Elastic Lid Research Articles

Crustal rheology of southern Tibet constrained from lake-induced viscoelastic deformation

We probe the rheology of the Tibetan lithosphere using the rebound that accompanied climate-driven lake level variations. At the modern decadal time scale, we used deformation around Siling Tso measured from InSAR. At the millennial time scale, we use Holocene paleoshorelines around Siling Tso and Zhari Nam Tso. We use chronological constraints from the literature and Digital Elevation Models to constrain their ages and geometry. We observe a small post-highstand subsidence of the area near the center of mass of the paleolake-load and a low-amplitude short-wavelength outer bulge. In the context of a model consisting of an elastic lid over a viscous channel with a rigid base, these observations preclude the existence of a thick low viscosity channel and require a thin elastic lid. Based on Monte Carlo inversion, we constrain the range of possible equivalent elastic thickness of the lid (<5 km), the viscosity (2×1018–1020 Pa.s) and thickness of the crustal channel (<10–20 km). By contrast, the modern data requires a stiffer lid with equivalent elastic thickness >20 km and a >20 km thick channel with lower crustal viscosity (<5×1018 Pa.s). The different rheologies inferred at these different time-scales could be explained by a Burgers body rheology of the middle and lower crust, with a short-term viscosity of 1018 Pa.s and long-term viscosity of 1020 Pa.s, or even better by vertical variations of viscosity. To illustrate the latter claim, we show that the observations at the decadal and Holocene time scales can be reconciled by assuming a low viscosity zone (1018 Pa.s) at mid-crustal depth (between ∼10 and 30 km depth) embedded in a higher viscosity crust (>1020 Pa.s). In both cases, the interferences in space of the deformation signals induced by the lakes geometry, and in time through the viscoelastic response to the lake level variations results in limited distortion of the paleo-shorelines. While the elastic lid in the upper crust needs in any case to be thin (<10 km), the low amplitude distortion requires significant viscoelastic support from the lower crust and upper mantle; this explains the relatively high effective elastic thickness (>20 km) inferred in some previous studies of Holocene paleoshorelines. In the longer term, the effective elastic thickness of the lithosphere must drop asymptotically to the value of the elastic lid in the upper crust (<10 km); this explains the low effective elastic thickness derived from gravity studies.

On the frequency spectrum of free vibrations of membranes and plates in contact with a fluid

A parallelepiped-shaped container, which is completely filled with a perfect incompressible fluid, is considered. The container is covered with an elastic lid, which is modeled by a membrane or a constant-thickness plate. The other faces of the container are nondeformable. The frequency spectrum of small free vibrations of the lid has been obtained taking into account the apparent mass of the fluid the movement of which is assumed to be potential. The main specific feature of the problem formulation is that the volume of the fluid under the cover remains unchanged in the course of vibrations. As a result, the shape of the deflection of the lid should satisfy the equation of constraint, which follows from the condition of preservation of the volume of the fluid under the lid.

Postseismic relaxation in Kashmir and lateral variations in crustal architecture and materials

AbstractThirty horizontal displacement time series from GPS sites in the area around the 2005 Kashmir earthquake show lateral spatial variations in displacement magnitude and relaxation time for the postseismic interval from 2005 to 2012. The observed spatial pattern of surface displacements can only be reproduced by finite element models of postseismic deformation in elastic over viscoelastic crust that include lateral differences in both the thickness of the elastic layer and the viscosity of the viscoelastic layer. Solutions reproducing the sign of horizontal displacements everywhere in the epicentral region also require afterslip on the portion of the fault dislocation in the viscoelastic layer but not in the elastic lid. Although there are substantial tradeoffs among contributions to postseismic displacements of the surface, the observations preclude both crustal homogeneity and shallow afterslip. In the best family of solutions, the thickness of the elastic upper crust differs by a factor of 5 and the viscosity of the middle and lower crust by an order of magnitude between domains north and south of a suture zone containing the Main Boundary Thrust and Main Mantle Thrust.

