The role of rheology and slab shape on rapid mantle flow: Three … · 2014. 5. 5. · The role of rheology and slab shape on rapid mantle flow: Three-dimensional numerical models

The role of rheology and slab shape on rapid mantle flow:Three-dimensional numerical models of the Alaska slab edge

M. A. Jadamec1,2 and M. I. Billen1

Received 31 May 2011; revised 6 December 2011; accepted 8 December 2011; published 9 February 2012.

[1] Away from subduction zones, the surface motion of oceanic plates is wellcorrelated with mantle flow direction, as inferred from seismic anisotropy. However,this correlation breaks down near subduction zones, where shear wave splitting studiessuggest the mantle flow direction is spatially variable and commonly non-parallel toplate motions. This implies local decoupling of mantle flow from surface plate motions,yet the magnitude of this decoupling is poorly constrained. We use 3D numericalmodels of the eastern Alaska subduction-transform plate boundary system to furtherexplore this decoupling, in terms of both direction and magnitude. Specifically, weinvestigate the role of the slab geometry and rheology on the mantle flow velocity at aslab edge. The subducting plate geometry is based on Wadati-Benioff zone seismicityand tomography, and the 3D thermal structure for both the subducting and overridingplates, is constrained by geologic and geophysical observations. In models using thecomposite viscosity, a laterally variable mantle viscosity emerges as a consequence ofthe lateral variations in the mantle flow and strain rate. Spatially variable mantlevelocity magnitudes are predicted, with localized fast velocities (greater than 80 cm/yr)close to the slab where the negative buoyancy of the slab drives the flow. The samemodels produce surface plate motions of less than 10 cm/yr, comparable to observedplate motions. These results show a power law rheology, i.e., one that includes theeffects of the dislocation creep deformation mechanism, can explain both observationsof seismic anisotropy and decoupling of mantle flow from surface motion.

Citation: Jadamec, M. A., and M. I. Billen (2012), The role of rheology and slab shape on rapid mantle flow: Three-dimensionalnumerical models of the Alaska slab edge, J. Geophys. Res., 117, B02304, doi:10.1029/2011JB008563.

1. Introduction

[2] Plate boundaries are inherently three-dimensional (3D)tectonic features with variations in geometry and physicalproperties along their length [Jarrard, 1986; Gudmundssonand Sambridge, 1998; Bird, 2003; Lallemand et al., 2005;Sdrolias and Muller, 2006; Syracuse and Abers, 2006;Rychert et al., 2008]. For example, subduction zones havesignificant changes in slab dip along strike, including flatslab segments, as in the eastern Alaska subduction zone, thePeru-Chile Trench, the Cascadia subduction zone, and thesouthwestern Japan Trench [Gudmundsson and Sambridge,1998; Gutscher et al., 2000; Ratchkovski and Hansen,2002; Lallemand et al., 2005; Syracuse and Abers, 2006;Tassara et al., 2006]. In addition, many plate boundaries arenot simply end-member subduction zones, transform faults,or spreading centers in isolation, but rather are hybrid sys-tems. For example, plate boundary corners with slab edges

formed by the intersection of a subduction zone with atransform fault occur in eastern Alaska, the northern Kuril-Kamchatka subduction zone, the southernmost Marianatrench near the Yap trench, the northern Tonga trench, andthe north and south boundaries of the Antilles and the Scotiasubduction zones [Gudmundsson and Sambridge, 1998;Bird, 2003]. Subduction-transform intersections also occurin non-corner geometries, as in the termination of the Ker-madec Trench against the Alpine fault in New Zealand andthe north and south terminations of the Cascadian subduc-tion zone [Gudmundsson and Sambridge, 1998; Bird, 2003].The three-dimensionality in both surface and subsurfacestructure can influence the relative motion of the mantle withrespect to the surface plates. Thus, in many cases a two-dimensional (2D) approach to studying plate boundary pro-cesses can miss critical aspects of the dynamics resultingpurely from the geometry.[3] Away from subduction zones, the surface motion of

oceanic plates is well correlated with mantle flow direction,as inferred from seismic anisotropy [Kreemer, 2009; Conradet al., 2007; Becker et al., 2003]. However, observations ofseismic anisotropy from numerous subduction zones displayseismic fast directions that are non-parallel to plate motions,e.g., the Peru-Chile, Kamchatka, Tonga, Marianas, South

1Geology Department, University of California, Davis, California,USA.

2School of Mathematical Sciences and School of Geosciences, MonashUniversity, Clayton, Victoria, Australia.

Copyright 2012 by the American Geophysical Union.0148-0227/12/2011JB008563

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, B02304, doi:10.1029/2011JB008563, 2012

B02304 1 of 20

http://dx.doi.org/10.1029/2011JB008563

Sandwich, Cascadia, Costa Rica-Nicaragua, and easternAlaska subduction zones [Russo and Silver, 1994; Peytonet al., 2001; Smith et al., 2001; Pozgay et al., 2007; Mulleret al., 2008; Zandt and Humphreys, 2008; Long and Silver,2008; Abt et al., 2009; Christensen and Abers, 2010]. Ifthe seismic fast directions are tracking mantle flow [Savage,1999; Kaminiski and Ribe, 2002; Kneller and van Keken,2007; Long and Silver, 2009; Jadamec and Billen, 2010],this implies that local decoupling between the plates andunderlying mantle may be a common feature in subductionzones. This also indicates differential motion, at least interms of direction, of the mantle close to subduction zonesversus that farther away from them.[4] Several 3D semi-analytic, numerical, and laboratory

experiments have investigated mantle flow dynamics insubduction zones [Zhong and Gurnis, 1996; Zhong et al.,1998; Buttles and Olson, 1998; Hall et al., 2000; Kincaidand Griffiths, 2003; Schellart, 2004; Funiciello et al., 2006;Piromallo et al., 2006; Royden and Husson, 2006; Schellartet al., 2007; Kneller and van Keken, 2008; Giuseppe et al.,2008; Jadamec and Billen, 2010]. For example, 3D subduc-tion studies, commonly in the context of slab rollback, indi-cate a toroidal component of mantle flow dominates near theslab edge, where material is transported from beneath the slabaround the slab edge and into the mantle wedge [Kincaid andGriffiths, 2003; Schellart, 2004; Funiciello et al., 2006;Piromallo et al., 2006; Stegman et al., 2006]. This compo-nent of flow cannot be captured in 2D models of subduction[Tovish et al., 1978; Garfunkel et al., 1986]. In addition,numerical models investigating the effect of variable slab dipand curvature on flow in the mantle wedge show that thevariable geometry can induce pressure gradients that drivetrench parallel flow [Kneller and van Keken, 2007, 2008].Thus, both observations of seismic anisotropy and 3D fluiddynamics simulations indicate a difference between thedirection of mantle flow and the surface plate motion, indi-cating local decoupling of the surface plates from the mantlein subduction zones [Jadamec and Billen, 2010].[5] In this paper, we use 3D instantaneous regional models

of the eastern Alaska subduction-transform plate boundarysystem to further explore this decoupling of mantle flowfrom surface plate motion, in terms of both direction andmagnitude. The 3D models of the subduction-transformplate boundary system in southern Alaska use a subductingplate geometry based on Wadati-Benioff zone seismicity anda 3D thermal structure for both the subducting and overrid-ing plates, constrained by geologic and geophysical obser-vations. No kinematic boundary condition is prescribed tothe subducting plate, rather the negative buoyancy of theslab drives the flow. We employ a composite viscosity,which includes both the diffusion and dislocation creepmechanisms (i.e., Newtonian and non-Newtonian viscosity).[6] This study builds on the 3D numerical models

presented by Jadamec and Billen [2010] that investigatedthe effect of the slab shape and Newtonian versus non-Newtonian rheology on rapid mantle flow and comparedthe results to observations of seismic anisotropy fromChristensen and Abers [2010]. In this paper, we explore alarger range in model parameters and specifically addresshow these affect the velocity magnitude in the mantlesurrounding the slab, the overall pattern of mantle flowaround the slab edge, as well as implications of the non-

Newtonian rheology as a mechanism for plate-mantledecoupling in subduction zones. In addition, we discussimplications specific to Alaskan tectonics. The approachtaken for models presented in this paper, as well as those ofJadamec and Billen [2010], differs from that in previous 3Dnumerical models of subduction in that previous models[Moresi and Gurnis, 1996; Zhong and Gurnis, 1996; Billenet al., 2003; Billen and Gurnis, 2003; Piromallo et al.,2006; Stegman et al., 2006; Schellart et al., 2007; Knellerand van Keken, 2007; Giuseppe et al., 2008; Kneller andvan Keken, 2008] either use a simplified plate geometry,prescribe a velocity boundary condition to the subductingplate, do not include an overriding plate, or use a Newtonianrheology in the mantle.

