Gravitational Potential Energy Differences Research Articles

A methodology to predict the run-out distance of submarine landslides

In this paper, the method of computational fluid dynamics (CFD) is proposed to simulate a fluidized submarine landslide with shear thinning non-Newtonian fluids over a seabed under different contact conditions in the ambient water. The CFD method is first validated using data of physical channel and non-Boussinesq lock-exchange experiments with different rheological characteristics and is found to provide good accuracy. Various CFD-based experiments with different initial velocities of the submarine landslide and different seabed contact conditions are then performed systematically. During the movement of the submarine landslide in ambient water, stress state and causes of the submarine landslide mass are revealed, and the submarine landslide-seabed contact relation is clarified as a decisive influencing factor. Furthermore, based on the principle of energy conservation, a methodology to predict the run-out distance of the submarine landslide mass by using the initial geometry of the submarine landslide masses with different scales and the total initial kinetic energy (including the initial kinetic energy and the gravitational potential energy difference caused by the self-slumping) of the submarine landslide mass is presented, equations to quantify the process are established, and the proposed methodology and equations are validated by the numerical result, which provides a significant basis for the prediction of marine engineering geological and hydrodynamic hazards with special reference to submarine landslides.

A powerful interferometer works by holding, not dropping, its atoms

After 20 seconds in an optical lattice, the gravitational potential-energy difference between two wavepackets separated by micrometers generates megaradians of phase.

Surface Motions and Continental Deformation in the Indian Plate and the India‐Eurasia Collision Zone

AbstractThe collision of the Indian plate with Eurasia has played a major role in controlling the dynamics of central Asia leading to the world's largest continental deformation zone. In order to study the deformation within the Indian plate as well as the India‐Eurasia collision zone, we model the lithospheric stress field by calculating the two primary sources of stress, one arising due to topography and shallow lithospheric structure estimated by gravitational potential energy differences and the other arising from basal tractions derived from density‐driven mantle convection. We use several tomography models to calculate horizontal tractions using the convection code HC for two radially varying viscosity structures. We also take into account lateral viscosity variations in the lithosphere model arising from stiff cratons, weak plate boundaries, and strength variations due to old and young oceanic lithosphere. We do a quantitative comparison of our predicted deviatoric stresses, strain rates, and plate velocities with surface observables and find that the regional tomography model of Singh et al. (2014) embedded in the global S wave model S40RTS does a remarkable job of fitting the observations of GPS velocities and strain rates as well as intraplate stress field from the World Stress Map.

A new crustal model of the Anatolia–Aegean domain: evidence for the dominant role of isostasy in the support of the Anatolian plateau

The engines of surface deformation in the Anatolia-Aegean region are a matter of debate, including the origin of the high elevations of the Anatolian plateau. Recent publications based on geological and thermomechanical modelling emphasize the role of dynamic topography in the plateau uplift. However, quantitative estimates of the contribution of dynamic topography are affected by large uncertainties due to insufficient knowledge of the crustal structure, in particular crustal thickness and density. To reduce these uncertainties, we provide a new accurate crustal thickness map of the Anatolia-Aegean domain computed from a large volume of broadband seismic data. In addition, we display high-resolution seismic sections of the internal structure of the crust in Western and Central Anatolia. Density contrasts are derived from the same seismic data set and Bouguer gravity anomaly computed from the EGM2008 model. Our crustal thickness model is highly correlated with the topography suggesting that the Anatolian plateau is close to isostatic equilibrium. The average density difference between crust and upper mantle computed from our crustal model and Bouguer gravity anomaly is low compared to the global average, ∼0.315 ×10 3 kg m −3. The ratio of surface elevation to crustal thickness is lower than average, 1/9.4, which also indicates a low-density crust. Differences between isostatic topography and observed topography are overall small (<500 m). The east-to-west gradients of crustal thickness and topography changes are nearly constant in between the Taurides and Pontides at the northern and southern borders of Anatolia. The observed constant crustal thickness gradient may indicate a low viscosity lower crust supported by the thin mantle lithosphere evidenced by seismic tomography beneath the Anatolian plateau. We propose that viscous flow in the lower crust has smoothed out lateral changes in the crustal structure expected for such a heterogeneous collage of continental fragments. This flow may originate from gravitational potential energy differences between Eastern Anatolia (thick crust, high elevations) and the Aegean Sea (thin crust, low elevations), suggesting that gravity plays an integral part in the westward escape of Anatolia.

