lithosphere tearing at step faults: response to edges of ... · lithosphere tearing at step faults:...

tters 236 (2005) 505–523

www.elsevier.com/locate/epsl

Earth and Planetary Science Le

Lithosphere tearing at STEP faults: Response to edges of

subduction zones

R. Govers*, M.J.R. Wortel1

Department of Geosciences, Utrecht University, P.O. Box 80.021, 3508 TA Utrecht, Netherlands

Received 29 September 2004; received in revised form 21 March 2005; accepted 30 March 2005

Available online 20 June 2005

Editor: S. King

Abstract

Slab edges are a relatively common feature in plate tectonics. Two prominent examples are the northern end of the Tonga

subduction zone and the southern end of the New Hebrides subduction zone. Near such horizontal terminations of subduction

trenches, ongoing tearing of oceanic lithosphere is a geometric consequence. We refer to such kinks in the plate boundary as a

Subduction-Transform Edge Propagator, or STEP. Other STEPs are the north and south ends of the Lesser Antilles trench, the

north end of the South Sandwich trench, the south end of the Vrancea trench, and both ends of the Calabria trench. Volcanism

near STEPs is distinct from typical arc volcanism. In some cases, slab edges appear to coincide with mantle plumes. Using 3D

mechanical models, we establish that STEP faults are stable plate tectonic features in most circumstances. In the (probably rare)

cases that the resistance to fault propagation is high, slab break-off will occur. Relative motion along the transform segment of

the plate boundary often is non-uniform, and the STEP is not a transform plate boundary in the (rigid) plate tectonics sense of

the phrase. STEP propagation may result in substantial deformation, rotation, topography and sedimentary basins, with a very

specific time-space evolution. Surface velocities are substantially affected by nearby STEPs.

D 2005 Elsevier B.V. All rights reserved.

Keywords: geodynamics; Tonga trench; New Hebrides trench; Mediterranean region; Lesser Antilles trench; South Sandwich trench

1. Introduction

Near the majority of horizontal terminations of

subduction trenches, continual tearing of the litho-

0012-821X/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsl.2005.03.022

* Corresponding author. Tel.: +31 302 534 985; fax: +31 302 535

030.

E-mail addresses: [email protected] (R. Govers),

[email protected] (M.J.R. Wortel).1 Tel.: +31 302 535 074; fax: +31 302 535 030.

sphere is a geometric consequence [1]. With time,

the intersection between the subduction fault and the

transform segment propagates through the lithosphere,

thereby effectively increasing the area of the trans-

form-like fault (Fig. 1). We refer to the tearing trans-

form fragment as a Subduction-Transform Edge

Propagator (STEP) fault.

Following the identification of current plate bound-

aries, plate-tearing configurations were hypothesized

(bscissors type faultingQ [2], bhinge faultingQ [3,4]).

oceanic lithosphere

(a)

STEPSTEP

(b)

STEPSTEP

(c)

Fig. 1. Map view of a schematic evolution of a Subduction-Transform Edge Propagator (STEP). To highlight the characteristics of STEPs, we

assume that no east–west motion occurs between left and right boundaries of the region (rollers). (a) Subduction of the oceanic lithosphere

beneath the overriding plate is facilitated by trench rollback and back-arc extension (light grey area). Lithospheric tearing occurs along the

dashed line. Vectors represent relative velocities. (b) Later stage of development, where the STEP has propagated to the east. Back-arc extension

is assumed to have migrated east along with the trench. Principal lithospheric strain rates are indicated by arrows. Non-zero block rotation rates

occur along the STEP fault segment from the trench to the west end of the back-arc extension zone. (c) Alternative, where relative motion

between the overriding and subducting plate is possible at the left boundary. No in-plate deformation is necessary, except at plate boundaries.

The STEP fault acts like regular transform plate boundary.

R. Govers, M.J.R. Wortel / Earth and Planetary Science Letters 236 (2005) 505–523506

Tearing has been occurring in the following regions in

the last couple of million years (Fig. 2); the northern

termination of the Tonga trench, the southern end of

the New Hebrides trench, the northern and southern

ends of the Lesser Antilles trench, the northern end of

the South Sandwich trench, the southern end of the

Hikurangi trench (North Island, New Zealand), the

southern end of the Vrancea trench (Carpathians), on

both ends of the Calabria trench (Sicily), both ends of

the Hellenic trench, and possibly the Gibraltar arc.

This list is not complete in that it does not include

collision examples.

