Zeumann et al-2015-Tectonics

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Tectonics
RESEARCH ARTICLE
10.1002/2015TC003867
Key Points:
• Deformation pattern depends on
ridge orientation and forearc structure
• For migrating ridges, areas of extension
and shortening shift along margin
• Results allow better understanding of
natural ridge-related forearc deformation
Deformation of erosive and accretive forearcs during
subduction of migrating and non-migrating aseismic
ridges: Results from 3-D finite element models and
application to the Central American, Peruvian,
and Ryukyu margins
Stefanie Zeumann1 and Andrea Hampel1
1
Supporting Information:
• Figures S1–S4
Correspondence to:
S. Zeumann,
zeumann@geowi.uni-hannover.de
Citation:
Zeumann, S., and A. Hampel (2015),
Deformation of erosive and accretive
forearcs during subduction of migrating
and non-migrating aseismic ridges:
Results from 3-D finite element models
and application to the Central American,
Peruvian, and Ryukyu margins, Tectonics,
34, 1769–1791, doi:10.1002/
2015TC003867.
Received 25 FEB 2015
Accepted 18 JUL 2015
Accepted article online 23 JUL 2015
Published online 5 SEP 2015
Institut für Geologie, Leibniz Universität Hannover, Hannover, Germany
Abstract Subduction of aseismic oceanic ridges causes considerable uplift and deformation of the upper
plate and may lead, for example, to the indentation of the forearc, the formation of marine terraces, or
distinct fault patterns in the upper plate. Depending on the orientation of the ridge relative to the plate
convergence direction, the ridge may either be stationary or migrate along the margin. Here we use
three-dimensional numerical models to investigate the tectonic evolution of forearcs affected by ridge
subduction. In different experiments, we distinguish between migrating/non-migrating ridges and
accretive/erosive margins, respectively. Our results reveal that displacement and strain fields above
migrating and non-migrating ridges are asymmetric with respect to the ridge axis unless both ridge and
plate convergence direction are perpendicular to the trench. As the asymmetric deformation pattern shifts
along the margin through time, uplift caused by the underthrusting ridge is followed by subsidence when
the ridge crest passed by, and regions initially experiencing shortening may subsequently undergo
extension and vice versa. If the forearc comprises an accretionary prism, the ridge-induced reentrant is
larger than those in models with erosive forearcs and strain localizes in the frontal part of the wedge.
Additional models with a setup adjusted to the Cocos and Gagua Ridges provide constraints on the onset
of their subduction at the Central American and Ryukyu margins at ~2 Ma and 1 Ma, respectively.
Displacement and strain fields from a model for the Nazca Ridge collision zone show good agreement
with geological data from marine terraces and Quaternary faulting.
1. Introduction
The present-day ocean floor is occupied by a large number of oceanic plateaus, aseismic ridges, and seamount
chains, which are bound to be subducted with the oceanic plate that carries them (note that in the following
only “aseismic” bathymetric highs are considered; i.e., active spreading ridges are excluded). Some of these
bathymetric highs have already entered a subduction zone, with notable effects on the geometry and
tectonic evolution of the affected margin [e.g., McCann and Habermann, 1989]. Among these effects are the
indentation of the frontal part of the upper plate accompanied by a landward shift of the trench [e.g.,
Bouysse and Westercamp, 1990; Schnürle et al., 1998; Lallemand et al., 1999] and uplift of the forearc, which
may lead to formation of marine terraces at the coast [e.g., Corrigan et al., 1990; Gardner et al., 1992, 2013;
Hsu, 1992; Macharé and Ortlieb, 1992; Saillard et al., 2011]. Farther landward, ridge subduction may induce
uplift and shortening [e.g., Fisher et al., 2004; Sitchler et al., 2007; Espurt et al., 2007; Regard et al., 2009] and
enhance the exhumation of rocks [Wipf et al., 2008; Spikings and Simpson, 2014]. At deeper levels, ridges and
subducted plateaus may contribute to the formation of flat slabs [e.g., Gutscher et al., 2000; van Hunen et al.,
2002; Espurt et al., 2008] although the link between ridge subduction and slab flattening is not yet confirmed
and other factors like slab rollback and a trenchward advance of a thick overriding plate may also play a role
[van Hunen et al., 2004; Manea and Gurnis, 2007; Manea et al., 2012]. From their abundance in the present-day
oceans, it can be assumed that a number of bathymetric highs have also been subducted in the past and
probably influenced the topographic and tectonic evolution of the affected margin [e.g., Gutscher et al., 1999a;
Rosenbaum et al., 2005; Spikings and Simpson, 2014].
©2015. American Geophysical Union.
All Rights Reserved.