Weak ductile shear zone beneath a major strike‐slip fault: Inferences from earthquake cycle model constrained by geodetic observations of the western North Anatolian Fault Zone

AbstractGPS data before and after the 1999 İzmit/Düzce earthquakes on the North Anatolian Fault Zone (Turkey) reveal a preseismic strain localization within about 25 km of the fault and a rapid postseismic transient. Using 3‐D finite element calculations of the earthquake cycle in an idealized model of the crust, comprising elastic above Maxwell viscoelastic layers, we show that spatially varying viscosity in the crust can explain these observations. Depth‐dependent viscosity without lateral variations can reproduce some of the observations but cannot explain the proximity to the fault of maximum postseismic velocities. A localized weak zone beneath the faulted elastic lid satisfactorily explains the observations if the weak zone extends down to midcrustal depths, and the ratio of relaxation time to earthquake repeat time ranges from ~0.005 to ~0.01 (for weak‐zone widths of ~24 and 40 km, respectively) in the weakened domain and greater than ~1.0 elsewhere, corresponding to viscosities of ~1018 ± 0.3 Pa s and greater than ~1020 Pa s. Models with sharp weak‐zone boundaries fit the data better than those with a smooth viscosity increase away from the fault, implying that the weak zone may be bounded by a relatively abrupt change in material properties. Such a change might result from lithological contrast, grain size reduction, fabric development, or water content, in addition to any effects from shear heating. Our models also imply that viscosities inferred from postseismic studies primarily reflect the rheology of the weak zone and should not be used to infer the mechanical properties of normal crust.

Fluid-Solid Interaction of Incompressible Media Using h, p, k Mathematical and Computational Framework

This paper considers multi-media interaction processes in which the interacting media are incompressible elastic solids and incompressible liquids such as Newtonian fluids, generalized Newtonian fluids, dilute polymeric liquids described by Maxwell, and Oldroyd-B models or dense polymeric liquids with Giesekus constitutive model. The mathematical models for both solids and liquids are developed using conservation laws in Eulerian description for isothermal conditions with velocities, pressure, and deviatoric stresses as dependent variables. The constitutive equations for the solids and the liquids provide closure to the governing differential equations resulting from the conservation laws. For Newtonian and generalized Newtonian fluids, the commonly used constitutive equations are well known in terms of first convected derivative of the strain tensor, stress tensor, and the transport properties of the fluids. For dilute and dense polymeric liquids that are viscous as well as elastic, the mathematical models have been derived and used using a number of different choices of stress variables. All such choices eventually result in a system of coupled nonlinear partial differential equations in terms of chosen stresses, convected derivative of the stress and strain tensors, and the transport properties. An appropriate choice of stress variables is crucial for transparent interaction of such fluids with other fluids and solids. The choice of velocities as dependent variables necessitates rate constitutive equations for solids [1] that are utilized in the present work. A novel feature of the mathematical models presented here is that a single mathematical model describes physics of all media of an interaction process, thereby the media interactions are inherent in the mathematical model and thus do not require constraint equations at the interfaces between the interacting media as in the case of currently used methodologies. These mathematical models result in a system of nonlinear partial differential equations in space coordinates and time, i.e. initial value problems (IVPs) that are solved numerically using the space-time finite element method in h, p, k mathematical and computational framework with space-time variationally consistent (STVC) space-time integral forms. This computational methodology permits higher order global differentiability approximations for all variables in space as well as time, and ensures time-accurate evolutions as well as results in unconditionally stable computations during the entire evolution. 1D and 2D numerical examples of interaction processes are presented using elastic solids, Newtonian fluid, dilute polymeric liquid (Maxwell fluid and Oldroyd-B fluid), and polymer melts (Giesekus fluid). Model problems consist of 1D wave propagations, 2D elastic lid driven cavity, and flow between parallel plates with rigid as well as elastic boundaries.