From their inventory of seismicity in STEP

regions, Bilich et al. [5] find a bconspicuousscarcityQ of strike-slip earthquakes. This finding is

consistent with the nature of STEP faults, as

explained next (Fig. 1a–b). A STEP fault allows sub-

duction to continue. The amount of transform motion

is not necessarily uniform along the STEP fault. To

illustrate this point, consider a tectonic setting like the

Central Mediterranean, where relative motion between

continental Europe and Africa has nearly come to a

halt and subduction of the Ionian slab is accompanied

by slab roll-back. In such bland-locked basinsQ [6], theoverriding plate shows back-arc extension in response

to the movement of the trench. Relative horizontal

motion across the STEP fault only occurs up to the

back-arc domain. STEP propagation acts like a wave

traveling through the landscape; at any location along

the STEP path, strains and rotations build up until it

Fig. 2. Current STEP regions. Lines schematically indicate active plate boundary zones. Rotation symbols show the regionally observed sense of motion on transform faults, or

paleomagnetic rotations about a vertical axis.

R.Govers,

M.J.R

.Wortel

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andPlaneta

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236(2005)505–523

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has passed by. Accurate timing of deformation and

paleomagnetic rotation is therefore crucial to detect

STEP propagation geologically. In the alternative

case that rigid motion of the overriding plate is possi-

ble (Fig. 1c), strike-slip motion will occur across the

STEP fault that in this case behaves more like a

classical transform plate boundary. Whether the over-

riding plate can rigidly trail the trench during rollback,

or even actively overrides the subducting plate without

deforming internally, depends on boundary conditions

(left side of Fig. 1a–c) and internal strength.

Schellart et al. [7] use analogue models to study the

geological consequences of trench retreat for the North

Fiji back-arc basin. Implicit in their experimental ap-

proach is the assumption that the STEP fault at the

southern end of the New Hebrides trench propagates

easily. Prescribed saloon door kinematics on the edge

of the basin are shown to reproduce the observed

structural development within the overriding plate.

Return flow around slab edges is addressed in some

recent model studies. Kincaid and Griffiths [8] show

that return flow depends on velocities of subduction,

slab-steepening, and rollback. Vice versa, the kinemat-

ics of subduction are significantly affected by the pres-

ence of a slab edge, resulting in a geometry of edge-

bounded subduction zones that differs from the typical

concave shape towards the overriding plate [9–11].

We first review some of the main characteristics of

existing STEP regions. The inferred range of plate

tectonic settings in which STEPs occur, inspires end-

member dynamic models of STEP regions. These

models are intentionally simple, and without a focus

on any specific region. We will show that STEP faults

are stable in that, once a STEP geometry exists, it will

grow upon itself except in relatively extreme cases.

Another outcome of the models is that very particular

patterns of surface deformation result from tear prop-

agation, which may be geodetically and geologically

detectable. Finally, we predict some first order geo-

logical imprints from the models.

2. Characteristics of STEP regions

2.1. North Fiji Basin (Fig. 2a)

Following the classical work by Isacks et al. [2,3],

Millen and Hamburger [12] show that seismicity and

focal mechanisms are indicative of progressive down-

warping and tearing of the Pacific plate as it enters the

northernmost segment of the Tonga subduction zone.

Dip-slip faulting along shallow (18–57 km) near-ver-

tical planes that are oriented parallel to the slab edge is

inferred from large (5.6–7.5 mb) earthquakes. Sinis-

tral strike-slip activity on the STEP fault tapers to-

wards the northwestern most end of active back-arc

extension [13]. Montelli et al. [14] image a deeply

rooted plume at the northern end of the Tonga sub-

duction zone. Lavas from the northern Tonga islands

are interpreted to contain geochemical imprints of the

Samoa plume by Wendt et al. [15]. Smith et al. [16]

conclude that seismic anisotropy and He isotopes

from the Samoa hotspot are indicative of return flow

around the slab edge.

The New Hebrides Trench marks the eastward

subduction of the Australia plate beneath the North

Fiji basin. Near the southern end of the trench we

expect a STEP fault. No shallow (b50 km depth)

tear faulting mechanisms were recorded in the pe-

riod 1977–2002 in this region, so it is more diffi-

cult to identify the exact location of the active

STEP fault. The Hunter fracture zone likely repre-

sents the inactive portion of the STEP fault. Con-

sistent with the STEP fault behavior discussed in

Fig. 1, (sinistral strike-slip) seismic moment release

dwindles to zero along the STEP fault towards the

ENE [17].

2.2. Mediterranean subduction zones (Fig. 2b)

The Mediterranean region currently hosts multiple

STEPs. Paleogeographic reconstructions show that the

Calabria trench has been retreating ESE at a rate of 30

mm/yr during the last few million years (e.g., [18]).

