thermal-rheologic controls on deformation within oceanic...

Furlong et al. Oceanic Transform Rheology

Thermal-Rheologic Controls onDeformation within Oceanic Transforms

Kevin P. Furlong*Steven D. Sheaffer1Rocco Malservisi

Geodynamics Research Group, Department of GeosciencesPennsylvania State University, University Park, PA USA

* Corresponding author. Department of Geosciences, Penn State University, University Park, PA16802, USA. E-mail: [email protected].

1 Present address: Department of Geophysics, Colorado School of Mines, Golden, CO 18401,USA. E-mail: [email protected]; [email protected].

Reference:Furlong, KP, Sheaffer, SD, Malservisi, R., 2001. Thermo-rheological controls on deformationwithin Oceanic Transforms. In: Holdsworth, RE, Strachan, RA, Magloughlin, JF, Knipe, RJ (eds),The Nature and Tectonic Significance of Fault Zone Weakening. Geological Society, London,Special Publications, 186, 65-84.


Abstract: Transform faults that offset mid-ocean ridgesegments accommodate plate motion throughdeformations that involve complex thermal andmechanical feedbacks involving both brittle andtemperature-dependent ductile rheologies. Through theimplementation of a 3-D coupled thermal-mechanicalmodeling approach, we have developed a more detailedpicture of the geometry of plate boundary deformationand its dependence on plate velocity and the age offsetof MOR transforms. The modeling results show thatcooling of near-ridge lithosphere (lateral heat transfer)has significant effects in the ductile mantle lithospherefor both the location and style of deformation. Theregion where strain is accommodated in the subjacentmantle lithosphere is systematically offset from theposition of the overlying linear transform fault in thebrittle crust. This offset causes the boundary to beoblique to plate motions along much of the transformslength, producing extension in regions of significantobliquity modifying the location of the surface faultsegments. An implication of this complex plate-boundary geometry is that in the near-ridge region, theolder (cooler) lithosphere will extend beneath the ridgetip, restricting the upwelling of mantle to the mid-ocean ridge. The melt to generate the oceanic crustadjacent to the transform must migrate laterally fromits offset source resulting in a reduced volume andthinner crust. This near-ridge plate boundary structurealso matches the pattern of core-complex extensionobserved at inside corners of many slow-spreadingridges. The oblique extensional structure may alsoexplain magmatism that is observed along "leaky"transforms, which could ultimately result in thegeneration of new ridge segments that effectively"split" large transforms.

Mid-oceanic ridge transform boundaries havecomplex thermal and rheological structures andtherefore potentially complex kinematic behavior.Even though deformation at the surface appears to occurin narrow linear zones along brittle faults, deformationin the deeper lithosphere below the brittle-ductiletransition may be more complicated. Below the depthof faulting, the structure of the shear zone where platemotions are accommodated will be determined bycoupled thermal-mechanical effects, and thus can be athree-dimensional regime that does not necessarilymimic the overlying brittle faults, but may perturbtheir behavior.

Improvements in tools to image bathymetricfeatures of transform zones allow detailed descriptionsof the geometry and localization of shear deformationwithin transform zones to be determined (see forexample, Searle 1992). The actual transform fault zone(TFZ) within the transform tectonized zone (TTZ) isoften slightly oblique to the TTZ (Fox and Gallo 1984;Searle 1986, 1992; Searle et al. 1994). The patterns ofdeformation observed in the TTZ appear to vary withspreading rate. How these near-surface patterns of plateboundary deformation relate to deeper plate boundaryshear is not well resolved and serves as a focus of thisresearch.

An exciting set of recent research results is thedocumentation of core-complex-like “mega-mullions”at the inside corners of many ridge-transformintersections (e.g. Cann et al. 1997; Blackman et al.1998; Tucholke et al. 1998; Escartin and Cannat 1999),particularly associated with low-velocity plateboundaries. These extensional structures expose lower-crustal gabbros and upper-mantle peridotites and requirea significant change in deformational style in thevicinity of the ridge-transform intersection. The rolethat the lithosphere-scale deformation plays in drivingthis deformation is an issue requiring investigation.

An idealized model comprising two elasticplates separated by a linear strike-slip fault is oftenemployed in transform studies. Any plate boundarystrength below the brittle-ductile transition is oftendisregarded. However, this ductile material may havesignificant shear strength, particularly as one movesfrom the ridge into the older lithosphere along thetransform. Ocean-ridge transforms with large age-offsetmay show patterns of deformation that result from thisvariation in mechanical strength of the plate boundaryregion. Furthermore, although the ductile strengthtends to decrease with depth (increasing temperature),this weaker mantle lithosphere may still play animportant role in transform behavior.


We have developed a 3-D coupled thermal-deformational model to investigate the nature ofdeformation along mid-ocean transform systems. Thevariation in deformational geometries as a function ofplate velocity and age-offset along the transform are theprimary targets of this modeling.

The modeling approach we are taking isessentially an extension of the oceanic transform modelof Forsyth and Wilson (1984), which describes theresults of a three-dimensional thermal model of thetransform regime using finite difference methods. Theyassumed a transform that is a vertical strike-slipboundary at all depths and prescribed a uniform velocityfield on either side parallel to the transform strike,except under the ridges where upwelling was defined.This model resulted in a three-dimensional temperaturefield that included the effects of lateral heat conductionacross the transform. Limitations of this modelapproach which we have tried to address in our modelsare that the kinematics were completely prescribed, andit did not account for the effects of variations intemperature on rheology. Below the depth of faulting,the “plate boundary” is presumably a shear zone. Theresults of our modeling indicate that these factors havesignificant effects on both the thermal structure and thekinematics of the transform.

In addition to the purely conductive model ofForsyth and Wilson (1984), Phipps-Morgan andForsyth (1988) coupled the thermal calculation to asub-lithosphere velocity field based on upper-mantleflow calculations. A semi-analytical solution for three-dimensional linear viscous flow from an assumedtransform plate geometry was employed to determinethe velocity field in the viscous regions. This field wasthen used in a finite difference thermal calculation toestimate the large scale transform temperature field.This model assumed a linear rheology with constant,temperature independent viscosity, and the calculatedvelocity field depended only on the plate geometry. Inessence, the thermal field depended on the calculatedvelocity field, but the velocity field was independent ofthe thermal field. In our study, we have explicitlyincluded the feedbacks between the thermal anddeformational fields in modeling the plate boundarydeformation zone, in order to evaluate the influence ofthese interactions in controlling the pattern of plateboundary deformation. We have focused on thedeformational response of the lithospheric part of theMOR-transform system. These results are generallycompatible with a suite of modeling studies that havefocused more on the linkages between the induced flowfield in the asthenospheric mantle and the overlyingMOR-transform lithosphere (Shen and Forsyth 1992;Blackman and Forsyth 1992; Blackman 1997).