2. Alaskan Subduction-Transform Boundary

[7] The Aleutian-Alaska subduction zone accommodatesconvergence between the northernmost Pacific plate and theAlaskan part of the North American plate (Figure 1). Thesubduction zone length is greater than 3000 km, and alongthis length the sense of curvature changes from convex tothe south in the central Aleutians to convex to the north insouth central Alaska [Page et al., 1989; Gudmundsson andSambridge, 1998; Ratchkovski and Hansen, 2002; Bird,2003]. Offshore south central Alaska, the observed Pacificplate motion with respect to North America is N16°W at5.2 cm/yr [DeMets and Dixon, 1999]. The easternmost partof the subduction zone forms a plate boundary corner wherethe Aleutian trench terminates against the northwest trend-ing Fairweather-Queen Charlotte transform fault (Figure 1)[Bird, 2003]. In this plate boundary corner, the dip of thesubducting plate shallows to form a flat slab [Ratchkovskiand Hansen, 2002], and the Yakutat block, a buoyantoceanic plateau, is subducting beneath the North Americanplate [Bruns, 1985; Pavlis et al., 2004; Ferris et al., 2003](Figure 1).[8] East of approximately 212° longitude, where the sub-

duction zone approaches the transform boundary, there is anabrupt decrease in seismicity at depths greater than 25 km(Figure 1). Despite the decrease in seismicity, several seis-mic studies suggest there is a steeply dipping slab, theWrangell slab, in this region of the plate boundary cornerbeneath the active adakitic Wrangell Volcanoes (Figures 1and 2) [Stephens et al., 1984; Skulski et al.,1991; Preeceand Hart, 2004]. There is debate over the geometry of theWrangell slab as well as its continuity with the main Aleu-tian slab to the west [Perez and Jacob, 1980; Stephens et al.,1984; Page et al., 1989; Zhao et al., 1995; Ratchkovski andHansen, 2002; Eberhart-Phillips et al., 2006; Fuis et al.,2008]. Therefore, we construct two slab geometries, onewith and one without the Wrangell slab, to test the influenceof the slab geometry on the mantle flow in this plateboundary corner (Figure 1).

3. Methodology

[9] We present eighteen 3D numerical fluid dynamicsexperiments of the subduction-transform plate boundarysystem in southern Alaska, in which we varied the viscositystructure (Newtonian versus composite viscosity), the sub-ducting plate geometry (slabE325 versus slabE115), the yield

JADAMEC AND BILLEN: RHEOLOGY, SLAB SHAPE, RAPID MANTLE FLOW B02304B02304

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plate. In contrast, we use a low viscosity zone to decouplethe Pacific plate from the southern edge of the model domain(see below). This allows the Pacific plate to move freely inresponse to the local driving forces. 2D tests were also usedto determine the necessary box depth and width in order tominimize boundary condition effects on the flow in thesubduction zone. These are all instantaneous flow simula-tions designed to explore the present-day balance of forces,lithosphere and mantle structure.

3.2. Subducting Plate Geometry[13] We construct two 3D slab shapes, slabE325 and

slabE115, to test competing hypotheses for the geometry andcontinuity of the subducted oceanic lithosphere beneath

south central Alaska (Figure 1). We assume that the Wadati-Benioff zone represents the shape of the subducting litho-sphere, and use seismic data to constrain the shape and depthextent of the slab (Figure 1; Table 4; and references therein).In models using slabE325, the depth of the slab is everywhere325 km, and thus the Aleutian and Wrangell slabs arecontinuous. In contrast, in models using slabE115, east of212° longitude the slab surface extends to only to 115 kmdepth. Thus in models using slabE115, the slab is shorterbeneath the Wrangell Mountains and barely protrudesbeneath the lithosphere of the overriding plate in this regionof the model (Figure 1; Table 4).[14] The 3D slab surfaces (Figure 1) were generated using

a tensioned cubic spline algorithm in GMT [Wessel and

Figure 2. Temperature structure for 3D geodynamic model. (a) Seafloor ages for Pacific plate and ther-mal domains in upper plate used in half-space cooling model. Seafloor ages fromMuller et al. [1997]. Seetext for constraints on upper plate age assignment. (b) Temperature profiles for domains in upper plate:I - forearc, II - magmatic arc, III - Cordillera, IV - Ancestral North America. Note temperature profilesfor domains I and IV overlap because the two regions have the same effective age. (c) Radial slicethrough temperature at 26 km depth, which is the same for models using slabE325 and slabE115. Radialslice at 152 km depth for models with (d) slabE325 and (e) slabE115. (f) Cross section through flat slabregion (AA′), which is the same for models using slabE325 and slabE115. Cross section through the WrangellVolcanics (BB′) for models using (g) slabE325 and (h) slabE115. Note, Figures 2b–2h are shown for subset ofmodel domain.


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Smith, 1991]. The slab surface was then mapped onto thefinite element grid using the SlabGenerator code by calcu-lating the perpendicular distances of the finite element meshpoints to the slab surface. In this way, the varying strike, dipand depth of the slab are smoothly represented on the modelgrid. From these perpendicular distances, the initial 3Dthermal structure and 3D plate boundary shear zone structureare constructed.

3.3. Subducting Plate Thermal Structure[15] A 3D thermal structure constrains the temperature-

dependent viscosity and the density anomaly that drives theflow in the geodynamic models. The thermal structure isbased on geologic and geophysical observables, for both thesubducting and overriding plates, thereby capturing theregional variability in the plate boundary system (Figure 2).[16] The 3D thermal structure for the subducting plate,

generated by the SlabGenerator code, is constructed using asemi-infinite half-space cooling model in which the thick-ness of the thermal lithosphere is a function of the plate age[Turcotte and Schubert, 2002]:

T ¼ Tm " Tsð Þerf d

2ffiffiffiffiffikt

p" #

þ Ts ð1Þ

where Tm = 1400°C, Ts = 0°C, k = 1 & 10"6 m2/s, d is depthperpendicular from the slab surface, and t is the plate age.The half-space cooling model is an appropriate approxima-tion of the thermal structure of oceanic lithosphere where theplate age is less than approximately 80 Myr [Turcotte andSchubert, 2002; Hillier and Watts, 2005], which is the casefor the majority of the Pacific plate included in our models(Figure 2a) [Muller et al., 1997].[17] Along the length of the Aleutian trench, the seafloor

age decreases eastward, from approximately 70 Myr at185° E longitude to approximately 30 Myr in the plateboundary corner (Figure 2a). The seafloor age at the trenchis extrapolated onto the subducted part of the Pacific plate so

that there is also an eastward decrease in the age of the slab.The eastward decrease of plate age creates an the eastwarddecrease in thermal and mechanical thickness of the Pacificplate. Note, that we do not include a compositional densityanomaly corresponding to the Yakutat block in our models,and therefore, in the plate boundary corner, we assume theage of the seafloor beneath the Yakutat block is the same asthat just southwest of the Transition fault (Figure 2).[18] To simulate conductive warming of the slab in the

mantle, a depth-dependent correction factor based on alength-scale diffusion analysis is applied to d, the distanceperpendicular from the slab surface used in equation (1). Weadjust the minimum value of d as a function of increasing

Table 1. Summary of Model Parameters and Resultsa

Model Slab Top Rheology sy Max. (MPa) PBSZ (Pa s) Vpacsurf (cm/yr, Azimuth) Vop (cm/yr, Azimuth) Vwedge (cm/yr, Azimuth)

A1n 325 var Newtonian 500 1 & 1020 2.11, 338.91° 0.23, 263.09° 2.56, 185.80°A2n 325 var Newtonian 500 1 & 1021 0.76, 328.64° 0.18, 285.15° 2.43, 183.03°A3n 325 var Newtonian 1000 1 & 1020 2.10, 338.39° 0.23, 261.17° 2.25, 187.02°A4n 325 var Newtonian 1000 1 & 1021 0.74, 327.29° 0.18, 282.83° 2.07, 183.67°A1c 325 var Composite 500 1 & 1020 5.28, 345.92° 0.06, 280.92° 31.68, 189.84°A2c 325 var Composite 500 1 & 1021 2.58, 345.89° 0.06, 290.08° 28.52, 189.51°A3c 325 var Composite 1000 1 & 1020 5.17, 342.93° 0.06, 275.49° 15.40, 180.79°A4c 325 var Composite 1000 1 & 1021 2.47, 342.73° 0.06, 283.39° 12.12, 179.42°B1n 115 var Newtonian 500 1 & 1020 1.92, 332.63° 0.24, 264.99° 3.15, 204.87°B2n 115 var Newtonian 500 1 & 1021 0.69, 320.38° 0.19, 279.15° 2.86, 203.13°B3n 115 var Newtonian 1000 1 & 1020 1.92, 332.11° 0.24, 263.61° 2.88, 207.91°B4n 115 var Newtonian 1000 1 & 1021 0.68, 318.90° 0.19, 277.28° 2.52, 206.48°B5n 115 unif Newtonian 500 1 & 1021 0.74, 318.45° 0.26, 264.21° 3.16, 203.42°B1c 115 var Composite 500 1 & 1020 4.40, 339.59° 0.07, 276.41° 65.78, 225.59°B2c 115 var Composite 500 1 & 1021 2.04, 339.45° 0.07, 284.45° 79.79, 226.71°B3c 115 var Composite 1000 1 & 1020 4.40, 336.57° 0.07, 273.33° 40.82, 225.39°B4c 115 var Composite 1000 1 & 1021 2.02, 336.18° 0.06, 279.12° 32.32, 225.24°B5c 115 unif Composite 500 1 & 1021 2.10, 340.39° 0.08, 273.39° 94.76, 225.81°

aTop is temperature structure of overriding plate, either (var) laterally variable effective age or (unif) laterally uniform effective age with both using anage-dependent temperature formulation. Vpacsurf is the Pacific plate surface velocity offshore south central Alaska at 217.3° longitude, 57.0° latitude. Vop

is the surface velocity in the overriding plate at 210.5° longitude, 64.5° latitude. Vwedge is the velocity in mantle wedge at 210.5° longitude, 64.5° latitude,and 100 km depth. At this location in the mantle wedge, horizontal velocities dominate with vertical velocities less than 3% of the horizontal velocitymagnitude. Vertical velocities increase with proximity to the pivoting slab tip.

