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Shear-Driven Upwelling Induced by Lateral Viscosity Variations
and Asthenospheric Shear: A Mechanism for Intraplate Volcanism
Clinton P. Conrad*
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Department of Geology and Geophysics, SOEST, University of Hawaii, Honolulu HI 96816
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Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore MD 21218
Benjun Wu
Eugene I. Smith
Ashley Tibbetts
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Department of Geoscience, University of Nevada at Las Vegas, Las Vegas NV 89154
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Corresponding Author: clintc@hawaii.edu
Submitted to Physics of the Earth and Planetary Interiors, March XX, 2009
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Abstract
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Volcanism that occurs away from ridges and subduction zones does not have an obvious plate
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tectonic explanation, but instead must arise from sub-lithospheric processes that generate
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upwelling flow and decompression melting. Several convective processes, such as mantle
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plumes, convective instability, edge-driven convection, and Richter rolls, produce upwelling via
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the action of gravity on density heterogeneities in the mantle. Here we investigate an alternative
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mechanism, the shear-driven upwelling (SDU), which instead generates upwelling flow solely
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through the action of asthenospheric shear flow on viscosity heterogeneity. Using a numerical
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flow model, we examine the effect of viscosity heterogeneity on viscous shear flow induced
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within an asthenospheric layer. We demonstrate that for certain geometries and viscosity ratios,
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circulatory flow develops within a “cavity” or “step” embedded into the lithospheric base, or
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within a low-viscosity “pocket” embedded within the asthenospheric layer. For an asthenosphere
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accommodating 5 cm/yr of shear, we estimate that SDU can produce upwelling rates of up to
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~0.2 cm/yr within a continental rift, ~0.5 cm/yr along the vertical edge of a craton, or ~1.0 cm/yr
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within a “pocket” of low-viscosity asthenosphere. In the last case, the pocket must feature an as-
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pect ratio of more than 5 and be at least 100 times less viscous than the surrounding astheno-
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sphere. Such viscosity heterogeneity may be associated with thermal, chemical, melting, volatile,
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or grain-size heterogeneity, and is consistent with tomographic constraints on asthenospheric
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variability. We conclude that SDU could provide an explanation for some intraplate volcanism
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occurring above rapidly shearing asthenosphere, for example in the Basin and Range region of
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North America.
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Keywords: Intraplate Volcanism; Asthenospheric Upwelling; Upper Mantle Flow; Plate Motions;
Viscous Shear; Viscosity Heterogeneity; Melting Instability
1. Introduction
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Most of the volcanism around the globe occurs at subduction zones and mid-ocean
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ridges, and is well-explained by the theory of plate tectonics. Volcanism that occurs away from
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plate boundaries, however, is less easily explained, but has often been attributed to hot plumes
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that rise from deep within the mantle [Morgan, 1971]. Such plumes are a natural consequence of
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mantle convection and provide an explanation for the numerous linear chains of volcanoes
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around the globe [e.g., Richards et al., 1989]. Recently, however, the plume explanation for in-
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traplate volcanism has been challenged [e.g., Foulger & Natland, 2003], and alternative explana-
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tions such as lithospheric cracking have been proposed [e.g., Anderson, 2000]. Recent studies
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have suggested that relatively few (less than 10) volcanic chains are caused by deep mantle
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plumes [e.g. Courtillot et al., 2003], out of upwards of 30 to 40 hotspot tracks that have previ-
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ously been attributed to plumes [e.g., Sleep, 1990; Steinberger, 2000]. Thus, regardless of
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whether the major hotspots (e.g., Iceland, Hawaii, Louisville) are plume-generated, an alternative
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explanation is needed to explain intraplate volcanism not fed by plumes.
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Furthermore, several other intraplate volcanic features, such as seamounts that pervade
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Pacific basin [Hillier & Watts, 2007], are not associated with classic hotspot tracks [Clouard &
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Bonneville, 2001]. Instead most Pacific seamounts were emplaced during Cretaceous along with
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the large Pacific oceanic plateaus [Wessel, 1997]. More recently, the southwestern US has be-
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come dotted by Quaternary to recent basaltic volcanic fields, such as the Death Valley-Lunar
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Crater belt, the Saint George volcanic Field, and the Jemez lineament. These features do not re-
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semble plume-induced volcanism in terms of their temporal and spatial patterns [Smith et al.,
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2002; Smith & Keenan, 2005], associated uplift [Parsons et al., 1994], or volumetric output
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[Bradshaw et al., 1993; Hawkesworth et al., 2005]. Other examples of non-plume intraplate vol-
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canism, such as in the Harrat Ash Shaam field in the Middle East [e.g., Shaw et al., 2003], and
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the Changbai volcano in Northeast Asia [Lei & Zhao, 2005], have been noted in several locations
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around the world.
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Without a source of excess heat coming from the deep mantle, most alternative explana-
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tions for intraplate volcanism invoke some source of regional asthenospheric upwelling that in-
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duces decompression melting. This melting may be augmented by “melting instabilities” that
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involve positive feedback between decompression melting and the subsequent upwelling caused
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by the presence of this melt [Raddick et al., 2002; Hernlund et al., 2008a; 2008b]. This feedback
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can result in sustained volcanism above asthenosphere near its melting temperature. Thus, the
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search for a non-plume source of intraplate volcanism generally involves a search for mecha-
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nisms that can initiate upwelling flow within the asthenosphere. Several upwelling mechanisms
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have been proposed. First, the presence of extension generates passive upwelling flow [e.g.,
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McKenzie & Bickle, 1988], but this flow should be extremely slow unless it becomes localized in
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some way. In addition, numerical models show that melting instabilities may be inhibited or de-
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layed by the presence of active lithospheric extension [Hernlund et al., 2008b]. Alternatively, the
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temperature differential between the lithosphere and asthenosphere sets up an inverted density
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structure that can lead to persistent steady-state thermal convection in the asthenosphere [e.g.,
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Haxby & Weissel, 1986; van Hunen & Zhong, 2006; Ballmer et al., 2007] or occasional “drips”
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of dense lithosphere sinking into the upper mantle [e.g., Le Pourhiet et al., 2006]. Both convec-
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tion and “dripping” involve asthenospheric upwelling that can lead to volcanism, and may be
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enhanced by viscosity heterogeneity or lithospheric deformation [e.g., Conrad, 2000]. Finally,
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small-scale convection in the asthenosphere may be enhanced near the edges of cratons or other
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sharp gradients in lithospheric thickness because the associated lateral temperature gradients can
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produce an “edge-driven” convective circulation in the asthenosphere [e.g., King & Anderson,
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1998] that can lead to volcanism [King & Ritsema, 2000].