Here we describe our attempt to obtain animproved picture of transform plate boundarydeformation by utilizing a model that fully couples thethermal and mechanical fields, and incorporateselastic/brittle material and brittle faulting at shallowdepth, with a non-linear temperature dependent ductilerheology at depth.

Our modeling shows that the resulting thermaland mechanical structures associated with platekinematics are significantly different from those seen inprevious models. Specifically, the localized shear zonethat accommodates plate motions in the ductile mantlelithosphere does not mimic the overlying transformfault. It is offset at the mid-ocean ridge (MOR) tipsbecause of the effects of lateral cooling on the non-linear ductile rheology of the upper mantle. As aresult, much of the boundary at depth is oblique to thetransform strike. Such a geometry may tend to driveoblique faulting at shallow levels, and produceextension, upwelling, and thinning along thetransform, leading to leaky transform magmatismsometimes observed along transforms. In addition, theplate boundary geometry and pattern of strain at theridge-transform intersection may serve as the root zonefor the formation of oceanic core-complexes.

Conceptual Model

We assume that near the surface, mid-oceanic-ridge transforms are dominated by weak, linear faultsthat are aligned with plate motions to within a fewdegrees (Spitzak and DeMets 1996). Although thedetails of the TTZ are clearly more complex than this(Searle 1992), we have assumed this simplifiedgeometry in our modeling, but address the implicationsof our models for the near surface deformation patternslater in the paper. This shallow plate boundary structureis implemented in our model as a single vertical faultof low frictional resistance cutting the elastic layer, thatstrikes normal to the ridge axes and parallel to platemotions. Seismic analyses suggest that the maximumdepth of faulting in these regimes is approximatelycoincident with the depth of the 600° C isotherm (e.g.Engeln, et al. 1986). For our models we use thistemperature to define the brittle-elastic layer, beneathwhich temperature dependent plastic deformation isassumed.

Lateral heat conduction across the transformwill cool young near-ridge material due to its proximityto cooler, older material on the opposite side. Thermalmodeling (e.g. Forsyth and Wilson 1984; Phipps-Morgan and Forsyth 1988) shows that there is a zonethat can extend more than 10 km on either side of thesurface transform within which this cooling will lowertemperatures by more than 100° C with respect to plate


material of equivalent age and depth far from thetransform. Although these temperature variations areusually interpreted as being significant primarily interms of their density/gravity effects (Escartin andCannat 1999); they can produce significant contrasts inductile strength (for temperature-dependent power-lawcreep in the upper mantle). Temperature variations of100° C can produce up to an order of magnitudedifference in dislocation-creep flow strength in “dry”olivine (Karato and Wu 1993).

With the effects of lateral cooling, young near-ridge mantle material in the transform zone will beanomalously strong compared to material of the sameage and depth in the rest of the plate. The weaker partof the plate (and thus the potential locus of localizedplate boundary strain) will not lie directly below theoverlying fault, but will be offset into the young platein regions where the temperature contrasts betweenplates are significant. The net result will be a narrowdeformation zone in the mantle where plate motions areaccommodated, but that is not everywhere aligned withthe overlying linear fault. This deformation zone willdefine the plate boundary in the mantle, and will bereferred to as such in the rest of the paper, even thoughit does refer to a shear zone of finite width.

Figure 1 shows a cartoon illustration of thisconcept. The plate boundary structure is complex andthree-dimensional in nature. The largest offset betweenthe near surface plate boundary (transform fault) and thedeeper shear zone will be near the ridges where thetemperature contrast across the transform is thegreatest. Here the lateral cooling effect requires that theolder plate extend beneath the younger plate (and MOR)at depth. In this region, the details of the magmasupply to the ridge will be complex. The magmarequired to generate new crust in this zone must migratelaterally over the offset and therefore might be reducedin volume (Fig 1b). This is consistent with studies ofthe crust along fracture zones that show it to beanomalously thin and have a fundamentally differentvelocity structure, both of which have been attributedto a reduced magma supply (Detrick, et. al. 1993).

The shape of the boundary itself will result inmismatch between the strike of the near-surface faultsand the deeper shear zone. This may lead to a re-orientation of surface faults and also result in transformparallel extension along parts of the mantle boundarythat are oblique to the transform strike (Fig 1a.). Suchextension and the associated upwelling may producethinning and magmatism along the transform if theupwelling velocity (thinning rate) is large compared tothe competing secular cooling rate. Near the ridge, theplate boundary may include a sub-horizontal sectionconnecting the base of the brittle fault to the deepershear zone (Fig. 1b). Such a low-angle shear zone may

help nucleate core-complex extension on the insidecorners of slow spreading ridge-transform intersections.

Numerical Models

We modeled these structures using twoseparate numerical codes. The mechanical code is athree-dimensional finite element (FE) code based onTECTON (Melosh and Raefsky 1980, 1981, 1983)which was modified to be fully 3-D and to allowtemperature dependent viscous rheologies (Govers andWortel 1995). Deformation is elasto-viscous, exceptalong faults which are included via the “slippery node”technique (Melosh and Williams 1989).

This finite element code is based on aLagrangian FE formulation, where nodal points areattached to material points and therefore move alongwith the deforming material. The large amounts ofrelative displacement across the transform boundarycreates problems for such a formulation, which isrestricted in terms of total displacement. However, weare primarily interested in the final, dynamic steady-state thermal and deformational fields. Throughcoupling the deformation model with an Eulerianthermal formulation (i.e. the material moves throughthe mesh according to a prescribed kinematics; andarbitrarily large displacements are allowed) we canovercome this shortcoming.

The separate thermal model, which isemployed to calculate the thermal structures outside theTECTON model, is based on a three-dimensional finitedifference (Method of Lines) solution to the heatconduction equation where it is decomposed to a systemof coupled linear ordinary differential equations (seeFurlong, et al. 1982). The solution to the resultingsystem is obtained numerically using the LawrenceLivermore ODEPACK solver (Hindmarsh 1983). Theeffects of heat advection from material kinematics areadded by shifting the nodal grid between conductionsteps based on a set of externally defined nodal velocityvectors, as in the model of Forsyth and Wilson (1984).However here the nodal velocities are not arbitrary butare determined by the 3-D mechanical model.

