Variations In Gravitational Potential Energy Research Articles

Comparing Earthquake Cycles on Normal and Reverse Faults Based on Simulations With a Dynamic Elasto‐Plastic Model

AbstractShear stress levels on reverse faults are anticipated to be several times higher than on normal faults with the same pore pressure ratio. In addition, ruptures on normal faults release gravitational potential energy, whereas earthquakes on reverse faults expend work in uplifting rocks. In this study, I investigate the significance of these differences for earthquake cycles and I question whether the source of energy driving earthquakes is the same on reverse and normal faults. Based on the assumption that normal and reverse faults have the same background frictional properties and pore pressure states, I use numerical simulations with a two‐dimensional dynamic elastic‐plastic model to show that due to stress differences, earthquakes on reverse faults tend to occur less frequently, produce more coseismic slip and stress drop and involve higher slip rates than ruptures on normal faults with equivalent dimensions. The analysis also shows differences in the energy changes associated with earthquake cycles on reverse and normal faults. However, the earthquakes on both fault types result from abrupt release of elastic strain energy, which proceed and essentially drive variations in gravitational potential energy. Thus, ruptures on both normal and reverse faults are consistent with elastic rebound theory.

Origin of Three‐Dimensional Crustal Stress Over the Conterminous United States

AbstractThe crustal stress field determines continental deformation, including intraplate seismicity and topographic undulations. However, the sources of observed crustal stress patterns remain debated, with proposed mechanisms including lateral variations in gravitational potential energy and mantle flow, the latter of which comprises plate boundary interactions and basal tractions. Here, we present a series of geodynamic models that simultaneously consider lithospheric and mantle dynamics in the same physical framework, based on which we investigate the sources of crustal stress over the conterminous U.S. The data‐oriented nature of these models allows us to systematically explore the relative contributions of different dynamic sources to the three‐dimensional crustal stress field. These models reveal that forces from the plate boundaries play a dominant role in generating the directional pattern of long‐wavelength horizontal crustal stress across the conterminous U.S. In the central U.S., especially regions of high‐topography, lithospheric density heterogeneities locally modify the crustal stress field. Similarly, mantle flow beneath the North American plate modulates crustal stress orientation in the eastern U.S., particularly in regions with thin lithosphere. Furthermore, we find that a denser‐than‐ambient lithospheric mantle beneath the central and eastern U.S. is required to match the observed continental‐scale E‐W topographic contrast.

Crustal Stress State in Taiwan: Moderately Strong Crust Supporting Gravitational and Flexural Loading

AbstractIn Taiwan and other contractional tectonic wedges, there is evidence that the basal detachment is very weak and the overlying crust is relatively strong. In this study, we compute the absolute deviatoric 3‐D stress field in Taiwan using focal mechanism data and coseismic stress changes for the 1999 M7.6 Chi‐Chi earthquake. We estimate a minimum coefficient of friction of 0.3 in the upper 15 km crust, assuming hydrostatic pore pressure, consistent with a moderately strong crust. The estimated stress state is consistent with primary tectonic structures of Taiwan. The maximum compressive stress in the fold and thrust belt and the Coastal Range is approximately aligned with relative motion of the Eurasian and the Philippine Sea Plates, but the minimum and intermediate principal stresses vary laterally and with depth. A reverse‐faulting stress regime wraps around the Peikang high in western Taiwan suggesting inherited basement structure influences crustal stress state. Vertical maximum compressive stress is inferred under the high topography of the Central Range mountains. We present a simple stress model for Taiwan assuming spatial variations in gravitational potential energy are supported elastically. The model stress state is broadly consistent with the stress inversion result. The model shows that vertical maximum compressive stress in the Central Range is a result of high topography and thick crustal root. Consistent with a moderately strong crust, the model deviatoric stresses in areas of high seismicity in Taiwan are of the order 50–100 MPa. Lower deviatoric stresses under the Central Range are consistent with low rates of observed seismicity.