ZEUMANN AND HAMPEL
An important point to consider when unraveling the spatiotemporal evolution of forearc deformation
patterns caused by subducting bathymetric highs is that elongated submarine ridges migrate laterally
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along the active margin unless they are parallel to the convergence direction of the oceanic plate [cf. Hampel,
2002]. As a consequence, the ridge-induced deformation will generally sweep along the margin through
time, as is the case for most currently subducting ridges such as the Nazca Ridge (Peru), the Gagua Ridge
(Ryukyu Island Arc), the Louisville Ridge (Tonga), and the Juan Fernandez Ridge (Chile). Notable exceptions
are the Cocos Ridge, which subducts approximately stationary beneath Central America, and the
d’Entrecasteaux Ridge subducting beneath the New Hebrides Island Arc. Furthermore, geophysical and
geological data from ridge collisions zones worldwide suggest that the style of ridge-induced deformation
differs between margins with accretionary prisms and margins that are characterized by subduction
erosion. At accretive margins, subducting ridges tend to cause a large indentation and partial removal of
the accretionary prism and reduce the input of sediments from the oceanic plate. Examples include the
Gagua Ridge, which indents the accretionary prism of the Ryukyu margin [Dominguez et al., 1998; Schnürle
et al., 1998; Lallemand et al., 1999], and the Juan Fernandez Ridge at the central Chilean margin [von Huene
et al., 1997; Ranero et al., 2006]. In contrast, the frontal wedge of tectonically erosive margins is generally
less indented, as indicated by the examples of the Nazca and Carnegie Ridges at the Andean margin [e.g.,
Hagen and Moberly, 1994; Gutscher et al., 1999b; Spikings et al., 2001; Hampel et al., 2004a], the Cocos Ridge
at the Central American margin [Gardner et al., 1992; Ranero and von Huene, 2000], and the Louisville Ridge
at the Tonga-Kermadec margin [Ballance et al., 1989; Clift and MacLeod, 1999]. Typically, the subduction of
an aseismic ridge enhances the rate of tectonic erosion [Bangs and Cande, 1997; Clift and MacLeod, 1999;
Yáñez et al., 2001; Clift et al., 2003; Clift and Vannucchi, 2004; Vannucchi et al., 2006, 2013; Stern, 2011]
besides causing uplift and steepening of the forearc.
The subduction of aseismic ridges has been investigated by both analogue and numerical models, of which
so far only the analogue models were able to capture the oblique subduction of the oceanic plate and the
migration of the aseismic ridge due to their three-dimensional (3-D) setup. One of these analogue models
[Dominguez et al., 1998] was adapted to the Gagua Ridge, which subducts beneath the accretionary prism
of the Ryukyu margin. The experiment showed that the ridge causes a deep indentation of the
accretionary prism, thrust and strike-slip faulting and temporarily inhibits the accretion of new sediments.
The 3-D analogue experiments performed by Hampel et al. [2004b], which had a setup adjusted to the
Nazca Ridge subducting beneath the erosive Peruvian margin, showed that the indentation is minor for
erosive forearcs and that normal faulting occurs above the leading flank of the migrating ridge. Recently,
Martinod et al. [2013] presented results from analogue models of larger scale (i.e., including the
lithospheres of the downgoing and upper plates as well as the sublithospheric mantle), which shed light
on the feedback mechanisms between the subducting ridge, the deformation of the upper plate, and the
downgoing slab. The authors found that ridge subduction results in slab flattening and indentation and
uplift of the upper plate. In Martinod et al.’s [2013] experiments, the plate convergence direction was
always perpendicular to the margin; migrating ridges were realized by oblique orientation of the model
ridge with respect to the trench.
In contrast to the analogue models, numerical models of ridge subduction were mostly two-dimensional and
focused on the question if flat-slab subduction is caused by the buoyancy of subducting aseismic ridges.
According to Gerya et al. [2009], the subduction of a ridge does not result in major changes of slab dynamics
compared to normal subduction. Similarly, van Hunen et al. [2002] suggested that the flat slab beneath Peru
rather results from the westward motion of South America than from the subduction of the Nazca Ridge.
Owing to their two-dimensional setup, both numerical models had, however, to neglect the effects of ridge
migration along the margin. Upper plate deformation due to an obliquely subducting ridge was considered
by Geist et al. [1993], who used a thin viscous sheet model with vertically constant material properties to
analyze the deformation and stress fields at a ridge-arc collision zone. So far, the only published fully 3-D
model on ridge migration uses a simplified setup, in which the plate interface is a vertical boundary between
two block-shaped plates and the subducting ridge is implemented as a basal velocity boundary condition
[Wallace et al., 2009]. Despite these simplifications, the results showed that the lateral migration of a ridge
might be responsible for the formation of a major left-lateral fault zone in SW Japan, which underlines the
necessity of using 3-D models when investigating the deformation induced by a subducting ridge.
In our study, we use 3-D finite element models to investigate the effects of ridge subduction on the frontal
part of the upper plate (i.e., the submarine forearc and the coastal region). In the first part of the study, we
focus on two major aspects, which are (a) the deformation patterns resulting from a variety of possible
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angles between the ridge, margin, and plate convergence direction and (b) the extent to which forearc
deformation during ridge subduction is governed by the internal structure of the forearc inherited from
accretion or subduction erosion. Our models consist of a subducting oceanic plate carrying the ridge and a
forearc with a realistic wedge shape. The internal structure of the model forearc is varied to reflect the
structure of natural forearcs that have been shaped by accretion or subduction erosion prior to the arrival
of the ridge. The setup of our models allows simulating the effects of ridge subduction for many different
orientations between ridge, margin, and the plate convergence direction, most of which have not been
realized in previous analogue models. In the second part, we present three models adjusted to the natural
case studies (Cocos Ridge, Nazca Ridge, and Gagua Ridge), respectively. The Cocos Ridge and the Nazca
Ridge subduct beneath erosive margins but differ in their orientation relative to the plate convergence
direction, whereas the Gagua Ridge subducts beneath the accretive Ryukyu Island Arc. The results of our
adjusted models contribute to a better understanding of the deformation patterns induced by these ridges.