As we are interested in studying the final"dynamic steady-state" regime for a particular platevelocity - age-offset scenario, these codes are utilizedin a two step process where we iterate between the twomodels, using the result of one as the input for theother. This process allows the mechanical model to berun for a sufficient deformation to provide theappropriate kinematics for the thermal calculation,which produces a new thermal regime used in thedeformation model, etc. The entire process begins withthe assumption of an idealized, uniform velocity fieldto “seed” the model. This velocity field is used in the


thermal code to calculate the steady-state temperaturefield produced by the assumed plate kinematics (akin tothe model approach Forsyth and Wilson (1984)). Thesetemperatures are then interpolated onto the finiteelement mesh and used as initial temperatures in thedeformational model. Appropriate boundary conditionsare applied and the deformational model produces avelocity field compatible for the thermal regime(keeping the total strain small so that the thermalstructure is not significantly disturbed spatially underthe limitations of the Lagrangian approach). This newvelocity field is then applied to the next iteration of thethermal model, producing a refined dynamic steady-statethermal field for the transform. These temperatures arethen used in the next iteration of the mechanical model,resulting in more refinements to the velocity field.This iterative process is continued to convergence (i.e.the point at which there are no longer significantchanges in either temperature or kinematics betweeniterations) providing a final estimate of the fully-coupled thermal-mechanical field of the transform. Inpractice after about 3-5 iterations, the change in eitherthe temperature field or the strain field are quite small,on the order of 1-2% of the total change from theinitial temperature and strain fields.

Model geometry is shown in Figure 2. Ourconvention is that the x-direction is in the transformparallel direction, the y-direction is ridge parallel, and z-direction is vertical. For the mechanical deformationmodel, displacement rate (velocity) boundary conditionsare applied to the sides of the model in the direction ofrelative plate motion as shown by the large arrows inFigure 2. The ridge-parallel ends of the model are freeto move as needed; although the location of the ridgeitself is specified along the top surface of the model.The top surface of the model is fixed in a verticaldirection, but the bottom of the model can movevertically as needed to accommodate any thinning in themodel. Since there is no gravity acting in this modelsimulation, the fixing of the top boundary does not inany way affect the patterns of deformation; although thecombination of not gravity and the boundary conditionpreclude directly observing the topographic response.The transform-parallel width of the model is fixed; i.e.the model is not allowed to expand or contract in the y-direction. The near-surface transform is specified and inthe model results shown was allowed to slip freelyusing ‘slippery nodes’. Models were also run (notshown here) with up to 10 MPa of sliding frictionalong the transform with no significant change in eitherthe final temperature or deformation fields. Models withhigh sliding friction or with locked faults showeddistinctly different patterns of strain, with little strainlocalization, particularly for low plate-velocitymodels. We believe models with low or no slidingfriction best simulate the long term evolution oftransform systems.

In the deformation model the vertical nodalspacing was fixed at 5 km; the y-direction (cross-transform ) had a variable spacing ranging from 2.5 kmnear the transform to 12.5 km at the edges of themodel; the x-direction (transform-strike direction) wasconstant for each model but changed depending on thetotal offset of the transform ranging from 4.2 km forthe short offset (100 km) models to 12.6 km for thelong offset (300 km) models. In all cases there were3450 nodes (x:y:z /23:15:10) and 2772 elements in thedeformational models. These nodal dimensions aresmall enough to capture the primary effects of thevariable temperature and rheology, while allowing thetotal model domain to be computationally tractable.

The thermal models covered the same modeldomain with uniform spacing of nodes in each directionbut variable between directions. The y-direction (21nodes) was spaced at 3.8 km; the z-direction (15 nodes)was spaced at 3 km; the x-direction (23 nodes) variedfrom approximately 4 km to 12 km depending oftransform offset. Boundary conditions for the thermalmodels were 0°C top boundary (ocean floor) and1300°C on the bottom boundary (asthenosphere).Boundary nodes on the ends of the models werespecified as parts of ridges (1300°C) or points ofmaterial ‘flow’ where temperatures were set based onthe local plate kinematics – to simulate the thermalconditions of material flowing across that boundary.Ridges were assumed to be passive and their length wasdetermined entirely by the specified velocity field(obtained from the previous iteration mechanicalmodel). The remaining sides of the model were set tohave zero heat flow (in the direction perpendicular tothe boundary).

The model lithosphere rheology for the resultspresented here is based on a “dry” olivine compositionwith the material parameters listed in Table 1.Observations and laboratory experiments suggest thatoceanic lithosphere near the mid-ocean ridges isundersaturated by water and "dry" parameters areappropriate in the upper 100 km of the oceaniclithosphere (Karato and Wu 1993; Hirth and Kolstedt1996).

Modeling Results

The results from our coupled thermal-deformational model differ from previous models inboth the resulting temperature structure and plateboundary geometry. The thermal field from our coupledmodel produces very different plate boundary structuresand kinematics than implicitly assumed in previousmodels, i.e. where the thermal regime evolved toinclude effects of lateral conduction, but the kinematicswere prescribed (Forsyth and Wilson 1984; Phipps-


Morgan and Forsyth 1988). We compare three sets ofsimulations with the age offset and plate velocityconditions given in Table 2.

Thermal Structure

The thermal structure of the transform regimeis substantially modified by the effects of a 3-Dkinematic field. Advection of heat within thelithosphere (3-D kinematics) couples with the lateral-cooling conductive effects (Forsyth and Wilson 1984)to modify both the kinematics and the resulting thermalfield. Phipps-Morgan and Forsyth (1988) showed theeffects of advective heat transport from a convectiveflow field in the mantle; we have focused on the effectsof the strain field local to the transform regime indriving a significant component of the heat transferalong the transform.