New heat flow determination in northern Tarim Craton, northwest China

Tarim Craton is a Precambrian block situated in northwest China, just north of the Tibetan Plateau, where a large sedimentary basin with abundant hydrocarbon potential has developed. Accurate heat flow data for Tarim is vital for understanding the lithospheric evolution and hydrocarbon generation in this area; however, there were unavailable until now, due to a lack of high quality steady-state temperature logging data. Here, we report 10 new heat flow values derived from steady-state temperature logging and measured thermal conductivity data. New heat flow values range from 40.1 to 49.4 mW m−2, with a mean of 43.1 ± 3.0 mW m−2. In addition, radiogenic heat production from the sediments accounts for 20 per cent of the observed surface heat flow, whilst the mantle heat flow is estimated to be as low as 6–15 mW m−2; this indicates a dominant contribution from crustal heat, to the observed heat flow. The average heat flow and crustal temperature in the Tarim Craton are markedly lower than those in the Tibetan Plateau, whilst the calculated rheological strength of the lithosphere, beneath Tarim, is sufficiently large to resist the elevation-induced gravitational potential energy difference between Tarim and Tibet. This inherited thermal and rheological contrast, between the craton and Plateau, can be traced back to before the India–Asia collision; this accounts for the differential active deformation pattern in the Tarim Craton and adjacent areas.

Refined models of gravitational potential energy compared with stress and strain rate patterns in Iberia

This study examines the role of gravitational potential energy (GPE) in generating second-order (spatial scale ∼102km) variations in the Iberia stress and strain-rate patterns. We present a new map of present-day strain rate field derived from the secular velocity field computed using all available continuously operating Global Navigation Satellite Systems (GNSS) stations in Iberia. The estimated strain rate field is generally consistent with the tectonic framework of the Iberian region, even though sporadic sharp local variations downgrade its correlation with the regional stress patterns. Many of the sharp spatial variations in the strain rate map are consistent with local changes of deformation style determined by prevailing faults. To obtain a more accurate estimate of GPE we use new data on the structure of the crust and apply a thin sheet approach using a 3-D definition of deviatoric stress. The GPE is derived from two isostatically compensated models (GPEd and GPEe compensated by density and elevation adjustment, respectively) and from the truncated geoid (GPEg). The GPE stresses are then summed with the first-order stress field due to the Eurasia–Nubia (EU–NU) convergence and the results compared with both the stress and strain rate data. In agreement with previous studies, we find that the GPE does not significantly change the NW–SE average direction of the most compressive stress (SHmax) imposed by the EU–NU collision, its main effect being to cause spatially changing stress regimes. From the analysis of the different GPE models we find: (1) in the Pyrenees, the tectonic forces have a secondary role when compared to the GPE. In this region, the model that best correlates with observations is the one emphasizing the role of surface elevation as a source of GPE (GPEe); (2) in the Iberian Chain and the Betics, the GPE imposes NE–SW extension consistent with a strike-slip regime and is equally (GPEe) or more (GPEg) important than the tectonic forces. In these regions, both deep heterogeneities associated with mantle convection and elevation are important sources of GPE; (3) in western Iberia, the GPE differences work against dominant tectonic forces by reducing the SHmax magnitude. The GPEg model is the one that best predicts the average strike-slip regime in Galicia; and finally (4) in the Gulf of Cadiz the gravitational potential stresses have a minor role and the style of deformation is clearly controlled by the tectonic forces.

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.

Predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

The way in which basal tractions, associated with mantle convection, couples with the lithosphere is a fundamental problem in geodynamics. A successful lithosphere‐mantle coupling model for the Earth will satisfy observations of plate motions, intraplate stresses, and the plate boundary zone deformation. We solve the depth integrated three‐dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection. The contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences. The basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations. We simultaneously fit stresses and plate motions in order to delineate a best‐fit lithosphere‐mantle coupling model. We use both the World Stress Map and the Global Strain Rate Model to constrain the models. We find that a strongly coupled model with a stiff lithosphere and 3–4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints. Our predicted deviatoric stresses, which are dominated by contribution from mantle tractions, range between 20–70 MPa. The best‐fitting coupled models predict strain rates that are consistent with observations. That is, the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates. Comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving, although in a few regions, including western North America, tractions are resistive.

Coeval thrusting and extension during lower crustal ductile flow – implications for exhumation of high‐grade metamorphic rocks

AbstractNumerical models of tectonic processes in large hot orogens offer insight into the styles, controls and consequences of ductile flow of middle and lower orogenic crust. We present results from crustal‐scale thermal‐mechanical models illustrating contrasting styles of syn‐ and post‐convergent ductile flow. Crustal viscosity in the models is controlled by temperature‐dependent flow laws, scaled to represent lithological strength variations. An additional viscosity decrease at high temperature can be imposed to represent weakening during incipient partial melting. Two end‐member tectonic styles, in which lower crustal flow is driven either by gravity or tectonics, develop in response to the initial properties and evolving strength of the model crust. Homogeneous channel flow, driven by the gravitational potential energy difference between a plateau and its foreland, is characteristic of Himalayan–Tibetan (HT‐series) models with relatively weak, laterally homogeneous crust and moderately high heat production. In contrast, Grenville Orogen (GO‐series) models with relatively strong, laterally heterogeneous crust do not reach the low effective viscosity (ηeff≤1019 Pa.s) required for gravity‐driven channel flow. Instead, tectonically driven lateral flow and explusion of lower crust is triggered by underthrusting of a strong indentor. The dominant structures are ductile fold nappes that may be transported hundreds of kilometres towards the foreland. When tectonic convergence is turned off, the model orogens undergo gravitational spreading, in which ductile middle and lower crust flow laterally from the plateau towards the foreland, driving thrusting on the orogenic flanks and ductile thinning in the orogenic core. The resulting geometry can resemble that produced by syn‐convergent ductile flow, except for the development of regional‐scale normal‐sense shear zones in the post‐convergent stage. Model feasibility is tested against data from the western Grenville Orogen in Ontario. The comparison suggests that high‐grade metamorphic rocks in the orogenic core record the effects of protracted syn‐ and post‐convergent ductile flow, whereas those on the flanks record mainly post‐convergent thrusting and extension. The models suggest a number of ways to distinguish among different styles of syn‐ and post‐convergent ductile flow; metamorphic P–T–t paths alone are not diagnostic of tectonic process without additional information on crustal‐scale structure and timing. In combination with erosion, both types of flow may contribute to exhumation of regionally extensive high‐grade gneiss terranes.

Contribution of gravitational potential energy differences to the global stress field