For the Cocos and Gagua Ridges, our models yield constraints on the debated onset of ridge subduction.
2. Model Setup
For constructing and computing the models, we used the commercial finite element software package
ABAQUS. The models consist of a wedge-shaped forearc and an oceanic plate carrying the aseismic ridge
(Figure 1a). As our study focuses on the deformation of the upper plate, only the forearc wedge is
deformable, whereas the oceanic plate and ridge are implemented as rigid model parts. To simulate
subduction, we apply a modified version of the approach by Cailleau and Oncken [2008], who
implemented the subducting oceanic plate as a rotating segment of a circle with a radius of 225 km. In our
3-D model, the oceanic plate has the shape of segment of a cylinder with a radius of 225 km. To
investigate the effect of the subduction radius on the results, we also applied a radius of 300 km. The plate
interface is modeled as the contact between the oceanic plate (including the ridge) and the bottom of the
forearc wedge (Figure 1). The upper part of the plate interface has a friction coefficient of μ = 0.3; at
depths greater than 30 km, the plate interface is frictionless. A value of μ = 0.3 represents an intermediate
friction coefficient, based on critical taper analyses and analogue models of forearc wedges [Davis et al.,
1983; Dahlen, 1990; Lallemand et al., 1994; Gutscher et al., 1996, 1998]. Thermomechanical numerical
models and models including a subduction channel tend to use low friction coefficients (μ ≤ 0.1) [Manea
et al., 2004; Sobolev and Babeyko, 2005; Gerbault et al., 2009], whereas models with a frictional contact
interface between upper and lower plate—as in our model—usually use higher friction coefficients [Cattin
et al., 1997; Hassani et al., 1997; Hampel and Pfiffner, 2006; Cailleau and Oncken, 2008].
The ridge is oriented either perpendicular or oblique to the forearc (angle ϕ in Figure 1a). It has an arc-shaped
cross section with the highest elevation at the ridge crest. The tip of the ridge is constructed as a semicircle
with a radius of 25 km. For the general models (section 3), we use a 100 km long and 1 km high ridge. In
different experiments, we varied—in steps of 30°—the plate convergence direction (angle α in Figure 1a)
as well as the angle between the ridge and the margin (angle ϕ in Figure 1a). Angles α and ϕ have
identical values for non-migrating ridges (Figure 1b) and different values for migrating ridges (Figure 1c).
The forearc wedge has a surface slope of 4° and extends 150 km from the trench to its rear (“landward”) side,
which is fixed in the x direction but may move in the vertical and y directions. Forearc sides in the xz plane are
fixed in the y direction and allowed to move in the x and z directions. To distinguish between forearcs that
experienced accretion or tectonic erosion, respectively, prior to ridge subduction, we created two types of
model forearcs that differ with respect to their internal structure and mechanical strength. Note that we
define the mechanical strength of a model domain as a combination of Young’s modulus and the plastic
yield stress. In other words, we use the term “mechanically strong” for a model domain with a high
Young’s modulus and a high plastic yield stress, whereas “mechanically weak” implies a low Young’s
modulus and a low plastic yield stress (Figures 1d and 1e). The erosive forearc (Figure 1d) is represented
by a mechanically strong forearc (light grey domain) overlain by a 1 km thick top layer of mechanically
weaker sediments (grey layer). This structure reflects—in a simplified way—the general architecture of
erosive forearcs as revealed by seismic reflection and refraction data [e.g., Ranero et al., 2000; von Huene
and Ranero, 2003; Hampel et al., 2004a]. The accretive forearc in the model consists of a 50 km wide frontal
part representing the accretionary prism and a 100 km wide backstop (Figure 1e). The model accretionary
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Figure 1. Model setup. (a) Perspective view of the model with a deformable wedge-shaped forearc and a rigid oceanic
plate carrying the oceanic ridge [cf. Cailleau and Oncken, 2008]. The angles between the ridge and the margin (ϕ) and the
plate convergence direction (α) are varied in different experiments. Gravity is included in the model. The rear (“landward”) side
of the forearc is fixed in the x direction and free to move in the vertical and y directions. Forearc sides in the xz plane are fixed
in the y direction and allowed to move in the x and z directions. Thick black line indicates the segment of the plate interface
with a friction coefficient of μ = 0.3. The downdip end of the frictional part of the plate interface is located at 30 km depth;
at greater depths, the plate interface is modeled as frictionless. (b) Schematic sketches showing in top view the setup of the
three experiments with non-migrating (“stationary”) ridges. (c) Schematic sketches (top view) of the models with migrating
ridges. Results for configurations indicated by grey arrows and angles α are shown in the supporting information. (d) Cross
section of the model forearc (erosive type). (e) Cross section of the model forearc (accretive type). Note that the terms “erosive”
or “accretive” only describe the internal structure of the forearc (i.e., there is no actual material transfer between the lower
and upper plates in the model). Rheological parameters are Young’s modulus (E), density (ρ), and plastic yield stress (σ y).