Figure 3 shows the thermal modeling resultsfor the low plate velocity-small age offset model(Model 5.04). The isotherms (at a depth of 20 km) thatresult from the kinematics determined by our finaldeformational model, are shown in Figure 3a. Acomparison of these results with other models oftransform thermal structure and with standard (i.e. ‘half-space’ in which temperature varies as the error function(erf)) thermal models highlights the importance of theconductive and advective components of heat transport.Figure 3b shows the basic conductive (lateral) coolingeffect at a depth of 20 km for the idealized transform(vertical fault-uniform velocity) by plotting thedifference between an error function lithosphere (half-space cooling) and the idealized initial-model thermalstructure (which includes effects of lateral cooling).This is analogous to the anomalous temperature plottedin Forsyth and Wilson (1984). It can be seen thatanomalies of > 80° C exist in regions near thetransform. Figure 3c shows the combined conductive(lateral) cooling and the advective effect on the thermalstructure from the final deformational model, byplotting the difference between it (Figure 3a.) and anerror function lithosphere. It is clear that thecombination of heat transfer effects is significant,producing anomalies >100° C along the transform.Figure 3d shows the difference between the idealizedthermal model (conduction alone) and the final thermalmodel (conductive plus advective effects). Significantdifferences in the temperature exist, focused near theridge-transform intersections. These differences arelarge enough to affect interpretations of crustal structureand/or magma influx derived from gravity analyses(Escartin and Cannat 1999).

Figure 4 shows a similar series of plots forthe high plate velocity transform (Model 5.12). Asmight be expected there is a greater difference in finaltemperature structure between the idealized case and our

result. This can be best seen in Figure 4c, where thereis a very large region of > 100° C lateral cooling effect,and Figure 4d., where the difference between the idealand final models is more significant than in the lowvelocity model (Figure 3d.).

Model 5.04 and Model 5.12 can be normalizedaccording to crustal age. In both models crustal agespans 0 m.y to 5 m.y, and the pattern of age differenceacross the transform is the same. In the idealized model,both of these models produce the same thermalstructure in the age normalized reference frame.However when the feedbacks between thermal structureand deformation are included, as well as the effects ofadvective and conductive heat transfer, significantthermal differences result. Figure 5 shows the differencebetween Models 5.04 and 5.12 (normalized for crustalage) at depths of 10 km and 20 km. At both depths (10km and 20 km) shown, the slow plate velocity modelis hotter than the fast plate velocity model. This is aresult of both the relative geometry of the plateboundary zone which extends further into the ‘young’side of the transform in the faster case, and slightlymore thinning occurring in the low velocity model as aconsequence of plate boundary curvature (describedlater).

KinematicsThe influence of the thermal field on the

patterns of plate kinematics is shown in Figure 6,where the velocity distribution across the modeltransform is shown at a depth of 20 km (below thebrittle-ductile transition; at the depth of the temperatureresults shown in Figures 3 and 4); a depth where therheology is very dependent on temperature. The upperplot shows results for Model 5.04; the lower plot is theequivalent result for model 5.12. Three velocitymodels are compared in each case. The step-functionshows the velocity distribution assumed in the idealizedtransform model with uniform velocity on either side ofa vertical transform. The set of dashed curves showsthe velocity distributions at various positions along thetransform (from near the ridge to the center of thetransform) as determined by the deformational modelusing the idealized (step function) thermal model. Thisis the result one gets using the Forsyth and Wilson(1984) temperature model to determine plate boundarydeformation, and is the result we obtain after the firstiteration of our modeling sequence. The velocity modelproduced by the assumed thermal model is inconsistentwith the velocity model which produced the thermalfield! To correct this inconsistency, we follow theiterative process described earlier to couple the thermaland mechanical fields and produce internally consistentthermal and deformational conditions. The velocitydistribution at the same points along the transform ofour final model, after model convergence, is shown by


the solid curves, and will be referred to as the finaldeformational model.

For the low plate-velocity transform case, themotion is accommodated in a shear zone roughly 20km wide (Fig. 6). The middle of the deformation zone(the ‘plate boundary’) is offset near the ridge onto the“old side” of the transform by 10 km. Although thereare significant differences between idealized (step-function) kinematics and those produced by the coupleddeformational model, there is a relatively smalldifference between the initial and final deformationalmodels, except as we approach the ridge (e.g. the 10km curve in the upper panel of Figure 6). Thissuggests that for low plate velocity transforms, theidealized thermal structure (Forsyth and Wilson 1984;Phipps-Morgan and Forsyth 1988)) produces areasonable approximation of the transform kinematicsaway from the ridges.

In the high plate velocity model (Fig. 6) theshear zone is wider (~ 25 km) and the offset into theyoung side of the transform is greater. The difference inthe kinematics between the initial and final deformationmodels are again greater near the ridge-ends of thetransform. These results suggest that in the near ridgeenvironment, the idealized thermal structure (derivedfrom simple step-function kinematics) does not producea good approximation to the deformation field and acoupling of the thermal and mechanical processes isrequired to determine the final mechanicalconfiguration.

3-D Deformation Along Transforms

Our model provides 3-D simulations of thestrain field occurring along mid-ocean transforms underthe thermal conditions which develop in this self-consistent thermal-deformational modeling strategy.Visualizing the 3-D deformation patterns is difficult andwe have used a series of 2-D slices (both horizontal andvertical) through the three-dimensional data blocks tohelp define patterns of strain and the geometry of theplate boundary. In each cross-section, the color shadingshows strain rates and small arrows represent nodalvelocities; which vary with model simulation toaccommodate the variations in strain rates and velocitywith spreading rate.

Figure 7 shows the results for Model 5.12(high velocity) which has a transform length of 300km. Shear strain rate, ε̇ xy , (shear strain rate in the

transform parallel direction on the vertical planeperpendicular to the ridge (y-z) plane) is shown in mapview slices at depths of (a) 5 km, within thebrittle/elastic layer; and (b) 25 km in the upper mantle.Vertical sections perpendicular to the transform are

shown in (c) 5km from the ridge, (d) 60 km from theridge, and (e) 100 km from the ridge. The shear zonethat acts as the mantle plate boundary can clearly beseen and displays the basic offset form described by theconceptual model in relation to the overlying brittletransform fault (cf. Fig 1). The plate boundary,represented by the “zero” line across which thevelocities change direction, is indicated on the plots.The 3-D shape of the plate boundary can be inferredfrom the set of cross-sectional views of the strain-ratefield in Figure 7c-e. The location of the brittle fault inthe elastic-brittle layer is shown by the gray dashedline, and the orange dashed line traces the zero velocityfiber through the high shear zone, which again displaysthe form shown in the conceptual model, and the older(cooler) plate can be seen to extend into the youngerplate beneath the ridge tips.