Stress and deformation mechanisms at a subduction zone: insights from 2-D thermomechanical numerical modelling

SUMMARY Numerous processes such as metamorphic reactions, fluid and melt transfer and earthquakes occur at a subducting zone, but are still incompletely understood. These processes are affected, or even controlled, by the magnitude and distribution of stress and deformation mechanism. To eventually understand subduction zone processes, we quantify here stresses and deformation mechanisms in and around a subducting lithosphere, surrounded by asthenosphere and overlain by an overriding plate. We use 2-D thermomechanical numerical simulations based on the finite difference and marker-in-cell method and consider a 3200 km wide and 660 km deep numerical domain with a resolution of 1 km by 1 km. We apply a combined visco-elasto-plastic deformation behaviour using a linear combination of diffusion creep, dislocation creep and Peierls creep for the viscous deformation. We consider two end-member subduction scenarios: forced and free subduction. In the forced scenario, horizontal velocities are applied to the lateral boundaries of the plates during the entire simulation. In the free scenario, we set the horizontal boundary velocities to zero once the subducted slab is long enough to generate a slab pull force large enough to maintain subduction without horizontal boundary velocities. A slab pull of at least 1.8 TN m–1 is required to continue subduction in the free scenario. We also quantify along-profile variations of gravitational potential energy (GPE). We evaluate the contributions of topography and density variations to GPE variations across a subduction system. The GPE variations indicate large-scale horizontal compressive forces around the trench region and extension forces on both sides of the trench region. Corresponding vertically averaged differential stresses are between 120 and 170 MPa. Furthermore, we calculate the distribution of the dominant deformation mechanisms. Elastoplastic deformation is the dominant mechanism in the upper region of the lithosphere and subducting slab (from ca. 5 to 60 km depth from the top of the slab). Viscous deformation dominates in the lower region of the lithosphere and in the asthenosphere. Considering elasticity in the calculations has an important impact on the magnitude and distribution of deviatoric stress; hence, simulations with increased shear modulus, in order to reduce elasticity, exhibit considerably different stress fields. Limiting absolute stress magnitudes by decreasing the internal friction angle causes slab detachment so that slab pull cannot be transmitted anymore to the horizontal lithosphere. Applying different boundary conditions shows that forced subduction simulations are stronger affected by the applied boundary conditions than free subduction simulations. We also compare our modelled topography and gravity anomaly with natural data of seafloor bathymetry and free-air gravity anomalies across the Mariana trench. Elasticity and deviatoric stress magnitudes of several hundreds of MPa are required to best fit the natural data. This agreement suggests that the modelled flexural behaviour and density field are compatible with natural data. Moreover, we discuss potential applications of our results to the depth of faulting in a subducting plate and to the generation of petit-spot volcanoes.

Extension and Dynamics of the Andes Inferred From the 2016 Parina (Huarichancara) Earthquake

AbstractTheMw6.1 2016 Parina earthquake led to extension of the south Peruvian Andes along a normal fault with evidence of Holocene slip. We use interferometric synthetic aperture radar, seismology, and field mapping to determine a source model for this event and show that extension at Parina is oriented NE‐SW, which is parallel to the shortening direction in the adjacent sub‐Andean lowlands. In addition, we use earthquake source models and GPS data to demonstrate that shortening within the sub‐Andes is parallel to topographic gradients. Both observations imply that forces resulting from spatial variations in gravitational potential energy are important in controlling the geometry of the deformation in the Andes. We calculate the horizontal forces per unit length acting between the Andes and South America due to these potential energy contrasts to be 4–8 ×1012 N/m along strike of the mountain range. Normal faulting at Parina implies that the Andes in south Peru have reached the maximum elevation that can be supported by the forces transmitted across the adjacent foreland, which requires that the foreland faults have an effective coefficient of friction0.2. Additionally, the onset of extension in parts of the central Andes following orogen‐wide compression in the late Miocene suggests that there has been a change in the force balance within the mountains. We propose that shortening on weak detachment faults within the Andean foreland since ∼5–9 Ma reduced the shear tractions acting along the base of the upper crust in the eastern Andes, leading to extension in the highest parts of the range.

