Internal Buoyancy Forces Research Articles

The Dynamics of the India‐Eurasia Collision: Faulted Viscous Continuum Models Constrained by High‐Resolution Sentinel‐1 InSAR and GNSS Velocities

AbstractThe distribution and magnitude of forces driving lithospheric deformation in the India‐Eurasia collision zone have been debated over many decades. Here we test a two‐dimensional (2‐D) Thin Viscous Shell approach that has been adapted to explicitly account for displacement on major faults and investigate the impact of lateral variations in depth‐averaged lithospheric strength. We present a suite of dynamic models to explain the key features from new high‐resolution Sentinel‐1 Interferometric Synthetic Aperture Radar as well as Global Navigation Satellite System velocities. Comparisons between calculated and geodetically observed velocity and strain rate fields indicate: (a) internal buoyancy forces from Gravitational Potential Energy acting on a relatively weak region of highest topography (>2,000 m) contribute to dilatation of the high plateau and contraction on the margins; (b) a weak central Tibetan Plateau (∼1021 Pa s compared to far‐field depth‐averaged effective viscosity of at least 1022–1023 Pa s) is required to explain the observed long‐wavelength eastward velocity variation; (c) localized displacement on fault systems enables strain concentration and clockwise rotation around the Eastern Himalayan Syntaxis. We discuss the tectonic implications for rheology of the lithosphere, distribution of geodetic strain, and partitioning of active faulting and seismicity.

Mantle structure and dynamics at the eastern boundary of the northern Cascadia backarc

The tectonics of southwestern Canada are dominated by the Cascadia subduction zone. The northern Cascadia backarc encompasses a > 400 km wide region of the Southern Canadian Cordillera. Geophysical observations, including seismic tomography and surface heat flow, show that the backarc is characterized by a hot, thin lithosphere (60–70 km). The eastern limit of the backarc approximately underlies the Rocky Mountain Trench, where there is an abrupt eastward increase in lithosphere thickness to the ∼250 km thick North American (Laurentian) Craton. Seismic tomography studies show that the transition in lithosphere thickness occurs over a horizontal distance of 50–100 km, resulting in a subvertical to west-dipping lithosphere step, with a dip angle of 75–90°. Using numerical models, we show that such a structure can be readily destabilised by internal buoyancy forces, edge-driven convection, and shearing by regional mantle flow. To maintain a subvertical step for > 50 Myr, the lowermost craton mantle lithosphere must be both dry and moderately chemically depleted. The observed westward dip may reflect partial lateral extrusion of the lowermost craton lithosphere, as well as shearing from west-directed mantle flow associated with the Cascadia subduction zone. The models also show that the backarc mantle must be relatively weak, such that vigorous convection maintains the hot, thin lithosphere. This also provides a mechanism to explain the observed lateral seismic gradient between the low-velocity backarc mantle and high-velocity craton. Our models demonstrate that the eastern limit of the Cascadia backarc is a region of active mantle flow, including possible slow deformation of the craton edge.

The adjoint equations for thermochemical compressible mantle convection: derivation and verification by twin experiments.

The adjoint method is an efficient way to obtain gradient information in a mantle convection model relative to past flow structure, allowing one to retrodict mantle flow from observations of the present-day mantle state. While adjoint equations for isochemical mantle flow have been derived for both incompressible and compressible flows, here we extend the method to thermochemical mantle flow models, and present thermochemical adjoint equations in the elastic-liquid approximation. We verify the method with twin experiments, and retrodict the flow history of a thermochemical reference model (reference twin) assuming for the final state, either a consistent thermochemical interpretation, using the thermochemical adjoint equations, or an inconsistent purely thermal interpretation, using the isochemical adjoint equations. The consistent simulation correctly retrodicts the flow evolution of the reference twin. The inconsistent case, instead, restores a false flow history whereby internal buoyancy forces and convectively maintained topography are overestimated. Because the cost function is reduced in either case, our results suggest that the adjoint method can be used to link assumptions on the role of chemical mantle heterogeneity to geologic inferences of dynamic topography, thus providing additional means to test hypotheses on mantle composition and dynamics.