Figure 3. 3D model set-up. NAM- North American plate;PAC- Pacific plate; Slab- subducted part of Pacific platewith portion of slab geometry that is varied outlined withshort-dashed black line; PBSZ- plate boundary shear zone;SMSZ - southern mesh boundary shear zone; and JdFR -Juan de Fuca Ridge. Cross sections A and B correspond tothose in Figure 2.


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vertical depth in the model, such that the minimum value ford on the slab surface increases from 0 km for the unsub-ducted part of the Pacific plate to 15 km on the slab surfaceat 300 km depth. Before this correction is added, T = 0°Ceverywhere on the slab surface, even on the parts of the slabsurface that are at 300 km depth. After this correction, theminimum temperature on the slab surface smoothly increa-ses with increasing slab depth, simulating the warming thatwould occur as the slab is immersed within the mantle, withthe deeper parts having been immersed longer and hencewarmed longer. The slab thermal field is then blended intothe ambient mantle thermal field using a sigma-shapedsmoothing function.

3.4. Overriding Plate Thermal Structure[19] The 3D thermal structure for the overriding North

American plate, constructed with SlabGenerator, alsoassumes a semi-infinite half-space cooling model (equation(1)), but uses effective thermal ages assigned to the conti-nental regions as a proxy to capture the temperature structurewithin the continental lithosphere (Figures 2a and 2b). Weelect this approach rather than using surface heat flowobservations to directly invert for the temperature as a func-tion of depth, because there are few coupled surface heat flowand radiogenic heat production measurements in Alaska.Without coupled measurements, the relative contribution ofheat from radioactive decay within the crust cannot bequantitatively separated from the contribution of heat fromthe underlying mantle [Turcotte and Schubert, 2002].[20] Thus, using equation (1), we construct a spatially

variable depth-dependent thermal structure for the overridingplate, with the overriding plate subdivided into four thermaldomains: the Cordilleran region, the magmatic arc, theforearc, and ancestral North America (Figures 2a and 2b).We base these subdivisions on a synthesis of regional geo-physical and geologic observations, including the surfaceheat flow [Blackwell and Richards, 2004], location ofNeogene volcanism (Alaska Volcano Observatory) [Plafkeret al., 1994], seismic profiles [Fuis et al., 2008], mohotemperature estimates, major terrane boundaries [Greningeret al., 1999], and the integrative work characterizing thethermal structure of the lithosphere in western Canada byCurrie and Hyndman [2006] and Lewis et al. [2003]. For theCordilleran domain, we assume the relatively warm Cordil-leran back arc lithosphere in western Canada [Currie andHyndman, 2006; Lewis et al., 2003] extends into mainlandAlaska (Figures 2a and 2b), and assign this region aneffective age of 30 Myr, corresponding to the lithosphericthickness of a continental mobile belt [Blackwell, 1969;Hyndman et al., 2005]. The magmatic arc is assigned aneffective age of 10 Myr, giving it the thinnest (warmest)lithosphere with the 1200°C isotherm at approximately40 km. The forearc and ancestral North America (effectiveages of 80 Myr) have the thickest lithosphere reaching1200°C at approximately 110 km depth (Figure 2b). Theresultant 3D thermal structure is shown in Figures 2c–2e.[21] To test the effect of the lateral variations in the

overriding plate thermal structure, we also construct a depth-dependent thermal structure that uses a single effective ageand thus has a laterally uniform thermal field throughoutthe entire overriding plate. We choose an effective age of30 Myr, which corresponds to a lithospheric thickness of

approximately 60 km at the 1200°C isotherm and 90 km atthe 1350°C isotherm (Figure 2b), and is comparable to thatof warm continental back arcs [Blackwell, 1969; Hyndmanet al., 2005].

3.5. Plate Boundary Shear Zone[22] In numerical models of subduction the plate interface

is typically represented either as a discrete fault surface[Kincaid and Sacks, 1997; Zhong et al., 1998; Billen et al.,2003] or a narrow low viscosity layer [Gurnis and Hager,1988; Kukacka and Matyska, 2004; Billen and Hirth,2007]. We model the plate interface as a narrow 3D lowviscosity layer in which the imposed reduction in viscosityrepresents a number of processes including the shear heat-ing, variation in grain size, and the presence of water andsediments. We use the SlabGenerator code to define theplate interface, referred to as the plate boundary shear zone(PBSZ), that is at least 40 km wide and extends to 100 km indepth [Jadamec, 2009; Jadamec and Billen, 2010]. Therheological implementation of the narrow 3D low viscositylayer (PBSZ) is described in section 3.7. The orientation ofthe PBSZ is spatially variable following the strike and dip ofthe subducting plate and is continuous with the vertically-oriented Fairweather-Queen Charlotte transform boundary(Figures 1 and 3). The PBSZ location is fixed in space,which is appropriate for these models of the present-daydeformation [Sdrolias and Muller, 2006]. We also include anarrow vertical low viscosity layer located along the south-ern edge of the Pacific plate in our model to decouple thePacific plate from the southern model boundary. This lowviscosity layer is implemented by the same method as for thePBSZ. No low viscosity layer is imposed on the Juan deFuca ridge, because the localized warm temperatures at thespreading center decouple the plates in that region. In addi-tion, no weak zone is imposed on the western-most bound-ary as this was found to have little affect on the modelresults.

3.6. Governing Equations and Numerical Method[23] The open source finite element code, CitcomCU

[Zhong, 2006], based on CITCOM [Moresi and Solomatov,1995; Moresi and Gurnis, 1996], is used to solve for theviscous flow in the 3D models of the Alaska plate boundarycorner. CitcomCU solves the Navier-Stokes equation for thevelocity and pressure, assuming an incompressible fluidwith a high Prandlt number, given by the conservation ofmass:

r⋅u ¼ 0 ð2Þ

and conservation of momentum:

r⋅s þ roa T " Toð Þgdrr ¼ 0 ð3Þ

where u, s, ro, a, T, To, g, and drr are the velocity, stresstensor, density, coefficient of thermal expansion, tempera-ture, reference temperature, acceleration due to gravity, andKronecker delta, respectively [Moresi and Solomatov, 1995;Zhong, 2006]. The models are instantaneous, therefore theenergy equation is not solved.


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[24] The constitutive relation is defined by

sij ¼ "Pdij þ heffɛ̇ij ð4Þ

where P is the dynamic pressure, heff is the effective vis-cosity defined in equation (9), and ɛ̇ij is the strain rate tensor.The models are defined and solved in spherical coordinates.The equations of motion are non-dimensionalized by theRayleigh number, Ra, is defined by

Ra ¼ roagDTR3

khrefð5Þ

where DT = To"Tsurf and ro, a, g, R, href, and k are asdefined in Table 2.

3.7. 3D Model Rheology[25] Experimental studies and the observation of seismic

anisotropy throughout the upper mantle, suggest that dislo-cation creep is the dominant deformation mechanism ofolivine in the upper mantle [Hirth and Kohlstedt, 2003]. Thenon-linear relationship between stress and strain rate fordeformation by dislocation creep leads to a faster rate ofdeformation (higher strain rates) for a given stress, whichcan be expressed as a reduction in the effective viscosity(i.e., heff ¼ s=2 _ɛ). Previous 3D numerical modeling studiesusing only Newtonian viscosity (diffusion creep) haveshown that imposing a region of low viscosity in the mantlewedge provides a better fit to the geoid and topography[Billen and Gurnis, 2001; Billen et al., 2003; Billen andGurnis, 2003]. Because mantle flow strain rates are high inthe corner of the mantle wedge, the imposed low viscosityregion in these previous models may be due to the weakeningeffect of the dislocation creep mechanism, providing oneexample of the possible importance of including the non-Newtonian (dislocation creep) viscosity. Therefore follow-ing the implementation of Billen and Hirth [2007], in our3D models of the Alaska subduction zone, we modifiedCitcomCU to use a composite viscosity in the upper mantle,that includes the effects of both dislocation (ds) and thediffusion (df) creep deformation mechanisms [Jadamec andBillen, 2010].[26] For deformation under a fixed stress (driving force)

the total strain rate is the sum of the contributions fromdeformation by the diffusion and dislocation creepmechanisms:

ɛ̇com ¼ ɛ̇df þ ɛ̇ds ð6Þ

where ɛ̇ without the subscripts i-j refers to the secondinvariant of the strain rate tensor, ɛ̇II . Substituting, s ¼2hcom ɛ̇, the composite viscosity, hcom, can be defined by

hcom ¼ hdfhdshdf þ hds

ð7Þ

[27] The viscosity components, hdf and hds, are definedassuming the experimentally-determined viscous flow lawgoverning deformation for olivine aggregates [Hirth andKohlstedt, 2003] such that

hdf ;ds ¼dp

ACrOH

" #1n

ɛ̇1"nn exp

E þ PlVnR T þ Tadð Þ

$ %ð8Þ

where Pl is the lithostatic pressure, R is the universal gasconstant, T is non-adiabatic temperature, Tad is the adiabatictemperature (with an imposed gradient of 0.3 K/km), and A,n, d, p, COH, r, E, and V are as defined in Table 3, assumingno melt is present [Hirth and Kohlstedt, 2003].[28] For diffusion creep, the strain rate depends linearly on

the stress (n = 1) but non-linearly on the grain size (p = 3)[Hirth and Kohlstedt, 2003]. A grain size of 10 mm is usedfor the upper mantle giving a background viscosity of 1020