Structures of Helicobacter pylori Shikimate Kinase Reveal a Selective Inhibitor-Induced-Fit Mechanism

Shikimate kinase (SK), which catalyzes the specific phosphorylation of the 3-hydroxyl group of shikimic acid in the presence of ATP, is the enzyme in the fifth step of the shikimate pathway for biosynthesis of aromatic amino acids. This pathway is present in bacteria, fungi, and plants but absent in mammals and therefore represents an attractive target pathway for the development of new antimicrobial agents, herbicides, and antiparasitic agents. Here we investigated the detailed structure–activity relationship of SK from Helicobacter pylori (HpSK). Site-directed mutagenesis and isothermal titration calorimetry studies revealed critical conserved residues (D33, F48, R57, R116, and R132) that interact with shikimate and are therefore involved in catalysis. Crystal structures of HpSK·SO4, R57A, and HpSK•shikimate-3-phosphate•ADP show a characteristic three-layer architecture and a conformationally elastic region consisting of F48, R57, R116, and R132, occupied by shikimate. The structure of the inhibitor complex, E114A•162535, was also determined, which revealed a dramatic shift in the elastic LID region and resulted in conformational locking into a distinctive form. These results reveal considerable insight into the active-site chemistry of SKs and a selective inhibitor-induced-fit mechanism.

Temporal Gravity Variations near Shrinking Vatnajökull Ice Cap, Iceland

Repeated gravity measurements were carried out from 1991 until 1999 at sites SE of Vatnajokull, Iceland, to estimate the mass flow and deformation accompanying the shrinking of the ice cap. Published GPS data show an uplift of about 13 ± 5 mm/a near the ice margin. A gravity decrease of –2 ± 1 μGal/a relative to the Hofn base station, was observed for the same sites. Control measurements at the Hofn station showed a gravity decrease of –2 ± 0.5 µGal/a relative to the station RVIK 5473 at Reykjavik (about 250 km from Hofn). This is compatible, as a Bouguer effect, with a 10 ± 3 mm/a uplift rate of the IGS point at Hofn and an uplift rate of ~20 mm/a near the ice margin. Although the derived gravity change rates at individual sites have large uncertainties, the ensemble of the rates varies systematically and significantly with distance from the ice. The relationship between gravity and elevation changes and the shrinking ice mass is modelled as response to the loading history. The GPS data can be explained by 1-D modelling (i.e., an earth model with a 15-km thick elastic lithosphere and a 7·1017 Pa·s asthenosphere viscosity), but not the gravity data. Based on 2-D modelling, the gravity data favour a low-viscosity plume in the form of a cylinder of 80 km radius and 1017 to 1018 Pa·s viscosity below a 6 km-thick elastic lid, embedded in a layered PREM-type earth, although the elevation data are less well explained by this model. Strain-porosity-hydrology effects are likely to enhance the magnitude of the gravity changes, but need verification by drilling. More accurate data may resolve the discrepancies or suggest improved models.

Topography and geoid anomalies due to density heterogeneities at the base of the thermal lithosphere: application to oceanic swells and small-wavelength geoid lineations

SUMMARY The surface topography, gravity and geoid associated with loads situated at the base of the thermal lithosphere are computed. The model lithosphere is composed of a viscous lower layer with depth-dependent viscosity overlain by an elastic lid. When the viscosity varies strongly with depth, the amplitude of the surface topography decreases rapidly as the wavenumber characterizing the mass anomaly increases. The response for this two-layer lithosphere differs substantially from the response computed for the loading from below of an elastic lid. If the 200km wavelength geoid anomalies observed in the oceans are due to convective instabilities at the base of the lithosphere, a positive geoid anomaly with an amplitude reaching 30 to 50cm is expected over a cold downwelling for ages greater than 10 Myr. No detectable topography associated with the lineations should be present for ages greater than 20 Myr. Our model predicts that some topographic anomalies might be visible for younger ages. If 1000 km broad swells are due to light material at a depth of about 100 km, the associated geoid-over-topography ratios are quite reduced compared to those predicted by the long-wavelength linear relationship usually employed for estimating the apparent compensation depth.