Constraints from GPS measurements on the dynamics of the zone of convergence between Arabia and Eurasia

AbstractWe investigate the dynamics of deformation in the zone of convergence between the Arabian and Eurasian plates using a physical model that treats the lithosphere as a thin fluid sheet deforming in response to lateral variations in gravitational potential energy (GPE). This model has two free material parameters, the power law exponent, n, of the vertically averaged rheology of the lithosphere and the Argand number, Ar, which expresses the relative importance of GPE and stresses required to deform the lithosphere. With boundary conditions described by three additional free parameters, the model fits the observed deformation, as measured by 367 GPS velocities, with a root‐mean‐square residual of <2.4 mm/yr. We find negligible improvement when variations in material properties are introduced that represent increases or decreases in the lithospheric strength of the Central Iranian and Turkish‐Iranian Plateaux and the Zagros Mountains. Effective viscosity of the lithosphere ranges from 5 × 1022 Pa s at 10 nanostrain/yr to 1022 Pa s at 100 nanostrain/yr. As well as matching the decadal time scale strain rates determined from GPS, the computed distribution of strain rates is also consistent with the distribution and types of earthquake focal mechanism. Significant historical earthquake activity is seen in regions with strain rates lower than 20 nanostrain/yr, implying that it is prudent to base assessments of seismic hazard on regional strain rates.

Constraints from GPS measurements on the dynamics of deformation in Anatolia and the Aegean

AbstractWe estimate the strength of the lithosphere in Anatolia and the Aegean, and the boundary forces acting upon it, using a dynamical model that treats the lithosphere as a thin fluid sheet deforming in response to variations in gravitational potential energy. This model has one free material parameter, the power law exponent, n, of the vertically averaged rheology of the lithosphere, and two parameters that specify the forces per unit length applied to its edges. Solutions to this model that best fit the velocities of 346 reliable GPS sites require an effective viscosity of the lithosphere of 1022 to 1021 Pa s at strain rates of 10 to 100 nanostrain per year. The best‐fitting force at the Arabia‐Anatolia boundary is consistent with the lithostatic pressure due to the high topography there, and the force at the Nubia‐Aegean boundary is consistent with the contrast in lithostatic pressure across that boundary. No additional force, from “slab rollback” or basal tractions due to convection in the mantle, is required to explain the observations. These results are supported by scaling relations derived from approximate analytical solutions. The inverse relationship between the viscosity of the lithosphere and deviatoric stress produces strong slowly deforming regions in the Southern Aegean and Central Anatolia whose motions resemble those of microplates. The distribution of geodetic strain rates within the region, and the partitioning between normal and strike‐slip faulting, are explained by the interplay between boundary conditions, internal variations in gravitational potential energy, and the power law rheology of the lithosphere.

Gravitational potential energy and active deformation in the Apennines

We use velocity measurements from a network of continuous GPS sites spanning the Apennines of peninsular Italy to test the hypothesis that the active deformation of the region is explained by variations in gravitational potential energy of the lithosphere. The simple geometry of the mountain chain allows us to treat the deformation as two-dimensional, neglecting gradients of velocity along the strike of the chain. Under this assumption, the integral of gravitational potential energy per unit area of the lithosphere (GPE) in the direction perpendicular to the chain is related by a simple expression to the velocity in the same direction. We show that the observed velocities match this expression with an RMS misfit of 0.5mm/yr. This agreement suggests that deformation of the Apennines reflects a balance, within the mountain chain itself, between lateral variations in GPE and the stresses required to deform the lithosphere. Forces arising from processes external to the belt are not required to explain the observations.

Relationship between tectonic overpressure, deviatoric stress, driving force, isostasy and gravitational potential energy