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The density inversion between the lithosphere and asthenosphere is not the only energy
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source that can drive small-scale asthenospheric circulation and upwelling. For example, the as-
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thenosphere accommodates up to a few cm/yr of relative motion between the lithospheric plates
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and the convecting mantle via a shearing deformation that can be detected by observations of
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seismic anisotropy [e.g., Silver & Holt, 2002; Conrad et al., 2007]. When asthenospheric shear
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occurs simultaneously with small-scale convection, the density heterogeneity produced by con-
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vection becomes elongated into roll-like circulatory structures known as “Richter Rolls” [e.g.,
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Richter & Parsons, 1975; Korenaga & Jordan, 2003]. Less well-studied, however, is the re-
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sponse of a shear flow to viscosity heterogeneity, either within the asthenospheric layer (e.g., as-
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sociated with thermal or chemical heterogeneities or pockets of melt) or associated with lateral
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variations in lithospheric thickness (e.g., near a ridge or a cratonic “edge”). In some engineering
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applications, for example, the presence of a shear flow beneath an open fluid-filled “cavity” can
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produce circulatory flow within the cavity at low Reynolds numbers [e.g., Shen & Floryan,
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1985; Pakdel et al., 1997; Shankar & Deshpande, 2000]. Applied to the asthenosphere, this
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“shear-driven cavity flow” may produce a type of upwelling that is not associated with any con-
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vective process. Instead, the driver for this type of upwelling is the relative motion between the
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plates and mantle; upwelling flow is excited in this case by viscosity heterogeneity, rather than
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density heterogeneity (e.g., Fig. 1). In this study, we examine how asthenospheric shear flow
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may combine with asthenospheric or lithospheric viscosity heterogeneity to produce upwelling
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flow in the asthenosphere. We then examine the dynamical situations where this type of “shear-
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driven upwelling” (SDU hereafter) may generate mantle upwelling, and thus intraplate volcan-
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ism.
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2. Lithospheric Viscosity Variations: Shear-Driven Cavity Flow
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We first examine the response of asthenospheric shear flow to a variation in the basal to-
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pography of the lithosphere. Such variations are expected in the vicinity of mid-ocean ridges,
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continental rifts, and cratonic roots. To describe asthenospheric shear flow beneath these fea-
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tures, we turn first to the engineering literature, where the fluid mechanics of highly viscous (low
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Reynolds number) flows have been well studied. Here we examine flow beneath lithospheric
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thickness variations in terms of the classic engineering problem known as “lid-driven” (e.g.,
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Pakdel et al., 1997; Shankar & Deshpande, 2000; Gürcan, 2005) or “shear-driven” (e.g., Shen &
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Floryan, 1985; Pakdel et al., 1997; Shankar & Deshpande, 2000) flow within a cavity. For the
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shear-driven cavity flow, most published literature deals with a rectangular cavity added to one
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wall of a channel (Fig. 2); motion of the opposite wall generates shear within the channel that
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excites flow within the cavity.
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2.1 Model Setup
We study cavity flow using the finite element code ConMan [King et al., 1990], which is
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designed for two-dimensional study of viscous flow within the Earth’s mantle. We generate a
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flow field (e.g., Fig. 1) by imposing a dimensionless velocity V on the base of an asthenospheric
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channel that is Hasth=100 km thick and contains fluid of viscosity asth. Above the asthenosphere
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lies a lithospheric layer with a high viscosity of 10,000asth, which serves to impose stationary
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conditions on the top of the asthenospheric channel (meaning that we are studying shear flow in
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the reference frame of the surface plate; V then represents the full velocity contrast across the
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asthenosphere). We embed a cavity (with width WC, height HC, and viscosity C) within the
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lithospheric layer (Fig. 2) in order to study flow patterns induced in the cavity by the driven
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asthenospheric shear. Dimensionless cavity heights and widths are defined using the aspect ratio
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AC WC HC and the asthenospheric thickness ratio TC  H asth H asth  H C  (TC expresses the
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relative asthenospheric thicknesses with and without the cavity). A 30 km buffer zone (Fig. 2) is
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included between the cavity walls and the side boundary conditions that allow free horizontal
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flow into and out of the calculation. The calculations performed here use resolutions of 0.5, 1.0,
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or 2.0 km (depending on the cavity size), and thus require up to 300,000 finite elements.