Pa s at 250 km. In contrast, for dislocation creep of olivine,the strain rate dependence is non-linear for dislocation creepof olivine (n = 3.5), but there is no grain-size dependence,giving the same background viscosity at 250 km for a strainrate of 10"15 s"1 [Hirth and Kohlstedt, 2003]. For higherstrain rates, the composite viscosity will lead to lowereffective viscosity due to most of the deformation beingaccommodated by the dislocation creep mechanism.[29] The lower mantle viscosity is included using the

Newtonian flow law for olivine, with a larger effective grainsize (70 mm) in order to create a viscosity jump by a factorof 30 from the upper to lower mantle. This simplified vis-cosity structure for the lower mantle is consistent with themagnitude of the viscosity jump constrained by post-glacialrebound [Mitrovica, 1996] and models of the long wave-length geoid [Hager, 1984], as well as the lack of observa-tions of seismic anisotropy in the lower mantle and the fewexperimental constraints on the viscous behavior ofperovskite.[30] Close to the earth’s surface and within the cold core

of the subducted slab, the viscosity values determined byequation (7) become unrealistically large in that they imply arock strength much greater than that predicted by laboratoryexperiments [Kohlstedt et al., 1995]. To allow for plastic

Table 2. Dimensionalization Parameters

Parameter Description Value

Ra Rayleigh number 2.34 & 109

g acceleration due to gravity, m/s2 9.8To reference temperature, K 1673Tsurf temperature on top surface, K 273R radius of Earth, m 6371 & 103

href reference viscosity, Pa⋅s 1 & 1020

ro reference density, kg/m3 3300k thermal diffusivity, m/s2 1 & 10"6

a thermal expansion coefficient, K"1 2.0 & 10"5

Table 3. Flow Law Parameters, Assuming Diffusion and Disloca-tion Creep of Wet Olivinea

Variable Description Creepdf Creepds

A pre-exponential factor 1.0 9 & 10"20

n stress exponent 1 3.5d grain size, mm (if A in mm) 10 & 103 –p grain size exponent 3 –COH OH concentration, H/106 Si 1000 1000r exponent for COH term 1 1.2E activation energy, kJ/mol 335 480V activation volume, m3/mol 4 & 10"6 11 & 10"6

aValues from Hirth and Kohlstedt [2003].


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yielding where the stresses calculated in the model exceedthose predicted from laboratory experiments, the stressescalculated in the model are limited by a depth-dependentyield stress. The yield stress increases linearly with depth,assuming a gradient of 15 MPa per km, from 0.1 MPa at thesurface to a maximum value of either 500 MPa or 1000 MPa(Table 1), with the maximum value based on constraintsfrom experimental observations, low-temperature plasticity,and the dynamics in previous models [Kohlstedt et al., 1995;Weidner et al., 2001; Hirth, 2002; Billen and Hirth, 2005,2007].[31] We thus define the effective viscosity, heff:

heff ¼ hcom; if sII < sy& '

ð9Þ

¼ sy

ɛ̇II

" #; if sII > sy

( )ð10Þ

where hcom, sII, ɛ̇II , and sy are the composite viscosity,second invariant of the stress tensor, second invariant of thestrain rate tensor, and yield stress, respectively. The effectiveviscosity is solved for as an additional solution loop inCitcomCU that iterates until the global difference betweenthe velocity field of consecutive solutions is less than somespecified value, typically 1% [Billen and Hirth, 2007].Themodels allow for viscosity variations of up to seven ordersof magnitude, with a minimum viscosity cutoff value of5 & 1017 Pa s and a maximum value of 1 & 1024 Pa s.[32] To incorporate the 3D PBSZ defined by SlabGen-

erator into CitcomCU, we modified CitcomCU to read in aweak zone field, such that the weak regions indicative of theplate boundaries are smoothly blended into the backgroundviscosity, heff, using

hwk ¼ ho101"Awkð Þlog10 heff =hoð Þ ð11Þ

where heff is the effective viscosity as defined in equation (9),and ho is the reference viscosity equal to 1 & 1020 Pa s[Jadamec, 2009; Jadamec and Billen, 2010]. Awk is thescalar weak zone field, defined using SlabGenerator,assuming a sigma-function with values ranging from 0 to 1[Jadamec, 2009; Jadamec and Billen, 2010]. Values of 1correspond to fully weakened regions in the center of theshear zone and values of 0 correspond to unweakened

regions. The hwk value serves as an upper bound on the vis-cosity in the shear zone and will be overwritten if the vis-cosity calculated by equation (9) is lower. Thus, the finalform of the viscosity, hf, becomes

hf ¼ min heff ; hwkð Þ ð12Þ

[33] Although we cannot compare the complex 3Dnumerical models presented in our paper to an analyticsolution, previous 2D modeling by Moresi and Solomatov[1995] and Moresi et al. [1996] using CITCOM indicatesthat for models with large viscosity variations, error can bereduced by limiting the viscosity jump across each element,preferably to a factor of 3 or less. CitcomCU implements thefull multigrid method to accelerate convergence [Zhong,2006], which was found to save on valuable compute timein the high resolution regional models of the Alaska plateboundary containing large viscosity variations [Jadamec,2009]. In our models, to limit the viscosity jump in thePBSZ, the PBSZ width varies with the resolution of thefinite element mesh so that the PBSZ always spans a mini-mum number of elements. We found that numerical stabilitycould be obtained using 8 elements to span four orders ofmagnitude of viscosity, i.e., we allow for viscosity jumps ofup to a factor of 5 across the elements in the PBSZ. Thisimplementation was tested on a series of 3D models with asimplified subduction zone geometry and we found thatviscosity contrasts on this order led to good convergencebehavior [Jadamec, 2009].

3.8. 3D Visualization[34] The increasing incorporation of high performance

computing and massive data sets into scientific research hasled to the need for high fidelity tools to analyze and interpretthe information [Erlebacher et al., 2001; Kreylos et al.,2006; Chen et al., 2008; Kellogg et al., 2008]. Immersive3D visualization facilities provide one approach to fill thisgap in the workflow, especially when working with complexspatially varying data and nonlinear model behavior [e.g.,Kreylos et al., 2006; Billen et al., 2008].[35] The open source software 3DVisualizer [Kreylos

et al., 2006; Billen et al., 2008; Jadamec et al., 2008] wasused in the Keck Center for Active Visualization in the EarthSciences (KeckCAVES) for rapid inspection and interactive

Table 4. Seismic Constraints on Slab Deptha

Study Data Type daleut (km) dakp (km) dscak (km) dwr (km)

Qi et al. [2007] 3D teleseismic tomography – >400 300–400 90Eberhart-Phillips et al. [2006] 3D tomography – >200 160–180 50–60Zhao et al. [1995] 3D tomography – >190 165 >90Kissling and Lahr [1991] 3D tomography – – 120–150 –Fuis et al. [2008] Seismic reflection, refraction earthquake hypocentral locations – 240 175 100Ferris et al. [2003] Teleseismic receiver function analysis – – 150 –Ratchkovski and Hansen [2002] Earthquake hypocentral locations – 210 165–185 –Page et al. [1989] Seismic reflection, refraction earthquake hypocentral locations – – – >100Engdahl and Gubbins [1987] Simultaneous time travel inversion 400 – – –Stephens et al. [1984] Earthquake hypocentral locations – – – 85Boyd and Creager [1991] Local seismicity and teleseismic residual sphere analysis 600 – – –Gudmundsson and Sambridge [1998] RUM seismic model 300 250 150 –

aAbbreviations, daleut, dakp, dscak, and dwr, refer to the depth of the subducting plate beneath the Aleutians, the Alaska Peninsula, south central Alaska, andthe Wrangell Mountains. Data suggest a decrease in slab depth from west to east. Note, there is a range in depth resolution for studies listed in the table.


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exploration of the 3D plate boundary geometry and thermalstructure output from the SlabGenerator code. In this way,the quality and smoothness of the features mapped onto themodel grid, containing over 100 million finite elementnodes, could be assessed efficiently. This was especiallyuseful because of the large model size (which amounted to

inspecting almost two thousand 2D model slices for each 3Dmodel) and because of the geometrically complex slab andplate boundary configuration.[36] 3DVisualizer was also used in the KeckCAVES for

inspection and exploration of the composite viscosity field,velocity field, and strain rate output from CitcomCU for

Figure 4. Flow field, viscosity and strain rate for models using (left) slab325 with composite viscosity,(middle) slab115 with composite viscosity, and (right) slabE115 with Newtonian viscosity. Viscosity isosur-face and velocity slices for (a, d) model A1c, (b, e) model B1c, and (c, f) model B1n. Cross section of vis-cosity and second invariant of the strain rate tensor for (g, j) model A1c, (h, k) model B1c, and (i, l) modelB1n. Profiles at 64.5°N (location of vertical line in Figures 4g–4l) for (m) models A1c-A4c, (n) modelsB1c-B5c, and (o) models B1n-B5n. Figures show subset of model domain.