3
Density is 2700 kg/m , and Poisson ratio is 0.25 for the forearc wedge.
prism comprises imbricate, landward dipping domains (note that the thrust faults separating these imbricate
structures in nature are not included in the models). The imbricate domains have different values for Young’s
modulus and plastic yield stress, which increase toward the backstop to simulate an increasing mechanical
strength. Again, we base this structure of the model forearc on geophysical images of accretive margins
[e.g., Kopp et al., 2000; Kopp and Kukowski, 2003]. For the model domain beneath the weak top layer
(erosive forearc, Figure 1d) and the backstop of the accretive forearc (Figure 1e) we use a depthdependent plastic yield stress, which was chosen such that the forearc becomes plastic only in case of
ridge subduction. All model domains have a density of 2700 kg/m3 and a Poisson ratio of ν = 0.25.
Gravity acts on the entire model domain (acceleration due to gravity: 9.81 m/s2). Note that our model setup
does not allow capturing isostatic effects at the bottom of the forearc wedge, as the wedge is always in
contact with the rigid oceanic plate underneath; hence, we restrict the interpretation of our results to the
frontal part of the wedge, where most deformation can be expected to result from the topography of the
ridge itself and isostatic uplift can be considered as less important. Eustatic sea level changes, which may
affect the location of the seismogenic zone and the seismic coupling along the plate interface [e.g.,
Bourgois et al., 2007], are not considered in our models. Also not considered are erosion and sedimentation
of the forearc wedge, with the consequence that our models cannot provide constraints, for example, on
rates of rock exhumation above subducting ridges [cf. Wipf et al., 2008; Spikings and Simpson, 2014].
To minimize the initial deformation purely caused by gravity, we pursue the following approach [cf. Wang
and He, 1999; Cailleau and Oncken, 2008]. First, both model types (i.e., with erosive and accretive forearc,
respectively) are computed without plate movement. At this stage, the forearc is purely elastic and has a
Poisson ratio of 0.48, i.e., close to incompressible. The stress fields resulting from these models are used as
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initial condition for the models with a Poisson ratio of 0.25 [cf. Cailleau and Oncken, 2008; Ellis et al., 2006]. In
the first analysis step, gravity and initial conditions are applied. In the second step, the oceanic plate starts to
move at a velocity of 9 cm/a over a period of three million model years. In models with oblique convergence
directions, this value is the total velocity, which is composed of the trench-parallel and trench-perpendicular
component. The convergence velocity is varied in the case studies for the Cocos Ridge (9.2 cm/a), Nazca
Ridge (7.7 cm/a), and Gagua Ridge (6.6 cm/a) and in an additional experiment (4.5 cm/a). Ridge subduction
starts after ~200 ka in all models. All models were calculated using ABAQUS/Standard, which applies an
implicit solution technique based on the Lagrangian method, where the mesh is bounded to the material
and therefore follows its changes in shape during deformation. The average edge length of the brickshaped elements is 3 km; it decreases to 800 m toward the tip of the wedge. In the model with the erosive
forearc, the top layer consists of four layers of elements. For reference, all models were also computed
without a subducting ridge. To isolate the effect of ridge subduction, we subtracted the results of the
models without a ridge from the model results including the ridge. This applies to all general models
presented in section 3. All model parameters are summarized in Table 1.
3. Results From General Models
In this section, we present the results from the general models. We first analyze the deformation patterns for
different orientations between ridge, trench, and plate convergence direction using the setup with an erosive
forearc (section 3.1). In section 3.2, we evaluate the differences between erosive and accretive forearcs for
selected orientations of the ridge.
3.1. Results for Different Orientations of Ridge and Plate Convergence Direction From Models With
Erosive Forearc
3.1.1. Non-migrating (“Stationary”) Ridges
Figure 2a shows the results from the experiment, in which both the plate convergence direction and the
ridge axis are perpendicular to the margin. In this case, displacement and strain patterns are symmetric
with respect to the ridge axis and perpendicular to the strike of the margin. The time series of the vertical
displacement shows that the ridge induces a maximum uplift above its crest. Despite the constant ridge
height, the distribution of uplift along the ridge axis is not uniform but has two maxima near the tip of the
ridge and near the trench, respectively. Uplift rates averaged over 100 ka vary both spatially and
temporally. At model times of 0.5 and 1 Ma, they are highest (3.8 mm/a and 3.5 mm/a, respectively) where
the elevation of the ridge increases gradually to its maximum. At 1.5 Ma, the size of the uplifted area
increases while the maximum uplift rate decreases to 2.2 mm/a. Trenchward of the uplifted area, slight
subsidence ( 0.3 mm/a) occurs. The temporal evolution of the total horizontal displacement through
model time shows that the forearc material is pushed radially away from the frontal part of the ridge. This
displacement pattern results in contractional strain in front of the ridge and extensional strain above the
ridge tip (Figure 2). At the ridge flanks, shortening prevails. Through model time, zones with shortening
also develop trenchward of the extended area. A comparison of the trench-normal and trench-parallel
components of the total horizontal displacement at 1.5 Ma of model time reveals that the margin-normal
displacement has two maxima along the ridge crest with an area of less displacement in between. As a
consequence, the margin-normal horizontal strain changes along the ridge axis from shortening at the
ridge tip to extension above the frontal part of the ridge to shortening again. Near the trench, low
extensional strain prevails. Margin-parallel displacements show opposite movement directions and the
highest values around the frontal part of the ridge. In this region, extensional strain occurs near the ridge
axis and shortening at the flanks.