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2.2 Numerical Results
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Cavity dimensions largely determine the flow patterns that occur within the cavity. For
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narrow cavities, we observe a circulatory flow pattern that fills the entire cavity (AC=2 and
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TC=0.85, Fig. 3a). This circulation is driven from below by asthenospheric shear and includes
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shear-driven upwelling (SDU) flow along the downstream wall of the cavity, return flow along
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the cavity ceiling, and downwelling along the upstream wall. As the aspect ratio grows (AC=4
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and TC=0.85, Fig. 3b), the walls of the cavity become increasingly separated and the returning
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flow along the cavity ceiling diminishes. In this case, circulatory flow and associated SDU is
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confined to the two inner corners of the cavity while the rest of the cavity becomes filled with a
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broad widening of the background asthenospheric shear flow. As the cavity widens further (AC=6
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and TC=0.85, Fig. 3c), the penetration of the asthenospheric shear flow into the cavity dominates
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the cavity flow field. Note that in this case, SDU occurs on the downstream side of the cavity as
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part of the corner circulation, and on the upstream side of the cavity as part of the widening shear
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flow. These patterns of cavity flow have been documented previously [Shankar & Deshpande,
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2000] in laboratory [Shen & Floryan, 1985] and analytical [Gürcan, 2005] studies.
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We characterize the full range of cavity flow behavior by varying AC and TC. By examin-
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ing the maximum upwelling velocity within the cavity (Fig. 4a), we find that the fastest
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upwelling flow occurs for the widest (large AC) and deepest (small TC) cavities. As discussed
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above, a wide cavity permits penetration of the asthenospheric shear flow into the cavity; a deep-
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er cavity requires a more extensive penetration of this flow, and thus permits a faster upwelling
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velocity. By examining the horizontal velocity at the cavity centerline at a point 10% of the cavi-
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ty thickness from the cavity ceiling (Fig. 4b), we can determine the pattern of flow in the cavity.
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For narrow cavities (small AC), these velocities are negative and represent return flow from the
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cavity circulation (Fig. 3a). For wider cavities, these velocities are positive and represent pene-
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tration of asthenospheric shear flow into the cavity (Fig. 3c). The boundary between these two
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regimes occurs when the horizontal velocity is approximately zero at this depth (Fig. 4b). Shen &
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Floryan [1985] showed that this transition occurred at an aspect ratio of about 3; we find that the
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critical aspect ratio depends on TC, but is between 3 and 4 for TC>0.55. Shen & Floryan’s [1985]
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study assigns cavity dimensions consistent with TC~0.94, but employ a Poiseuille-Couette flow
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field that amplifies shear near the cavity mouth, leading to a somewhat smaller effective TC. For
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TC~0.7, we find a critical aspect ratio close to (but slightly larger than) the value of ~3 that Shen
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& Floryan [1985] observed, indicating a broad consistency of our results with the engineering
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literature.
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Because SDU within the cavity may induce asthenospheric melting, which would de-
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crease the viscosity within the cavity, we also examined the case in which C is smaller than asth
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by a factor of 10 (Fig. 5). The lower viscosity in the cavity causes more of the deformation of the
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system to move from the channel into the lower-viscosity cavity. This enhanced deformation of
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the cavity fluid allows circulatory flow within the cavity for higher aspect ratios (compare Fig.
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5b and Fig. 4b), and generally increases the magnitude of SDU for the circulatory flow regime
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(compare Fig. 5a and Fig. 4a).
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2.3 Shear-Driven Cavity Flow within Earth’s Asthenosphere
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On Earth, cavities within the lithosphere are found beneath mid-ocean ridges and conti-
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nental rifts. However, because plate spreading is associated with both of these tectonic environ-
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ments, the presence of persistent asthenospheric shear in one direction is unlikely. Furthermore,
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volcanism in these systems can already be well explained by passive upwelling associated with
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localized extension. Nevertheless, if spreading ceases or becomes overwhelmed by a shear flow
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induced by global mantle flow, then the sub-lithospheric cavities associated with mid-ocean
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ridges or continental rifts might serve as hosts to SDU. The “edge” of a thick craton, if present
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above asthenospheric shear, may also excite SDU, and can be examined in terms of shear-driven
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cavity flow if we assume a very wide cavity.
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To evaluate the capacity of these geometrical configurations to produce SDU, we esti-
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mate the ratios TC and AC, and refer to Figures 4a and 5a to estimate the maximum rate of SDU
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relative to the driving shear flow. To evaluate the style of cavity flow, we refer to Figures 4b and
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5b. Full circulation within the cavity is indicated by the blue regions of these figures; in these
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cases SDU should occur on the “downstream” wall of the cavity (e.g., Fig. 3a; here and below,
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“downstream” refers to the direction of the shear flow with respect to the stationary plate; “up-
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stream” is the opposite direction). In the red regions of these figures, flow primarily follows the
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contours of the lithospheric base (e.g., Fig. 3c). Although upwelling does occur as the shear flow
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enters the cavity, the associated upwelling is generally diffuse and therefore slow. These cases
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also show small circulatory “vortices” also occur within the inside corners of the upstream-
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facing steps (e.g., Fig. 3c). These vortices produce SDU with amplitudes only ~0.1% of the shear
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velocity amplitude, and will only occur if these interior corners are sufficiently sharp. Therefore,
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we do not expect significant SDU to be associated with these interior vortices for most geologic
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scenarios. As a result, we will only consider SDU from a cavity flow to be significant if there is a
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closed circulation within the cavity (as in Fig. 3a), as indicated by the blue regions of Figs. 4b
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and 4c.
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For a mid-ocean ridge, we estimate TC and AC by noting that the thickness of the oceanic
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lithosphere increases rapidly away from the ridge. At 10 Myr, the base of the lithosphere (ap-
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proximated by the 1000C isotherm) should be ~30 km deep [e.g., Stein & Stein, 1992]. For the
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slowest spreading ridges (e.g., the mid-Atlantic ridge, which spreads at ~2 cm/yr in places), the
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two 10 Myr isochrons are about 400 km apart. This yields TC~0.9 if the base of the astheno-
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sphere is 300 km deep, and AC~13. The upwelling rate associated with SDU in this cavity is ra-
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ther slow (Fig. 4A) and does not involve circulatory flow (it is in the red area of Fig. 4b), primar-
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ily because the cavity depth is small relative to the asthnospheric thickness, and does not induce
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significant velocity gradients near the cavity base. Slow and non-circulating flows are expected
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even if the cavity is filled with low-viscosity fluid (Fig. 5), as expected if excess heat or melting
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is present beneath the ridge. Therefore, shear-driven cavity flow may only form beneath a ridge
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if asthenospheric shear becomes concentrated within a much shallower (~100 km) region imme-
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diately beneath the ridge, perhaps via viscous layering of the asthenosphere.
