Yury Y. Podladchikov

A new multilayered model for intraplate stress-induced differential subsidence of faulted lithosphere, applied to rifted basins

In-plane horizontal stresses acting on predeformed lithosphere induce differential flexural vertical motions. A high-precision record of these motions can be found in the sedimentary record of rifted basins. Originally, it was proposed that rifted basins experience flank uplift and basin center subsidence in response to a compressive change of in-plane stress, which agrees well with observed differential motions. Subsequently published models predicted that the vertical motions may be opposite because of the flexural state of the lithosphere induced by necking during extension. However, the total, flexural and permanent, geometry of the lithosphere underlying the rifted basin is the controlling parameter for the in-plane stress-caused vertical motions. The largest part of this preexisting geometry is caused by faulting in the uppermost brittle part of the crust and ductile deformation in the underlying parts of the lithosphere. We present a new multilayered model for stress-induced differential subsidence, taking into account the technically induced preexisting geometry of the lithosphere, including faults in the upper crust. As continental lithosphere may exhibit flexural decoupling due to a weak lower crustal layer, the new multilayer in-plane stress model discriminates the geometries of the separate competent layers. At a basin-wide scale, the new model predicts that a compressive change of in-plane force results in basin center subsidence and flank uplift, confirming the original hypothesis. Compared to all previous models, the new model requires a lower horizontal stress level change to explain observed differential vertical motions.

A rheological model of a fractured solid

Abstract Experiments to study the behavior of various materials point to the relation that exists between elastic properties and the type of stress. The influence of the state of stress on the elasticity of a fractured material will be discussed for a physically non-linear model of an elastic solid. The strain-dependent moduli model of material, presented in this paper, makes it possible to describe this feature of a solid. It also permits to simulate a dilatancy of rocks. A damage parameter, introduced into the model using a thermodynamical approach, allows to describe a rheological transition from the ductile regime to the brittle one, and to simulate the rocks memory, narrow fracture zone creation and strain rate localization. Additionally, the model enables the investigation of the final geometry of fracture zones, and also to simulate their creation process, taking into account pre-existing fracture zones. The process of narrow fracture zone creation and strain rate localization was simulated numerically for single axis compression and shear flow.

A Hydromechanical Model for Lower Crustal Fluid Flow

Metamorphic devolatilization generates fluids at, or near, lithostatic pressure. These fluids are ultimately expelled by compaction. It is doubtful that fluid generation and compaction operate on the same time scale at low metamorphic grade, even in rocks that are deforming by ductile mechanisms in response to tectonic stress. However, thermally-activated viscous compaction may dominate fluid flow patterns at moderate to high metamorphic grades. Compaction-driven fluid flow organizes into self-propagating domains of fluid-filled porosity that correspond to steady-state wave solutions of the governing equations. The effective rheology for compaction processes in heterogeneous rocks is dictated by the weakest lithology. Geological compaction literature invariably assumes linear viscous mechanisms; but lower crustal rocks may well be characterized by non-linear (power-law) viscous mechanisms. The steady-state solutions and scales derived here are general with respect to the dependence of the viscous rheology on effective pressure. These solutions are exploited to predict the geometry and properties of the waves as a function of rock rheology and the rate of metamorphic fluid production. In the viscous limit, wavelength is controlled by a hydrodynamic length scale δ, which varies inversely with temperature, and/or the rheological length scale for thermal activation of viscous deformation l A , which is on the order of a kilometer. At high temperature, such that δ < l A , waves are spherical. With falling temperature, as δ → l A , waves flatten to sill-like structures. If the fluid overpressures associated with viscous wave propagation reach the conditions for plastic failure, then compaction induces channelized fluid flow. The channeling is caused by vertically elongated porosity waves that nucleate with characteristic spacing δ. Because δ increases with falling temperature, this mechanism is amplified towards the surface. Porosity wave passage is associated with pressure anomalies that generate an oscillatory lateral component to the fluid flux that is comparable to the vertical component. As the vertical component may be orders of magnitude greater than time-averaged metamorphic fluxes, porosity waves are a potentially important agent for metasomatism. The time and spatial scales of these mechanisms depend on the initial state that is perturbed by the metamorphic process. Average fluxes place an upper limit on the spatial scale and a lower limit on the time scale, but the scales are otherwise unbounded. Thus, inversion of natural fluid flow patterns offers the greatest hope for constraining the compaction scales. Porosity waves are a self-localizing mechanism for deformation and fluid flow. In nature these mechanisms are superimposed on patterns induced by far-field stress and pre-existing heterogeneities.