SUMMARY Modelling the lithospheric stress field has proved to be an efficient means of determining the role of lithospheric versus sublithospheric buoyancies and also of constraining the driving forces behind plate tectonics. Both these sources of buoyancies are important in generating the lithospheric stress field. However, these sources and the contribution that they make are dependent on a number of variables, such as the role of lateral strength variation in the lithosphere, the reference level for computing the gravitational potential energy per unit area (GPE) of the lithosphere, and even the definition of deviatoric stress. For the mantle contribution, much depends on the mantle convection model, including the role of lateral and radial viscosity variations, the spatial distribution of density buoyancies, and the resolution of the convection model. GPE differences are influenced by both lithosphere density buoyancies and by radial basal tractions that produce dynamic topography. The global lithospheric stress field can thus be divided into (1) stresses associated with GPE differences (including the contribution from radial basal tractions) and (2) stresses associated with the contribution of horizontal basal tractions. In this paper, we investigate only the contribution of GPE differences, both with and without the inferred contribution of radial basal tractions. We use the Crust 2.0 model to compute GPE values and show that these GPE differences are not sufficient alone to match all the directions and relative magnitudes of principal strain rate axes, as inferred from the comparison of our depth integrated deviatoric stress tensor field with the velocity gradient tensor field within the Earth's plate boundary zones. We argue that GPE differences calibrate the absolute magnitudes of depth integrated deviatoric stresses within the lithosphere; shortcomings of this contribution in matching the stress indicators within the plate boundary zones can be corrected by considering the contribution from horizontal tractions associated with density buoyancy driven mantle convection. Deviatoric stress magnitudes arising from GPE differences are in the range of 1–4 TN m−1, a part of which is contributed by dynamic topography. The EGM96 geoid data set is also used as a rough proxy for GPE values in the lithosphere. However, GPE differences from the geoid fail to yield depth integrated deviatoric stresses that can provide a good match to the deformation indicators. GPE values inferred from the geoid have significant shortcomings when used on a global scale due to the role of dynamically support of topography. Another important factor in estimating the depth integrated deviatoric stresses is the use of the correct level of reference in calculating GPE. We also elucidate the importance of understanding the reference pressure for calculating deviatoric stress and show that overestimates of deviatoric stress may result from either simplified 2-D approximations of the thin sheet equations or the assumption that the mean stress is equal to the vertical stress.

Three-dimensional numerical modeling of contemporary mantle flow and tectonic stress beneath the Central Mediterranean

The structure, density and effective viscosity of the crust and uppermost mantle beneath the Central Mediterranean influence lithospheric deformation, mantle flow, and tectonic stress state. To estimate the contribution of buoyancy forces to regional dynamics, three-dimensional finite-element models are developed to determine contemporary uppermost mantle flow and tectonic stresses. We use density models for the crust and uppermost mantle derived from S-wave seismic velocities and constrained by gravity data. The viscosity model is constrained by the observed strain rate and regional heat flow data. The modeled movement of the uppermost crust is consistent with the northeast-oriented motion of the lithosphere and is in an agreement with the geodetic measurements. The modeled flow patterns of the lower crust and uppermost mantle are consistent with the regional observations. The models predict (i) northwest-oriented movements beneath the southeast part of the Adriatic Sea region, (ii) the northeastern subduction beneath the western part of the Adriatic Sea, (iii) the upwelling beneath the Tyrrhenian Sea and its eastern coast, (iv) the western movement of the Ionian Sea sub-plate, and (v) the subduction beneath the western Calabria region. Our models predict also a distinct compressional regime along the northeast part of the Italian peninsula and to the east of Sicily, and a tensional regime beneath the Tyrrhenian Sea, Umbria–Marche region, and Ionian Sea. The predicted tectonic stress regimes in the northern and central Apennines are in agreement with stress regimes derived from earthquake fault-plane solutions. Changes in the predicted crustal stress pattern and magnitude are likely to be caused by buoyancy-driven mantle circulation beneath the region rather than by gravitational potential energy differences in the crust itself. Based on the model results, we conclude that the buoyancy forces play an important role in the contemporary tectonics of the region.

Joint modeling of lithosphere and mantle dynamics elucidating lithosphere‐mantle coupling

We provide new insights into the lithosphere‐mantle coupling problem through a joint modeling of lithosphere dynamics and mantle convection and through comparison of model results with the high resolution velocity gradient tensor model along the Earth's plate boundary zones. Using a laterally variable effective viscosity lithosphere model, we compute depth integrated deviatoric stresses associated with both gravitational potential energy (GPE) differences and deeper mantle density buoyancy‐driven convection. When deviatoric stresses from horizontal basal tractions, associated with deeper density buoyancy‐driven convective circulation of the mantle, are added to those from GPE differences, the fit between the model deviatoric stress field and the deformation indicators improves dramatically in most areas of continental deformation. We find that the stresses induced by the horizontal tractions arising from deep mantle convection contribute approximately 50% of the magnitude of the Earth's deviatoric lithospheric stress field. We also demonstrate that lithosphere‐asthenosphere viscosity contrasts and lateral variations within the lithospheric plate boundary zones play an important role in generating the right direction and magnitude of tractions that yield an optimal match between deviatoric stress tensor patterns and the deformation indicators.

