Andrew M. Freed

Evidence of power-law flow in the Mojave desert mantle.

Studies of the Earths response to large earthquakes can be viewed as large rock deformation experiments in which sudden stress changes induce viscous flow in the lower crust and upper mantle that lead to observable postseismic surface deformation. Laboratory experiments suggest that viscous flow of deforming hot lithospheric rocks is characterized by a power law in which strain rate is proportional to stress raised to a power, n (refs 2, 3). Most geodynamic models of flow in the lower crust and upper mantle, however, resort to newtonian (linear) stress–strain rate relations. Here we show that a power-law model of viscous flow in the mantle with n = 3.5 successfully explains the spatial and temporal evolution of transient surface deformation following the 1992 Landers and 1999 Hector Mine earthquakes in southern California. A power-law rheology implies that viscosity varies spatially with stress causing localization of strain, and varies temporally as stress evolves, rendering newtonian models untenable. Our findings are consistent with laboratory-derived flow law parameters for hot and wet olivine—the most abundant mineral in the upper mantle—and support the contention that, at least beneath the Mojave desert, the upper mantle is weaker than the lower crust.

Delayed triggering of the 1999 Hector Mine earthquake by viscoelastic stress transfer

Stress changes in the crust due to an earthquake can hasten the failure of neighbouring faults and induce earthquake sequences in some cases. The 1999 Hector Mine earthquake in southern California (magnitude 7.1) occurred only 20 km from, and 7 years after, the 1992 Landers earthquake (magnitude 7.3). This suggests that the Hector Mine earthquake was triggered in some fashion by the earlier event. But uncertainties in the slip distribution and rock friction properties associated with the Landers earthquake have led to widely varying estimates of both the magnitude and sign of the resulting stress change that would be induced at the location of the Hector Mine hypocentre—with estimates varying from -1.4 bar (ref. 6) to +0.5 bar (ref. 7). More importantly, coseismic stress changes alone cannot satisfactorily explain the delay of 7 years between the two events. Here we present the results of a three-dimensional viscoelastic model that simulates stress transfer from the ductile lower crust and upper mantle to the brittle upper crust in the 7 years following the Landers earthquake. Using viscoelastic parameters that can reproduce the observed horizontal surface deformation following the Landers earthquake, our calculations suggest that lower-crustal or upper-mantle flow can lead to postseismic stress increases of up to 1–2 bar at the location of the Hector Mine hypocentre during this time period, contributing to the eventual occurrence of the 1999 Hector Mine earthquake. These results attest to the importance of considering viscoelastic processes in the assessment of seismic hazard.

Topography of the Northern Hemisphere of Mercury from MESSENGER Laser Altimetry

Mercury Inside and Out The MESSENGER spacecraft orbiting Mercury has been in a ∼12-hour eccentric, near-polar orbit since 18 March 2011 (see the Perspective by McKinnon). Smith et al. (p. 214, published online 21 March) present the most recent determination of Mercurys gravity field, based on radio tracking of the MESSENGER spacecraft between 18 March and 23 August 2011. The results point to an interior structure that differs from those of the other terrestrial planets: the density of the planets solid outer shell suggests the existence of a deep reservoir of high-density material, possibly an Fe-S layer. Zuber et al. (p. 217, published online 21 March) used data obtained by the MESSENGER laser altimeter through to 24 October 2011 to build a topographic map of Mercurys northern hemisphere. The map shows less variation in elevation, compared with Mars or the Moon, and its features add to the body of evidence that Mercury has sustained geophysical activity for much of its history. Mercury’s topography indicates sustained geophysical activity for most of the planet’s geological history. Laser altimetry by the MESSENGER spacecraft has yielded a topographic model of the northern hemisphere of Mercury. The dynamic range of elevations is considerably smaller than those of Mars or the Moon. The most prominent feature is an extensive lowland at high northern latitudes that hosts the volcanic northern plains. Within this lowland is a broad topographic rise that experienced uplift after plains emplacement. The interior of the 1500-km-diameter Caloris impact basin has been modified so that part of the basin floor now stands higher than the rim. The elevated portion of the floor of Caloris appears to be part of a quasi-linear rise that extends for approximately half the planetary circumference at mid-latitudes. Collectively, these features imply that long-wavelength changes to Mercury’s topography occurred after the earliest phases of the planet’s geological history.

The Origin of Lunar Mascon Basins

Lunar Mascons Explained The origin of lunar mass concentrations (or mascons), which appear as prominent bulls-eye patterns on gravitational maps of both the near- and far side of the Moon, has been a mystery since they were originally detected in 1968. Using state-of-the-art simulation codes, Melosh et al. (p. 1552, published online 30 May; see the Perspective by Montesi) developed a model to explain the formation of mascons, linking the processes of impact cratering, tectonic deformation, and volcanic extrusion. A detailed model of impact basin formation explains the gravity signatures near two lunar craters. [Also see Perspective by Montesi] High-resolution gravity data from the Gravity Recovery and Interior Laboratory spacecraft have clarified the origin of lunar mass concentrations (mascons). Free-air gravity anomalies over lunar impact basins display bull’s-eye patterns consisting of a central positive (mascon) anomaly, a surrounding negative collar, and a positive outer annulus. We show that this pattern results from impact basin excavation and collapse followed by isostatic adjustment and cooling and contraction of a voluminous melt pool. We used a hydrocode to simulate the impact and a self-consistent finite-element model to simulate the subsequent viscoelastic relaxation and cooling. The primary parameters controlling the modeled gravity signatures of mascon basins are the impactor energy, the lunar thermal gradient at the time of impact, the crustal thickness, and the extent of volcanic fill.

