Carl W. Gable

Convection in three dimensions with surface plates: Generation of toroidal flow

This work presents numerical calculations of mantle convection that incorporate some of the basic observational constraints imposed by plate tectonics. The model is three-dimensional and includes surface plates; it allows plate velocity to change dynamically according to the forces which result from convection. We show that plates are an effective means of introducing a toroidal component into the flow field. After initial transients the plate motion is nearly parallel to transform faults and in the direction that tends to minimizes the toroidal flow field. The toroidal field decays with depth from its value at the surface; the poloidal field is relatively constant throughout the layer but falls off slightly at the top and bottom boundaries. Layered viscosity increasing with depth causes the toroidal field to decay more rapidly, effectively confining it to the upper, low-viscosity layer. The effect of viscosity layering on the poloidal field is relatively small, which we attribute to its generation by temperature variations distributed throughout the system. The generation of toroidal flow by surface plates would seem to account for the observed nearly equal energy of toroidal and poloidal fields of plate motions on the Earth. A low-viscosity region in the upper mantle will cause the toroidal flow to decay significantly before reaching the lower mantle. The resulting concentration of toroidal flow in the upper mantle may result in more thorough mixing there and account for some of the geochemical and isotopic differences proposed to exist between the upper and lower mantles.

Dynamics of mantle flow and melting at a ridge-centered hotspot: Iceland and the Mid-Atlantic Ridge

The dynamics of mantle flow and melting of a ridge-centered plume were investigated with three-dimensional variable-viscosity numerical models, focusing on three buoyancy sources: temperature, melt depletion, and melt retention. The width, W, to which a plume spreads along a ridge axis, depends on plume volume flux, Q, full spreading rate, U, buoyancy number, B, and ambientrplume viscosity contrast g . When all melting effects are considered, our numerical . 1 r 2 . 0.04 results are best parameterized by Ws 2.37 Qr UB g . Thermal buoyancy is first-order in controlling along-axis plume spreading while latent heat loss due to melting, and depletion and retention buoyancy forces contribute second-order . effects. We propose two end-member models for the Iceland plume beneath the Mid-Atlantic Ridge MAR . The first has a broad plume source with temperature anomaly DT of 758C, radius, a, of 300 km, and Q of 1.2 = 10 7 km 3 rmy. The second p is of a narrower and hotter plume source with DT of 1708C, a radius of 60 km, and Q of 2.1 = 10 6 km 3 rmy. The broad p plume source predicts successfully the observed seismic crustal thickness, topographic, and gravity anomalies along the MAR, but predicts an along-axis geochemical plume width substantially broader than that suggested by the observed 87 Srr 86 Sr anomaly. The narrow plume source model predicts successfully the total excess crustal production rate along the

Interaction of mantle plumes and migrating mid‐ocean ridges: Implications for the Galápagos plume‐ridge system

We investigate the three-dimensional interaction of mantle plumes and migrating mid-ocean ridges with variable viscosity numerical models. Numerical models predict that along-axis plume width W and maximum distance of plume-ridge interaction xmax scale with (Q/U)½, where Q is plume source volume flux and U is ridge full spreading rate. Both W and xmax increase with buoyancy number ⊓b which reflects the strength of gravitational-versus plate-driven spreading. Scaling laws derived for stationary ridges in steady-state with near-ridge plumes are consistent with those obtained from independent studies of Ribe [1996]. In the case of a migrating ridge, the distance of plume-ridge interaction is reduced when a ridge migrates toward the plume because of the excess drag of the faster moving leading plate and enhanced when a ridge migrates away from the plume because of the reduced drag of the slower moving trailing plate. Given the mildly buoyant and relatively viscous plumes investigated here, the slope of the lithospheric boundary and thermal erosion of the lithosphere have little effect on plume flow. From observed plume widths of the Galapagos plume-migrating ridge system, our scaling laws yield estimates of Galapagos plume volume flux of 5–16×106km3 m.y.−1 and a buoyancy flux of ∼2×103 kg s−1. Model results suggest that the observed increase in bathymetric and mantle-Bouguer gravity anomalies along Cocos Plate isochrons with increasing isochron age is due to higher crustal production when the Galapagos ridge axis was closer to the plume several million years ago. The anomaly amplitudes can be explained by a plume source with a relatively mild temperature anomaly (50°–100°C) and moderate radius (100–200 km). Predictions of the along-axis geochemical signature of the plume suggest that mixing between the plume and ambient mantle sources may not occur in the asthenosphere but, instead, may occur deeper in the mantle possibly by entrainment of depleted mantle as the plume ascends from its source.