The displacement and strain patterns described above become asymmetric both relative to the ridge axis
and along strike of the margin if the plate convergence direction and the ridge are oblique (60°) to the
trench (Figure 2b). The area with the highest uplift rates (3 mm/a at 1.5 Ma) has shifted toward one of the
ridge flanks and is followed in the trenchward direction by a zone of slight subsidence ( 0.3 mm/a). As in
the model with a margin-perpendicular ridge, the total displacement shows that the forearc material
moves radially away from the frontal part of the ridge, which results in shortening in front of the ridge and
extension above the ridge tip. Initially, the displacement and strain fields are approximately symmetric
relative to the ridge axis, but they become strongly asymmetric with time. At 1.5 Ma of model time, the
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Table 1. Summary of Model Parameters
Parameter
Symbol
Gravitational acceleration
Oceanic plate width (y parallel to trench)
Oceanic plate radius
Plate convergence velocity
g
ocw
ocr
v
α
Angle between plate convergence
Direction and margin
Ridge width; height
w; h
Angle between ridge axis and margin
Forearc width (parallel to trench)
Forearc length (normal to trench)
Forearc thickness (landward edge)
Density of forearc
Poisson ratio of forearc
Young’s modulus
ϕ
fw
fl
ft
ρ
ν
E
Plastic yield stress
σy
Friction coefficient on plate interface
Location of downdip end of coupling zone
μ
de
Value
Model
2
9.81 m/s
1500 km
225 km; 300 km
90 mm/a; 45 mm/a
92 mm/a
77 mm/a
66 mm/a
30°; 60°; 90°; 60°; 30°
90°
60°
40°
100 km; 1 km
300 km; 2 km
200 km; 1.5 km
25 km; 2.5 km
90°; 60°; 30°
1000 km
150 km
68 km
3
2700 kg/m
0.25
10 GPa
60 GPa
10 to 60 GPa
60 GPa
100 MPa
400 to 1700 MPa
100 to 400 MPa
400 to 1700 MPa
0.3
30 km
All models
All models
General models
General models
Cocos Ridge model
Nazca Ridge model
Gagua Ridge model
General models
Cocos Ridge model
Nazca Ridge model
Gagua Ridge model
General models
Cocos Ridge model
Nazca Ridge model
Gagua Ridge model
General models
All models
All models
All models
All models
All models
Erosive forearc (sedimentary layer)
Erosive forearc (continental crust)
Accretive forearc (frontal prism)
Accretive forearc (backstop)
Erosive forearc (sedimentary layer)
Erosive forearc (continental crust)
Accretive forearc (frontal prism)
Accretive forearc (backstop)
All models
All models
zone with the highest contractional total strain has shifted to one side of the ridge tip, whereas the highest
total extensional strain occurs above the other ridge flank. Margin-normal displacements vary across the
ridge, resulting in areas of margin-normal shortening at the ridge tip and of margin-normal extension
where the maximum uplift rate occurs. Margin-parallel displacements and strain also show different
maximum values above the two ridge flanks. Similar results were obtained from the experiment with an
angle of 30° between margin and ridge (Figure S1 in the supporting information).
3.1.2. Migrating Ridges
In the first two experiments, we consider ridges that are perpendicular to the trench but migrate along the
margin because the plate convergence direction is oblique (60° and 30°; Figure 3). The vertical
displacement field at 1.5 Ma of model time obtained from these experiments is almost the same as for a
ridge oriented perpendicular to the margin, but the distribution of the vertical displacement rates
averaged over 100 ka shows an asymmetric pattern (Figures 3a and 3b). In the experiment with a plate
convergence direction of 60°, the maximum uplift rate of 2.8 mm/a occurs above the ridge tip (Figure 3a).
Above the leading and trailing ridge flanks, uplift and subsidence rates of up to 1.7 mm/a are observed.
Both uplift and subsidence rates increase for a plate convergence direction of 30° (Figure 3b). In both
experiments, the total horizontal displacements as well as the total strain are asymmetric relative to the
ridge axis with the highest contractional strain occurring above the leading ridge flank. The margin-normal
displacement fields show only a slight asymmetry relative to the ridge crest and two maxima at the ridge
tip and near the trench, respectively. In contrast, margin-parallel displacements and strains are
characterized by a more pronounced asymmetry, which increases for the lower plate convergence direction.
From the series of experiments, in which we varied the plate convergence direction and the orientation of the
ridge, we show selected examples in Figure 4 (for results from other experiments see Figure S2 in the
supporting information). In all experiments, the vertical displacement reflects the shape of the ridge, but
rates of uplift and subsidence vary between different experiments. If the plate convergence direction is
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Figure 2. Displacement and strain fields (shown in top view for the central part of the forearc wedge) obtained from
experiments with a non-migrating ridge and an erosive forearc. (a) Ridge and plate convergence are perpendicular to
the margin (α = ϕ = 90°). (b) Ridge and plate convergence direction form an angle of 60° with the margin (α = ϕ = 60°).