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Continental rifting may provide a greater opportunity for SDU because existing continen-
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tal lithosphere can be thicker than new oceanic lithosphere, and therefore produce a deeper cavi-
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ty. For example, tomographic studies of the Rio Grande rift [West et al., 2004], show a ~200 km
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wide low-velocity anomaly extending 100-200 km beneath the surface and surrounded by a 100
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km thick layer with a faster velocity anomaly [van Wijk et al., 2008]. Again assuming a 300 km
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depth to the asthenospheric base, we estimate T~0.67 and a cavity aspect ratio of only about 2.
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This combination of parameters allows for circulatory flow within the cavity (blue regions of
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Figs. 4b and 5b), with amplitudes of up to about 4% of the shear flow amplitude if the cavity is
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filled with low-viscosity fluid (Fig. 5a). Since the amplitude of asthenospheric shear cannot be
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greater than the rate of plate motions, which can be up to about 5 cm/yr for continental plates,
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then SDU within a continental rift could induce upwelling rates of up to about 0.2 cm/yr within
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the rift, particularly against the downstream wall of the sub-lithospheric rift cavity.
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We also investigate the possibility of SDU forming against the edge of a large variation
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in lithospheric thickness, such as the side of a cratonic root, by considering only one wall of a
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large aspect ratio cavity (e.g., AC>10, Figs. 4 & 5). Cratons may penetrate as deeply as 200 to
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300 km or more [e.g., Jaupart & Mareschal, 1999], which indicates TC  0.5 if the surrounding
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lithosphere is 100 km thick and the asthenospheric base is 300 km deep. For a uniform viscosity
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asthenosphere, the flow field within the “cavity” (in this case the portion of the asthenosphere
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bounded by the step) is non-circulatory (red area of Fig. 4b) and simply responds to the changing
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asthenospheric thickness; the shear flow is downward beneath an upstream-facing step and up-
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ward beneath a downstream-facing step (Fig. 3c). If the asthenosphere is layered, however, such
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that the fluid next to the step is low-viscosity, then our calculations show that a large step induc-
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es a “return flow” in the upper asthenosphere (Fig. 5b is blue for TC<0.6). In this case, we expect
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upwelling against an upstream-facing step (e.g., Fig. 3a, but for large aspect ratio) with an ampli-
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tude that can be 10% of the shear amplitude (Fig. 5a), or 0.5 cm/yr for a 5 cm/yr shear flow.
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Finally, rapid variations in lithospheric thickness may occur in non-cratonic regions as
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well, such as near the Basin and Range province, where a sharp ~50 km increase in lithospheric
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thickness has been documented [Zandt et al., 1995] near volcanism that seems to arise from as-
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thenospheric melting [Wang et al., 2002]. When added above asthenosphere that is at least 150
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km thick, we estimate TC  0.7 for these non-cratonic lithospheric steps. These shallower steps
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do not produce a return flow in the asthenosphere (Fig. 4b), even for a low-viscosity upper as-
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 5b). Thus, although large steps (TC>0.5) may produce SDU for either upthenosphere (Fig.
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stream- or downstream-facing orientations, smaller steps (TC>0.7) will only generate SDU if they
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face downstream.
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3. Asthenospheric Viscosity Variations: Circulatory Flow in a Low-Viscosity “Pocket”
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A geophysically-interesting variation of the shear-driven cavity flow, which has not been
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explored in the engineering literature, involves relaxing the rigidity of the cavity-containing lay-
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er. In this case, the “cavity” becomes a region of relatively low-viscosity that is embedded within
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the shearing layer (Fig. 6). The viscosity heterogeneity in this case may result from the presence
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of “pockets” of mantle with unusually high temperature, volatile concentration, or melt fraction,
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or small grain size, which produce regions of anomalously low viscosity within a shearing as-
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thenospheric layer. Here we examine how a low-viscosity “pocket” with given dimensions may
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deform when subjected to rapid asthenospheric shear.
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3.1 Model Setup
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To study the response of asthenospheric viscosity heterogeneity to imposed shear flow,
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we again set up viscous flow calculations using the finite element code ConMan [King et al.,
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1990]. As before, we induce shear flow in a 100 km thick asthenospheric layer (viscosity asth)
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by imposing a basal velocity V while holding the high-viscosity lithosphere viscosity
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10,000asth) stationary (Fig. 6). To introduce lateral heterogeneity into the asthenospheric layer,
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we assign low viscosities (LV < asth) to a rectangular region (width WLV and height HLV) that is
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located a depth DLV beneath the base of the lithosphere (Fig. 6). We can then define the dimen-
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sionless aspect ratio
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DLV  DLV H asth , and pocket viscosity LV  LV asth to describe the characteristics of the low
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 We use 1 km resolution for these
viscosity region.
calculations, and extend the studied box by
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
100 km and 20 km on the upstream
and downstream sides of the pocket, respectively. To main-
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tain a basic shear flow pattern within the asthenosphere, we utilize free flow conditions on the
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left side, and impose a simple Couette flow (for a uniform viscosity layer) condition on the right
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side (Fig. 6).