Hydrogeologic Controls on Induced Seismicity in Crystalline Basement Rocks Due to Fluid Injection into Basal Reservoirs

A series of Mb 3.8-5.5 induced seismic events in the midcontinent region, United States, resulted from injection of fluid either into a basal sedimentary reservoir with no underlying confining unit or directly into the underlying crystalline basement complex. The earthquakes probably occurred along faults that were likely critically stressed within the crystalline basement. These faults were located at a considerable distance (up to 10 km) from the injection wells and head increases at the hypocenters were likely relatively small (∼70-150 m). We present a suite of simulations that use a simple hydrogeologic-geomechanical model to assess what hydrogeologic conditions promote or deter induced seismic events within the crystalline basement across the midcontinent. The presence of a confining unit beneath the injection reservoir horizon had the single largest effect in preventing induced seismicity within the underlying crystalline basement. For a crystalline basement having a permeability of 2 × 10(-17)  m(2) and specific storage coefficient of 10(-7) /m, injection at a rate of 5455 m(3) /d into the basal aquifer with no underlying basal seal over 10 years resulted in probable brittle failure to depths of about 0.6 km below the injection reservoir. Including a permeable (kz  = 10(-13)  m(2) ) Precambrian normal fault, located 20 m from the injection well, increased the depth of the failure region below the reservoir to 3 km. For a large permeability contrast between a Precambrian thrust fault (10(-12)  m(2) ) and the surrounding crystalline basement (10(-18)  m(2) ), the failure region can extend laterally 10 km away from the injection well.

The dynamics of off-axis plume-ridge interaction in the uppermost mantle

Two decades of geochemical and geophysical observations have led to the plume channel model whereby buoyant, off-axis mantle plumes feed and interact with diverging plates at mid-ocean ridge axes which act as sinks of upper mantle material. Here we present results from two-dimensional (2-D) numerical experiments which incorporate the essential physics and fluid dynamic aspects of the plume-ridge-upper mantle system in order to test the feasibility of this plume-ridge interaction model. Specifically, experiments test the relative importance of physical effects such as strong viscosity variations and thermal and chemical buoyancy forcing in plume-ridge dynamics. Results indicate that both transient and steady-state connections may be established between off-axis plumes and ridges for a range of realistic mantle conditions. The presence of a strongly sloping rheological boundary layer (RBL) is a necessary condition for long-term communication between an off-axis buoyant upwelling and a spreading ridge. The flux of buoyant material to the ridge is also shown to increase with increasing plume-to-mantle density contrast, decreasing plume viscosity and smaller plume-ridge separation distances. Plume-ridge interaction regimes are defined based on the competing effects of plate-driven and buoyancy-driven flow. Thermal erosion of the viscous lithosphere strongly inhibits long-term plume-ridge interaction by enhancing the plates ability to deflect the plume, both head and conduit, away from the ridge axis.

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

Abstract dfn W orks is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using dfn G en , which combines fram (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the L a G ri T meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in an intrinsically parallel fashion. Flow through the network is simulated in dfn F low , which utilizes the massively parallel subsurface flow and reactive transport finite volume code pflotran . A Lagrangian approach to simulating transport through the DFN is adopted within dfn T rans to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO2 sequestration are also included.

