Shear-Driven Upwelling

Clinton P. Conrad¹, Todd A. Bianco² & Eugene I. Smith³

¹Dept. Geology & Geophysics, Univ. Hawaii at Manoa, Honolulu HI 96822, clintc@hawaii.edu

²Dept. Geology & Geophysics, Univ. Hawaii at Manoa, Honolulu HI 96822, tbianco@hawaii.edu

³Dept. Geoscience, Univ. Nevada at Las Vegas, Las Vegas NV 89154, gene.smith@unlv.edu

This webpage is a summary of: Conrad, C.P., B. Wu, E.I. Smith, T.A. Bianco, and A. Tibbetts, Shear-driven upwelling induced by lateral viscosity variations and asthenospheric shear: A mechanism for intraplate volcanism, Physics of the Earth and Planetary Interiors, 178, 162-175, 2010.

 Introduction

Most of the volcanism around the globe occurs at subduction zones and mid-ocean ridges, and is well-explained by the theory of plate tectonics. Volcanism that occurs away from plate boundaries, however, is less readily explained, but has often been attributed to hot plumes that rise from deep within the mantle [Morgan, 1971]. However, several intraplate volcanic features are not associated with classic hotspot tracks (e.g., the Cretaceous seamounts that pervade the western Pacific basin [Hillier & Watts, 2007] or the mid-Miocene to contemporary basaltic volcanic fields of the southwestern US [Smith et al., 2002]). Without a deep-mantle source of excess heat, most alternative explanations for intraplate volcanism invoke some source of regional asthenospheric upwelling that induces decompression melting of near-solidus fertile mantle [Raddick et al., 2002; Hernlund et al., 2008]. Several upwelling mechanisms have been proposed such as small-scale thermal convection in the asthenosphere [e.g., Haxby & Weissel, 1986; van Hunen & Zhong, 2006; Ballmer et al., 2007; Ed: see also Small-scale Convection], return flow from occasional “drips” of dense lithosphere sinking into the upper mantle [e.g., Le Pourhiet et al., 2006], and “edge-driven” convection near sharp gradients in lithospheric thickness [e.g., King & Anderson, 1998; King & Ritsema, 2000; Ed: see also Edge Convection]. These mechanisms for driving asthenospheric upwelling utilize the density inversion between the lithosphere and asthenosphere as an energy source.

Conrad et al. [2010] demonstrated an alternative mechanism for generating intraplate upwelling. This mechanism, named “Shear-Driven Upwelling” (SDU), is based on asthenospheric shear, which accommodates the few cm/yr of relative motions between surface plates and the convecting mantle. SDU is a variation of “shear-driven cavity flow”, a classic engineering problem in which shear flow in a channel induces circulatory flow within an adjacent fluid-filled cavity [e.g., Shen & Floryan, 1985; Pakdel et al., 1997; Shankar & Deshpande, 2000]. Applied to the asthenosphere, the driver for SDU is the relative motion between the plates and mantle; upwelling flow is excited in this case by lateral viscosity heterogeneity (e.g., Figure 1), rather than by density heterogeneity. Below, we summarize the analysis of Conrad et al. [2010] of how SDU can generate mantle upwelling and intraplate volcanism.

Figure 1: Diagram showing two mechanisms by which asthenospheric shear can act on lateral viscosity heterogeneity to induce Shear-Driven Upwelling (SDU). Asthenospheric shear is generated by relative motion between the mantle and the lithosphere, and is drawn here in a lithospheric reference frame. Shearing asthenosphere can induce (a) “shear-driven cavity flow” within a variation in lithospheric thickness or (b) circulatory flow within a “pocket” of low-viscosity asthenosphere. Both flows induce upwelling; if the asthenospheric mantle is fertile and near its solidus, melting and surface volcanism can result.

SDU within a Lithospheric Cavity

To examine the response of asthenospheric shear flow to a variation in the basal topography of the lithosphere, we use the two-dimensional finite element code ConMan [King et al., 1990] and generate asthenospheric shear flow by imposing rigid velocity boundary conditions above and a dimensionless velocity V below a viscous asthenospheric channel (Figure 2a). Above the asthenosphere lies a stationary high viscosity lithospheric layer in which a cavity is embedded. For narrow cavities, circulatory flow fills the entire cavity (Figure 3a) and SDU occurs along the downstream wall of the cavity. As the aspect ratio grows (Figure 3b), the circulatory flow is confined to the two inner corners of the cavity while the rest of the cavity becomes filled with a broad widening of the background asthenospheric shear flow. As the cavity widens further (Figure 3c), the penetration of asthenospheric shear into the cavity dominates the cavity flow field and generates SDU on the upstream side of the cavity.

Figure 2: Drawings of asthenospheric shear flow (driven by an imposed basal velocity of V) beneath a stationary lithosphere that features (a) a “cavity” of variable height HC and width WC and viscosity , and (b) an embedded “pocket” of low-viscosity fluid of variable height HLV, width WLV, depth DLV, and viscosity hLV, as shown.

Figure 3: Calculations of the flow field within the cavity shown in Figure 2a, for three different cavity aspect ratios (AC,=WC/HC) and a single cavity depth given by the athenospheric thickness ratio TC= Hasth /(Hasth+HC) =0.85. Arrows indicate direction of flow, and colors indicate velocity magnitude as fraction of V, the imposed velocity at the base of the asthenosphere. Three different patterns of flow are shown. (a) For small aspect ratios (AC=2), the cavity is narrow enough that the asthenospheric shear flow cannot penetrate into the cavity and a closed circulation develops. (b) In a wider cavity (AC=4), asthenospheric shear penetrates into the cavity and individual circulatory cells develop in the corners of the cavity. (c) For larger aspect ratios (AC=6), asthenospheric shear dominates in the center of the cavity, but weak circulation persists in the cavity corners.