Shown for model times of 0.5, 1, and 1.5 Ma are the vertical displacement, the rate of vertical displacement (averaged over
100 ka), the total horizontal displacement (shown color coded and by black arrows in the region above the ridge), and the
total horizontal strain. Positive and negative strain values indicate shortening and extension, respectively. Note that the
total strain is derived from the largest absolute value of the principal strains (i.e., a value of 0.01 implies that the minimum
principal strain at this point shows extension and has a larger absolute value than the maximum principal strain; this strain
measure therefore allows differentiating between areas of net extension or shortening). The horizontal displacement and
strain field normal and parallel to the margin, respectively, are shown at 1.5 Ma of model time. Except for the rate of vertical
displacement, all results are shown relative to the beginning of the model run (i.e., 0 Ma model time). Thick white arrows
indicate the plate convergence direction, and dashed white lines denote the ridge position underneath the forearc. Results for
α = 30° are shown in Figure S1 (supporting information).
perpendicular to the margin (Figures 4a and 4b) or has the opposite orientation than the ridge relative to the
margin (Figures 4c and S2), maximum rates of uplift and subsidence occur above the leading and trailing
ridge flanks, respectively. Furthermore, uplift and subsidence rates have similar values and increase for
lower plate convergence angles (Figure S2). In contrast, the highest uplift rates occur above the frontal
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Figure 3. Displacement and strain fields (shown in top view for the central part of the forearc wedge) obtained from
experiments with migrating ridges oriented perpendicular to an erosive forearc. Shown are, at a model time of 1.5 Ma and
for plate convergence directions of (a) α = 60° and (b) α = 30°, the vertical displacement, the rate of vertical displacement
(averaged over 100 ka), the total horizontal displacement (color coded and black arrows in the region above the ridge) and its
trench-normal and trench-parallel components, the total strain, and the trench-normal and trench-parallel horizontal strain.
Positive and negative strain values indicate shortening and extension, respectively. Thick white arrows indicate the plate
convergence direction, and dashed white lines denote the ridge position underneath the forearc.
part of the ridge if the arrow of the plate convergence direction points in the same direction as the ridge
(Figures 4d and S2c). Also, uplift rates are generally higher than the subsidence rates in these experiments.
The total displacement and strain fields are asymmetric with respect to the ridge axis. Maximum
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Figure 4. Displacement and strain fields (shown in top view for the central part of the forearc wedge) from selected
experiments with migrating ridges oriented oblique to an erosive forearc (cf. Figure 1c). (a) Plate convergence direction
is α = 90°, and ridge is oriented ϕ = 60° with respect to the margin; (b) α = 90° and ϕ = 30°; (c) α = 60° and ϕ = 30°; and
(d) α = 60° and ϕ = 30°. Shown at a model time of 1.5 Ma are the vertical displacement, the rate of vertical displacement, the
total horizontal displacement (color coded and black arrows in the region above the ridge), and the total horizontal
strain. Positive and negative strain values indicate shortening and extension, respectively. Thick white arrows indicate
the plate convergence direction, and dashed white lines denote the ridge position underneath the forearc. Results for other
oblique ridge orientations (cf. Figure 1c) are shown in Figure S2 (supporting information).
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shortening occurs in front of the ridge and at the toes of the leading ridge flank. Near the ridge crest,
extension prevails.
3.2. Results From Experiments With Accretive Forearcs
All experiments were also performed with a forearc structure that includes an accretionary prism (Figure 5).
As for the models with erosive forearcs, the displacement and strain patterns are symmetric relative to the ridge
axis only if the ridge axis and convergence direction are perpendicular to the trench. The forearc material moves
radially away from the frontal part of the ridge (Figure 5a). Generally, the amount and rate of the vertical
displacement are similar to the models with an erosive forearc (not shown in figure), whereas the horizontal
displacement and strain patterns differ in magnitude and distribution (cf. Figures 2–5). Notably, the
maximum of the total horizontal displacement is located above the frontal part of the wedge in the accretive
models, while most erosive models show the maximum displacement above the ridge tip. Hence, the
models with an accretive forearc show an elongated, margin-parallel zone of shortening between trench
and landward end of the accretionary prism. The strain distribution in this zone depends on the orientation
of ridge, trench, and plate convergence direction. Most models show strain localization at the landward end
of the accretionary prism (e.g., Figures 5a–5e). However, in the experiments with ridges that form an angle of
30° with the margin, the strain is distributed rather homogeneously (Figure 5g) or may even change to
extension above the trailing ridge flank (Figure 5h). In the shortened area in front of the ridge and in the
extended area above the ridge tip, the accretive models show slightly lower values than the erosive models.
4. Results From Models for the Cocos, Nazca, and Gagua Ridges
In the following, we present the results from three models, in which we adjusted the ridge height and width
as well as the plate convergence direction and velocity to the settings of the Cocos, Nazca, and Gagua Ridges.
In contrast to the results from the general models, which are shown as the difference between the
experiments with and without a ridge, the results for the case studies are shown without subtracting the
results from experiments without a ridge. Therefore, the modeled displacement, strain, and stress fields
can be directly compared with geological data (see section 5).
4.1. Cocos Ridge Model
The ~2 km high and ~300 km wide Cocos Ridge (Figure 6a) extends for ~1000 km across the Cocos Plate in
the eastern Pacific and subducts beneath the Central American margin that is characterized by subduction
erosion [e.g., Ranero and von Huene, 2000]. The Cocos Ridge formed in the Miocene and represents the
trace of the Galapagos hotspot [Barckhausen et al., 2001; Meschede and Barckhausen, 2001]. Although the
exact values of plate convergence directions and velocities vary in different publications, all estimates show
that the Cocos Ridge is approximately parallel to the convergence direction of the Cocos Plate, with the
result that the collision zone has remained almost stationary since the ridge started to subduct [e.g., Gardner
et al., 1992, 2013; Sitchler et al., 2007; Morell et al., 2011]. The onset of ridge subduction is still under debate,
with estimates reaching from 8–5 Ma [e.g., Abratis and Wörner, 2001] to 1–0.5 Ma [Lonsdale and Klitgord,
1978; Gardner et al., 1992]. More recent studies suggest that ridge subduction started 3–1.5 Ma ago
[MacMillan et al., 2004; Morell et al., 2012; Gardner et al., 2013].