Far-reaching transient motions after Mojave earthquakes require broad mantle flow beneath a strong crust

[1] Geodeticallyobservedpostseismicsurfacedisplacements in the 7 years following the 1999 Hector Mine earthquake demonstrate a previously unrecognized broad pattern of transient deformation throughout southern California and into Nevada, more than 200 km from the epicenter. Unlike previous postseismic observations in which trade-offs between postseismic mechanisms and the depth of flow lead to non-unique solutions, this deformation pattern can only be explained by viscoelastic flow in a region of the mantle 100s of km wide and below a depth of 40 km. This result enables two robust conclusions regarding the nature of lithospheric strength in this region: the mantle is weaker than the lower crust, and flow occurs over a wide region of mantle as opposed to within a narrow shear zone beneath

Triggering of New Madrid seismicity by late-Pleistocene erosion

The spatiotemporal behaviour of earthquakes within continental plate interiors is different from that at plate boundaries. At plate margins, tectonic motions quickly reload earthquake ruptures, making the location of recent earthquakes and the average time between them consistent with the faults’ geological, palaeoseismic and seismic histories. In contrast, what determines the activation of a particular mid-continental fault and controls the duration of its seismic activity remains poorly understood. Here we argue that the concentration of magnitude-7 or larger earthquakes in the New Madrid seismic zone of the central United States since the end of the last ice age results from the recent, climate-controlled, erosional history of the northern Mississippi embayment. We show that the upward flexure of the lithosphere caused by unloading from river incision between 16,000 and 10,000 years ago caused a reduction of normal stresses in the upper crust sufficient to unclamp pre-existing faults close to failure equilibrium. Models indicate that fault segments that have already ruptured are unlikely to fail again soon, but stress changes from sediment unloading and previous earthquakes may eventually be sufficient to bring to failure other nearby segments that have not yet ruptured.

Time‐dependent changes in failure stress following thrust earthquakes

Two-dimensional (2-D) viscoelastic finite element models were used to calculate the time-dependent changes in Coulomb failure stresses following thrust earthquakes due to respective effects of relaxation of viscous lower crust or upper mantle and postseismic creep on the main fault or its downdip extension. Results suggest that thrust earthquakes cause a coseismic increase in Coulomb stress along antithetic lobes normal to the slip plane. Following a quake, creep processes that reduce stresses in a ductile lower crust or upper mantle are calculated to cause a transfer of stress to the upper crust. Under certain conditions, transfer of stress may lead to a further buildup of high Coulomb stress along the base of the upper crust, potentially shortening the time to failure of other faults in the region. The conditions under which an antithetic lobe of high Coulomb stress are favored to expand at the base of the upper crust postseismically within a few decades include the following: the lower crust or upper mantle has an effective viscosity not greater than 1019 Pa s; the thrust fault has a moderate dip angle (40°–50°); the brittle/ductile transition is deep enough to provide a corridor at the base of the upper crust for expansion; and the crust has a low apparent coefficient of friction (<0.2). Postseismic increases in Coulomb stress within the upper crust may also be caused by aseismic creep on the fault. Stress changes due to this mechanism are maximized with a high apparent coefficient of friction. Analysis of experimentally determined non-Newtonian flow laws suggests that wet granitic, quartz, and feldspar aggregates may have a viscosity of the order of 1019 Pa s. The calculated rate of stress transfer from a viscous lower crust or upper mantle to the upper crust becomes faster with increasing values of the power law exponent and the presence of a regional compressive strain rate. Results of this 2-D analysis suggest a potentially important role of viscous flow in controlling time-dependent postseismic stress changes that warrant further investigation using 3-D viscoelastic analysis.