The 2003 earthquake swarm in Anjalankoski, south-eastern Finland

During May 2003 a swarm of 16 earthquakes ( M L = 0.6–2.1) occurred at Anjalankoski, south-eastern Finland. The activity lasted for three weeks, but additional two events were observed at the same location in October 2004. A comparison of the waveforms indicated that the source mechanisms and the hypocentres of the events were nearly identical. A relative earthquake location method was applied to better define the geometry of the cluster and to identify the fault plane associated with the earthquakes. The relocated earthquakes aligned along an ENE–WSW trending zone, with a lateral extent of about 1.0 km by 0.8 km. The relative location and the waveform-modelling of depth sensitive surface wave (Rg) and S-to-P converted body wave (sP) phases indicated that the events were unusually shallow, most likely occurring within the first 2 km of the surface. The revised historical earthquake data confirm that shallow swarm-type seismicity is characteristic to the area. The focal mechanism obtained as a composite solution of the five strongest events corresponds to dip-slip motion along a nearly vertical fault plane (strike = 250°, dip = 80°, rake = 90°). The dip and strike of this nodal plane as well as the relocated hypocentres coincide with an internal intrusion boundary of the Vyborg rapakivi batholith. The events occur under a compressive local stress field, which is explained by large gravitational potential energy differences and ridge-push forces. Pore-pressure changes caused by intrusion of ground water and/or radon gas into the fracture zones are suggested to govern the swarm-type earthquake activity.

Dynamic modeling for crustal deformation in China: Comparisons between the theoretical prediction and the recent GPS data

Using a dynamic method, we present a quantitative model for the present-day crustal movement in China. We consider not only the effect of the India–Eurasia collision, the gravitational potential energy difference of the Tibet Plateau, but also the contribution of the shear traction on the bottom of the lithosphere induced by the global mantle convection. By solving a system of force balance equations using a finite element method, we obtain the crustal movement velocity in China with respect to the Eurasia plate. The comparison between our result and the velocity field obtained from the GPS observation shows that our model satisfactorily reproduces the general picture of crustal deformation in China. Numerical modeling results reveal that the shear traction at the base of the lithosphere induced by the mantle flow is probably a considerable factor that causes the movement and deformation of the lithosphere in China continent. But its effect focus on the eastern China.

Gravitational potential energy of the Tibetan Plateau and the forces driving the Indian plate

We present a study of the vertically integrated deviatoric stress field for the Indian plate and the Tibetan Plateau associated with gravitational potential energy (GPE) differences. Although the driving forces for the Indian plate have been attributed solely to the mid-oceanic ridges that surround the entire southern boundary of the plate, previous estimates of vertically integrated stress magnitudes of ~6–7 x 1012 N/m in Tibet far exceed those of ~3 x 1012 N/m associated with GPE at mid-oceanic ridges, calling for an additional force to satisfy the stress magnitudes in Tibet. We use the Crust 2.0 data set to infer gravitational potential energy differences in the lithosphere. We then apply the thin sheet approach in order to obtain a global solution of vertically integrated deviatoric stresses associated only with GPE differences. Our results show large N-S extensional deviatoric stresses in Tibet that the ridge-push force fails to cancel. Our results calibrate the magnitude of the basal tractions, associated with density buoyancy driven mantle flow, that are applied at the base of the lithosphere in order to drive India into Tibet and cancel the N-S extensional stresses within Tibet. Moreover, our deviatoric stress field solution indicates that both the ridge-push influence (~1 x 1012 N/m) and the vertically integrated deviatoric stresses associated with GPE differences around the Tibetan Plateau (~3 x 1012 N/m) have previously been overestimated by a factor of two or more. These overestimates have resulted from either simplified two-dimensional approximations of the thin sheet equations, or from an assumption about the mean stress that is unlikely to be correct.