Post-seismic motion following the 1997 Manyi (Tibet) earthquake: InSAR observations and modelling

SUMMARY On November 8 1997 a Mw 7.6 earthquake occurred in the Manyi region of northern Tibet, near the western end of the Kunlun Fault. Over 7 m of left-lateral slip occurred on a 200-kmlong fault. Here we use InSAR observations of post-seismic surface deformation following the Manyi earthquake to investigate possible causal mechanisms. Time-series of deformation are constructed from 26 interferograms, covering the entire length of the fault for nearly 4 yr after the earthquake. Three different modelling approaches are used to try and understand the observed variations in surface displacement. First order poroelastic models predict displacement fields which do not match those observed. Modelling of viscoelastic stress relaxation in a half-space with standard linear solid rheology beneath an elastic lid provides a reasonable fit to the observations, and demonstrates that two relaxation times are needed to characterize the post-seismic transient. The best-fitting viscosity is 4 £ 10 18 Pa s, and the fully-relaxed shear modulus is 32 per cent of the purely elastic value. A model with a Maxwell viscoelastic halfspace underlying the lid cannot explain the observations: at later times, larger viscosities are required than at earlier times. This increase in effective viscosity with time may be consistent with stress relaxation occurring in a power-law rheology. The time-series are also inverted for distributed afterslip on an extension of the coseismic rupture. Along-strike correlation of coseismic and post-seismic slip maxima suggests that afterslip is a plausible mechanism. The maximum slip in the afterslip model is 0.72 m after 3 yr, and the equivalent moment release is approximately 20 per cent of the coseismic moment. This study shows that it is possible to rule out certain mechanisms as the dominant post-seismic process, but with the current InSAR data set it is difficult to distinguish between other plausible options.

Au-quartz mineralization near the base of the continental seismogenic zone

Abstract The base of the continental seismogenic zone is defined within individual fault zones by the transition with depth from pressure-sensitive factional (FR) faulting to temperature-sensitive quasi-plastic (QP) ductile shearing. The depth of this FR-QP transition fluctuates principally as a consequence of variations in geothermal gradient and crustal lithology but other factors (e.g. fluid pressure level, strain rate) also play a role. For quartz-dominant and feldspar-dominant lithologies, respectively, it corresponds approximately to isotherms at 300–350°C and c. 450 °C., defining an undulating transition zone in the mid-crust with a relief of the order of 5–10 km. This transition zone correlates with the greenschist-facies metamorphic environment where the bulk of mesozonal Au-quartz lodes form in mixed continuous-discontinuous shear zones. In areas of crustal convergence and thickening, where fluid release results from prograde metamorphic dehydration, especially at the greenschistamphibolite-facies transition in the middle to deep crust, the seismogenic carapace acts as an upper crustal stress guide and low-permeability lid to overpressured metamorphic fluids migrating through shear zone conduits. Under appropriate combinations of stress and fault architecture in the brittle carapace, substantial fluid volumes may be trapped beneath this elastic lid at sufficient overpressure to generate dilatant fault-fracture meshes discharging episodically by fault-valve action following fault rupture, with permeability locally enhanced by aftershock activity distributed about the rupture zones. Topographic irregularities in the seismic-aseismic transition determine rupture nucleation sites and probably play a critical role in focusing the discharge of overpressured metamorphic fluids into the seismogenic layer. This helps to account for the observed spacing of mesozonal lode systems along transcrustal shear zones.

Centrifugo-magnetic pump for gas-to-liquid sampling

This paper describes a novel gas micropump realized on a centrifugal microfluidic platform. The pump is integrated on a passive and microstructured polymer disk which is sealed by an elastomer lid featuring paramagnetic inlays. The rotational motion of this hybrid over a stationary magnet induces a designated sequence of volume displacements of the elastic lid, leading to a net transport of gas. The pumping pressure was determined as a function of the frequency of rotation, with a maximum observable pressure of 4.1 kPa without further optimization. The first application of this rotary device is the production of gas–liquid flows by pumping ambient air into a continuous centrifugal flow of liquid. The injected gas volume segments the liquid stream into a series of liquid compartments. Apart from such multi-phase flows, the new pumping technique supplements a generic air-to-liquid sampling method to centrifugal microfluidic platforms.