Geodynamical models of lithospheric deformation, rotation and extension of the Pannonian Basin of Central Europe

The two major crustal blocks of the Pannonian basin, Alcapa (Alpine–Carpathian–Pannonian) and Tisza, underwent a complex process of rotation and extension of variable magnitude during the Tertiary. The northward push of the Adriatic Block initiated the eastward displacement and rotation of both the Alcapa and Tisza blocks. We have constructed geodynamical models of the rotation and extension of the two Pannonian blocks. We analyse this process in terms of the competing influences of a NE push by the Adriatic block, a NE pull from a retreating subduction zone on the eastern Carpathians, and the internal buoyancy forces arising from crustal thickness variations. Deformation of the blocks included substantial strike-slip movements, together with shortening and possible extension across the Mid-Hungarian Line, which now separates the two domains. We use an idealised thin viscous sheet model of the continental lithosphere in which deformation is described by a nonlinear viscous constitutive relationship. Our approach is based on the finite element method, and we consider several distinct models of initial geometry, boundary conditions, and constitutive parameters. Rotation and deformation vary across both blocks, with anticlockwise rotation occurring in the Alcapa plate, and clockwise rotation in the Tisza block. The opposite rotations of the two plates led to NW–SE convergence in the space between the two Intra-Carpathian terranes. Subsequently both domains underwent extension dominantly in the NE–SW direction. Extension and internal rotation can be represented using a thin sheet model in which deformation is driven by an east- or northeast-directed outward traction of order 1 to 3 MPa. Internal buoyancy forces produced by thick crust from a prior phase of Alpine-style convergence appear to be a necessary element in the force balance that drives the extension process.

The dynamics of western North America: stress magnitudes and the relative role of gravitational potential energy, plate interaction at the boundary and basal tractions

Summary We investigate the forces involved in driving long-term large-scale continental deformation in western North America, and quantify the vertically averaged deviatoric stress field arising from internal buoyancy forces and the accommodation of relative plate motions. In addition, we investigate the ability of regional models to resolve the level of tractions acting at the base of the lithosphere. We directly solve force-balance equations for vertically averaged deviatoric stresses associated with differences in values of 1/(lithospheric thickness) times the gravitational potential energy per unit area (GPE). The GPE values are inferred using both the ETOPO5 topographic data set and the CRUST2.0 crustal thickness model. Deviatoric stresses associated with basal tractions are calculated globally, with inputs determined from an isoviscous upper mantle (η = 1021 Pa s) 3-D large-scale convection model in which mantle density variations were inferred from tomographic data and the history of subduction. In a 211-parameter iterative inversion we then solve for a stress field boundary condition by fitting stress field indicators (i.e. the directions and relative magnitudes of the principal axes of kinematic strain rates). Magnitudes of the total vertically averaged deviatoric stress field (sum of GPE solution with the boundary condition solution) range from 5 to 10 MPa within a 100-km thick lithosphere. These magnitudes are calibrated by the GPE differences, along with the spatial variation in deformation style. There is a trade-off between the scaling of the basal traction deviatoric stress field and the boundary condition solution. However, the combined boundary conditions plus basal traction solution is robust (in both magnitude and style), and when added to the contribution from GPE differences provides a global minimum of misfit between the total deviatoric stress solution and the stress field indicators. GPE variations account for ∼50 per cent of the deviatoric stress magnitudes driving deformation, while boundary condition stresses account for the remaining ∼50 per cent of deviatoric stress magnitude. By comparing possible end-member strength profiles with our vertically averaged deviatoric stresses we infer that the bulk of the strength within the lithosphere in western North America lies within the brittle seismogenic layer.

Influence of past and present-day plate motions on spherical models of mantle convection: implications for mantle plumes and hotspots