Bubbles attenuate elastic waves at seismic frequencies: First experimental evidence

The migration of gases from deep to shallow reservoirs can cause damageable events. For instance, some gases can pollute the biosphere or trigger explosions and eruptions. Seismic tomography may be employed to map the accumulation of subsurface bubble-bearing fluids to help mitigating such hazards. Nevertheless, how gas bubbles modify seismic waves is still unclear. We show that saturated rocks strongly attenuate seismic waves when gas bubbles occupy part of the pore space. Laboratory measurements of elastic wave attenuation at frequencies <100 Hz are modeled with a dynamic gas dissolution theory demonstrating that the observed frequency-dependent attenuation is caused by wave-induced-gas-exsolution-dissolution (WIGED). This result is incorporated into a numerical model simulating the propagation of seismic waves in a subsurface domain containing CO2-gas bubbles. This simulation shows that WIGED can significantly modify the wavefield and illustrates how accounting for this physical mechanism can potentially improve the monitoring and surveying of gas bubble-bearing fluids in the subsurface.

Tectonic subsidence of the Lomonosov Ridge

The Cenozoic sedimentary record revealed by the Integrated Ocean Drilling Programs Arctic Coring Expedition (ACEX) to the Lomonosov Ridge microcontinent in 2004 is characterized by an unconformity attributed to the period 44–18 Ma. According to conventional thermal kinematic models, the microcontinent should have subsided to >1 km depth owing to rifting and subsequent separation from the Barents–Kara Sea margin at 56 Ma. We propose an alternative model incorporating a simple pressure-temperature ( P - T ) relation for mantle density. Using this model, we can explain the missing stratigraphic section by post-breakup uplift and erosion. The pattern of linear magnetic anomalies and the spreading geometry imply that the generation of oceanic crust in the central Eurasia Basin could have been restricted and confined by non-volcanic thinning of the mantle lithosphere at an early stage (ca. 56–40 Ma). In response to a rise in temperature, the mantle mineral composition may have changed through breakdown of spinel peridotite and formation of less dense plagioclase peridotite. The consequence of lithosphere heating and related mineral phase transitions would be post-breakup uplift followed by rapid subsidence to the deep-water environment observed on the Lomonosov Ridge today.

Coupling changes in densities and porosity to fluid pressure variations in reactive porous fluid flow: Local thermodynamic equilibrium

Mineralogical reactions which generate or consume fluids play a key role during fluid flow in porous media. Such reactions are linked to changes in density, porosity, permeability, and fluid pressure which influence fluid flow and rock deformation. To understand such a coupled system, equations were derived from mass conservation and local thermodynamic equilibrium. The presented mass conservative modeling approach describes the relationships among evolving fluid pressure, porosity, fluid and solid density, and devolatilization reactions in multicomponent systems with solid solutions. This first step serves as a framework for future models including aqueous speciation and transport. The complexity of univariant and multivariant reactions is treated by calculating lookup tables from thermodynamic equilibrium calculations. Simplified cases were also investigated to understand previously studied formulations. For nondeforming systems or systems divided into phases of constant density, the equations can be reduced to porosity wave equations with addition of a reactive term taking the volume change of reaction into account. For closed systems, an expression for the volume change of reaction and the associated pressure increase can be obtained. The key equations were solved numerically for the case of devolatilization of three different rock types that may enter a subduction zone. Reactions with positive Clapeyron slope lead to an increase in porosity and permeability with decreasing fluid pressure resulting in sharp fluid pressure gradients around a negative pressure anomaly. The opposite trend is obtained for reactions having a negative Clapeyron slope during which sharp fluid pressure gradients were only generated around a positive pressure anomaly. Coupling of reaction with elastic deformation induces a more efficient fluid flow for reactions with negative Clapeyron slope than for reactions with positive Clapeyron slope.

