buoyancy of the body, solidus temperature of the magma, and rheological parameters of the wall rock. The results show that when the wall rock behaves as a power law fluid, the diapirs ascent rate increases, without a similar increase in the rate of heat loss. In this way, diapirs rising at 10 to 102 m/yr can ascend into the middle or upper crust before solidification. Strain rate softening rather than thermal softening is the mechanism that allows diapirism to occur at such rates. The thermal energy of the diapir is used to soften the country rock only at late stages of ascent. The transport of magmas through the lower crust and mantle as diapirs is shown to be as effective as magmatic ascent through fractures.

Transition from passive to active rifting: Relative importance of asthenospheric doming and passive extension of the lithosphere

We present quantitative modeling results of the dynamic interplay of passive extension and active convective thinning of the mantle lithosphere beneath intracontinental rift zones investigating the relative importance of thermal buoyancy forces associated with asthenospheric doming and far-field intraplate stresses on the style of rifting. To this aim we employ a two-dimensional numerical code based on a finite element method formulation for nonlinear temperature dependent viscoelastoplastic rheology. Brittle behavior is modeled using Mohr-Coulomb plasticity. The models support a scenario in which passive stretching leads to an unstable lithospheric configuration. Thermal buoyancy related to this asthenospheric doming subsequently drives active upwelling in a lithosphere scale convection cell. In the late synrift to early postrift the lithospheric horizontal stresses caused by the active asthenospheric upwelling may start to compete with the far-field intraplate stresses. At this stage the domal forces may dominate and even drive the system causing a change from passive to active rifting mode. If this transition occurs, the model predicts (1) drastic increase of subcrustal thinning beneath the rift zone, (2) lower crustal flow towards the rift flanks, (3) middle crustal flow towards the rift center, (4) the coeval occurrence of tensional stresses within and compressive stresses around the upwelling region, and (5) possible surface uplift. Late postrift thermal cooling removes the thermal buoyancy forces. At this stage the far-field forces dominate the stress state again and the lithosphere becomes more sensitive to small changes in the intraplate stresses. The model results may explain several key observations that are characteristic of a large number of intracontinental rift basins. These features include differential thinning of extending lithosphere, the discrepancy between fault-related extension and crustal thinning, late (end of synrift to early postrift) mantle related volcanism, surface domal uplift succeeding rifting, and rift flanks uplift associated with extension of a weak lithosphere.

Hydrothermal vent complexes associated with sill intrusions in sedimentary basins

Abstract Subvolcanic intrusions in sedimentary basins cause strong thermal perturbations and frequently cause extensive hydrothermal activity. Hydrothermal vent complexes emanating from the tips of transgressive sills are observed in seismic profiles from the Northeast Atlantic margin, and geometrically similar complexes occur in the Stormberg Group within the Late Carboniferous-Middle Jurassic Karoo Basin in South Africa. Distinct features include inward-dipping sedimentary strata surrounding a central vent complex, comprising multiple sandstone dykes, pipes, and hydrothermal breccias. Theoretical arguments reveal that the extent of fluid-pressure build-up depends largely on a single dimensionless number (Ve) that reflects the relative rates of heat and fluid transport. For Ve >> 1, ‘explosive’ release of fluids from the area near the upper sill surface triggers hydrothermal venting shortly after sill emplacement. In the Karoo Basin, the formation of shallow (< 1 km) sandstone-hosted vents was initially associated with extensive brecciation, followed by emplacement of sandstone dykes and pipes in the central parts of the vent complexes. High fluid fluxes towards the surface were sustained by boiling of aqueous fluids near the sill. Both the sill bodies and the hydrothermal vent complexes represent major perturbations of the permeability structure of the sedimentary basin, and are likely to have long time-scale effects on its hydrogeological evolution.

Dynamic modeling of the transition from passive to active rifting, application to the Pannonian Basin

We examine a number of first-order features of Pannonian basin evolution in terms of the feedback relation between passive far-field-induced extension and active Raleigh Taylor instable upwelling of the astheno- sphere. We show that active mantle upwelling following a phase of passive extension are viable mechanisms ex- plaining the Pannonian basin formation. The dynamic interplay between far-field-driven passive extension and active thinning of the mantle lithosphere by convective upwelling beneath the rift zone is modeled using ther- momechanical finite element methods. Our modeling results predict a first phase of passive lithospheric thin- ning which is followed by a second phase of late synrift to postrift active mantle lithosphere thinning due to buoyancy-induced flow beneath the rift zone. We argue that the pattern of coeval extension in the thinning re- gion and compression in the flanking regions may be explained by the buoyancy forces due to lithosphere thinning. It is demonstrated that timescales of and stresses generated by both processes are comparable. The model appears also to explain the occurrence of late shallow mantle-related decompression melts in the Pannonian region and late regional doming.

FRACTAL PLASTIC SHEAR BANDS

We present a numerical study model of shear bands in rocks with a non-associated plastic flow rule. The system drives spontaneously into a state in which the length distribution of shear bands follows a power law and where the spatial organization of the shear bands appears to be fractal. The distribution of local gradients in deviatoric strain rate has different scaling exponents for each moment which we calculate and discuss. Samples of granodiorite from the Pyrenees sheared under high confining pressure are analyzed and their properties compared with the numerical results.