The southern edge of the Ionian slab is currently

imaged near Sicily [19], where Carminati et al. [20]

infer a STEP-like plate boundary. In Fig. 2b, the line

north of Sicily schematically indicates the 100 km

wide dextral shear zone between the Ustica-Eolie

line in the Tyrrhenian basin, and the Kumeta-Alcan-

tara line in N-Sicily [21]. Clockwise paleomagnetic

rotation observations on Sicily [22,23] are consistent

with dextral strike-slip along the STEP fault. The

current southern edge of the Calabria trench appears

to be propagating along a Mesozoic weakness zone,

the Malta Escarpment [24,25]. No M N4 tearing

R. Govers, M.J.R. Wortel / Earth and Planetary Science Letters 236 (2005) 505–523 509

events have been recorded in this region. Seismic

strain is dominated by the convergence between

Africa and Europe in a direction that is approximately

perpendicular to the direction of trench retreat [26].

GPS velocities in the Central Mediterranean suggest

that retreat of the Ionian trench may currently have

halted [27]. This may be explained by detachment of

the Ionian slab as was suggested by Wortel and Spak-

man [28] on the basis of observed rapid uplift of

Calabria. However, regional uplift may also be influ-

enced by the plume that was imaged below Sicily by

Montelli et al. [14]. The STEP is located close to

Mount Etna, Aeolian and Tyrrhenian volcanoes. The

geodynamic cause for their peculiar magma chemistry

evolution has been the topic of debate in the last

couple of years (plume [29], plate detachment [30],

lithosphere delamination [31], return flow [32]).

Civello and Margheriti [33] conclude that return

flow causes shear wave splitting in the south-central

Mediterranean.

The northern edge of the Ionian slab [19] may

require a STEP fault through the Lucanian Apennines.

The line in Fig. 2b indicating this fault zone is poorly

constrained. Fast (~258/0.5 My), recent, counter-

clockwise paleomagnetic rotations about a vertical

axis in southern Italy are consistent with such STEP

fault zone [24,34–37]. Catalano et al. [38] show that

sinistral strike-slip along NW–SE faults in the south-

ern Apennines was principal the mode of deformation

during middle (0.8–0.2 Ma) and late Pleistocene (0.8–

0 Ma). Support for a STEP fault zone from seismicity

is lacking.

The Hellenic trench is also laterally bounded by

STEP regions. The Kephallinia fault zone in the west

should probably be considered as a STEP. In the

east, a STEP fault is located somewhere between

the eastern Aegean region near Rhodes [39] and

the Isparta angle [40]. The strike-slip character of

this boundary is evident from focal mechanisms. At

depth, the eastern edge of the Hellenic slab was

interpreted as a bvertical ruptureQ by de Boorder et

al. [41].

The narrow Vrancea slab is currently constrained

in the south by STEP faulting near the Intramoesian

Fault and in the north by a STEP near the Trotus

fault (e.g., [42]). Alternating periods of migration of

slab detachment along the Carpathians [28] and

STEP tectonics may have resulted in multiple gen-

erations of STEP faults along the north end of the

slab.

The Betic-Rif mountain belt has been proposed to

have resulted from westward subduction of a ~200

km wide slab [43,44]. Important building stones of

this scenario are paleomagnetic rotations on either

side of the Gibraltar arc, which are interpreted to

reflect STEP fault activity at lateral slab edges. Here

too, no plate tearing events have yet been identified.

2.3. Eastern Caribbean plate (Fig. 2c)

VanDecar et al. [45] tomographically image the

aseismic edge of the Lesser Antilles slab beneath

continental South America, showing that the Lesser

Antilles subduction zone is distinct from the Caribbe-

an subduction zone further to the west. In the absence

of tear faulting seismicity in this region, we speculate

that the STEP fault zone approximately follows the

continental margin. Carlos and Audemard [46] argue

that the cumulative (geological) slip on major faults in

northern Venezuela is substantially less than what

would be expected on the basis of large scale recon-

structions. Similarly, seismic moment release in the

southeast Caribbean is limited to the active STEP

region [47].

The edge at the north end of the Lesser Antilles

trench is geometrically complicated. Here, the exis-

tence of a microplate (Gonave, Hispaniola, and Puerto

Rico (GHPR) blocks) along the northern STEP

fault is a major complication that requires further

study.

2.4. Sulawesi, Indonesia (Fig. 2d)

The western end of the North Sulawesi trench

marks the edge of the slab [48]. Sinistral strike-slip

on the Palu fault on Sulawesi [49,50] is consistent

with this being a very active STEP fault.

2.5. Scotia-Sandwich plates (Fig. 2e)

Forsyth [4] was the first to examine focal

mechanisms along the Scotia and Sandwich plates.