SUMMARY We explore the influence of tectonic plate motions, given by the no-net-rotation (NNR)NUVEL-1 model, on a 3-D spherical model of mantle convection in which plates can be coupled to the underlying mantle flow in a dynamically consistent manner. We first derived a reference convection model in which only the NUVEL-1 geometry of the tectonic plates is prescribed. The plate rotations are then predicted on the basis of the buoyancy forces in the mantle, ensuring a dynamical balance of torques acting on the plates. This dynamically consistent reference convection model, which is based on a simple two-layer viscosity profile, yields the main features of plate tectonics: linear subduction zones, passive diverging zones and four mantle plumes. We next developed a time-dependent convection model, which is initiated with the average radial temperature field extracted from the reference convection model, and in which we imposed the NNR-NUVEL-1 plate velocities. This convection simulation yields six focused upwelling plumes, whose location and number is very similar to the primary terrestrial hotspots which have been recently identified (Courtillot et al. 2003). In all convection models incorporating the NNR-NUVEL-1 plate motions, we find that the surface heat flow and mantle potential temperature stay essentially constant, demonstrating the compatibility between the observed NNR-NUVEL-1 velocities and the internal buoyancy forces in the mantle. To determine the robustness of these results we carried out complementary convection simulations incorporating the past 120 Ma history of tectonic plate evolution. These simulations yielded shifting ‘hotlines’ at the core‐mantle boundary, but the locations of the overlying hotspot plumes remained relatively stable. The configuration of the hotlines in the convection experiments with and without evolving surface plate geometries are very similar to each other, showing that convection models with present-day plate configurations are sufficient for capturing the essential characteristics of the present-day thermal structure in the mantle. In a final experiment, the prescribed NNR-NUVEL-1 plate velocity constraint is released, allowing the plates to rotate freely in response to the underlying mantle flow. We find that the initial evolution of this model is characterized by a strong stability of the mantle thermal structures, in particular the upwelling plumes. An important and novel feature of the convection model with free plate motions is the predicted opening of the African plate along the East African Rift boundary, which occurs in response to the large-scale mantle flow and does not appear to require the presence of upwelling plumes directly beneath the rift.

Material versus local incompressibility and its influence on glacial-isostatic adjustment

SUMMARY We present an analytical form of the layer propagator matrix for the response of a locally incompressible, layered, linear-viscoelastic sphere to an external load assuming that the initial density stratification ϱ0(r) within each layer is parametrized by Darwin's law. From this, we show that the relaxation of a sphere consisting of locally incompressible layers is governed by a discrete set of viscous modes. The explicit dependence of the layer propagator matrix on the Laplace transform variable allows us to determine the amplitudes of the viscous modes analytically. Employing Darwin's parametrization, we construct three simplified earth models with different initial density gradients that are used to compare the effects of the local incompressibility constraint, div (ϱ0u)=0, and the material incompressibility constraint, div u=0, on viscoelastic relaxation. We show that a locally incompressible earth model relaxes faster than a materially incompressible model. This is a consequence of the fact that the perturbations of the initial density are zero during viscoelastic relaxation of a locally incompressible medium, so that there are no internal buoyancy forces associated with the continuous radial density gradients, only the buoyancy forces generated by internal density discontinuities. On the other hand, slowly decaying internal buoyancy forces in a materially incompressible earth model cause it to reach the hydrostatic equilibrium after a considerably longer time than a locally incompressible model. It is important to note that the approximation of local incompressibility provides a solution for a compressible earth model that is superior to the conventional solutions for a compressible earth with homogeneous layers because it is based on an initial state that is consistent with the assumption of compressibility.

Present-Day deformation across the basin and range province, western united states

The distribution of deformation within the Basin and Range province was determined from 1992, 1996, and 1998 surveys of a dense, 800-kilometer-aperture, Global Positioning System network. Internal deformation generally follows the pattern of Holocene fault distribution and is concentrated near the western extremity of the province, with lesser amounts focused near the eastern boundary. Little net deformation occurs across the central 500 kilometers of the network in western Utah and eastern Nevada. Concentration of deformation adjacent to the rigid Sierra Nevada block indicates that external plate-driving forces play an important role in driving deformation, modulating the extensional stress field generated by internal buoyancy forces that are due to lateral density gradients and topography near the province boundaries.