The effect of inplane force variations on a faulted elastic thin‐plate, Implications for rifted sedimentary basins

Studies of flexural motions of lithosphere commonly apply a differential equation based on the thin-plate approach. In this approximation, the flexural response to a changing horizontal inplane force depends only on the curvature of the midplane of the thin-plate representing the mechanical behaviour of the lithosphere. However, in cases where an abrupt change of the geometry of the lithosphere occurs the midplane of the thin-plate is offset. We demonstrate that the combination of the offset with an inplane horizontal force produces an additional, rheology independent moment at the position of the geometry change. This effect has been overlooked by previous studies of lithosphere deflections, and thin-plate problems in general. In the presented analysis, the thin-plate with an abrupt change in plate geometry represents lithopshere with a mechanically healed, inactive fault. However, the derived analytical solutions are general and can be used to study problems with similar abrupt geometry changes.

Thermodynamic equilibrium at heterogeneous pressure

Recent advances in metamorphic petrology point out the importance of grain-scale pressure variations in high-temperature metamorphic rocks. Pressure derived from chemical zonation using unconventional geobarometry based on equal chemical potentials fits mechanically feasible pressure variations. Here, a thermodynamic equilibrium method is presented that predicts chemical zoning as a result of pressure variations by Gibbs energy minimization. Equilibrium thermodynamic prediction of the chemical zoning in the case of pressure heterogeneity is done by constrained Gibbs minimization using linear programming techniques. In addition to constraining the system composition, a certain proportion of the system is constrained at a specified pressure. Input pressure variations need to be discretized, and each discrete pressure defines an additional constraint for the minimization. The Gibbs minimization method provides identical results to a geobarometry approach based on chemical potentials, thus validating the inferred pressure gradient. The thermodynamic consistency of the calculation is supported by the similar result obtained from two different approaches. In addition, the method can be used for multi-component, multi-phase systems of which several applications are given. A good fit to natural observations in multi-phase, multi-component systems demonstrates the possibility to explain phase assemblages and zoning by spatial pressure variations at equilibrium as an alternative to pressure variation in time due to disequilibrium.

Shear heating-induced strain localization across the scales

We investigate the dynamics of thermally activated shear localization in power law viscoelastic materials. A two-dimensional (2D) thermomechanical numerical model is applied that uses experimentally derived flow laws for rock. We consider viscous and viscoelastic rheologies and show that the numerical solutions for shear bands are mesh insensitive and energetically conservative. Deformation under long-term tectonic strain rates () yields to shear localization on the scale of kilometres. Although viscous and viscoelastic models exhibit comparable shear zone thickness, the timing of shear localization and stress magnitudes are affected by viscoelasticity. Large values of shear modulus ( Pa) promotes fast stress loading (within strain) and localization ( strain), whereas lower values ( Pa) delays localization ( strain) and reduces the maximum effective stress by a factor two. High stress exponents (up to ) focuses the deformation into narrow shear zones ( m) while maintaining a relatively high average stress level in the material outside the shear zone (stress drop of ). Conversely, Newtonian materials produce broad shear zones ( larger than for ) and exhibit a stronger thermal weakening (stress drops of ). Finally, we evaluate the thickness of shear zones for a wide range of strain rates (from to ) using both numerical models and an analytical scaling law. Our results suggest that thermally activated shear localization may occur from the scale of kilometre down to the nanometre.

Pore Fluid Extraction by Reactive Solitary Waves in 3‐D

In the lower crust, viscous compaction is known to produce solitary porosity and fluid pressure waves. Metamorphic (de)volatilization reactions can also induce porosity changes in response to the propagating fluid pressure anomalies. Here we present results from high-resolution simulations using Graphic Processing Unit parallel processing with a model that includes both viscous (de)compaction and reaction-induced porosity changes. Reactive porosity waves propagate in a manner similar to viscous porosity waves, but through a different mechanism involving fluid release and trap in the solid by reaction. These waves self-generate from red noise or an ellipsoidal porosity anomaly with the same characteristic size and abandon their source region to propagate at constant velocity. Two waves traveling at different velocities pass through each other in a soliton-like fashion. Reactive porosity waves thus provide an additional mechanism for fluid extraction at shallow depths with implications for ore formation, diagenesis, metamorphic veins formation, and fluid extraction from subduction zones.