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10° westward so that it is focused around the most northernpart of the slab. This leads to a stronger component of west-ward directed trench parallel flow beneath the magmatic gapin south central Alaska for models with slabE115.[40] Figures 4d–4f show the poloidal component of flow,

where the sinking of the slab draws material into the mantlewedge toward the slab. Beneath the Pacific plate, a broaderregion of poloidal flow is induced in the mantle where thesurface part of the Pacific plate is pulled into the subductionzone. Cross sections AA′ through the poloidal flow in themantle wedge show velocity vectors that are steeper than theslab dip (Figures 4d–4f), indicating steepening of the slabdip with time, or retrograde slab motion [Garfunkel et al.,1986] if the models were to run forward in time. However,in cross section BB′ for models with slabE115, there isessentially no poloidal flow component in the mantle wedgeabove the Wrangell slab (Figures 4e and 4f). This is becauseslabE115 is too short in this region of the model to induce thepoloidal motion of mantle material.[41] The toroidal and poloidal flow in the mantle around

the subduction zone are not independent. Figures 4a–4c andFigures 5a–5c show there is motion along strike associatedwith the poloidal flow and motion in the vertical directionassociated with the toroidal flow. For example, in all models,the poloidal flow in cross section AA′ contains a westwardtrench parallel velocity component in the mantle wedge,suggesting the flow of material away from the slab nosetoward the arcuate central Aleutian subduction zone (Figures4d–4f). The trench parallel flow component around thenorthernmost part of the slab is stronger in models withslabE115, because the center of the toroidal flow is morewestward, i.e., at 212° rather than 222° longitude.[42] In addition, in all models, the toroidal flow around the

slab edge, whether it is centered at 212° or 222° longitude, isassociated with an upward component of flow (Figures 4a–4c and Figure 5a–5c). This upward flow component occurswhere the toroidal flow emerges from beneath the slab, i.e.,on the eastern side of the counterclockwise flow pattern inAlaska. The magnitude of the upward flow varies dependingon slab shape, slab strength, and mantle rheology, and canhave values greater than 10 cm/yr (Figures 5a–5c). Crosssection BB′ shows the upward component of flow at 100 kmdepth for models that use slabE325 with the composite vis-cosity (Figure 5d), slabE115 with the composite viscosity(Figure 5e), and slabE115 with the Newtonian viscosity(Figure 5f). Note the upward component of flow associatedwith the slab edge forms a 3D lenticular feature, and thus itsmagnitude varies laterally as well as with depth, with themaximum vertical component occurring at approximately200 km depth.[43] The upward component of mantle flow associated

with the toroidal flow at the slab edge combines with theupward component of the poloidal flow in the mantle wedgeabove the slab. The vertical motion of mantle material nearslab edges may play a role in forming melts from bothdecompression melting and melting of the slab edge (i.e.,adakites), as this part of the subduction zone is continuouslyexposed to upward advected warm mantle material. Theimplications for the adakitic Wrangell Mountains in easternAlaska, which are situated at approximately 216° longitude,are discussed in section 5.4.

4.2. 3D Variable Viscosity and Mantle Flow[44] Cross sections through the viscosity structure and

strain rate field are shown for the three representative mod-els: Model A1c (Figures 4g and 4j), Model B1c (Figures 4hand 4k), and Model B1n (Figures 4i and 4l). Figure 4 alsoshows vertical profiles through the viscosity and strain ratefor all models using slabE325 and the composite viscosity(Figure 4m), slabE115 and the composite viscosity (Figure 4n),and slabE115 and the Newtonian viscosity (Figure 4o).[45] Models using the composite viscosity formulation

have higher strain rates and lower mantle viscosities thanmodels using the Newtonian viscosity. In these models usingthe composite viscosity, a laterally variable viscosity emer-ges in the mantle as a consequence of the lateral variations inthe flow (Figures 4g, 4h, 4j, 4k, 4m, and 4n). Viscosities inthe mantle wedge can be lower than 1018 Pa s, where strainrates are high, on the order of 10"12 s"1. The weakest vis-cosities in the mantle wedge occur as elliptical regionsimmediately beneath the overriding plate and immediatelyabove the slab, again correlating to where strain rates arehigh ( Figures 4g, 4h, 4j, 4k, 4m, and 4n). Note that althoughshown in cross section only, these low viscosity (high strainrate) regions form three-dimensional ellipsoids in the mantlewedge that follow the strike of the slab.[46] For models using slabE115 and the composite viscos-

ity, the high strain rate and low viscosity region in the mantlewedge along cross section AA′ is broader than for modelsusing slabE325 (Figure 4h versus Figure 4g). This is becausethe velocity gradients and hence strain rates are higher whereboth toroidal and polodial flow occur leading to the lowerviscosity, as shown in cross section AA′ for model B1c.Models that use the composite viscosity and either slabshape also have high strain rates and low viscosity beneathand subparallel to the downgoing Pacific plate and slab(Figures 4g, 4h, 4j, and 4k).[47] In the Newtonian models, viscosities in the mantle

wedge are higher (1019 to 1020 Pa s) and strain rates arelower (10"13 to 10"14 s"1). In these models, the mantleviscosity is laterally uniform, except for temperature-dependent variations, because there is no power law relationbetween the stress and strain rate. Therefore, the viscosity isnot reduced in regions of high strain rate as was the case formodels using the composite viscosity (Figure 4).[48] The weakening effect of the strain rate dependent

viscosity in models using the composite viscosity formula-tion leads to viscosity contrasts that can be up to sevenorders of magnitude between the mantle and lithosphere.However, away from the driving force of the slab, strainrates decrease, and mantle viscosities increase to on theorder of 1020 Pa s. The localized regions of low viscosity andhigh strain rate around the slab and beneath the plates sig-nificantly reduces the coupling between the lithosphere andthe mantle near the subduction zone.[49] It is the magnitude of the driving forces that ulti-

mately limits the amount of weakening that occurs in themodels with the composite viscosity formulation, with thegreater amount of weakening in the mantle close to wherethe sinking slab is driving the flow. In this way, using thisviscosity formulation redistributes how the stresses areaccommodated in the model by weakening in some regions(the mantle) while strengthening in others (the lithosphere).


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leading to faster mantle flow velocities (Figure 6), as seen byBillen and Hirth [2005], Jadamec and Billen [2010], andStadler et al. [2010]. For example, mantle wedge velocitiesin models using the composite viscosity can be greater thanten times that in models using the Newtonian viscosity(66.8 cm/yr versus 6.5 cm/yr in maximum horizontalvelocity magnitude for models B1c versus B1n at 100 kmdepth) (Figure 6). This implies greater decoupling of mantleflow from surface plate motions for models with the com-posite viscosity. Note that for both types of upper mantlerheology, surface plate motions are less than 6 cm/yr (seesection 4.4).[54] Figures 4–6 illustrate how the velocities are sensitive

to the rheology, including both to the slab strength and thesurrounding mantle viscosity. For models that use the com-posite rheology, high strain rates located where the slabbends into the mantle, lead to viscous yielding within theslab and deformation by dislocation creep on the undersideof the slab, resulting in a narrower and weaker slab core(Figures 4g, 4h, 4j, and 4k). For example, whereas the slabcore remains on the order of 1024 Pa s in models with theNewtonian viscosity (Figure 4i), in models with the com-posite rheology, the viscosity of the slab is reduced to on theorder of 1022 Pa s in the slab hinge (Figures 4g and 4h). As aresult, less weight of the slab can be supported by the slabstrength, allowing for the slab to pivot faster and generatefaster velocities in the mantle (Figures 4–6).[55] When varying the yield strength, models with a

weaker slab (yield strength of 500 MPa) generate mantlevelocities that are almost twice as fast as the equivalentmodels with a stronger slab (yield strength of 1000 MPa)(black lines versus gray lines in Figures 6d–6f). Again,models with the lower yield strength allow less of the weightof the slab to be supported by the slab strength, thus leadingto a slab that is sinking faster and thereby generates morevigorous mantle flow.

[56] Mantle wedge velocities also vary depending onwhether toroidal and poloidal flow are both occurring. Forexample, where both poloidal and toroidal flow are actingtogether flow velocities in the mantle are stronger (Figures 5and 6). This can be seen for example, in comparison ofModel B1c (slabE115) and A1c (slabE325) along cross sec-tions AA′ in Figure 6. The velocities are higher for ModelB1c in which the flow from the toroidal and poloidal cellscombine in the mantle wedge.[57] In addition, models that use the uniform overriding

plate thermal structure and the composite viscosity havefaster mantle velocities, because the overriding plate is rel-atively thinner and thus the shallow mantle is warmer,allowing for lower viscosities and less resistance to flow(Figure 6e, models B2 versus B5).

4.4. Predicted Surface Motions[58] The predicted Pacific plate velocity vectors offshore

south central Alaska are shown in Figure 7. For models thatuse slabE325 and the Newtonian viscosity, the predictedvelocity of the Pacific plate ranges from 327.3° at 0.74 cm/yrto 338.9° at 2.11 cm/yr (Figure 7a). For models that useslabE115 and the Newtonian viscosity, the predicted platemotion ranges from 318.9° at 0.68 cm/yr to 332.6° at1.92 cm/yr (Figure 7b). Thus, models that use slabE325 havea more northerly and faster Pacific plate velocity than thesame models using slabE115. This is because models usingslabE325 have more slab pull in the eastern part of the slabwhere it extends to325 km beneath the Wrangell Mountains(Figure 1). This pattern is also seen in models using thecomposite viscosity, where the predicted Pacific platevelocity ranges from 343° at 2.47 cm/yr to 346° at 5.28 cm/yrfor models using slabE325 (Figure 7c) and from 336° at2.02 cm/yr to 340° at 4.4 cm/yr for models using slabE115(Figure 7d).