ALV WLV H LV , pocket height
H LV  H LV H asth , pocket depth
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3.2 Numerical Results
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To examine the variety of flow patterns that are excited within the low viscosity pocket
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by the shear flow, we first varied both the height H 
LV and aspect ratio ALV of the pocket re-
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gion, while keeping the surface of the pocket flush with the base of the lithosphere ( D
LV  0 ).
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 pocket (Fig. 7b) because the
For some cases, we find that circulatory 
flow develops within the
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shear flow imposes a horizontal velocity condition on the base of the pocket while the surface of
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the pocket is held fixed by the presence of the high-viscosity stationary lithosphere. Because the
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fluid in the pocket is low-viscosity, these two external forces produce a circulatory flow within
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the pocket, similar to what occurs for the cavity flow described above. Superimposed on this cir-
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culatory flow, however, is the background shear flow of the surrounding asthenospheric layer. If
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the low-viscosity pocket’s vertical extent spans a large fraction of the asthenosphere height (i.e.,
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H LV  0.7 ), then this background shear flow tends to overwhelm the circulatory flow. Alterna-
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tively, a wider and thinner pocket causes the system to behave as a layered structure, concentrat-
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ing asthenospheric shear within the pocket where the low-viscosity permits more rapid defor-
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mation.
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As an example, first consider flow in a cavity extending through 80% of the astheno-
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sphere ( H 
LV  0.8 and ALV  4 , Fig. 7a). In this case the background shear flow dominates and
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there is no return flow within the cavity, but the presence of weak circulatory behavior is evident
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by upward- and
 downward-deflected velocities on the upstream and downstream sides of the
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pocket (respectively). On the other hand, if the pocket aspect ratio is less than about 2 ( ALV  2 ),
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then the pocket becomes too small for a significant circulation to develop in response to the
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background shear. This is because circulatory flow requires the pocket fluid
to turn around the
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corners of the pocket, and for smaller pockets the energy required for this turning deformation
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become prohibitive. Thus, smaller pockets exhibit shear deformation similar to the rest of the
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asthenosphere (Fig. 7c), rather than generating their own internal circulation. These examples
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show that we should expect circulatory flow (e.g., as in Fig. 7b) to be excited within the pocket
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only for a limited range of pocket geometries. Because pocket deformation depends strongly on
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the viscosity of the pocket, we expect this range to depend on the rheological contrast between
311
the pocket and the background asthenosphere ( LV  LV asth ).

Conrad et al.: Shear-Driven Upwelling
-12-
2/15/16
312
To look for the geometrical conditions that lead to circulatory pocket flow, we measured
313
the maximum upwelling velocity within the pocket region (Figs. 8a-8d) and the horizontal veloc-
314
ity at a location 10% of H 
LV below the top of the pocket (Figs. 8e-8h). For a large viscosity
315
contrast between the pocket and the asthenosphere ( LV  0.01, as in Fig. 7), we detect upwelling
316
flow for ALV  3 and 0.1 H 
LV  0.7 (Fig. 8a). The presence of a negative horizontal velocity
317
near the top of the pocket confirms that 
this upwelling is part of a circulatory flow within the
318

pocket (Fig. 
8e). For a pocket that that is 100 times less viscous than the asthenosphere
319
( LV  0.01), the maximum upwelling velocity in the pocket can be up to about 20% of the max-
320
imum shear velocity contrast for ALV  6 and 0.3 H 
LV  0.5 (Fig. 8a). As the viscosity of the
321
pocket increases toward the asthenosphere viscosity, the pocket geometries that produce circula-
322

 but the vigor of circulatory flow within the pocket detory flow remain approximately
the same,
323
creases (Fig. 8). For LV  0.03 , the maximum upwelling velocity is less than 10% of the shear
324
velocity contrast (Fig. 8b), while at LV  0.1 it has decreased to less than 3% (Fig. 8c) and is
325
undetectablefor LV  0.3 (Fig. 8d). The amplitudes of the horizontal velocities near the top of
326
 (Figs. 8e-8h), as does a plot of the maximum upwelling velocity
the pocket confirm these trends
327
(for any H LV or ALV ) as a function of LV (Fig. 9, red line).
observed
328
Finally, we find that the positioning of the pocket deeper within the asthenospheric layer
329
 DLV ),tends to decrease the magnitude

(increasing
of circulatory flow within the pocket (Fig. 9).
330
This is because the lithosphere forms a solid unmoving upper boundary for the pocket if
331
  0 , but the deformability of the fluid above the pocket increases as DLV increases. If the
DLV
332
fluid above the pocket is deformable, then the shear flow can redistribute itself into the fluid
 333
 and the circulatory deforabove the pocket. In this case, the pocket rides along with the flow,
334
mation within the pocket is diminished.
335
336
3.3 Interaction of a Low-Viscosity “Pocket” with a Lithospheric Step
Conrad et al.: Shear-Driven Upwelling
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2/15/16
337
Because SDU is produced by shear flow acting on both lithospheric steps and astheno-
338
spheric pockets, we can ask whether types of flow could act together to augment upwelling rates.
339
To test this, we placed a low-viscosity pocket (Fig. 1, using ALV  5 , H 
LV =0.3 or 0.4, and
340
LV  0.01) upstream of a lithospheric step function (height 30 km) and measured the maximum
341
 to thestep, the maximum upwelling
upwelling as before. We found that as the pocket gets closer
 342
velocity decreases slightly. This is because near the lithospheric step, the pocket upwelling oc-
343
curs where the step forces the flow downward (Fig. 1); the two flows partially cancel. Similarly,
344
if the pocket is located downstream from a downstream-facing lithospheric edge (e.g., if the di-
345
rection of shear is reversed in Fig. 1), then by symmetry the upwelling flow around the step
346
would partially cancel the downwelling flow of (now reversed) circulation within the low-
347
viscosity pocket. We found that the effect of combining the two flows was larger for thinner as-
348
thenosphere because the relative deflection of the flow by the step is larger. However, the fastest
349
upwelling is generated by the low-viscosity pocket, and as a result pocket flow is only slightly
350
affected (by at most about 20%, and only if the pocket is within 40 km of the lithospheric step
351
for the example in Fig. 1) by the presence of a lithospheric step.