Distributed Nubia-Somalia relative motion and dike intrusion in the Main Ethiopian Rift

SUMMARY The Main Ethiopian Rift (MER) in central Ethiopia extended in the rift-normal direction at a mean rate of 4.0 ± 0.9 mm yr −1 (1σ ) during the period 1992‐2003, nearly a factor of two slower than the opening rate estimated from global plate motion inversions. Rift opening near a geodetic array during this period was accommodated by a single dike injection event in 1993, spatially coincident with active magmatic segments, probably triggered by observed seismicity. Following dike injection, the crust in the rift relaxed as a layered medium, with a ∼15-km-thick elastic lid over a viscous half space of 10 18 Pa s. Diking, rather than normal faulting on rift-bounding faults, appears to be the predominant mechanism of extension in the MER, explaining the very low regional rates of moment release. The length scale and temporal behaviour of surface displacements require viscoelastic rheology in the rift.

Controls on maximum fluid overpressure defining conditions for mesozonal mineralisation

The mesozonal environment for mineralisation (∼10±5 km depth) occurs towards the base of the seismogenic zone in the upper continental crust which, in areas of strong fluid release, acts as a stressed elastic lid containing overpressured hydrothermal fluids derived from metamorphic dehydration at depth. Au–quartz lodes in this environment are hosted by fault–fracture meshes comprising dilatant extensional and extensional-shear fractures interlinked by low-displacement faults. They form in a range of tectonic regimes but are most extensively developed in compressional/transpressional settings. A brittle failure mode plot contrasting compressional and extensional stress regimes demonstrates that: (i) high fluid overpressures are easier to sustain in compressional regimes that also allow the highest amplitude fluid-pressure cycling; (ii) dilatant mesh structures serve as high-permeability conduits only under high fluid-pressure and low differential stress in the absence of through-going cohesionless faults that are well-oriented for reactivation; and, (iii) the critical interdependence of differential stress and sustainable overpressure ensures that changes in stress state are accompanied by fluid redistribution. The specialised circumstances allowing high-flux flow of overpressured fluids are generally short-lived and are terminated by the formation of through-going, favourably oriented faults.

A mechanism for tectonic deformation on Venus

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface‐density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.

Shortening of continental lithosphere: the neotectonics of Eastern Anatolia — a young collision zone

Summary We use the tectonics of Eastern Anatolia to exemplify many of the different aspects of collision tectonics, namely the formation of plateaux, thrust belts, foreland flexures, widespread foreland/hinterland deformation zones and orogenic collapse/distension zones. Eastern Anatolia is a 2 km high plateau bounded to the S by the southward-verging Bitlis Thrust Zone and to the N by the Pontide/Minor Caucasus Zone. It has developed as the surface expression of a zone of progressively thickening crust beginning about 12 Ma in the medial Miocene and has resulted from the squeezing and shortening of Eastern Anatolia between the Arabian and European Plates following the Serravallian demise of the last oceanic or quasioceanic tract between Arabia and Eurasia. Thickening of the crust to about 52 km has been accompanied by major strike-slip faulting on the right-lateral N Anatolian Transform Fault (NATF) and the left-lateral E Anatolian Transform Fault (EATF) which approximately bound an Anatolian Wedge that is being driven westwards to override the oceanic lithosphere of the Mediterranean along subduction zones from Cephalonia to Crete, and Rhodes to Cyprus. This neotectonic regime began about 12 Ma in Late Serravallian times with uplift from wide-spread littoral/neritic marine conditions to open seasonal wooded savanna with colluvial, fluvial and limnic environments, and the deposition of the thick Tortonian Kythrean Flysch in the Eastern Mediterranean. Earthquake hypocentres are scattered throughout the region but large earthquakes are concentrated mainly on the major faults and are mostly shallow, supporting the idea of a brittle elastic lid with hypocentres concentrated towards its base with more ductile deformation in the middle and lower crust. Neotectonic magmatic suites are nepheline-hypersthene normative alkali basalts of mantle origin, and silicic/intermediate/mafic calcalkaline suites, both suites occurring in pull-apart basins in strike-slip regimes and along N-S extensional fissures, and both suites showing a strong change to central activity in the Pliocene. Upper-crustal strains appear to be discontinuous in space and time, with zones of strong shortening representing shoaling of crustal detachment zones flattening between 5 and 10 km. Approximately NW- (dextral) and NE- (sinistral) trending lineaments bound less deformed wedges (low relief seismically ‘dead’ areas) and vary from simple strike-slip faults to complicated braided transform-flake boundaries with pull-apart and compressional segments (N and E Anatolian Transform Faults). Volcanoes lie in grabens on N-S ‘cracks’ that extend into the Arabian Foreland and in transcurrent pull-aparts. Major extensional basins lie at plate (Adana) and flake (Karliova) triple junctions and result from compatibility problems.