The E–W trending fault at the north end of the South

Sandwich Trench qualifies as a STEP fault which

accommodates eastward rollback of the westward

dipping South America plate. The plate boundary


geometry along the southern Sandwich plate is not

well constrained; from the southernmost East Scotia

spreading ridge to the southern end of the South

Sandwich Trench the plate boundary does not have

a clear bathymetric expression and seismicity is

limited. It is however likely that this also is a

STEP fault. Beyond the STEP further to the east,

the South America and Antarctica plates are direct

neighbors along an east–west oriented transform

plate boundary (bSouth America–AntarcticaQ (SA-

A) ridge). This has the consequence that STEP

fault lengthening here occurs along a pre-existing

plate boundary.

Motion of the Scotia and Sandwich plates relative

to the South America and Antarctica plates is con-

strained by Thomas et al. [51]. Rates of transform

motion along the northern and southern boundaries of

the Scotia plate are on the order of 10% of the

convergence rate at the South Sandwich Trench.

This is consistent with the STEP fault model we

propose.

2.6. Summary

Observations of STEP characteristics vary by the

region. Where available, focal mechanisms at STEPs

are consistent with tear propagation. Seismicity rates,

geological offsets and paleomagnetic rotations yield

support to the notion that STEP faults are dissimilar

from transform plate boundaries. Volcanism near

STEPs is distinct from typical arc volcanism. In

some cases, slab edges appear to coincide with mantle

plumes.

STEPS occur in plate tectonic settings ranging

from the landlocked (Mediterranean) situation in

Fig. 1a and 1b to the open subduction (Caribbean)

setting of Fig. 1c. We next focus on first order defor-

mation/kinematic expressions of STEPs in these end-

member cases. The distinct volcanism and the relation

with plumes is not addressed here.

3. STEP model setup

We use a finite element (FE) method to solve the

mechanical equilibrium equation for three-dimension-

al displacements. The code was developed from TEC-

TON version 1.3 (1989) [52,53]. Constitutive

equations are based on (compressible) elastic and

non-linear, incompressible viscous flow;

eexx ¼1

Errxx � m rryy þ rrzz

� ��

þ rE=geffð Þn�1

6geff

2rxx � ryy � rzz

� �

eeyy ¼1

Erryy � m rrxx þ rrzzð Þ� �


6geff

2ryy � rxx � rzz

� �

eezz ¼1

Errzz � m rrxx þ rryy

� ��


6geff

2rzz � rxx � ryy

� �

eexy ¼1þ mE

rrxy þrE=geffð Þn�1

2geff

rxy

eexz ¼1þ mE

rrxz þrE=geffð Þn�1

2geff

rxz

eeyz ¼1þ mE

rryz þrE=geffð Þn�1

2geff

ryz

where e]ij are components of the strain rate tensor, a

dot indicates differentiation with respect to time, E is

Young’s modulus, m is Poisson’s ratio, rij are compo-

nents of the Cauchy stress tensor, geff is the effective

viscosity, and rE is the effective stress, defined as

rE u

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=3 r2

xx þ r2yy þ r2

zz � rxxryy � rxxrzz � ryyrzz

� �þ r2

xy þ r2xz þ r2

yz

r

This formulation avoids problems related to main-

taining incompressibility. We account for geometric

non-linearity due to large deformation through the

formalism of McMeeking and Rice [54]. Simplex

elements are used to derive the FE equations. Matrix

equations are solved using PETSc ([55], http://

www.mcs.anl.gov/petsc), a suite of data structures

and routines for the scalable solution of partial differ-

http://www.mcs.anl.gov/petsc


ential equations. We adopt the conjugate gradient

implementation of the Krylov subspace method and

Eisenstat preconditioning (a good introduction is

given by Freund et al. [56]) to solve the algebraic

equations iteratively.

As it is our goal to establish the first order response

to subduction in STEP regions, our model geometry is

a stylized form of the STEP regions described above.

The model rheology is linear visco-elastic; highly

viscous in the lithosphere, and low viscosity in the

asthenosphere. Horizontal dimensions of the mechan-

ical model are 1100�750 km, which is substantially

larger than the elastic flexural parameter of the in-

volved lithospheres (Fig. 3). Continental and oceanic

lithospheres are assumed to have 100 km and 80 km

thicknesses (L), respectively. In the models presented

here, the flexural rigidity of the lithosphere is uniform

(5.5�1024 Nm). The bottom of the model lies at 200

km or alternatively at 300 depth. The top of the curved

subducting slab is defined by an error function

z xð Þ ¼ � Rffiffiffip

p

etan2#erf

x e

2Rtan #

��

where z represents depth, x is horizontal distance

perpendicular to the trench, R is the radius of curva-

ture, and # is the (deep) subduction angle. This rep-

resentation has the benefit of a smooth variation of

Fig. 3. View through the 3D model geometry. The grey plates

labeled Africa and Ionian Sea (referring to the south-central Med-

iterranean plate tectonic setting) are part of a single Africa plate, part

of which is subducting. The transparent box outlines the overriding

plate of the Ionian subduction zone. The asthenospheric part of the

model is indicated by the sub-lithospheric transparent box.

curvature, so that (strain inducing) displacement dis-

continuities are avoided. Becker et al. [57] show that

the radius of curvature is of the order of the thickness

of the lithosphere at the trench. In the present study,

we assume R= 1.60L and #=458. We modified the

slippery node technique [58] to allow for freely

deforming faults while minimizing overlaps or gaps.