352
353
3.4 Low-Viscosity Pocket Flow within Earth’s Asthenosphere
354
Tomographic studies of the asthenosphere show low-velocity anomalies with a variety of
355
geometries and sizes. For example, detailed tomography of the mantle beneath the Basin and
356
Range region shows several regions with anomalously slow seismic velocity that were first ob-
357
served by Humphreys & Dueker [1994], but appear differently in various tomographic studies
358
since. Dueker et al. [2001] show low-velocity regions that range in width from about 100 to 300
359
km, and in height from about 50 to 200 km; similarly narrow pockets of slow seismic velocity
360
have since been detected by Moschetti et al. [2007]. Considering an asthenospheric layer that is
361
~200 km thick, these values indicate that H 
LV may vary between 0.25 and 1.0, and ALV beConrad et al.: Shear-Driven Upwelling

-14-

2/15/16
362
tween 0.5 and 6. Other, lower resolution, tomographic images show wider anomalies, even in the
363
basin and range region [e.g., van der Lee & Frederiksen, 2005], which indicates that a wide vari-
364
ety of pocket aspect ratios are possible. The depth of the possible anomalies beneath the litho-
365
sphere is not well constrained, but Dueker et al. [2001] show low velocity anomalies that extend
366
up to ~50 km depth, close to others’ estimates of the depth to the lithospheric base [e.g., Zandt et
367
al., 1995]. Thus, D
LV may be as small as zero for the low-velocity anomalies detected by
368
Dueker et al. [2001]. Taken together, these constraints allow for the possibility that the interac-
369

tion of asthenospheric
shear flow with low-velocity anomalies may produce localized upwelling
370
flow on the downstream side of these anomalies with amplitudes up to 20% of the shear flow
371
magnitude (Fig. 8a). If we consider 5 cm/yr of shear flow, then the rate of upwelling flow could
372
be up to 1 cm/yr. This estimate can be regarded as an upper bound on the rate of asthenospheric
373
upwelling because the low-viscosity region must be more than 100 times less viscous than the
374
surrounding asthenosphere ( LV  0.01 ) and approximately 80 by 480 km wide (yielding
375
ALV  6 and H LV  0.4 for a 200 km thick asthenosphere). These sizes are close to the extreme
376
 Dueker et al.’s [2001] images and most anomalies feature a smaller aspect
values estimated from
 377
ratio.
378
The magnitude of the viscosity heterogeneity that could be associated with low-viscosity
379
pockets is not clear. The magnitude of the slow velocity anomalies in Dueker et al.’s [2001] im-
380
ages are up to about -1.5%. For a background shear wave speed of 4.5 km/s, this indicates a
381
shear velocity anomaly of about 70 m/s, which is half that of the slow-velocity anomalies of
382
~150 m/s estimated for the same region by van der Lee & Frederiksen [2005]. If the anomaly has
383
a thermal origin, then we can convert this 70-150 m/s velocity anomaly to a 10-20 kg/m3 density
384
anomaly and then to a 100-200 K thermal anomaly (assuming a density conversion factor of 0.15
385
g cm3 km-1 s [e.g., Conrad et al., 2007], a thermal diffusivity of 310-5 K-1, and a background
386
density of 3300 kg/m3). Because temperature-dependent viscosity tends to produce an order of
Conrad et al.: Shear-Driven Upwelling
-15-
2/15/16
387
magnitude decrease in viscosity for every 100 degrees of temperature increase [e.g., Kohlstedt et
388
al., 1995], a thermal anomaly of up to 200 K could be up to 2 orders of magnitude less viscous
389
than its surroundings, giving LV  0.01. As discussed above, pockets with this viscosity con-
390
trast could produce SDU with upwelling rates as large as 1 cm/yr if driven by 5 cm/yr of asthen-
391
ospheric shear.

392
If, on the other hand, the anomalies are associated with melting, then a melt fraction of
393
0.5 to 1% would be associated with a 1.5 to 3.0% shear-wave velocity anomaly (assuming a con-
394
version factor of 3.3% S-wave anomaly per percent melt fraction [Schmeling, 1985], as others
395
have used [e.g., Toomey et al., 1998; Rychert et al., 2005]). Generally, an order of magnitude
396
decrease in viscosity, which is necessary to produce SDU (Fig. 8), requires at least a ~4% melt
397
fraction [e.g., Hirth & Kohlstedt, 1995a; 1995b], although melt fractions of only a few percent
398
may be required for small grain sizes [Kohlstedt & Zimmerman, 1996]. On the other hand, some
399
studies have suggested that the presence of melt may tend to dehydrate the solid minerals, which
400
could increase net viscosity, not decrease it [Karato, 1986]. Thus, partial melt, especially occur-
401
ring within hydrated asthenosphere, is not likely to produce a sufficient reduction in viscosity to
402
generate SDU, unless this melt is accompanied by a thermal anomaly or grain-size reduction that
403
also reduces viscosity.