Figure 7. Predicted Pacific plate motion vectors offshore south central Alaska for Newtonian modelsusing (a) slabE325 and (b) slabE115 and for composite viscosity models using (c) slabE325 and (d) slabE115.Observed NUVEL–1A Pacific plate motion vector, assuming North America fixed, shown with thick graysolid line [DeMets and Dixon, 1999].


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[59] Comparison of models using the composite viscositywith those using the Newtonian viscosity show that, onaverage, models using the composite viscosity move in amore northerly direction and about 2.5 times faster(Figures 7a and 7b versus Figures 7c and 7d). This is becausethe strain rate dependence in models using the compositeviscosity leads to a viscosity reduction in the mantle sur-rounding the slab, reducing the viscous support of the slab bythe mantle. In addition, high strain rates along the plateboundary in models using the composite viscosity lead to alower viscosity and broader plate boundary shear zone,allowing less resistance along the plate boundary interfaceand consequently faster surface plate motions. Imposing ahigher viscosity of 1021 Pa s versus 1020 Pa s along the plateinterface decreases the surface plate motion by approxi-mately a factor of two, regardless of whether the composite orNewtonian viscosity is used (Figure 7, dashed versus solidlines). There is little difference in predicted plate motion formodels that use the uniform overriding plate thermal struc-ture versus those that use the variable overriding plate ther-mal structure (Figure 7, models B2 versus B5).[60] Comparison of the predicted Pacific plate velocity to

the observed NUVEL–1A Pacific plate velocity offshoreAlaska [DeMets and Dixon, 1999] is shown in Figure 7.There is good agreement between the predicted andobserved Pacific plate motion offshore south central Alaskafor models using the composite viscosity and plate boundaryviscosity of 1020 Pa s, regardless of slab shape (Figure 7).However, before considering how the model parametersaffect the match between the observed and predicted surfaceplate motion, it is important to realize that the entire Pacificplate is not included in the models because doing so wouldexceed the computational resources available. Instead, themodel domain was designed such that the bounds of thePacific plate included in the models are approximately rep-resentative of those of the actual Pacific plate, that is, asubduction zone to the north (Aleutian-Alaska trench),transform and spreading center to the east (Queen Charlotte-Fairweather transform and Juan de Fuca ridge), and aspreading center to the south (vertical weak zone at thesouthern boundary approximates the orientation of the east-west trending Antarctic spreading center). The main excep-tion is the western boundary, where the Pacific plate haswestward dipping subduction zones that are not included inthe models.[61] In order for a plate to remain rigid and move in

response to slab-pull and ridge-push forces on multipleboundaries, the orientations of the individual plate bound-aries must be roughly oriented such that the local drivingforce is mostly consistent with the overall plate motion. Inthe case of southern Alaska, plate reconstructions indicatethis plate boundary configuration has been stationary for thelast 40 Myr [Sdrolias and Muller, 2006] implying that thelocal driving forces and orientation of the plate boundary aredynamically consistent with the overall Pacific plate motion.Therefore, if the other model parameters are appropriate(e.g., mantle rheology), then the section of the Pacific plateand Aleutian slab included in our models should result inplate motions that are close to Pacific plate motion.[62] Thus, although we do not expect the models to achieve

an exact match with observed Pacific plate velocities, that

there is a good fit in the same models that produce rapid flowin the mantle indicates that rapid mantle flow is not incom-patible with surface plate motions. In other words, the same3D geodynamic models of the Alaska subduction-transformsystem that predict velocity magnitudes of greater than80 cm/yr in the mantle close to the subduction zone, alsopredict surface plate velocities comparable to observed platemotions.

5. Discussion

[63] The results from the 3D models of the Alaska sub-duction-transform system demonstrate the ranges in mantlevelocities that can be produced assuming an experimentallydetermined flow law for olivine and a realistic slab geometryand density structure. The results show larger velocity ran-ges as well as sharper velocity gradients in models using thecomposite viscosity formulation. The maximum mantlevelocity predicted by the 3D models of the Alaska subduc-tion-transform system ranges from less than 10 cm/yr in theNewtonian models to over 80 cm/yr in the composite vis-cosity models. The maximum velocity that occurs in themantle wedge, around the slab edge, and underneath the slabdepends on several factors: the (1) slab density anomaly, i.e.,the driving force; (2) slab strength, which depends in part onthe yield strength; (3) mantle viscosity; (4) plate boundarycoupling, i.e., viscosity along the plate interface; and (5) theproximity of the mantle to the slab edge.

5.1. Spatially Variable Slab and Mantle Viscosity[64] The consequence of using an experimentally derived

Newtonian and composite viscosity formulation in the 3Dnumerical models of the Alaska subduction-transform sys-tem is that the slab strength depends on the thermal structure,and on the strain rate for the composite viscosity formulation[Billen and Hirth, 2007; Jadamec and Billen, 2010].Therefore, a strong slab core emerges from the rheologicalflow law [Jadamec and Billen, 2010]. The depth dependentyield stress places a limit on the maximum strength of theslab determined from the experimentally derived flow law.[65] In models with the composite rheology, the slab hinge

area becomes locally weakened, with viscosities reducedfrom 1024 Pa s to on the order of 1022 Pa s (Figures 4g and4h). This gives a viscosity difference of three to four ordersof magnitude between the slab hinge and the mantle sur-rounding the slab, and of up to six orders of magnitudebetween the stronger parts of the slab and the weakest part ofthe mantle wedge (Figures 4g and 4h). In models using theNewtonian viscosity, the slab is not weakened in the slabhinge and maintains a viscosity on the order of 1024 Pa s inthe core, with a viscosity difference between the slab andmantle on the order of four orders of magnitude (Figure 4i).The viscosity ratios in our models are in the upper range ofthose suggested from previous 2D and 3D models of sub-duction, where the viscosity contrasts between the slab andthe mantle range from two to six orders of magnitude[Piromallo et al., 2006; Stegman et al., 2006; Royden andHusson, 2006; Billen and Hirth, 2007; Schellart et al.,2007; Kneller and van Keken, 2008; Schellart, 2008;Giuseppe et al., 2008; Jadamec and Billen, 2010; Ribe,2010].


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[66] The models of the Alaska subduction-transform sub-duction zone that use the composite viscosity formulationexhibit a localized lower viscosity in the mantle surroundingthe slab, and therefore locally reduced viscous support of theslab. This local reduction of the mantle viscosity does notoccur in Newtonian models, such as those of Piromallo et al.[2006], Stegman et al. [2006], and Schellart et al. [2007].Thus, although 3D Newtonian models of short slabs under-going slab rollback or slab steepening do show fastervelocities close to the slab [Kincaid and Griffiths, 2003;Schellart, 2004; Funiciello et al., 2006; Piromallo et al.,2006; Funiciello et al., 2006; Stegman et al., 2006;Schellart et al., 2007], the maximum velocities and thevelocity gradients are larger for models using the compositerheology because of the local reduction in mantle viscosity[Jadamec and Billen, 2010; Stadler et al., 2010]. This isconsistent with a non-Newtonian viscosity behavior where apower law dependence between stress and strain rate ischaracterized by larger velocity gradients than in a New-tonian viscosity [Turcotte and Schubert, 2002].[67] In order to match surface observables, several previ-

ous models have called upon mantle velocities in the mantlewedge and back-arc that are faster than plate motions,although the mechanism for the lower viscosities is typicallyattributed to the presence of water or to higher temperatures,rather than from the weakening effects of a strain ratedependent viscosity [Hyndman et al., 2005; Currie andHyndman, 2006]. Although we use a thermal model with awarm back-arc lithosphere, as do Blackwell [1969] andHyndman et al. [2005], the fast velocities in the mantlepredicted by our models are not a result of the warm, thinlithosphere imposed for our overriding plate, because thethermal structure is the same for the instantaneous New-tonian and composite viscosity models. The low viscosityregion in the mantle wedge that emerges from the strain ratedependent viscosity suggests that in some subduction zones,additional water or heat [Billen and Gurnis, 2001; Hyndmanet al., 2005; Currie and Hyndman, 2006] may not berequired to reduce the viscosity and that the strain ratedependent rheology may be as important of a contributor toreducing the viscosity in the mantle wedge.