Slippery nodes are used to represent the subduction

fault that extends throughout the assumed lithospheric

thickness of 80 km. The subduction fault is assumed

to be well-developed and therefore frictionless, con-

sistent with inferences by Zhong et al. [59]. Similarly,

the STEP fault consists of slippery nodes and, for

simplicity, is assumed to be a vertical lithosphere

cutting feature. The influence of friction on the

STEP fault will be investigated.

We adopt a Maxwell rheology with uniform elastic

parameters (E =1011 Pa, m =0.25). Linear viscosity geff

is selected to be 1024 Pa s in the lithosphere and 2–4

orders of magnitude lower in the asthenosphere,

depending on the model. We will show model evolu-

tion as function of multiples of the asthenospheric

Maxwell time sM, which is the shortest characteristic

response time in the models. As we restrict the total

integration time to a few hundred asthenospheric

Maxwell times, modeling results can be viewed as

the near-instantaneous response to body forces and

boundary conditions (BCs).

Flow in the model asthenosphere is assumed to

result from forcing within the model only, i.e., we do

not consider the effect of larger scale convective

motions. Lithosphere density is taken to be 3100

kg/m3, asthenosphere density 3050 kg/m3. Deviatoric

stresses resulting from gravity loading are assumed

to have relaxed so that gravity pre-stresses are hy-

drostatic, except in the slab. Pre-stresses are therefore

initialized with a 1-D layered density field not con-

tributing to the initial forcing, and an anomalous

density field that excites sinking of the slab. This

approach has the benefit of including the full gravity

field while not introducing flow due to self-gravita-

tion. In some of the models we assume that the slab

beyond the model domain exerts an explicit down-

pulling force, i.e., we assume that slab pull is not

locally compensated by shear on a slab segment or

by interaction with deeper phase boundaries. We use

Winkler normal pressure BCs along the bottom of

the model, causing a pressure increase of �qgz for a


downward deflection of the interface by z meters, or

a decrease in case of an upward deflection.

Viscous resistance to horizontal flow along the

model bottom boundary is applied through Maxwell

BCs; this is a combination of a classical Winkler

spring element and a dashpot, in series [60]. Here,

the spring constant is proportional to the elastic shear

modulus, and the viscosity is equal to that of the

overlying asthenosphere. An initial Winkler force

consequently decays at a rate that is controlled by

the dashpot viscosity. Boundary conditions on verti-

cal model boundaries vary, as discussed below. In

most of the models, Maxwell BCs act in a direction

perpendicular to the asthenospheric portion of these

boundaries.

We use GMSH version 1.53.2 [61], which is pri-

marily based on a Delaunay algorithm, to generate a

three-dimensional tessellation by tetrahedral elements.

For visualization of the FE results, we use Data

Explorer (http://www.opendx.org).

3.1. STEP1: subduction model

We consider the instantaneous response of the

mechanical model to body forces and boundary con-

ditions in order to predict the location and direction of

STEP propagation. Fault propagation itself is not

explicitly included in the dynamic model. Fig. 4

shows the resulting velocity field, normalized by the

highest velocity magnitude anywhere in the model. As

velocities scale linearly with the assumed astheno-

sphere viscosity and density anomaly, this is an effi-

cient display of results for a variety of densities and

asthenosphere viscosities. The model result was com-

puted for lithospheric lateral BCs that are fixed hori-

zontally, except for the overriding model lithosphere

to allow for subduction (Fig. 1c). Perpendicular as-

thenospheric Maxwell BCs have a characteristic

decay time that is much larger than the Maxwell

time of the asthenosphere; effectively, lateral astheno-

sphere BCs simulate the compressible asthenosphere

beyond the model domain in this case (cf. [62]).