404
Finally, a heterogeneous concentration of water or other volatiles may produce low-
405
viscosity pockets with anomalously slow seismic velocity. Hydration near the lithospheric base
406
can produce a velocity drop of up to about 4.3% [e.g., Rychert et al., 2005, based on Karato &
407
Jung, 1998 and Gaherty et al., 1999]. Because the effect of hydration on upper mantle viscosity
408
can be more than a factor of 100 [Hirth & Kohlstedt, 1996], the viscosity drop associated with
409
hydration should be sufficient to produce SDU. Thus, it is possible that low-viscosity “pockets”
410
of hydrated asthenosphere may lead to SDU if subjected to vigorous asthenospheric shear. Other
411
compositional heterogeneity, possibly associated with other volatiles, grain-size reduction, or a
Conrad et al.: Shear-Driven Upwelling
-16-
2/15/16
412
variable melt extraction history, may also contribute to the total viscosity heterogeneity. Thus,
413
there are several mechanisms (thermal, melting, volatile, chemical, or grain-size) that could con-
414
tribute to a factor of ~100 decrease in viscosity within “pockets” of asthenospheric mantle. We
415
estimate that SDU produced by the action of asthenospheric shear on these regions can produce
416
upwelling rates of up to 1 cm/yr. If asthenospheric source rocks are close to solidus, this
417
upwelling can generate melting, inducing melting instabilities and/or intraplate volcanism.
418
419
4. Discussion and Conclusions
420
We have shown that localized shear-driven upwelling (SDU) can be generated in the as-
421
thenosphere by vigorous asthenospheric shear acting on large heterogeneities in asthenospheric
422
or lithospheric viscosity. In particular, flow within a low-viscosity “cavity” embedded within the
423
lithospheric base, as might be associated with a continental rift, can produce upwelling flow with
424
magnitudes up to ~4% of the total velocity contrast across the asthenosphere. Flow near a step
425
function change in lithospheric thickness, as might be associated with a cratonic edge, can pro-
426
duce upwelling at rates up to ~10% of the shear magnitude. In these cases, SDU is located
427
against the cavity wall that faces the shear flow. A second type of SDU can develop within a
428
“pocket” of low-viscosity fluid, which can begin to circulate when exposed to asthenospheric
429
shear. In this case, upwelling only occurs if the viscosity contrast is more than a factor of 10, the
430
aspect ratio of the pocket is more than about 5, and the pocket occupies between ~20% and
431
~60% of the asthenospheric thickness. If the viscosity contrast is 100, then the upwelling arm of
432
the pocket (located on the downstream side of the pocket) can produce SDU with a rate up to
433
~20% of the asthenospheric shear magnitude. Thus, if the total magnitude of shear across the as-
434
thenosphere is 5 cm/yr, viscosity heterogeneity associated with a lithospheric cavity, lithospheric
435
step, or asthenospheric pocket can generate up to 0.2 cm/yr, 0.5 cm/yr, or 1.0 cm/yr of
436
upwelling, respectively.
Conrad et al.: Shear-Driven Upwelling
-17-
2/15/16
437
Although lateral variations in lithospheric viscosity may be associated with the litho-
438
sphere’s thermal, chemical, and deformational history, the causes of lateral viscosity variations
439
in the asthenosphere are less apparent. We describe above several possible ways in which ther-
440
mal, melting, chemical, volatile or grain-size anomalies can cause isolated regions of the asthen-
441
osphere to feature lower viscosities than the surrounding lithosphere. Of these, the most straight-
442
forward is probably the presence of anomalously high temperature, as would be associated with
443
an impinging plume, lithospheric drip, or convective upwelling. These high temperatures should
444
also be associated with low densities that should tend to enhance the upwelling flow associated
445
with asthenospheric shear. However, convective processes tend to be time-dependent and
446
ephemeral if not constantly replenished by a heat source. Thus, more analysis is required to de-
447
termine long-term evolution and stability of SDU for a thermal source of viscosity heterogeneity.
448
Even if low-viscosity pockets are not associated with density anomalies of their own
449
(e.g., if the pockets are caused by volatile or grain-size heterogeneity), these pockets should
450
evolve in the presence of asthenospheric shear and SDU. In addition, upwelling flow may be as-
451
sociated with melting, which can cause surface volcanism but may also decrease local viscosity
452
and thus enhance SDU. Thus, the time-dependent development and longevity of SDU is more
453
complicated than has been presented here for instantaneous flow caused by idealized low-
454
viscosity pockets that are rectangular pockets in shape. For example, we discussed above that the
455
rate of circulation for a pocket 80 by 480 km wide embedded within a 200 km thick lithosphere
456
is about 1 cm/yr for 5 cm/yr of asthenospheric shear and a pocket viscosity of LV  0.01. At this
457
rate, recirculation of the pocket occurring in ~100 Myr (1000 km at 1 cm/yr). Thus, pocket circu-
458
lation should be capable of supplying previously unmelted mantle 
to a shear-driven upwelling
459
for a time period much longer than the expected lifetime of the driving shear flow, which can be
460
reorganized on shorter times scales by changes in either mantle flow or plate motions. Therefore,
461
depletion of recirculating mantle by multiple melting events probably does not limit the longevi-
Conrad et al.: Shear-Driven Upwelling
-18-
2/15/16
462
ty of volcanism induced by SDU. Instead, we can expect volcanism to cease when the driving
463
shear flow diminishes or if the low-viscosity pocket evolves into a geometry that is unfavorable
464
for producing SDU. Indeed, tomographic studies of the asthenosphere show a variety of shapes
465
and sizes of low-velocity anomalies that may result from a variety of time-dependent processes.
466
As a result, further study is necessary to characterize the time-dependent behavior of SDU for a
467
variety of geometries, and in three-dimensions. Additional seismological and geochemical con-
468
straints on the sizes, shapes, and viscosity contrasts associated with asthenospheric heterogeneity
469
would significantly aid this effort.