On Earth, lithospheric thickness variations are found at mid-ocean ridges, continental rifts, and cratonic edges. Near a mid-ocean ridge, the lithospheric basal depth can vary by up ~30 km over a ~400 km wide region. Such a wide and shallow cavity is not conducive to SDU. Continental rifting may generate narrower and deeper cavities. For example, tomography of the Rio Grande rift [West et al., 2004] shows a ~200 km wide by ~100 km deep low-velocity anomaly [van Wijk et al., 2008]. Asthenospheric shear flow of 5 cm/yr beneath this cavity would induce a closed circulation (e.g., Figure 3a) and SDU of ~0.2 cm/yr (4% of the shear amplitude), along the rift cavity’s downstream wall. Finally, the downstream-facing edge of a craton extending from 100 to 200 km depth should generate SDU with magnitudes ~10% of the driving shear amplitude, or about 0.5 cm/yr for 5 cm/yr of driving shear. These rates of upwelling can generate melt at rates up to 0.3 and 0.8 km/Myr, respectively, assuming near-solidus asthenosphere and typical melt parameters [Phipps Morgan, 2001; Raddick et al., 2002].

SDU within an Asthenospheric Low-Viscosity “Pocket”

A geophysically-interesting variation of the shear-driven cavity flow, which has not been explored in the engineering literature, involves relaxing the rigidity of the cavity-containing layer. In this case, the “cavity” becomes a region of relatively low-viscosity embedded within the shearing layer (Figure 1b). To study the response of asthenospheric viscosity heterogeneity to imposed shear flow, we embed a rectangular “pocket” of low-viscosity fluid within a shearing asthenospheric layer (Figure 2b). We find that circulatory flow develops for a certain range of pocket aspect ratios and thicknesses because the deformation preferentially localizes within the low-viscosity pocket, rather than within the surrounding high-viscosity asthenosphere. If the pocket’s vertical extent spans a more than ~70% of the asthenosphere thickness (Figure 4a), then the background shear flow overwhelms circulatory flow. Alternatively, circulatory flow cannot develop within a small pocket (Figure 4c) because it is energetically inefficient. Only for pockets with aspect ratios greater than ~6 and thicknesses between 20% and 60% of the asthenospheric thickness is circulatory flow excited by the driving shear flow (Figure 4b). For a pocket that is 100 times less viscous than the asthenosphere, the maximum upwelling velocity occurs on the downstream edge of the pocket at rates up to ~20% of the maximum shear velocity contrast. Considering 5 cm/yr of driving shear flow, then the rate of upwelling flow could be up to 1 cm/yr.

Figure 4: The flow field within a low-viscosity “pocket” (as depicted in Figure 2b) with viscosity h´=hLV/hasth=0.01 for three different choices of pocket aspect ratio (ALV=WLV/HLV) and dimensionless height H´=HLV/Hasth. Arrows show the flow field direction, while colors present the magnitude of flow. A pocket that is (a) tall (H´>0.7) or (c) narrow (ALV<3) simply accommodates asthenospheric shear without inducing significant upwelling flow. Only within a wide pocket (ALV>6) of intermediate thickness (0.2<H´<0.6), as shown in (b), is circulatory flow, and thus upwelling and volcanism, excited.

Tomographic studies of the asthenosphere show low-velocity anomalies with a variety of geometries, including some that could excite SDU [e.g., Humphreys & Dueker, 1994; Dueker et al., 2001; Moschetti et al., 2007; van der Lee & Frederiksen, 2005]. Magnitudes of order -1.5% are typical, which, if caused by thermal anomalies [Kohlstedt et al., 1995] or hydration [Hirth & Kohlstedt, 1996], are consistent with a viscosity drop by up to a factor of ~100. If asthenospheric source rocks are close to solidus, we estimate that 1 cm/yr of upwelling can generate 2.5 km/Myr of melt that is potentially eruptible. This is faster than eruption rates observed at some locations of continental basaltic volcanism [Conrad et al., 2010].

Conclusions

Most explanations for intraplate volcanism invoke convection-related density heterogeneity: small-scale convection, return flow from lithospheric “drips”, edge-driven convection, and even plume impingement, are examples of how density heterogeneity induces upwelling flow. Here, we show that viscosity heterogeneity can also drive upwelling flow, even in the absence of any density heterogeneity, if it occurs in the presence of vigorous asthenospheric shear. This shear-driven upwelling (SDU) is fundamentally different than the upwellings associated with convective processes. As a result, SDU may provide a new explanation for intraplate volcanism that occurs above rapidly shearing asthenosphere. One current example may be the basaltic volcanic fields of western North America [Wannamaker et al., 2001], where intraplate volcanism is difficult to explain via other processes [Smith et al., 2002; Smith & Keenan, 2005] and the underlying lithosphere and asthenosphere are laterally heterogeneous and appear to be shearing vigorously [Humphreys & Dueker,1994; Zandt et al., 1995; Dueker et al., 2001; Silver & Holt, 2002; van der Lee & Frederiksen, 2005; Conrad et al., 2007].

Acknowledgements

We thank the Nevada Agency for Nuclear Projects for support.

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