For the lower plate velocity models (Model5.04 [Fig. 8]; Model 15.04 [Fig 9]), the structure ofthe shear zone is analogous to Model 5.12. Model 5.04shows a deformed zone which is less linear than Model5.12- the greater curvature (and obliquity) of the strainfield as compared with the plate surface-velocity fieldresults from the combination of a shorter transformlength with only a slightly smaller offset near theridges. The increase in the obliquity of the strain ratefield for the slower transform may affect the pattern ofdeformation within the transform domain (Searle 1992;Fox and Gallo 1986).

The results for Model 15.04 (Figure 9) showsome of the characteristics of models of similar strain(i.e. Model 5.04 with same plate velocities) and alsosome of the characteristics of models of similar faultoffset length (i.e. Model 5.12 with the same 300 kmoffset) on the patterns of transform deformation. Thegeometrical effects of a longer fault offset allow a morelinear plate boundary, reducing the obliquity andcurvature in the center of the transform. The region ofgreatest obliquity (and possible largest extensionalstrain) is closer to the ridge at a position about 50 kmfrom the ridge-transform intersection. However, theslow velocities and the additional cooling time combineto produce a stronger plate with more lateral cooling.As a consequence the plate boundary at depth migratesmuch further into the young side of the transform, asthe older plate approaches the ridge. In Model 5.04 theplate boundary extends ~ 7 km into the young side,while in Model 15.04 it is 15 km or more. Similarlythe width of the region experiencing plate boundarystrain has a 1/2 width of approximately 10 km inModel 5.04 while it is almost 20 km for the larger ageoffset case. The equivalence of plate velocities impliesthe same total integrated strain across both boundaries,but in the larger age offset case, the impact of coolerlithosphere is to widen the zone of deformation.


Implications of the Models for TransformTectonics

The models were developed to evaluate thepatterns of deformation within the ductile part of thetransform plate boundary. As a result, we did not solvefor the position of the near surface faults. However,based on the patterns of strain below the elastic-brittlelayer we can investigate the role that sub-crustal strainmay play in perturbing the deformation at the surface.Four aspects of ridge-transform tectonics are analyzed:(a) patterns of strain and faulting within the transformdomain; (b) magma supply and asymmetric accretion atridge tips; (c) development of MOR core complexes;and (d) development of leaky transforms and transformsplitting ridges.

Strain in Transform zones

Using the terminology of Searle (1992) (andalso Fox and Gallo 1986), we can compare componentsof the transform plate boundary regime withdeformation patterns developed in our modeling. TheTransform Domain (TD) contains all of the crustaffected by the transform system. The TD is a variablewidth (<10 km to > 50 km), generally wider for largeroffsets and slower slip velocities (Searle 1992). Thedeeper extent of the shear zone in our models showsthis behavior and thus we are tempted to link the broadregion of the TD with this zone. This region is alsolikely to encompass the region of thinner crust asdiscussed below.

Within the TD is the Transform TectonizedZone (TTZ) which includes the transform relatedfaulting. This zone often is oblique to the strike of theplate motion (Roest et al. 1984; Searle 1986). Thispattern of obliquity for the faults within the TD waswell documented for the Romanche Transform (Searleet al. 1994). This is a very large offset, slow velocitytransform. Based on the results shown in Figure 9, wemight expect the cross-over from one side of thetransform regime to the other to be located part-waybetween the ridge and the transform midpoint. Thefaults within the Romanche TD cross-overapproximately 150-200 km from the ridge (of anapproximately 1000 km long transform). The cross-over occurs in the vicinity of the sedimented VemaDeep (Searle et al. 1994). Within our modelconfiguration, the Vema deep would represent theregion of extension driven by the local curvature of thesubjacent mantle shear zone.

We would expect the patterns of faultobliquity to be more symmetric in shorter offsettransforms and such is the case for the Atlantis FractureZone (Parson and Searle 1986), a low-velocitytransform with less than 100 km of offset. The

obliquity of the surface faults relative to the platemotion is as much as 15° for the Atlantis (Parson andSearle 1986), consistent with the results of Model 5.04(Figure 8). Applying the modeling results further wemight expect that the lengths of faults segments wouldbe longer along the portions with less curvature, andshorter and/or more oblique to plate motion in theregions of high plate boundary curvature.

Magma Supply at Ridge Ends

Crustal thickness varies along the MOR withthe thinnest crust typically near ridge offsets andadjacent to transforms (Detrick et al. 1993), particularlyfor slow plate-velocity systems. A variety ofmechanisms have been proposed to explain thevariation in crustal structure (e.g. Cannat 1996;Cannat et al. 1995; Kuo and Forsyth 1988, Detrick etal. 1995) primarily as a consequence of reduction inmagma supply near the ridge tips. Our models provideevidence of an additional causative factor for thethinning of crust near the ridge-transform intersection(RTI). The plate boundary geometry near the RTI willmean that the same volume of mantle-derived meltmust produce the crust for a longer segment of ridgecrust (Figure 1, and Figures 6-9). This effect will begreatest (i.e. produce the most thinning of the crust) forlow-velocity large-offset boundaries (cf. geometry ofplate boundary structure in Figure 9 vs Figure 7).Detrick et al. (1995) show such a pattern of crustalthickness variation with offset length (thinner crustwith longer offset), as long as the offset is greater than50 km. In cases of fast plate velocities, the plateboundary offset is somewhat less (cf. Fig 7 vs Fig 9)

Patterns of asymmetric accretion have beenobserved at the ridge tips of slow spreading ridges(Allerton et al. 2000; Escartin et al. 1999; Tucholkeand Lin 1994). These appear to be related to regions ofanomalous crustal thickness with accretion occurringprimarily on the outside corner side of the ridge. Theplate boundary geometry from our models in the nearridge regime would favor that the magma supply thatreaches the ridge axis near the RTI preferentially flowsto the outside corner side as that is the direction ofmaterial flow in the model (e.g. Fig. 7b).

Core Complexes

The recent documentation of extensional core-complex style deformation at the inside corners ofmany RTIs (Cann et al. 1997; Blackman et al. 1998;Tucholke et al. 1998; Escartin and Cannat 1999; Dicket al. 1999), particularly at slow spreading segments isan exciting new development in ridge-transformtectonics. The processes which produce these ‘mega-mullion’ structures are not fully understood andcontinue to drive research. Several aspects of the


deformation regime produced by our model may help toidentify some of the conditions and processes that leadto development of core complex tectonics. Thecharacteristic MOR core complex is approximately 14-42 km (ridge parallel direction) by 16-35 km (transformparallel direction) with surface areas between 150 km2

and 800 km2 (Tucholke et al. 1998).They developprimarily at low velocity RTIs, form exclusively onthe inside corners of the RTI, and represent intervals oftime with little magmatic accretion on the corecomplex side of the ridge crest.