Episodic tectonic plate reorganizations driven by mantle convection

Abstract Periods of relatively uniform plate motion were interrupted several times throughout the Cenozoic and Mesozoic by rapid plate reorganization events [R. Hey, Geol. Soc. Am. Bull. 88 (1977) 1404–1420; P.A. Rona, E.S. Richardson, Earth Planet. Sci. Lett. 40 (1978) 1–11; D.C. Engebretson, A. Cox, R.G. Gordon, Geol. Soc. Am. Spec. Pap. 206 (1985); R.G. Gordon, D.M. Jurdy, J. Geophys. Res. 91 (1986) 12389–12406; D.A. Clague, G.B. Dalrymple, US Geol. Surv. Prof. Pap. 1350 (1987) 5–54; J.M. Stock, P. Molnar, Nature 325 (1987) 495–499; C. Lithgow-Bertelloni, M.A. Richards, Geophys. Res. Lett. 22 (1995) 1317–1320; M.A. Richards, C. Lithgow-Bertelloni, Earth Planet. Sci. Lett. 137 (1996) 19–27; C. Lithgow-Bertelloni, M.A. Richards, Rev. Geophys. 36 (1998) 27–78]. It has been proposed that changes in plate boundary forces are responsible for these events [M.A. Richards, C. Lithgow-Bertelloni, Earth Planet. Sci. Lett. 137 (1996) 19–27; C. Lithgow-Bertelloni, M.A. Richards, Rev. Geophys. 36 (1998) 27–78]. We present an alternative hypothesis: convection-driven plate motions are intrinsically unstable due to a buoyant instability that develops as a result of the influence of plates on an internally heated mantle. This instability, which has not been described before, is responsible for episodic reorganizations of plate motion. Numerical mantle convection experiments demonstrate that high-Rayleigh number convection with internal heating and surface plates is sufficient to induce plate reorganization events, changes in plate boundary forces, or plate geometry, are not required.

Origin and Extent of Fresh Paleowaters on the Atlantic Continental Shelf, USA

While the existence of relatively fresh groundwater sequestered within permeable, porous sediments beneath the Atlantic continental shelf of North and South America has been known for some time, these waters have never been assessed as a potential resource. This fresh water was likely emplaced during Pleistocene sea-level low stands when the shelf was exposed to meteoric recharge and by elevated recharge in areas overrun by the Laurentide ice sheet at high latitudes. To test this hypothesis, we present results from a high-resolution paleohydrologic model of groundwater flow, heat and solute transport, ice sheet loading, and sea level fluctuations for the continental shelf from New Jersey to Maine over the last 2 million years. Our analysis suggests that the presence of fresh to brackish water within shallow Miocene sands more than 100 km offshore of New Jersey was facilitated by discharge of submarine springs along Baltimore and Hudson Canyons where these shallow aquifers crop out. Recharge rates four times modern levels were computed for portions of New Englands continental shelf that were overrun by the Laurentide ice sheet during the last glacial maximum. We estimate the volume of emplaced Pleistocene continental shelf fresh water (less than 1 ppt) to be 1300 km(3) in New England. We also present estimates of continental shelf fresh water resources for the U.S. Atlantic eastern seaboard (10(4) km(3)) and passive margins globally (3 x 10(5) km(3)). The simulation results support the hypothesis that offshore fresh water is a potentially valuable, albeit nonrenewable resource for coastal megacities faced with growing water shortages.

Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy

We introduce the feature rejection algorithm for meshing (FRAM) to generate a high quality conforming Delaunay triangulation of a three-dimensional discrete fracture network (DFN). The geometric features (fractures, fracture intersections, spaces between fracture intersections, etc.) that must be resolved in a stochastically generated DFN typically span a wide range of spatial scales and make the efficient automated generation of high-quality meshes a challenge. To deal with these challenges, many previous approaches often deformed the DFN to align its features with a mesh through various techniques including redefining lines of intersection as stair step functions and distorting the fracture edges. In contrast, FRAM generates networks on which high-quality meshes occur automatically by constraining the generation of the network. The cornerstone of FRAM is prescribing a minimum length scale and then restricting the generation of the network to only create features of that size and larger. The process is f...

Thermal evolution of the mantle following continental aggregation in 3D convection models

The claim that supercontinents insulate the mantle is largely based on recognition that seismically slow mantle below the Atlantic-African geoid high coincides with the former location of Pangea. We investigate the viability of continental insulation by varying both plate geometries and mantle properties in six three-dimensional (3D) mantle convection models. The efficiency of continental insulation is quantified by calculating the rate of change of the average temperature in the subcontinental mantle. Our findings generally agree with two-dimensional (2D) modeling results. However, we conclude that 2D convection models may exaggerate subcontinental heating, particularly in largely bottom heated cases, and that subcontinental heating results from an absence of subduction in the subcontinental mantle rather than the insulation of active upwellings. Correspondingly, we find that when large degrees of internal heating are present in the mantle, hotter-than-average regions evolve below large oceanic plates.