We present analytical derivations and 2-D numerical simulations that quantify magnitudes of deviatoric stress and tectonic overpressure (i.e. difference between the pressure, or mean stress, and the lithostatic pressure) by relating them to lateral variations in the gravitational potential energy (GPE). These predictions of tectonic overpressure and deviatoric stress associated with GPE differences are independent of rock rheology (e.g. viscous or elastic) and rock strength. We consider a simple situation with lowlands and mountains (plateau). We use a numerical two-layer model consisting of a crust with higher Newtonian viscosity than that in the mantle, and also a three-layer model in which the two-layer lithosphere overlies a much less viscous asthenosphere. Our results (1) explain why estimates for the magnitude of stresses in Tibet, previously published by different authors, vary by a factor of two, (2) are applied to test the validity of the thin sheet approximation, (3) show that the magnitude of the depth-integrated tectonic overpressure is equal to the magnitude of the depth-integrated deviatoric stress if depth-integrated shear stresses on vertical and horizontal planes within the lithosphere are negligible (the thin sheet approximation) and (4) show that under thin sheet approximation tectonic overpressure is required to build and support continental plateaus, such as in Tibet or in the Andes, even if the topography and the crustal root are in isostatic equilibrium. Under thin sheet approximation, the magnitude of the depth-integrated tectonic overpressure is equal to the depth-integrated horizontal deviatoric stress, and both are approximately 3.5 × 10 12 N m −1 for Tibet. The horizontal driving force per unit length related to lateral GPE variations around Tibet is composed of the sum of both tectonic overpressure and deviatoric stress, and is approximately 7 × 10 12 N m −1 . This magnitude exceeds previously published estimates for the force per unit length required to fold the Indo-Australian Plate south of India, and hence the uplift of the Tibetan plateau could have folded the Indian Plate. We also discuss the mechanical conditions that are necessary to achieve isostasy, for which the lithostatic pressure is constant at a certain depth. The results show that tectonic overpressure can exist at a certain depth even if all deviatoric stresses are zero at this depth, because this tectonic overpressure is related to horizontal gradients of vertical shear stresses integrated across the entire depth of the lithosphere. The magnitude of the depth-integrated tectonic overpressure of 3.5 × 10 12 N m −1 implies that the pressure estimated from observed mineral assemblages in crustal rocks is likely significantly different from the lithostatic pressure, and pressure recorded by crustal rocks is not directly related to depth. In case of significant weakening of the entire lithosphere by any mechanism our analytical and numerical studies provide a simple estimation of tectonic overpressure via variations in GPE.

Gravitational potential stresses and stress field of passive continental margins: Insights from the south-Norway shelf

It is commonly assumed that the stress state at passive margins is mainly dominated by ridge push and that other stress sources have only a limited temporal and/or spatial influence. We show, by means of numerical modelling, that observed variations in lithosphere structure and elevation from a margin towards continental interiors may also produce significant gravitational potential stresses competing with those induced by ridge push forces. We test this hypothesis on an actual case where abundant geological and geophysical datasets are available, the shelf of southern Norway and adjacent southern Norwegian mountains (or Southern Scandes). The modelling results are consistent with the main features of three key-observables: (1) undulations of the truncated geoid (reflecting variations in gravitational potential energy in the lithosphere), (2) significant stress rotations both offshore and onshore and (3) the seismicity pattern of southern Norway. The contribution of the Southern Scandes to the regional stress pattern appears to be far more significant than previously anticipated. In addition, the modelling provides a physical explanation for the enigmatic seismicity of southern Norway. Gravitational potential stresses arising from variations in the lithospheric structure between a passive margin and its continental borderlands, can exert a significant control on the dynamic evolution of the margin in concert with ridge push.

Why are the continents just so?

Variations in gravitational potential energy contribute to the intraplate stress field thereby providing the means by which lithospheric density structure is communicated at the plate scale. In this light, the near equivalence in the gravitational potential energy of typical continental lithosphere with the mid-ocean ridges is particularly intriguing. Assuming this equivalence is not simply a chance outcome of continental growth, it then probably involves long-term modulation of the density configuration of the continents via stress regimes that are able to induce significant strains over geological time. Following this notion, this work explores the possibility that the emergence of a chemically, thermally and mechanically structured continental lithosphere reflects a set of thermally sensitive feedback mechanisms in response to Wilson cycle oscillatory forcing about an ambient stress state set by the mid-ocean ridge system. Such a hypothesis requires the continents are weak enough to sustain long-term (10 8 years) strain rates of the order of � 10 )17 s )1 as suggested by observations that continental lithosphere is almost everywhere critically stressed, by estimates of seismogenic strain rates in stable continental interiors such as Australia and by the low-temperature thermochronological record of the continents that requires significant relief generation on the 10 8 year time-scale. Furthermore, this notion provides a mechanism that helps explain interpretations of recently published heat flow data that imply the distribution of heat- producing elements within the continents may be tuned to produce a characteristic thermal regime at Moho depths.