Since the core complexes develop as shear onplanes oriented perpendicular to the transform plane, wehave analyzed the patterns of the ε̇ xz (shear strain rate

in the transform parallel direction on the horizontalplane) shear strain-rate for Model 5.04 (Figure 10). Wesee that a sub-horizontal region of high shear-strainforms with dimensions comparable to observed core-complex size (Fig 10a). The top of this shear zone (asseen in the transform parallel vertical cross-section inFig 10c), which could act as a detachment structure forcore complex initiation, is at a depth of approximately10 km, again compatible with the inferred depth extentof exhumed lower crust and upper mantle rocks (Cannet al. 1997). In Figure 10 we also show schematicallyhow the model results can be compared to geologicmodels of MOR core complexes (modified from Cannet al. 1997). Although our models are not optimallydesigned to simulate such tectonics, the generalagreement between model behavior and observationencourages us to pursue the implications of thetransform deformation regime for core-complexformation.

The conditions for core complex initiationimplied by our model results lead us to the followingspeculations. The sporadic nature of core complexactivity as seen in the separate structures observedalong several transforms (Blackman et al. 1998) mayreflect the implications of core complex extension onthe near ridge plate boundary geometry produced in ourmodel. After a large offset on the core-complexdetachment fault , much of the lithosphere blocking theinflux of mantle derived magma will have moved downstream allowing a relative abundance of magma to reachthe ridge tip. This would then weaken the MOR axismaking extension more easily accomplished at the axisthan along the core complex detachment fault. Thissequence of events would cycle, as plate motions wouldbring the plate boundary geometry back to our modeledconditions after a few million years or less (based onplate velocities and the dimensions of the extendedblocks).

The non-occurrence of these extensionalstructures at faster spreading centers may reflect thecombination of sufficient magma supply to keep the

MOR axis weak, and the more subdued nature of theoffset in the deeper plate boundary. For very large offset(but slow velocity) transforms (e.g. Model 15.4) thedetachment level is substantially deeper. This leads to athicker block of material moving away from the ridgethat may again make the MOR axis the preferredlocation to accommodate extension.

Leaky Transforms and Transform Splitting

Our results indicate that, as a consequence ofthe curvature and obliquity of the ductile plate boundaryshear zones (particularly for slow plate velocities),extension and the possible magmatism resulting fromassociated leaky transform behavior may becomponents of transform evolution and behaviorrelated to the thermal-rheological evolution of thetransform system. We believe that several observationscould be explained by this process.

There appear to be velocity limits for oceanictransforms, both in an absolute sense (Naar and Hey1989), and as a function of length (Burr and Solomon1978; Stoddard 1992). A perhaps better constrainedrelationship can be seen between the maximumobserved transform velocity and age-offset; a patternmore consistent with the idea that thermal (rheological)structure is the major control on the transform (Furlong1992). Figure 11 shows such a data set where the fullplate velocity is plotted against the age-offset(approximated as transform length divided by the half-spreading rate). The dashed line is a rough estimate ofthe stability limit for this relationship. It has beenhypothesized that this stability limit bounds the regionwhere transforms are in a mechanical equilibrium. Ifvelocity and/or plate age-offset conditions move atransform beyond the limit into the unstable region,new ridge segments will form, effectively “splitting”the transform into two or more shorter, more stableoffsets (Furlong 1992).

Large transform offsets, especially those nearthe inferred velocity limit and at high velocities, areoften observed to be magmatic, where there is somedegree of spreading occurring along the transform(“leaky” transforms). “Leaky” transforms are oftenattributed to the effect of changes in plate motions thatcause a transform that is originally parallel to spreadingto become oblique, causing extension and magmatism(Menard and Atwater 1969; Burr and Solomon 1978;Collette 1986; Searle 1986). Other investigations,though, have concluded that this scenario can notgenerally explain the occurrences of these transforms,many of which are not consistent with or can not beassociated with any change in plate motions (Garfunkel1986; Fornari, el. al. 1989). So while it is clear thatchanges in plate rotation poles can enhancemagmatism, “leakyness” in transforms appears to be a


more inherent feature of the offsets, as first suggestedby Garfunkel (1986), and may be caused by some otherupwelling mechanism.

The velocity and age-offset dependencies of theobserved transform stability limit are most likely thecombination of several components. Larger age offsetgenerally means larger temperature contrasts, andtherefore larger boundary obliquity by our model. Italso means increasing length, which will affect thestress distribution in the regime. Finally there is theissue of brittle failure. In conceptual terms, we couldconclude that lower age offset regimes are hotter andtherefore generally more ductile and able toaccommodate higher velocities (i.e. higher strain ratesand lower shear stress) than larger age offsets (small ageoffset transforms are often diffuse shear zones), but thereality is surely more complicated.

Our models are not specifically designed toaddress these issues. The definition of the stabilitylimit is somewhat subjective, based on observations ofsurface morphologies and generalized criteria todistinguish a single “leaky” transform from a set ofseveral small transforms. It is useful to examine atransform that has undergone the inferred process andattempt to correlate it to the stability limit.

Plate velocities are not constant in time, sothe location of any transform on a velocity-age-offsetplot such as Figure 11 will not be fixed. Changes invelocity will result in changes on both axes of the plot,and the transform will have some evolutionary paththrough that parameter space. It is possible that achange in spreading rate could push a previously stablelarge offset transform across the limit, causing a newsegment to form. If this has occurred, we have areasonable chance of identifying it as such. If thevelocity history and path in velocity-age-offset spacefor the original transform can be ascertained, we can tryto correlate the age of the segment with the crossing ofthe limit.

As an example, we have investigated theCharlie Gibbs Fracture Zone (CGFZ) system on theMid-Atlantic Ridge. The CGFZ consists of twoclosely space transforms, separated by a small ridgesegment (Searle 1981). From the relative lengths ofthe long and short sets of fracture zones, it can beinferred that the intervening segment is younger thanthe rest of the system. The short fracture zonesassociated with the segment allow magnetic anomalydating of the formation of the segment, which appearsto be roughly 40 Ma.