470
Most previous studies that invoke sub-lithospheric processes to explain localized in-
471
traplate volcanism do so by creating upwelling via density heterogeneity: small-scale convection,
472
return flow from lithospheric “drips”, edge-driven convection, and even plume impingement, are
473
all examples of how density heterogeneity, in these cases associated with convective processes,
474
can induce upwelling flow. Here, we have shown that viscosity heterogeneity can alternatively
475
drive upwelling flow if it occurs in the presence of vigorous asthenospheric shear. We note that
476
upwelling flow can be induced even in the absence of any density heterogeneity or convective
477
processes. Thus, the shear-driven upwellings (SDU) described here are fundamentally different
478
than the upwellings associated with convective processes. Even Richter Rolls [e.g., Richter &
479
Parsons, 1975; Korenaga & Jordan, 2003], which exist in the presence of a shear flow, rely on
480
density heterogeneity and convection to maintain themselves. By contrast, SDU, which requires
481
shear flow and viscosity heterogeneity only, may help explain numerous examples of intraplate
482
volcanism that occur above rapidly shearing asthenosphere. One current example may be the ba-
483
saltic volcanic fields of western North America [Wannamaker et al., 2001], where intraplate vol-
484
canism is difficult to explain via other processes [Smith et al., 2002; Smith & Keenan, 2005] and
485
the underlying lithospheric and asthenospheric layers appear to be both shearing vigorously [Sil-
Conrad et al.: Shear-Driven Upwelling
-19-
2/15/16
486
ver & Holt, 2002; Conrad et al., 2007] and laterally heterogeneous [Humphreys & Dueker,1994;
487
Zandt et al., 1995; Dueker et al., 2001; van der Lee & Frederiksen, 2005].
488
489
Acknowledgements. We thank the Nevada Agency for Nuclear Projects for support.
490
491
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Figure 1. Viscous flow calculation showing the effect of both a low viscosity “pocket” and a
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lithospheric step on asthenospheric shear flow. In (a), arrows indicate velocity direction and
638
magnitude, while colors indicate viscosity variations. A detailed view of the red-outlined box in
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(a) is shown in (b), where arrows indicate velocity direction and colors indicate magnitude of
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velocity. In (a) and (b), amplitudes of velocity are given as a fraction of the velocity that drives
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the shear flow at the base of the asthenosphere.
642
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Figure 2. Cartoon drawing of asthenospheric shear flow (driven by an imposed basal velocity of
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V) beneath a stationary lithosphere that features a “cavity” of variable height HC and width WC
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and viscosity C .

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Figure 3. Calculations of the flow field within the cavity depicted in Fig. 2, for three different
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aspect ratios of the cavity and TC=0.85. Arrows indicate direction of flow, colors indicate veloci-
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ty magnitude as fraction of V, the imposed velocity at the base of the asthenosphere. Three dif-
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ferent patterns of flow are shown. (a) For aspect ratio AC=2, the cavity is narrow enough that the
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asthenospheric shear flow cannot penetrate into the cavity. Instead, a closed circulation develops
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within the cavity, with upwelling occurring along the downstream wall of the cavity. (b) As the
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cavity widens, the asthenospheric shear flow begins to penetrate into the cavity. At about AC=4
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(shown here), this flow reaches the cavity lid, eliminating the closed circulation that occurs for
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smaller aspect ratios. Instead, individual circulatory cells develop in the corners of the cavity. (c)
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For larger aspect ratios, (AC=6 is shown here) the asthenospheric shear flow dominates in the
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center of the cavity, but circulation persists in the cavity corners.
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Figure 4. Measurements of (a) the maximum upwelling flow within the cavity and (b) the hori-
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zontal velocity at a point 10% of HC from the top of the cavity midpoint, as a function of the as-
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pect ratio AC and the cavity thickness ratio TC. The style of flow can be determined from the di-
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rection of horizontal flow in (b), where blue negative values indicate the presence of a closed
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circulation in the cavity (as in Fig. 3a), and red positive values indicate a cavity flow field domi-
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nated by shear flow (as in Fig. 3c). The boundary between these flows (lightest blue and pink
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interface) indicates the transition between these two flows (as in Fig. 3b).
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Figure 5. Similar to Fig. 4, but for a low viscosity fluid within the cavity. Here, the cavity fluid
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is 10 times less viscous than the fluid of the rest of the asthenosphere.
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Figure 6. Cartoon drawing of asthenospheric shear flow (driven by an imposed basal velocity of
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V) with an embedded “pocket” of low-viscosity fluid (the Low Viscosity Region, LVR) of varia-
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ble height HLV, width WLV, depth DLV, and viscosity LV, as shown.
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Figure 7. The flow field within a pocket of low-viscosity fluid (as depicted in Fig. 6) with vis-
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cosity LV  LV asth  0.01, for three different choices of pocket aspect ratio ALV and dimen-
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sionless height H 
LV . Arrows show the flow field direction, while colors present the magnitude
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of flow.

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Figure 8. Summary (similar to Fig. 4) of the upwelling flow and return flow within the low vis-
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cosity pocket. Here the pocket viscosity is LV  LV asth  0.01 for (a,e), 0.03 for (b,f), 0.1 for
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(c,g), and 0.3 for (d,h). As in Fig. 4a, parts (a,b,c,d) show the maximum upwelling velocity in the

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pocket. As in Fig. 4b, parts (e,f,g,h) show the horizontal velocity at a depth 10% of HLV from the
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top of the pocket, where red (positive) indicates downstream flow (as in Fig. 7a and 7c) and blue
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(negative) indicates circulatory flow within the pocket (as in Fig. 7b).
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Figure 9. The maximum upwelling velocity as a function of the pocket viscosity LV  LV asth
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and the depth D
LV of the top of the pocket beneath the lithospheric base ( D
LV  0 for red, 0.1
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for blue, and 0.3 for green).
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