Sinking of the slab (particularly visible in top

and bottom views of the vertical velocity vz) causes

slip along the subduction fault. At the trench, an

eastward pressure gradient from lateral density var-

iations results in a suction force that drives the

overriding plate towards the trench. The top view

of horizontal trench-perpendicular motions (vx)

shows the overriding plate moving towards the

trench. Resistance to continued subduction near the

STEP is clear from the increase in subduction ve-

locity with distance away from the STEP. Continuity

of normal stresses across the subduction fault result

in down-pulling of the overriding plate near the

trench. Subsidence of the lithosphere south of the

STEP fault, near the trench, is caused by viscous

coupling to the sinking slab. Uplift of the top

surface results from flexural bulging (elastic wave-

length~160 km) and asthenospheric flow. The real-

istic thickness of the model lithospheres has the

benefit of yielding equally realistic dimensions of

their contact surfaces. A consequence of the simple

rheology of the lithospheres is that their effective

elastic thickness is unrealistic, and we consequently

do not believe that either the horizontal wavelength

or the rates of predicted uplift due to flexure apply

to the Earth. However, the modeled phenomenon

that N–S flexural bulging of the subducting litho-

sphere also produces uplift of the non-subducting

lithosphere in the south is probably realistic. The

restricted mass flux through vertical asthenospheric

boundaries causes uplift of the lithosphere following

subduction; alternative models with more open lat-

eral boundaries show decreased uplift rates and

higher subsidence rates. Non-zero friction on the

STEP fault smoothes the velocity discontinuity

across the fault.

In the asthenosphere, sinking of the slab results in

high and low pressure regions beneath and above the

slab, respectively. The bottom view of vy shows the

resulting slab-parallel horizontal flow from beneath

the slab towards its edge, and above the slab towards

the wedge. Experiments show that flow rate in the

asthenosphere decreases with increasing compressibil-

ity. Return flow is suppressed in cases where more

flow is allowed through lateral model boundaries.

Fig. 5 shows velocities at the model surface and

the predicted change in topography along a profile

south of and parallel to the STEP fault, assuming

that the STEP propagates at constant rate of 9 cm/

yr. Fig. 6 shows total effective strain rates which

maximize near the STEP end. Both figures illustrate

that relatively complicated surface deformation

fields may be expected in a region within about a

100 km distance of the STEP.

http://www.opendx.org

Fig. 4. Normalized velocities of bsubduction modelQ STEP1 (10s; j mYjmax ¼ 1 cm/yr), and finite element grid (light grey). North arrow is shown to facilitate model description.

Velocity magnitude, (a) top view and (b) bottom view. This and following panels; breakdown into individual components of the 3D velocity field at model boundaries. East

(positive)–west (negative) velocity component vx, (c) top view and (d) bottom view. In these and the following panels, black lines show zero velocity contours. South (positive)–north

(negative) velocity component vy, (e) top view and (f) bottom view. Up (positive)–down (negative) velocity component vz, (g) top view and (h) bottom view.

R.Govers,

M.J.R

.Wortel

/Earth

andPlaneta

ryScien

ceLetters

236(2005)505–523

513

Fig.4(continued).


600 400 200 0 -200 -400km

km

-1.05

10 τ η=2.1021

v z (m

m/y

r)T

opog

raph

y (m

)

1.05mm/yr

0

100

200

300

400

500

600

700

-0.4

-0.2

-0.0

0.2

0.4

0

500

1000

1500

Fig. 5. Bottom panel; velocities of STEP1 model surface at integration time=10 asthenospheric Maxwell times. Horizontal velocities are shown

as arrows, vertical velocity as color contours. The largest horizontal velocity, in the overriding plate, is 1 cm/yr. Surface intersections of the

subduction fault and STEP fault are shown as red lines. Middle panel; vertical velocities along the horizontal (black) profile line in the bottom

panel. Top panel; topography along the profile line resulting from STEP propagation (9 cm/yr) up to its location in the bottom panel.


Coulomb stresses can be used to predict the lo-

cation and orientation of prospective faults. Fig. 7

shows Coulomb stresses in model STEP1 (friction

coefficient of 0.6). Stress magnitudes increase with

model time; the result shown is after 50 Maxwell

times. The location and timing of actual failure will

depend on the actual strength of the lithosphere,

which is infinite in our elastic model lithosphere.

Based on the modeled Coulomb stresses, STEP

propagation in a direction parallel to the assumed

STEP fault orientation is most likely. This mode is

similar to tear propagation in a tearing sheet of

paper. The results show that, alternatively, the slab

can break off along an inclined plane cutting the

slab. This will occur when the resistance to STEP

propagation/failure is larger than the resistance to

slab break-off. In reality, the total strength of the

(oceanic) subducting slab is most often equal to or

higher than the strength of the surface plate, espe-

cially when the surface plate involves continental

crust [63]. Consequently, we consider slab break-

off substantially less likely than incessant propaga-

tion of the STEP.

We investigated the sensitivity of the above

model response to variations in model geometry,

mesh density, forcing, boundary conditions and

visco-elastic material properties. The results of

STEP1 are found to be quite representative for

600 400 200 0 -200 -400km

km

0.37 45.46 nstrain/yr

10 τ0

100

200

300

400

500

600

700

Fig. 6. Effective total (i.e., sum of elastic and viscous) strain rates eeE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=2ee Vij ee

Vij

q� �along the STEP1 model surface. The inset panel shows

principal horizontal strain rates in the boxed sub-region of the contour figure. Near the STEP, strain rates maximize and show a fanning pattern.