Plate tectonics and the evolution of the British Isles

This paper is an essay on the rationalism and difficulties of the geological corollaries of plate tectonics, with illustrations particularly from the geological history of the British Isles. There is special emphasis on the mechanics of continental lithosphere in extension, when basins are formed and in convergence whereby continental lithosphere thinned in extension is shortened and restacked to form orogenic belts. An upper lithosphere stress-concentrating elastic lid suffers extremely complex inhomogeneous deformations above a simpler, viscoelastic lower lithosphere whose deformation drives strain and displacement in the elastic lid. The very nature of plate tectonics as relative motion among a multi-plate mosaic of plates provides a rational semi-quantitative framework for large-scale geological complexity in space and time. The Caledonian and Hercynian history of the British Isles may be explained semi-quantitatively in terms of plate boundary evolution but it is not possible to define unequivocal solutions. The rationalism of plate tectonics is exhibited on a smaller, more direct field-scale by many of the complexities of ophiolite complexes, such as Ballantrae (Scotland), that can be explained as the effects of the evolution of ridge/ridge transforms and by diachronous deformation and sedimentation in subduction accretion prisms such as the Southern Uplands. Deformational and sedimentary patterns in NW Europe from Triassic times to the present day resulted from a complex interaction of extensional events related to diachronous Atlantic opening and compressional events related to sequential Alpine shortening phases. Those widespread events are typical of intracontinental plate boundary systems and create great difficulties for the geologist wishing to decipher relative plate motion from geological sequences, because huge areas, much larger than the British Isles, must be analysed and synthesized before much sense can be extracted. Further difficulties arise from the palinspastic and preservation problems of convergent boundaries; orogenic shortening telescopes and partially subducts facies belts. Most orogenic belts were assembled as a collage of displaced and rotated terrain elements that were subsequently flattened, elongated and straightened to an apparent but deceiving simplicity. Therefore, while plate tectonics provides a rational geological framework against which, for example, British basin evolution can be tested and explained, we cannot yet use the geological effects of plate boundary evolution to reconstruct relative plate motion quantitatively.

On the use of the volumetric thermal expansion coefficient in models of ocean floor topography

The use of the volumetric thermal expansion coefficient, instead of the linear coefficient, in successful models of ocean floor topography implies that the elastic rigidity of the lithosphere relaxes, enabling isostasy to be achieved. However, the presence of a thin elastic lid in the lithosphere, inferred from gravity investigations, implies some rigidity at the top of the lithospheric column and suggests that the volumetric thermal expansion coefficient derived from rheologically uniform models of the topography is about 15% too small.

Oscillations of elastic lid and bottom of a cylindrical tank filled by an elastic medium

Oscillations of elastic lid and bottom of a cylindrical tank filled by an elastic medium