5.2. Short Slabs and Fast Velocities[68] The deepest part of the slab in the 3D models of the

Alaska subduction-transform system extends to approxi-mately 325 km based on seismic constraints (section 3.2).Therefore, although the model depth extends to 1500 km,and the models include an increase in mantle viscosity forthe lower mantle, the slab is not supported by the lowermantle. Thus, the slab in our model is considered a shortslab, and how the model parameters affect the slab dynamicsshould be considered in the context of that for short slabs inthis early phase of subduction, as identified by Schellart[2004], Funiciello et al. [2006], Piromallo et al. [2006],Billen and Hirth [2007], Giuseppe et al. [2008], andJadamec and Billen [2010]. Within this transient state, as aslab descends into the mantle it does not maintain its initialdip indefinitely, rather the slab will steepen due to the slabpull force [Spence, 1987; Conrad and Hager, 1999;Lallemand et al., 2008; Ribe, 2010]. This pivoting can beaccentuated by the presence of a slab edge, where returnflow can increase the rate of steepening, as indicated by the

occurrence of steeper slab dips near slab edges [Lallemandet al., 2005; Schellart et al., 2007].[69] Viscous yielding and deformation by dislocation

creep which weaken the slab hinge allowing the slab to bendmore easily also reduce the amount of slab pull that can bedirectly transmitted to the subducting plate. This effect isincluded in all the models and contributes to why the surfacepart of the subducting plate moves slower than the slab issinking. Some amount of yielding is required to allow theslab to pivot and sink into the mantle, but the reduction inslab strength in the hinge limits the amount of slab pull forcethat can be directly transmitted to the surface plate.[70] We expect that it is slabs in the transient state, not

supported by the higher viscosity mantle below the transitionzone, that are more likely to induce localized rapid mantleflow. Thus, other subduction zones with short slabs whererapid mantle flow may be expected include central America,Cascadia, the lesser Antilles, Scotia, and Vanuatu. Seismicand geochemical studies suggest this may be the casebeneath Costa Rica-Nicaragua. In this region, local S waveand teleseismic SK(K)S wave anisotropy measurementscontain trench parallel fast axes in the shallow and deeperparts of the mantle wedge, indicative of trench parallel flow[Abt et al., 2009, 2010]. Along the volcanic front there is asystematic northwestward increase in 143/144Nd and decreasein 208/204Pb suggesting northwestward flow of mantle[Hoernle et al., 2008]. Using the isotopic ages and withassumptions about the transport distance, velocity bounds of6.3–19.0 cm/yr have be placed on the trench parallel com-ponent of mantle flow in the mantle wedge [Hoernle et al.,2008], which is either slightly slower than or more thantwice as fast as the surface motion vector for the Cocos plate.We also point out that localized rapid flow may not belimited to subduction zones with slab edges, as previousstudies that include a non-Newtonian rheology predict alongstrike flow of up to 50 cm/yr in a low viscosity channelwithin the mantle wedge [Conder and Wiens, 2007] as wellas mantle plume ascent velocities on the order of 100 cm/yr[Larsen et al., 1999].

5.3. Seismic Anisotropy and Plate-Mantle Decoupling[71] Beneath south-central Alaska teleseismic shear wave

splitting observations show east-west and northeast-south-west trending (trench-parallel) fast directions in the mantlewedge north of the slab [Christensen and Abers, 2010]. Theseismic fast directions rotate to northwest-southeast (trench-perpendicular) to the south of the 100 km Aleutian slabcontour beneath south central Alaska and are northeast-southwest (trench perpendicular) to the southeast of the slabnose [Christensen and Abers, 2010]. In order to use theseismic anisotropy observations of Christensen and Abers[2010] as a constraint on the mantle flow field predicted bythe 3D Alaska subduction-transform models, Jadamec andBillen [2010] calculated infinite strain axes (ISAs) from thepredicted mantle flow field, according to the method ofConrad et al. [2007], and compared the ISAs to the obser-vations of seismic anisotropy.[72] Jadamec and Billen [2010] found that models using

slabE115 and the composite rheology provided the best fitbetween the predicted ISA orientations and the seismic fastdirections from the observed anisotropy. None of the modelswith slabE325, where the toroidal flow is located further to


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the east, were able to match the observed pattern of anisot-ropy. Models with slabE115, but that used the Newtonianviscosity, displayed less vigorous flow including a smallertoroidal flow component and lead to a poor fit to theanisotropy. Thus, the pattern of observed seismic anisotropyin this region of south central Alaska is consistent with rapidtoroidal flow around the slabE115 edge. This implies decou-pling of the mantle from surface plate motion in terms ofboth direction and speed within the Alaska subduction-transform system.[73] Shear wave splitting studies that probe the character

of the mantle in many other subduction zones find seismicfast directions that are nonparallel to the direction of sub-ducting plate motion [Russo and Silver, 1994; Fischer et al.,1998; Hall et al., 2000; Smith et al., 2001; Kneller and vanKeken, 2007; Pozgay et al., 2007; Hoernle et al., 2008;Long and Silver, 2008; Abt et al., 2010]. In addition, shearwave splitting measurements from the subduction-transformjunctures in northern Kamchatka and southern Cascadia alsodisplay a curved pattern of the seismic fast directions, sug-gestive of toroidal flow in the uppermost mantle around aslab edge [Peyton et al., 2001; Zandt and Humphreys,2008]. This suggests that partial decoupling of the surfaceplate motion from the underlying mantle flow field, at leastin terms of direction, may be common in subduction zones.Moreover, in some subduction zones the mantle may flow atrates significantly faster than the surface plate motion[Conder and Wiens, 2007; Hoernle et al., 2008; Jadamecand Billen, 2010; Stadler et al., 2010], implying decou-pling in speed as well.[74] A power law rheology, i.e., one that includes the

effects of the dislocation creep deformation mechanism, canexplain both observations of seismic anisotropy and thedecoupling of mantle flow from surface motion [Jadamecand Billen, 2010]. Dislocation creep of olivine in the uppermantle leads to lattice preferred orientation (LPO) in olivinewhich results in anisotropy in seismic waves [Savage, 1999;Kaminiski and Ribe, 2002; Karato et al., 2008; Long andSilver, 2009]. In addition, dislocation creep of olivine leadsto a lowering of the viscosity in regions of high strain rate inthe mantle, which in turn facilitates the decoupling of themantle from the surface plates [Billen and Hirth, 2005;Jadamec and Billen, 2010]. This is because the power lawrelationship between stress and strain rate for deformation bydislocation creep leads to a faster rate of deformation (higherstrain rates) for a given stress, which can be expressed as areduction in the effective viscosity [Hirth and Kohlstedt,2003; Karato et al., 2008]. This reduction can occur inregions of variable velocity, or high strain rate, such as in themantle wedge and near a slab edge [Billen and Hirth, 2005,2007; Jadamec and Billen, 2010].

5.4. Implications for Volcanics Above a Slab Edge[75] In the 3D models of the Alaska subduction-transform

system, where the slab edge is deep enough to inducetoroidal flow, the models indicate there is associated mantleupwelling within approximately 500 km outward of the slabedge. This is consistent with mantle flow patterns predictedby other 3D subduction models where there is a slab edgeand slab steepening [Funiciello et al., 2006; Piromallo et al.,2006; Stegman et al., 2006; Jadamec and Billen, 2010;Schellart, 2010b]. Thus, in these tectonic environments,

warm mantle is expected to be transported from underneaththe slab into the mantle wedge in an upward and arcuatepattern around the edge of the slab, which could lead todecompression melting within several hundred kilometersoutward of the slab edge as well as contribute to melting ofthe slab edge [Yogodzinski et al., 2001]. In addition, becausetoroidal flow is associated with rapid mantle velocities[Kincaid and Griffiths, 2003], which are significantly fasterfor a composite viscosity [Jadamec and Billen, 2010;Stadler et al., 2010], this may contribute to the preservationof primitive magmas that can be brought to the surface[Durance-Sie, 2009; McLean, 2010; P. M. J. Durance andM. A. Jadamec, Magmagenesis within the Hunter Ridge RiftZone resolved from olivine-hosted melt inclusions andgeochemical modelling with insights from geodynamicmodels, submitted to Australian Journal of Earth Sciences,2012].[76] Adakitic volcanics have been identified at several

subduction-transform plate boundaries, including the easternAlaska subduction-transform boundary, the Kamchatka-Aleutian plate boundary corner, the Cascadia-San Andreasfault juncture, in southern New Zealand where there is asubduction-transform transition, and in the New Hebridestrench-Hunter fracture zone region [Skulski et al., 1991;Peyton et al., 2001; Yogodzinski et al., 2001; Durance-Sie,2009]. However, the position of the volcanics with respectto the slab edge and upwelling in the mantle flow field hasonly recently been tested in 3D geodynamic models[Jadamec and Billen, 2010; Schellart, 2010b; McLean,2010; Durance and Jadamec, submited manuscript, 2012].[77] The Wrangell volcanics in Alaska, characterized by

adakitic geochemical signatures indicative of melting of theslab edge, are located east of and physically separate fromthe Aleutian-Alaska magmatic arc (Figure 2) [Skulski et al.,1991; Preece and Hart, 2004]. In our 3D models that useslab115, the Wrangells are located above the upward streamin the counterclockwise quasi-toroidal flow associated withthe deeper slab edge. In models using slabE325, the Wran-gells are located above the center line of the return flow fromthe slab edge. We suggest the Wrangell volcanics in Alaskamay be due in part to the upwelling associated with thedeeper edge of slabE115 at approximately 212° to 215° lon-gitude. These models do not investigate the link betweenmelt migration and solid state flow of the mantle, which is animportant and complex process especially in 3D, but beyondthe scope of this paper.