Tectonics of mascon loading: Resolution of the strike‐slip faulting paradox

Subsidence of lunar mascon maria, impact basins partly filled with mare basalt and sites of prominent positive gravity anomalies, typically led to the formation of concentric graben (arcuate rilles) around the flanks of the basin, while compressive features (mare ridges) formed in interior regions. Although previous numerical models of the response of the lunar lithosphere to mascon loading predict that an annulus of strike-slip faulting should also have formed around mascon maria, no such faults have been observed. This “strike-slip faulting paradox,” however, arises from an oversimplification of the earlier models. Viscoelastic finite element models of lunar mascon basins that include the effects of lunar curvature, heterogeneous crustal strength, initial stress conditions, and multistage load histories show that the width of a predicted annulus of strike-slip faulting may be small. The use of Andersons criterion for predicting fault styles may also overpredict the width of strike-slip faulting. A faulting-style criterion that takes into account transitional faulting, in which both strike-slip and dip-slip components are present, predicts zones of pure strike-slip faulting that are about half of the width predicted by the Anderson criterion. Furthermore, strike-slip faulting should be observed only in regions in which flexural stresses are sufficient to induce rock failure. However, since stress patterns consistent with strike-slip faulting around mascon loads represent a transition between compressional and extensional provinces, differential stresses tend to be low in these regions and for at least part of this region are not sufficient to induce rock failure. A mix of concentric and radial thrust faulting is observed in some mascon maria, at odds with previous models that predict only radial orientations away from the basin center. This apparent discrepancy may be partly explained by the multistage emplacement of mare basalt units, a scenario that leads to a stress pattern where concentric and radial orientations of thrust faults are equally preferred. Detailed models of the Serenitatis basin indicate a 25-km-thick lunar lithosphere at the time of rille formation and a 75-km-thick lithosphere at the time of late-stage mare ridge formation. The extent of observed mare ridges and the inferred cessation of rille formation around Serenitatis prior to the time of emplacement of the youngest mare basalt units is consistent with the superposition of a global horizontal compressive stress field generated by the cooling and contraction of the lunar interior with the local stresses associated with lithospheric loading.

Using short-term postseismic displacements to infer the ambient deformation conditions of the upper mantle

[1] To interpret short-term postseismic surface displacements in the context of key ambient conditions (e.g., temperature, pressure, background strain rate, water content, creep mechanism), we combined steady state and transient flow into a single constitutive relation that can explain the response of a viscoelastic material to a change in stress. The flow law is then used to investigate mantle deformation beneath the Eastern California Shear Zone following the 1999 M7.1 Hector Mine earthquake. The flow law parameters are determined using finite element models of relaxation processes, constrained by surface displacement time series recorded by 55 continuous GPS stations for 7 years following the earthquake. Results suggest that postseismic flow following the Hector Mine earthquake occurs below a depth of � 50 km and is controlled by dislocation creep of wet olivine. Diffusion creep models can also explain the data, but require a grain size (3.5 mm) that is smaller than the inferred grain size (10–20 mm) based on the mantle conditions at these depths. In addition, laboratory flow laws predict dislocation creep would dominate at the stress/grain size conditions that provide the best fit to diffusion creep models. Model results suggest a transient creep phase that lasts � 1 year and has a viscosity � 10 times lower than subsequent steady state flow, in general agreement with laboratory observations. The postseismic response is best explained as occurring within a relatively hot upper mantle (e.g., 1200–1300°C at 50 km depth) with a long-term background mantle strain rate of 0.1–0.2 mstrain/yr, consistent with the observed surface strain rate. Long-term background shear stresses at the top of the mantle are � 4 MPa, then decrease with depth to a minimum of 0.1–0.2 MPa at 70 km depth before increasing slowly with depth due to the pressure dependence of viscosity. These conditions correspond to a background viscosity of 10 21 Pa s within a thin mantle lid that decreases to � 5 � 10 19 Pa s within the underlying asthenosphere. This study shows the utility of using short-term postseismic observations to infer long-term mantle conditions that are not readily observable by other means.

Accelerated stress buildup on the southern San Andreas fault and surrounding regions caused by Mojave Desert earthquakes

A sequence of four Mw . 6 earthquakes, including the 1992 Mw 5 7.3 Landers and Mw 5 7.1 Hector Mine earthquakes, occurred in the Mojave Desert in the 1990s in close proximity to the southern San Andreas fault, inducing stress changes on several of its segments. We calculate that coseismic slip combined with postseismic relaxation of viscous lower crust and/or upper mantle has led to a Coulomb stress increase of 2.3‐3.5 bar on the San Bernardino Mountain segment of the southern San Andreas fault between 1992 and 2001, with a projected increase of 3.6‐4.9 bar by the year 2020. In comparison, the calculated coseismic stress increase is 1.8 bar for this segment. This accelerated buildup of stresses is predicted to bring the San Bernardino Mountain segment, which last ruptured more than 190 yr ago, closer to a potentially major rupture. Meanwhile we project a net stress decrease of as much as 23.5 bar between 1992 and 2020 for the western Coachella Valley segment if the fault is governed by low effective friction, or an increase of 1.5 bar if the fault is governed by high effective friction. Coulomb stresses are calculated to decrease on the Mojave segment by as much as 21 bar between 1992 and 2020. Accelerated stress buildup is also predicted to occur on parts of the San Jacinto, Elsinore, and Calico faults. The pattern of the observed post-Landers aftershock clustering and the calculated Coulomb stress buildup on the Calico fault is similar to that noted in the Hector Mine region prior to the 1999 Mw 5 7.1 earthquake. These results imply that the stress changes caused by an earthquake may still play a role in triggering future quakes in neighboring crust many years later through viscoelastic processes.