Coulomb stress (MPa)

STEP propagation

50

60

70

80

90

Fig. 7. Coulomb stresses larger than 50 MPa in the STEP1 model lithospheres (50s). Coulomb stresses maximize along the STEP fault edge.

The expected orientation of fault propagation is indicated by the densely hatched vertical fault plane. Coulomb stresses are also significant along

a plane cutting the subducted lithosphere. Whether the STEP will propagate or slab break-off will occur, depends on the relative strength of the

subducted oceanic lithosphere and the lithosphere that needs to break for STEP propagation.



the investigated first-order models. One exception is

the (lack of boundary conditions which allow) free

horizontal motion of the overriding plate. This will

be addressed in a following model.

3.2. STEP2: land-locked basin model

The second model we consider is inspired by, but

not aimed to reproduce, the tectonics of the south-

central Mediterranean around Sicily. Importantly, and

possibly distinct from the situation beneath southern

Italy, we assume that the slab is continuous to predict

the response to density sinking of the slab. Moreover,

boundary conditions in the model do not allow east–

west motion of the westernmost overriding lithospher-

ic boundary, which is more extreme than the south-

central Mediterranean, where there is little relative

motion between points on the 108 and 208 meridians,

but where intermediate back arc extension facilitates

subduction of the Ionian slab. Similar horizontal

stretching of our model overriding plate is not possi-

ble. Our extreme choice of locked boundary condi-

tions (similar to Fig. 1a and b), is motivated by our

objective to investigate the entire spectrum of STEP-

dominated responses. Fig. 8 is a display of model

velocities similar to that of Fig. 4. The inability of

the overriding plate to move substantially is the most

striking difference. Instead, the velocity field is dom-

inated by vertical sinking of the slab and overriding

plate-without significant slip along the (frictionless)

subduction fault. This illustrates that, in a land-locked

basin situation, subduction is only possible if simul-

taneous back-arc extension occurs. This implies that

there is a critical subduction velocity below which

subduction stops entirely; at lower speeds, the rate of

conductive cooling of the extending lithosphere is

higher than the rate of advective heating, so that the

overriding plate strengthens with time. In the model,

relative motion along the STEP fault is also negligi-

ble. Coulomb stresses near the STEP are accordingly

small, and slab break-off is predicted. Flow velocities

in the asthenosphere are higher than lithosphere ve-

locities, and the flow pattern is different in that flow

towards the subduction wedge does not occur.

Fig. 9 shows the model surface velocity field (cf.

Fig. 5). The fanning pattern of horizontal velocities

closely follows the pattern of subsidence and uplift.

The predicted topography along the profile is subdued

relative to Fig. 5; the vertical velocity wave of the

middle panel that migrates with time to the east (left)

through the landscape produces topography in front of

the STEP, and subsidence its wake.

Surface strain rates are displayed in Fig. 10 (cf.

Fig. 6). Most important is the different pattern; due to

the lack of fault slip, maximum strain rates at the

surface do not occur near the STEP. Principal strain

rate directions follow the fanning pattern defined by

vertical velocity gradients.

4. Discussion

Once established, STEPs are stable features in

that they continue to propagate as long as the litho-

spheric strength is less than or equal to the slab

strength. As subduction results from instability of

the cold and strong boundary layer, STEPs will

mostly be stable as seems to be evident from the

length of STEP faults in Fig. 2. However, subduction

of progressively younger lithosphere may result in a

combination of substantial slab pull and a weak

shallow slab causing slab break-off rather than con-

tinued STEP propagation.

STEPs propagate in a direction opposite to the

subduction direction in lithosphere with laterally uni-

form horizontal properties. Horizontal variations in

strength in front of the STEP, most prominently passive

margins, may focus and redirect the direction of STEP

propagation. We expect that STEPs mostly will follow

passive margins. As passive margins have generally

rugged shapes in map view, the trench will lengthen

and shorten at the STEP accordingly (e.g., the southern

ends of the Calabria and Lesser Antilles trenches).

Conductive heating near the slab edge will be more

efficient, affecting both the body forces and the

strength of the slab. Assuming that the slab is instan-

taneously exposed to asthenospheric temperatures

below 100 km, a slab subducting at a rate of 4 cm/yr

at a 458 angle will be affected to about 10 km hori-

zontal distance from the edge when arriving at 200 km

depth. Except for very slowly subducting slabs, hori-

zontal heat flow therefore has limited effects.