Deformation of subducted oceanic lithosphere

SUMMARY The deformation of subducted oceanic lithosphere is revealed by detailed studies of the distribution of seismicity in Benioff zones and by the increasingly well-resolved images of the upper mantle obtained by seismic P-wave tomography. By using numerical experiments based on a simplified dynamical model of a subducted lithospheric slab, we test the idea that the observed deformation of the subducted slab results from a balance between internal buoyancy forces and the viscous stresses associated with deformation. The simplified model assumes that the lithosphere has uniform physical properties, it is denser and much more viscous than the upper mantle, and its penetration below 670 km depth is resisted by a step-like density increase at that level. The primary determinant of the style of deformation is the buoyancy number, F, a ratio of buoyancy stress generated by the mass anomaly in the slab to the stress associated with viscous deformation at a strain rate U,/L, defined in terms of subduction rate U, and slab thickness L. For a small buoyancy number, deformation of the slab is dominated by viscous flexure. For large F, down-dip extension of the slab appears to dominate, and a buckling instability of the slab is observed if there is resistance to penetration of the 670 km level. The transition value of F at which this change in behaviour is observed is about 0.05 for constant viscosity, and about 0.2 for stressdependent viscosity with a stress versus strain-rate exponent of n = 3. With n = 3, a boudinage-type instability of the slab is observed for large F. Penetration of the slab below the 670 km level depends on the density contrast between slab and lower mantle. Resisted only by the density difference, the slab may initially penetrate several hundred kilometres below the 670 km level (for plausible density parameters) before a buckling instability causes this part of the slab to rotate and ascend. Comparison of the deforming slab geometry and stress field with seismicity distribution and tomographic images from the Tonga subduction zone suggests that the effective buoyancy number F for this slab is approximately equal to the transition value that we determined experimentally. We use this constraint to estimate average rheological parameters for the Tonga slab which, when compared with published creep deformation laws for olivine, are consistent with the average temperature of the slab being about 0.4 to 0.45 times the melting temperature, based on constitutive laws for olivine. At shallow depths (< 100 km) these temperatures correspond to around 590°C for wet olivine or around 700°C for dry olivine.

Effects of ventilation on the energy balance of a greenhouse with bare soil

Measurements of the radiation and energy balances in a polyethylene greenhouse covering a bare, dry sandy soil were used to determine the heat dissipation efficiency of four ventilation methods. The 62% of incident solar radiation transmitted by the roof provided the heat load on the system. The four ventilation treatments comprised passive ventilation obtained by rolling up opposite end walls, activating two fans mounted in one gable and opening the opposite wall, the same configuration but with a single fan, and completely closing the greenhouse. Opening opposite walls generated sufficient draught to exchange air at a rate of 44 volumes per hour. Operating one and two fans produced exchanges of 8 and 13 volumes per hour, respectively, much below the specified rating of the equipment, because of pressure losses across insect-proof nets on the vents. Closing the greenhouse limited the air exchange to three volumes per hour. For the climatic conditions of the experiment, external wind speed and internal buoyancy forces affected passive ventilation, but had no significant effects on fan ventilation. Despite the dryness of the top layer of soil, the latent heat flux remained a large term in the energy balance. High ventilation rates diminished soil heat flux, increased sensible heat flux and slightly reduced latent heat flux.

Mantle convection model with a dynamic plate: topography, heat flow and gravity anomalies

SUMMARY Surface observables have been calculated for a numerical convection model that includes a dynamic plate; that is, a stiff but mobile section of the upper boundary layer that is driven entirely by internal buoyancy forces. The results for heat flux and topography are virtually identical to those obtained from a partially kinematic model in which plate mobility results from an imposed horizontal velocity on the top surface. These results confirm the validity of the partially kinematic approach, which has been used previously. The partially kinematic approach is more efficient, computationally.

Geoid anomalies in a dynamic Earth

In order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces, we have calculated potential and surface deformation Love numbers for internal loading. These quantities depend on the depth and harmonic degree of loading. They can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Spherically symmetric, self‐gravitating flow models are constructed for a variety of radial Newtonian viscosity variations and flow configurations including both whole mantle and layered convection. We demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound, much less than the time scale for significant change in the convective flow pattern, by calculating relaxation times for a series of spherically symmetric viscous earth models. For uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads, resulting in net negative geoid anomalies for positive density contrasts. Geoid anomalies from intermediate‐wavelength density contrasts are amplified by up to an order of magnitude. Geoid anomalies are primarily the result of density contrasts in the interior of convecting layers; density contrasts near layer boundaries are almost completely compensated. Layered mantle convection results in smaller geoid anomalies than mantle‐wide flow for a given density contrast. Viscosity stratification leads to more complicated spectral signatures. Because of the sensitivity of the dynamic response functions to model parameters, forward models for the geoid can be used to combine several sources of geophysical data (e.g., subducted slab locations, seismic velocity anomalies, surface topography) to constrain better the structure and viscosity of the mantle.