Spontaneous Thermal Runaway as an Ultimate Failure Mechanism of Materials

The first theoretical estimate of the shear strength of a perfect crystal was given by Frenkel [Z. Phys. 37, 572 (1926)10.1007/BF01397292]. By assuming that two rigid atomic rows in the crystal would move over each other along a slip plane, he derived the ultimate shear strength to be about one-tenth of the shear modulus. Here we present a theoretical study showing that catastrophic failure of viscoelastic materials may occur below Frenkels ultimate limit as a result of thermal runaway. The thermal runaway failure mechanism exhibits progressive localization of the strain and temperature profiles in space, thereby producing a narrow region of highly deformed material, i.e., a shear band. We calculate the maximum shear strength sigma_{c} of materials and then demonstrate the relevance of this new concept for material failure known to occur at scales ranging from nanometers to kilometers.

Low-frequency reflections from a thin layer with high attenuation caused by interlayer flow

The 1D interlayer-flow (or White’s) model is based on Biot’s theory of poroelasticity and explains low-frequency seismic wave attenuation in partially saturated rocks by wave-induced fluid flow between two alternating poroelastic layers, each saturated with a different fluid. We have developed approximate equations for both the minimum possible value of the quality factor, Q , and the corresponding fluid saturation for which Q is minimal. The simple approximate equations provide a better insight into the dependence of Q on basic petrophysical parameters and allow for a fast assessment of the minimal value of Q . The approximation is valid for a wide range of realistic petrophysical parameter values for sandstones partially saturated with gas and water, and shows that values of Q can be as small as two. We ap-plied the interlayer-flow model to study the reflection coefficient of a thin (i.e., between 6 and 11 times smaller than the incident wavelength) layer that is partially saturated with gas and water. ...

Finite amplitude folding: transition from exponential to layer length controlled growth

Abstract A new finite amplitude theory of folding has been developed by the combined application of analytical, asymptotic and numerical methods. The existing linear folding theory has been improved by considering nonlinear weakening of membrane stresses, which is caused by the stretching of the competent layer during folding. The resulting theory is simple and accurate for finite amplitude folding and is not restricted to infinitesimal amplitudes, as is the classical linear theory of folding. Two folding modes relevant to most natural settings were considered: (i) both membrane and fiber stresses are viscous during folding (the ‘viscous’ mode); (ii) membrane stresses are viscous whereas fiber stresses are elastic (the ‘viscoelastic’ mode). For these two modes, the new theory provided a nonlinear, ordinary differential equation for fold amplification during shortening and an estimate for crossover amplitude and strain where the linear theory breaks down. A new analytical relationship for amplitude versus strain was derived for strains much larger than the crossover strain. The new relationship agrees well with complete 2D numerical solutions for up to threefold shortening, whereas the exponential solution predicted by the linear theory is inaccurate by orders of magnitude for strains larger than the crossover value. Analysis of the crossover strain and amplitude as a function of the controlling parameters demonstrates that the linear theory is only applicable for a small range of amplitudes and strains. This renders unreliable the large strain prediction of wavelength selection based on the linear theory, especially for folding at high competence contrasts. To resolve this problem, the new finite amplitude theory is used to calculate the evolution of the growth rate spectra during progressive folding. The growth rate spectra exhibited splitting of a single maximum (predicted by the linear theory) into two maxima at large strains. This bifurcation occurred for both deformation modes. In contrast, the spectra of the cumulative amplification ratio (current over initial amplitude) maintained a single maximum value throughout. The wavelength selectivity is found to decrease at large strains, which helps explain the aperiodic forms of folds commonly observed in nature and the absence of long dominant wavelengths for high competence contrast folding. Calculation of the cumulative amplification spectra for different initial amplitude distributions, ranging from white to red noise, showed that the initial noise has a strong influence on the amplitude spectra for small strains. For larger strains, however, the cumulative amplification spectra were similar despite the strong difference in the initial noise.

Dome structures in collision orogens: Mechanical investigation of the gravity/compression interplay

Domes and basins are evidence for vertical movements in both compression and extension tectonic environments. They are thus evidence for interplay between gravity and tectonic forces in structuring the continental crust. We employ analytical and numerical techniques to investigate the respective roles of gravity and compression during the growth of crustal-scale buckle anticlines and diapirs submitted to instantaneous erosion. The analytical perturbation method, which explores the onset of both types of instability, yields a “phase-diagram” discriminating eight folding-diapirism modes, fi ve of which are geologically relevant. Numerical simulations show that the phase diagram is applicable to evolved, fi nite amplitude stages. Calculated strain fi elds in both diapirs and folds show normal sense of shear at the interface if the upper layer is thick compared to the lower layer. We conclude that the present-day structural techniques applied for distinguishing diapiric domes and folds are ambiguous if detachment folding and intense erosion take place during deformation, and that domes displaying extensional structures do not necessarily refl ect extension.

Stress release in exhumed intermediate and deep earthquakes determined from ultramafic pseudotachylyte

Stresses released by coseismic faults during subduction toward lawsonite-eclogite facies conditions in the Alpine subduction complex of Corsica can be estimated based on the energy required to form pseudotachylyte fault veins where shear strain can be measured. Congruent peridotite melting at ambient conditions of 1.5 GPa and 470 °C requires a temperature increase of 1280 °C to 1750 °C. We assume that more than 95% of the work is converted to heat during faulting, hence that the stress drop is nearly proportional to the amount of melting and inversely proportional to shear strain. Minimum estimates of released stress are typically greater than 220 MPa and as high as 580 MPa. The abundance of pseudotachylyte on small faults in the studied peridotite suggests that melting is very common on intermediate and deep earthquakes and that shear heating is important for seismic faulting at depth.