Using magnetic anomaly data, the velocityhistory of the transform can be estimated. There hasbeen a significant variation in plate velocity throughtime (inset to Figure 11), including a large decrease,

that will lead to an increase in age offset (if the lengthremains constant). Assuming that prior to theformation of the short median ridge segment the singletransform length was approximately equivalent tocombined length of the two present-day transforms,then the path of that offset in velocity-age-offset spaceis as shown in Figure 11. This path takes the originaltransform across the stability limit, from the increasein age-offset driven by the decrease in plate velocity, atroughly 42 Ma. The new transform-splitting medianridge segment also formed at an off-center location,consistent with the locations of the zones of maximumextension in the slow velocity – large offset transformmodel (Model 15.04; Figure 9).

Conclusion

Transforms that offset mid-ocean ridgesdisplay complex deformational behavior that cannot beexplained by a simple strike-slip plate boundary.Transforms show broad deformation zonesencompassing a suite of tectonic structures, oftenstriking obliquely to relative plate motions.Extensional core-complex structures are identified atseveral ridge-transform intersections, almostexclusively at the inside corners of slow spreadingridges. Leakyness and the development of transformsplitting short ridge segments is also observed at somelong offset transforms. The model we have developed,which couples the thermal and deformational regimes,produces a deformation field that provides possibletectonic explanations for many of these observations.The effects of lateral cooling and a migration of thelocus of shear deformation along the ductile portion ofthe plate boundary produce a 3-D plate boundarygeometry compatible with patterns of deformationalong MOR – transform systems. Although simple,the coupled 3-D thermal-mechanical model providesimportant insights into deformational processes alongtransforms. More refined models can be developed tobetter define the tectonic processes at work along MORtransforms.

This work was supported by a Deike ResearchGrant (Penn State) to Kevin Furlong. Detailed and veryconstructive reviews by D.K. Blackman and R.C.Searle are greatly appreciated and helped improve thepaper. Insightful discussions with J. Escartin are alsoacknowledged.


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Figure Captions

Figure 1. Conceptual lithospheric and plateboundary structure. Top ( map view): Location ofcrustal faulting and the approximate location of themantle plate boundary at depth. Bottom: Cutawaycross-section at the ridge showing the form of theboundary and a schematic interpretation of the plateboundary geometry effect on magma supply.

Figure 2. Schematic of model domain andgeneralized boundary conditions for mechanicalmodeling. Plate velocity boundary conditions areapplied along the sides of the model. Thermal andmechanical models covered same domain with slightlydifferent nodal spacing. Width of model (y direction) isconstant (80 km) in all cases, length of model (xdirection) varies with transform offset (100 – 300 km),thickness of model is 45 km in most cases. It is thickerin the large-offset low-velocity models to accommodateincreased plate cooling.

Figure 3. Temperature model results for Model5.04 (depth = 20 km). a) Thermal field (isotherms) forour final coupled model which includes rheological andmechanical effects. b) Difference between the thermalfield of an idealized transform model consisting of avertical strike-slip fault at all depths with uniformvelocity on either side (including 3-dimensional heatconduction), and that of an error function lithosphere(infinite half-space) with no lateral heat conduction. c)Difference between (a), our final transform model, andan error function lithosphere. d) Difference betweenthermal fields for the idealized model and our transformmodel. All contours are °C.

Figure 4. Temperature model results for Model5.12 (depth = 20 km). (a) – (d) as in Fig. 3.

Figure 5. Difference in Temperature resultsbetween models 5.04 and 5.12 normalized for crustalage. Upper: Temperature difference at 10 km depthwithin elastic-brittle layer. Lower: Temperaturedifference results at 20 km depth within ductile region.Contours are labeled in °C. Negative values indicatemodel 5.04 is hotter than Model 5.12.

Figure 6. Velocity profiles across the transformmodel at a depth of 20 km for the a) low velocitymodel and the b) high velocity model. Both have anage offset of 5 Ma. Each graph shows the velocityprofiles for three different models. The step function isthe velocity distribution for an idealized transform withuniform velocity on either side of a vertical fault. Theopen symbols show profiles for the initialdeformational model, which results from the use of thethermal field from the idealized transform (i.e. the stepfunction) in the deformational model. It is shown at 3

points along the transform length: 10, 25, and 50 km,the last being at the mid-point. The solid symbolsgive the velocity profiles for the final deformationalmodel (at the same 3 locations along the transform),which is the steady-state dynamical result of repeatediterations of coupled thermal-mechanical steps.

Figure 7. Results from 3-D coupled model forModel 5.12. Strain rate, ε̇ xy , (shear strain rate in the

transform parallel direction on the vertical plane parallelto the transform orientation) is shown by colorcontours and arrows indicate velocities in plane of eachfigure. The plate boundary, represented by the “zero”line across which the velocities change direction, isindicated on the plots by the red dashed line. (a)Horizontal slice at depth of 5 km (within elastic-brittlelayer) showing near surface kinematics; (b) Horizontalslice at 25 km depth. Offset in plate boundary is shownby dashed orange line. Width of shear zone varies withposition relative to ridge. (c) Vertical cross-sectionalslice 5 km from left ridge end of model. (d) Verticalcross-sectional slice 60 km from left ridge end of modelin area of maximum plate boundary curvature; (e)Vertical cross-sectional slice 100 km from left ridge endof model near central portion of plate boundary.


transform parallel direction on the vertical plane parallelto the transform orientation) is shown by colorcontours and arrows indicate velocities in plane of eachfigure. The plate boundary, represented by the “zero”line across which the velocities change direction, isindicated on the plots by the red dashed line. (a)Horizontal slice at depth of 5 km (within elastic-brittlelayer) showing near surface kinematics; (b) Horizontalslice at 25 km depth. Offset in plate boundary is shownby dashed orange line. Width of shear zone varies withposition relative to ridge. (c) Vertical cross-sectionalslice 5 km from left ridge end of model. Inferredlocation of plate boundary shown by dashed line. (d)Vertical cross-sectional slice 20 km from left ridge endof model in area of maximum plate boundary curvature;(e) Vertical cross-sectional slice 35 km from left ridgeend of model near central portion of plate boundary.These locations compare in plate age with the cross-sections (c-e) in Figure 7 for the faster plate velocitycase.


transform parallel direction on the vertical plane parallelto the transform orientation) is shown by colorcontours and arrows indicate velocities in plane of eachfigure. The plate boundary, represented by the “zero”line across which the velocities change direction, is


indicated on the plots by the red dashed line. (a)Horizontal slice at depth of 25 km showing region ofhigh plate boundary curvature and low kinematicobliquity along the interior of the transform (b)Horizontal slice at 35 km depth. (c) Vertical cross-sectional slice 5 km from left ridge end of model.Inferred location of plate boundary shown by dashedline. (d) Vertical cross-sectional slice 100 km from leftridge end of model.