Gravitational and tectonic forces controlling postcollisional deformation and the present‐day stress field of the Alps: Constraints from numerical modeling

We perform numerical modeling to investigate the mechanisms leading to the postcollisional tectonic evolution of the Alps. We model the lithospheric deformation as a viscous thin sheet with vertically averaged rheology and coupled with surface mass transport. The applied kinematic boundary conditions simulate the convergence between the Adria indenter and the European foreland during the last 35 Myr. Model predictions of elevation, lithospheric structure, erosion/sedimentation pattern and vertical axis rotation are compared with observations of the planform shape of the chain, topography, crustal thickness, distribution of rock exhumation and sediment thickness, and paleomagnetic rotations. Thickening of the lithosphere in the Alpine region is shown to be highly sensitive to the assumed viscosity law, to the strength contrasts between the different regions and to the surface mass transport. Modeling results indicate that the large‐scale deformation of the Alps during the postcollisional phase is mainly controlled by accommodation of convergence in a weak orogenic zone caught between a nearly rigid Adria plate and a strong European foreland. Modeling of the present‐day stress field shows that (1) the present rotation of Adria is responsible for the change of extension direction from strike‐perpendicular in the western Alps to strike‐parallel in the east and (2) the strike‐perpendicular extension observed in the western Alps is likely due to lateral variations of gravitational potential energy. The results suggest a NNE shift of about 700 km of the Euler pole of Adria relative to Europe from its mean position during postcollisional deformation to the present day.

Thin-sheet modelling of lithospheric deformation and surface mass transport

We study the effects of incorporating surface mass transport and the gravitational potential energy of both crust and lithospheric mantle to the viscous thin sheet approach. Recent 2D (cross-section) numerical models show that surface erosion and sediment transport can play a major role in shaping the large-scale deformation of the crust. In order to study these effects in 3D (planform view), we develop a numerical model in which both the dynamics of lithospheric deformation and surface processes are fully coupled. Deformation is calculated as a thin viscous layer with a vertically-averaged rheology and subjected to plane stresses. The coupled system of equations for momentum and energy conservation is solved numerically. This model accounts for the isostatic and potential-energy effects due to crustal and lithospheric thickness variations. The results show that the variations of gravitational potential energy due to the lateral changes of the lithosphere–asthenosphere boundary can modify the mode of deformation of the lithosphere. Surface processes, incorporated to the model via a diffusive transport equation, rather than just passively reacting to changes in topography, play an active role in controlling the lateral variations of the effective viscosity and hence of the deformation of the lithosphere.

The relationship between the instantaneous velocity field and the rate of moment release in the lithosphere

SUMMARY Instantaneous velocity gradients within the continental lithosphere are often related to the tectonic driving forces. This relationship is direct if the forces are secular, as for the case of loading of a locked section of a subduction interface by the downgoing plate. If the forces are static, as for the case of lateral variations in gravitational potential energy, then velocity gradients can be produced only if the lithosphere has, on average, zero strength. The static force model may be related to the long-term velocity field but not the instantaneous velocity field (typically measured geodetically over a period of several years) because over short time intervals the upper lithosphere behaves elastically. In order to describe both the short- and long-term behaviour of an (elastic) lithosphere‐(viscoelastic) asthenosphere system in a selfconsistent manner, I construct a deformation model termed the expected interseismic velocity (EIV) model. Assuming that the lithosphere is populated with faults that rupture continually, each with a definite mean recurrence time, and that the Earth is well approximated as a linear elastic‐viscoelastic coupled system, I derive a simple relationship between the instantaneous velocity field and the average rate of moment release in the lithosphere. Examples with synthetic fault networks demonstrate that velocity gradients in actively deforming regions may to a large extent be the product of compounded viscoelastic relaxation from past earthquakes on hundreds of faults distributed over large ( >10 6 km 2 ) areas.