In our model adjusted to the Cocos Ridge, we use a 300 km wide and 2 km high symmetric ridge, which is
oriented perpendicular to the forearc, and a convergence velocity of 92 mm/a [DeMets et al., 1994, http://
www.unavco.org] parallel to the ridge axis. The deformation and strain patterns induced by the
subducting ridge are symmetric relative to the ridge axis (Figure 6). The distribution of the vertical
displacement shows that the uplift is not uniform along the ridge axis but that two zones of uplift exist
above the frontal part of the ridge and near the trench, respectively (Figure 6b). Maximum uplift rates
decrease over time from ~7.5 mm/a at 0.5 Ma after the onset of ridge subduction to 4 mm/a at 2 Ma
(Figure 6c). Seaward of the uplifted zone, the forearc subsides at rates of up to 1 mm/a. The total
horizontal displacement field shows a broad area with landward movements of the forearc, which reach a
maximum of ~3 km near the trench at 1.5 Ma (Figure 6d), which also represents the largest landward
indentation of the model forearc. Above the ridge flanks, the total displacement vectors gradually become
shorter toward the rear edge of the forearc wedge and change their direction from trench-normal to almost
trench-parallel close to the fixed landward edge of the forearc wedge. This displacement pattern results in
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Figure 5. Horizontal displacement and total strain fields (shown at 1.5 Ma model time in top view for the central part of the
forearc wedge) from selected experiments with an accretive forearc and stationary and migrating ridges (note that vertical
displacements are similar for erosive and accretive forearcs and hence not shown in this figure). Shown are results from
models with non-migrating ridges with trench-normal plate convergence direction and ridge axis (a) α = ϕ = 90° and
(b) α = ϕ = 60°. From experiments with migrating ridges, results are shown for the following plate convergence directions
and ridge orientations: (c) α = 60°, ϕ = 90°; (d) α = 30°, ϕ = 90°; (e) α = 90°, ϕ = 60°; (f) α = 90°, ϕ = 30°; (g) α = 60°, ϕ = 30°;
and (h) α = 60°, ϕ = 30°. Black arrows show total horizontal displacements in the region above the ridge. Thick white
arrows indicate the plate convergence direction, and dashed white lines denote the ridge position underneath the forearc.
Positive and negative strain values indicate shortening and extension, respectively.
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Figure 6. (a) Location map of the Cocos Ridge, which subducts approximately stationary beneath the erosive Central
American margin (TM: Talamanca Mountains; FC: Fila Costeña; OP: Osa Peninsula; BP: Burica Peninsula). Topographic/
bathymetric data are SRTM30_PLUS [Becker et al., 2009]. Results from the model, in which the ridge height and width as well
as the plate convergence direction and velocity were adjusted to the setting of the Cocos Ridge: shown at 0.5, 1, 1.5, and
2 Ma are (b) the vertical displacement, (c) the rate of vertical displacement (averaged over 100 ka), (d) the total horizontal
displacement (color coded and black arrows in the region above the ridge), and (e) the total strain. (f) Trench-normal
and trench-parallel strain as well as (g) the maximum and minimum principal stresses are shown at 2 Ma, which represents
our preferred scenario concerning the present position of the Cocos Ridge beneath Central America (see text for details).
Positive and negative strain values indicate shortening and extension, respectively. Thick white arrows indicate the plate
convergence direction, and dashed white lines denote the ridge position underneath the forearc. Dashed grey line
schematically indicates the approximate location of the present-day coastline.
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alternating zones dominated by trench-normal shortening and trench-parallel extension, respectively, which
are as wide as the model ridge and strike parallel to the trench (Figures 6e and 6f). At the end of the model
run (2 Ma), the center of the forearc shows a broad zone of trench-normal shortening (Figures 6e and 6f).
Near its landward edge, extension prevails. The broad zone of shortening is characterized by a subhorizontal
orientation of the maximum principal stress σ 1 and a subvertical orientation of the minimum principal stress
σ 3, whereas σ 1 and σ 3 have vertical and horizontal orientations, respectively, in the extended area (Figure 6g).
4.2. Nazca Ridge Model
The ~1.5 km high and 200 km wide Nazca Ridge stretches more than 1100 km across the southeastern Pacific
and subducts beneath the Peruvian continental margin (Figure 7a), whose forearc has been shaped by longterm tectonic erosion [von Huene and Lallemand, 1990; Clift et al., 2003; Hampel et al., 2004a]. Plate
reconstructions showed that the Nazca Ridge started to subduct 11 Ma ago at ~11.2°S and since then
migrated southeastward along the Peruvian margin to its present position between 14 and 16°S [Hampel,
2002]. The present collision zone has been affected by the Nazca Ridge since 4–5 Ma [Macharé and Ortlieb,
1992; Hampel, 2002; Rosenbaum et al., 2005].