Figure 10. Results from 3-D coupled model forModel 5.12. Strain rate, ε̇ xz , (shear strain rate in the

transform parallel direction on the horizontal plane) isshown by color contours and arrows indicate velocitiesin plane of each figure. The plate boundary, representedby the “zero” line across which the velocities changedirection, is indicated on the plots by the red dashedline. (a) Horizontal slice at depth of 15 km (belowelastic-brittle layer) near inferred initiation depth ofMOR core-complex structures showing spatial extentof potential detachment horizon; (b) Vertical cross-sectional slice 5 km from left ridge end of model.

Inferred location of plate boundary shown by dashedline; (c) Vertical slice parallel to and 2.5 km away fromtransform fault. Possible relationship of detachmentsurfaces are shown by white dashed lines and arrows. (d)Correlation of our model-derived core-complexgeometry with geologic model (adapted from Cann etal. 1997)

Figure 11. Global oceanic transform data, plottedwith transform velocity versus age offset,(approximated as length/half-spreading rate). Theinferred stability limit of for the age-offset velocityrelationship is shown by the dashed curve. Inset showsthe velocity time behavior for the Charlie GibbsFracture zone, showing a significant decrease in platevelocity at the approximate time of the transformsplitting event (~ 40 Ma). Path of the transform invelocity/age-offset space is shown by points labeled a-don main plot. At time of new ridge formation, the platekinematics had moved the transform into the Unstablefield.


Table 1. Material Parameters in Modeling

Parameter ValueThermal Properties

Thermal Conductivity (k) 3.0 W/m-KHeat Generation 0.0 µW/m3

Density (ρ) 3300 kg/m3

Elastic and Plastic PropertiesYoung's Modulus (E) 1x 1011 Pa

Poissons Ratio (υ) 0.25

Mohr-Coulomb Angle 35°

Creep Properties('Dry' Olivine)

Karato and Wu [1993]) Power Law exponent (n) 3.5Activation Energy (Q) 544 kJ/mole

Pre-exponent (A) 2.01359 x 10-16 Pa-3.5 s-1

Gas Constant (R) 8.31441 J mol-1 K-1

Table 2. Model Age/Offset Conditions

Model Age Offset(m.y)

Plate Velocity(cm/yr)

5.04 5 4

5.12 5 12

15.04 15 4

Plate velocity is full spreading rate and age offset is transform lengthdivided by half-spreading rate (i.e. the crustal age on the old side atthe ridge) .

Plate boundary in crust

Plate boundary in mantle

Plate boundary in mantle

Figure 1Furlong et al., 2000


z

x

y

Ridge

RidgeVelocity B.C.

Figure 3 Furlong et al., 2000

0 20 40 60 80 100-40

-20

0

20

40

12001100

1000

a) Final Isotherms

d) Idealized-Final

0 20 40 60 80 100-40

-20

0

20

40

0

4080

0

40

80

1000 20 40 60 80-40

-20

0

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40

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4080

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4080

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0 20 40 60 80 100-40

-20

20

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0

40

80

0

40

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1000 11001200

80

(km)(km)

(km)(km)

(km)

0

(km)(k

m)

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)

0 50 100 150 200 250 300-40

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0 50 100 150 200 250 300-40

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04080

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0 50 100 150 200 250 300-40

-20

0

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1200 1100 1000

a) Final Isotherms


(km

)(k

m)

(km

)(k

m)

(km)

(km)

(km)

(km)

40

20

0

-20

-40

40

20

0

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0 1 2 3 4 5

0 1 2 3 4 5

Crustal age (M.y.)

Crustal age (M.y.)

Dis

tanc

e (k

m)

Dis

tanc

e (k

m)

-60

-60

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-40

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-30

-30

-30

-50

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10 km depth

20 km depth



50 km - Final25 km - Final10 km - Final50 km - Initial25 km - Initial10 km - Initial

-40 -30 -20 -10 0 10 20 30 40-2.5

-2

-1.5

-1

0

-.5

.5

1

1.5

2

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Model 5.04

a)

Vel

ocity

(cm

/yr)

Distance from the transform fault (km)

150 km - Final75 km - Final15 km - Final150 km - Initial75 km - Initial15 km - Initial

-8

-6

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0

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6

8

Model 5.12

b)

Vel

ocity

(cm

/yr)

Distance from the transform fault (km)-40 -30 -20 -10 0 10 20 30 40

(c)

(d)

(e)

300 km

(a)

y

x

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5 km

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100 km


yz

y

z

y

z 80 km

45 k

m45

km

45 k

m

(b)25 km

y

x

0

1.0e-1

3

2.0e-1

3

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3

εxy (1/s)

12 cm/yr

0

0.4e-1

3

0.8e-1

3

1.2e-1

3

εxy (1/s)

25 km5 km

y

x

100 km 4 cm/yr

Figure 8Furlong et al.,2000

(a) (b)

5 km

y

z

45 k

m(c)

20 km

45 k

m

(d)

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45 k

m

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y

z

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0

0.4e-1

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1.2e-1

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εxy

(1/s)4 cm/yr

5 kmy

z

72 k

m

100 km

80 km80 km

300 km

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(c) (d)

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(a)

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εxz (1/s)

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z

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45 k

m

100 km

v v v v v

vv v vv

Corrugated surface with exposures of serpentinites and gabbros

Magmatic Axis2

4

6

8

10?

Nucleating Shear Zone

kmFigure 10Furlong et al.,2000

(a)

(c)

yz

5 km

45 k

m

80 km

(d)

(b)

0 10 20 30 40 500

2

4

6

8

10

12

14

16

Age Offset (m.y.)

Vel

ocity

(cm

/yr)

Unstable

a

b

cd

2

3

4

0 10 20 30 40 50 60 70

B

ATime (Ma)

Vel

ocity

(cm

/yr)

a

b

cd

Charlie Gibbs F.Z.


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