5.5. Slab and Trench Geometry in Alaska[78] The toroidal flow of the mantle around the eastern

Alaska slab edge and steepening of the slab dip predicted bythe 3D models of the Alaska subduction-transform systemare suggestive of slab rollback [Garfunkel et al., 1986;Kincaid and Griffiths, 2003; Schellart, 2004; Funiciello etal., 2006; Stegman et al., 2006] and thereby retreat of thetrench in eastern Alaska. 3D laboratory experiments of freesubduction indicate that during trench retreat, the trenchgeometry evolves into an arcuate shape with the concaveside directed away from subducting plate [Schellart, 2004;Funiciello et al., 2006; Schellart, 2010a]. Along the greaterthan 3000 km length of the Aleutian-Alaska subductionzone, the sense of curvature of the plate boundary changesconcavity [Page et al., 1989; Gudmundsson and Sambridge,


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1998; Ratchkovski and Hansen, 2002; Bird, 2003]. Althoughin the central Aleutians the trench is concave to the north,i.e., away from the subducting plate consistent with thatexpected for trench retreat, the trench in eastern Alaska isconcave to the south, i.e., toward the subducting plateinconsistent with that expected for trench retreat.[79] A comparison of global plate motion models

[Schellart et al., 2008] indicates that although the trench inthe central Aleutians may be retreating, the trench in easternAlaska shows little to no trench retreat, despite that it ter-minates into the Queen Charlotte-Fairweather transformfault forming a slab edge. In addition, plate reconstructionsindicate this portion of the plate boundary has been station-ary for at least 10 Myr [Sdrolias and Muller, 2006]. Theseobservations are unexpected, as along many plate bound-aries the rate of trench retreat tends to be greatest near a slabedge, and 3D numerical models indicate that the magnitudeof trench retreat along a subduction zone is greatest closestto a slab edge [Stegman et al., 2006; Schellart et al., 2007,2008]. Therefore, other features of the subduction zone maycontrol the shape of the trench in eastern Alaska or thesubduction zone may be in a transient state.[80] One such feature is the Yakutat terrane, the oceanic

plateau that is actively colliding with North America in theplate boundary corner of southern Alaska [Lahr and Plafker,1980; Bruns, 1983; Fletcher and Freymueller, 1999; Pavliset al., 2004; Meigs et al., 2008] and may be subducted to adepth of 150 km [Ferris et al., 2003]. 3D laboratory andnumerical models of the subduction of an oceanic plateauoriented at a high angle to a trench indicate that the shape ofthe trench becomes arcuate with the concave side toward thesubducting plate [Martinod et al., 2005;Mason et al., 2010].This is opposite to that predicted for slab rollback and con-sistent with the trench shape in eastern Alaska. At depth,these 3D laboratory and numerical models predict that after aplateau is subducted, the uppermost part of the slab shallowsin dip becoming a flat slab in the vicinity of the oceanicplateau with the flanks of the slab dipping more steeply andaway from the central shallow slab [Martinod et al., 2005;Mason et al., 2010]. This geometry is consistent with thatobserved in the subducted plate beneath south centralAlaska,where the flat slab is flanked by the more steeplydipping Aleutian portion of the slab to the west and thesteeply dipping, but shorter, Wrangell slab to the east[Stephens et al., 1984; Page et al., 1989; Gudmundsson andSambridge, 1998; Ratchkovski and Hansen, 2002; Fuis etal., 2008]. Thus, the toroidal flow around the slab edge insouth-central Alaska may not lead to the formation of aretreating trench, because the positive buoyancy of theYakutat terrane may prevent sinking of this upper portion ofthe slab and thus inhibit trench retreat. We point out that,although the geometry of the subducting plate in our modelsis based on Wadati-Benioff zone seismicity, which weexpect is due in part to the subducted Yakutat terrane, themodels do not include an additional compositional buoyancyforce representative of this plateau.[81] Alaska has long-lived subduction history [Wallace

and Engebretson, 1984; Lonsdale, 1988; Madsen et al.,2006; Sdrolias and Muller, 2006; Qi et al., 2007] suggest-ing that a slab could be present to the 660 km discontinuity.However, the seismicity and seismic tomography indicatethat, although the slab beneath the Aleutians may reach the

transition zone, the slab beneath south central Alaska likelydoes not extend deeper than 300 km, and that the slab beneatheasternmost Alaska is likely even shorter (see Table 4 andreferences therein). The lack of a slab continuous to thetransition zone beneath south central Alaska could resultfrom previous detachment of the deeper part of the subductedplate due to the subduction of the Yakutat terrane or due to aweakness in the subducting plate at depth because of sub-duction of the failed Kula-Farallon spreading center [Madsenet al., 2006; Qi et al., 2007]. Investigating the potentialdetachment of a slab with depth over the course of the sub-duction history of southern Alaska is beyond the scope of thispaper, but would be interesting to investigate using futuretime-dependent modeling studies and would likely be moretractable with future codes using adaptive mesh refinement[e.g., Stadler et al., 2010].[82] The seismicity, seismic tomography, and the agree-

ment between the models using slabE115 and the seismicanisotropy from the northern mantle wedge, suggest slabE115is representative of the actual slab shape beneath mainlandAlaska, and that slabE325 is not (Table 4 and Jadamec andBillen [2010]). The numerical models show that the rela-tive depth of the slab tip and base of the overriding litho-sphere influences whether there will be flow induced in themantle. Thus, for models using slabE115, although this slabshape has two slab edges, one at approximately 212° lon-gitude (beneath south central Alaska) and the other at223° longitude (near the northern end of the QueenCharlotte-Fairweather fault), only the deeper slab edge at212° induces toroidal flow. The lack of induced flow nearthe northern end of the Queen Charlotte-Fairweather faultimplies that there is little strain induced in the mantle wedgehere and therefore we would not expect a well developedLPO in the mantle wedge in the vicinity of the easternmostWrangell slab. If, however, the actual slab shape were two-tiered as in slabE115 but with the slab beneath the Wrangellsextending to 175 km, rather than to 115 km, we wouldexpect the tiered shape to produce two regions of toroidalflow in the mantle, one centered at 212° longitude and thesecond centered farther to the east at 223° longitude. In thiscase, one would expect a well developed LPO, and thusorganized pattern in the seismic anisotropy, in the mantlewedge near both 212° and 223° longitude. Additional seis-mic anisotropy measurements near the northern end of theQueen Charlotte-Fairweather fault would be useful to betterconstrain the depth of the shorter slab segment beneath theWrangell mountains.

6. Conclusions

[83] We have constructed 3D instantaneous regionalmodels of the eastern Alaska subduction-transform plateboundary system to investigate the role of slab geometry andrheology on the decoupling of mantle flow from surfaceplate motion, in terms of both direction and magnitude, atsubduction zones. The 3D models use a subducting plategeometry based on Wadati-Benioff zone seismicity andseismic tomography and a 3D thermal structure for both thesubducting and overriding plates, constrained by geologicand geophysical observations. The models test the effect of aNetwonian viscosity and a composite viscosity, whichincludes both the diffusion and dislocation creep


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mechanisms (i.e., Newtonian and non-Newtonian viscosity).The models in this paper differ from previous 3D numericalmodels of subduction in that previous models either use asimplified plate geometry, prescribe a velocity boundarycondition to the subducting plate, do not include an over-riding plate, or use a Newtonian rheology in the mantle.However, our models are limited in that they are instanta-neous, examining the spatial distribution of the flow ratherthan the time-dependent evolution.[84] Models using the composite viscosity formulation

have higher strain rates and lower mantle viscosities thanmodels using the Newtonian viscosity. In models using thecomposite viscosity, a laterally variable mantle viscosityemerges as a consequence of the lateral variations in themantle flow and strain rate. Spatially variable mantle velocitymagnitudes are predicted, with localized fast velocities(greater than 80 cm/yr) close to the slab where the negativebuoyancy of the slab drives the flow. The same models pro-duce surface plate motions of less than 10 cm/yr, comparableto observed plate motions. We expect that it is short slabsundergoing slab steepening, not supported by the higherviscosity mantle below the transition zone, that are morelikely to induce the localized rapid mantle flow. These resultsshow that a power law rheology, i.e., one that includes theeffects of the dislocation creep deformation mechanism, canexplain both observations of seismic anisotropy and thedecoupling of mantle flow from surface motion.[85] The incorporation of realistic slab geometries into 3D

models of subduction leads to a complex pattern of poloidaland toroidal flow in the mantle, with the spatial positions ofthe mantle flow components sensitive to the slab geometry.We conclude that slabE115 is representative of the actual slabshape beneath south central Alaska. The vertical motion ofmantle material near slab edges may play a role in formingmelts from both decompression melting and melting of theslab edge (i.e., adakites), as this part of the subduction zoneis continuously exposed to upward advected warm mantlematerial. The Wrangell volcanics may be due in part to theupwelling associated with the deeper edge of slabE115.

[86] Acknowledgments. We thank C. Matyska, W. P. Schellart, andan anonymous reviewer for thoughtful reviews of the manuscript. We thankD. Turcotte, L. Kellogg, S. Roeske, D. Eberhart-Phillips, T. Taylor, and L.Moresi for thoughtful discussions. We thank Oliver Kreylos and the UCDavis Keck Center for Active Visualization in the Earth Sciences (Keck-CAVES) for enabling the incorporation 3D immersive data visualizationinto this research. We thank the Computational Infrastructure for Geody-namics (CIG) for the CitcomCU source code. Figures were made withGMT and 3D Visualizer. High resolution models were run on the TeraGridsite, Lonestar, at the Texas Advanced Computing Center (TACC) throughTG-EAR080015N. This work was supported by National Science Founda-tion grants EAR-0537995 and EAR-1049545.

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