Dynamics of the India‐Eurasia collision zone

We present simple new dynamic calculations of a vertically averaged deviatoric stress field (over a depth average of 100 km) for Asia from geodetic, geologic, topographic, and seismic data. A first estimate of the minimum absolute magnitudes and directions of vertically averaged deviatoric stress is obtained by solving force balance equations for deviatoric stresses associated with gravitational potential energy differences within the lithosphere plus a first‐order contribution of deviatoric stresses associated with stress boundary conditions. This initial estimate of the vertically averaged deviatoric stress field is obtained independent of assumptions about the rheology of the lithosphere. Absolute magnitudes of vertically averaged deviatoric stresses vary between 5 and 40 MPa. Assuming bulk viscous behavior for the lithosphere, the magnitudes of deviatoric stresses, together with the magnitudes of strain rates inferred from Quaternary fault slip rate and GPS data, yield vertically averaged effective viscosities for Tibet of 0.5–5×1022 Pa s, compared with 1–2.5×1023 Pa s in more rigid areas elsewhere in the region. A forward modeling method that solves force balance equations using velocity boundary conditions allows us to refine our estimates of the vertically averaged effective viscosity distribution and deviatoric stress field. The total vertically averaged deviatoric stress and effective viscosity field are consistent with a weak lower crust in Tibet; they are consistent with some eastward motion of Tibet and south China lithosphere relative to Eurasia; and they confirm that gravitational potential energy differences have a profound effect on the spatially varying style and magnitude of strain rate around the Tibetan Plateau. Our results for the vertically averaged deviatoric stress argue for a large portion of the strength of the lithosphere to reside within the seismogenic upper crust to get deviatoric stress magnitudes there to be as high as 100–300 MPa (in accord with laboratory and theoretical friction experiments indicating that stress drops in earthquakes are small fractions of the total deviatoric stress).

What caused the March 25, 1998 Antarctic Plate earthquake?: Inferences from regional stress and strain rate fields

We investigate possible driving forces behind the occurrence of the 1998 Antarctic plate earthquake. We determine first a regional strain rate field associated with the accommodation of relative plate motion, and second, a vertically averaged minimum deviatoric stress field associated with lithospheric gravitational potential energy differences and deglaciation of the Antarctic ice cap. We find that the mechanism of this event is inconsistent with strain orientations inferred from kinematic modeling of a diffuse zone of deformation within the triple junction region. Stress perturbations associated with deglaciation cannot be ruled out as a triggering mechanism for this event.

Dynamics of the pacific-north american plate boundary in the western united states

The vertically averaged deviatoric stress tensor field within the western United States was determined with topographic data, geoid data, recent global positioning system observations, and strain rate magnitudes and styles from Quaternary faults. Gravitational potential energy differences control the large fault-normal compression on the California coast. Deformation in the Basin and Range is driven, in part, by gravitational potential energy differences, but extension directions there are modified by plate interaction stresses. The California shear zone has relatively low vertically averaged viscosity of about 10(21) pascal.seconds, whereas the Basin and Range has a higher vertically averaged viscosity of 10(22) pascal.seconds.

Macroscopic quantum interference from atomic tunnel arrays

Interference of atomic de Broglie waves tunneling from a vertical array of macroscopically populated traps has been observed. The traps were located in the antinodes of an optical standing wave and were loaded from a Bose-Einstein condensate. Tunneling was induced by acceleration due to gravity, and interference was observed as a train of falling pulses of atoms. In the limit of weak atomic interactions, the pulse frequency is determined by the gravitational potential energy difference between adjacent potential wells. The effect is closely related to the ac Josephson effect observed in superconducting electronic systems.

Neutron interference induced by gravity: New results and interpretations

We report the results of neutron interferometric experiments, extending the range and precision of the COW gravitationally-induced quantum interference experiment of Staudenmann and co-workers. These experiments provide a test of the principle of equivalence in the quantum limit. High precision data (1 part in 1000) is presented. The frequency of the quantum interference oscillations, and the loss of contrast observed as a function of increasing gravitational potential energy difference are compared with the recent interferometer dynamical diffraction calculations of Bonse and Wroblewski and of Horne. Theory and experiment are found to differ by 0.8%.