The scarcity of tear fault mechanisms in the cen-

tennial catalog is remarkable. We speculate that this is

caused by alternating periods of STEP propagation

and loading. Immediately after a STEP propagation

Fig. 8. Normalized velocities of bland-locked basin modelQ STEP2 (10s; j mYjmax ¼ 0:25 cm/yr), and finite element grid (light grey). North arrow is shown to facilitate model

description. Velocity magnitude, (a) top view and (b) bottom view. This and following panels; breakdown into individual components of the 3D velocity field at model boundaries.

East (positive)–west (negative) velocity component vx, (c) top view and (d) bottom view. In these and the following panels, black lines show zero velocity contours. South (positive)–

north (negative) velocity component vy, (e) top view and (f) bottom view. Up (positive)–down (negative) velocity component vz, (g) top view and (h) bottom view.

R.Govers,

M.J.R

.Wortel

/Earth

andPlaneta

ryScien

ceLetters

236(2005)505–523

518

Fig.8(continued).


600 400 200 0 -200 -400km

-1.22 1.22 mm/yr

10 τ η=2.1021

kmv z

(mm

/yr)

Top

ogra

phy

(m)

0

100

200

300

400

500

600

700

-0.4

-0.2

-0.0

0.2

-400-200

0200400600

Fig. 9. Bottom panel; velocities at the STEP2 model surface at integration time=10 asthenospheric Maxwell times. Horizontal velocities are

shown as arrows, vertical velocity as color contours. The largest horizontal velocity, in the overriding plate, is 0.8 mm/yr. See caption of Fig. 5

for further details.


event or period, the shallow slab dip near the STEP

may be too gentle. Depending on the sinking velocity,

it subsequently requires some time before the STEP is

reloaded. The observed tearing seismicity at north

Tonga implies that this region is in the propagation

mode.

STEPs are what Bilich et al. [5] refer to as two-

plate convex regions, or closed corner transitions [64],

in their global characterization of subduction-to-

strike-slip transitions. This nomenclature reflects the

perspective of an observer on the subducting plate.

Indeed, many of the hypothesized STEP regions have

rounded corners, and two-ocean plate boundaries spe-

cifically have a characteristic convex shape. Model

STEP1 alludes to a cause for this observation; resis-

tance to subduction near the STEP resulting from the

extra work that is required to break the lithosphere.

Duggen et al. [65] imply that two propagating

STEPs bounding the Strait of Gibraltar may result in

bands of neighboring lithospheric mantle to be

dragged along with the subducting lithosphere (be-

neath northern Africa and southern Spain). Depending

on the negative buoyancy of the lithospheric mantle

and the viscous coupling to the overlying crust this

appears a viable process, which may also occur in

other STEP regions. Subsequent decompression melt-

ing of infilling asthenospheric may explain the plume

petrologic signature of STEP-volcanoes. However,

return flow as found in model STEP1 may already

suffice to explain this observation.

600 400 200 0 -200 -400km

km

0.13 7.29 nstrain/yr

10 τ0

100

200

300

400

500

600

700

Fig. 10. Effective total strain rates along the STEP2 model surface. See caption of Fig. 6 for further details.


Our models do not include the dynamic effects of

phase transitions [66,67], interaction of the slab with

the upper-lower mantle discontinuity [68,69], and

(larger scale) convection not excited by model slab

subduction. Our first order description of the geome-

try, rheology and forcing in STEP regions allows us to

identify the base pattern of surface responses at such

features. Future work will focus on regional models to

investigate whether STEP evolution explains avail-

able observations. To this end, we will assimilate in

our models knowledge of geometry (seismology, po-

tential field data), temperature (heat flow, seismology)

to define rheology and body forces, and pre-existing

regional faults.

5. Conclusions

We identify a dozen or so STEP-type edges of

subduction zones, where continued subduction

requires tearing of the lithosphere. Observational sup-

port for STEP propagation varies strongly per region,

partly because of the remoteness or inaccessibility of

the area, but also because lithosphere tearing events

seem to occur infrequently. STEPs are basically dif-

ferent from transform plate boundaries, although they

may sometimes mimic the kinematic behavior of

transforms. Once established, STEPs are stable fea-

tures in that they continue to propagate in most cir-

cumstances. A STEP propagating through the

landscape has the potential to produce kilometer-

scale topography and major sedimentary basins. Geo-

logically recorded deformation and rotation at points

along the STEP path are expected to exhibit a, yet

undocumented, very specific temporal variation.

Acknowledgements

This research was performed as part of the ISES

program. The work was partly supported by the

EUROMARGINS Program of the European Science

Foundation, 01-LEC-EMA22F WESTMED project.

Reviews by Michael Hamburger, Ray Russo and

Wouter Schellart are greatly appreciated.

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