In our Nazca Ridge model, we use a 200 km wide and a 1.5 km high model ridge subducting beneath an
erosive forearc. We apply a plate convergence velocity of 77 mm/a and a convergence angle of 60° relative
to the margin [DeMets et al., 1994, http://www.unavco.org]. To take into account that the present collision
zone of the Nazca Ridge is not influenced by the deformation around the ridge tip, which is already
located beneath the Amazonian Basin [Hampel, 2002; Rosenbaum et al., 2005; Espurt et al., 2007], we
analyze the results for a time interval of 4 Ma after the tip of the model ridge has passed the landward side
of the forearc wedge. As the results at the end of the model run (= present) show, the vertical
displacements as well as uplift and subsidence rates are distributed almost symmetric relative to the ridge
axis (Figures 7b and 7c). The forearc above the leading flank of the ridge is uplifted at maximum rates of
1 mm/a, whereas the material above the trailing ridge flank subsides at rates of up to 1.1 mm/a. This
pattern of uplift and subsidence rates has migrated along the forearc wedge to its position at the end of
the model run (Figure 7c). In contrast to the vertical displacements, the total horizontal displacement and the
total strain fields are asymmetric with respect to the ridge axis (Figures 7d and 7e) and dominated by the
margin-parallel component (cf. Figures 7f–7i). The margin-normal displacements indicate an indentation
of the forearc of not more than a few hundred meters (Figure 7f), with the result that margin-normal
shortening of the forearc is negligible (Figure 7g). In the margin-parallel direction, extensional strain
occurs in a 100 to 150 km wide area above the ridge crest, whereas the transition zones between ridge
flanks and surrounding oceanic plate are characterized by shortening (Figure 7i). This pattern is
recognizable in the total strain (Figure 7e) and relates to the orientations of the maximum and minimum
principal stresses (Figure 7j). In the extended area, the maximum principal stress σ 1 is subvertical and
the minimum principal stress σ 3 is subhorizontal. In contrast, σ 1 and σ 3 are horizontal and vertical,
respectively, in the areas with contractional strain (Figure 7e).
4.3. Gagua Ridge Model
Located on the Philippine Sea Plate in the western Pacific, the 350 km long Gagua Ridge subducts beneath
the accretionary prism of the Ryukyu margin (Figure 8a) [e.g., Lallemand et al., 1999]. The N-S striking
Gagua Ridge is up to 4 km high, with an average elevation above the surrounding seafloor of ~2.5 km, but
only 25 km wide [Dominguez et al., 1998; Lallemand et al., 1999]. The plate convergence rate is 66 mm/a at
an angle of 40° relative to the Ryukyu margin [DeMets et al., 1994, http://www.unavco.org]. The oblique
convergence has led to strain partitioning, which is accommodated by a major right-lateral strike-slip fault
in the Ryukyu forearc [Lallemand et al., 1999]. With respect to the onset of ridge subduction, some authors
argue that the ridge has been subducted beneath the Ryukyu margin since at least the Pliocene [Sibuet
et al., 2002], whereas others argue that ridge subduction started less than 1 Ma ago [Dominguez et al., 1998].
In the model adjusted to the Gagua Ridge, we use a 25 km wide and 2.5 km high model ridge and the setup
for an accretive forearc. The results of the model, which is run for 3 Ma, are depicted in Figure 8. The vertical
displacement field shows an initially symmetric pattern of uplift at 1 Ma, with values equivalent to the ridge
height. Until 3 Ma, uplift above the ridge crest increases to more than 3 km. In the wake of the migrating
ridge, a zone of several hundred meters of subsidence develops (Figure 8b). Rates of uplift and subsidence
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Figure 7. (a) Location map of the Nazca Ridge, which migrates along the erosive Peruvian margin. Topographic/bathymetric
data are SRTM30_PLUS [Becker et al., 2009]. Results from the model, in which the ridge height and width as well as the plate
convergence direction and velocity were adjusted to the setting of the Nazca Ridge. Results are shown at the end of the model
run (=0 ka, i.e., the present). (b) Amount and rate of vertical displacement (the latter averaged over 100 ka). Dashed black line
marks the position of the profiles shown in Figure 7c. (c) Diagram showing the finite vertical displacement and the rate of
vertical displacement at four different model times along profile at a distance of the trench approximately equivalent to the
distance between Peruvian trench and coast in nature (dashed black line in Figure 7b; note that the profiles cover a longer
distance parallel to the trench than indicated in Figure 7b). Model time 0 Ma represents the present and refers to the end of the
model run, 1 Ma is equivalent to 1 Ma before present, and so on. Colored dashed lines indicate the position of the ridge axis at
the different model times. (d) Total horizontal displacement, (e) total strain, (f) trench-normal displacement, (g) trench-normal
strain, (h) trench-parallel displacement, (i) trench-parallel strain, and (j) maximum and minimum principal stresses at 0 Ma
(present). Positive and negative strain values indicate shortening and extension, respectively. Thick white arrows indicate the
plate convergence direction, and dashed white lines denote the ridge position underneath the forearc. Dashed grey line
schematically indicates the approximate location of the present-day coastline.
rates averaged over 100 ka attain values of >15 mm/a above the leading and trailing flanks of the ridge,
respectively (Figure 8c). The total horizontal displacement is dominated by margin-parallel movements due to
the low angle between plate convergence direction and the forearc wedge (Figure 8d). An asymmetric
reentrant (i.e., the horizontal indentation of the forearc away from the trench by the subducting ridge)
develops, whose depth increases from ~1 km at 0.5 Ma to ~6.5 km at 3 Ma (Figures 8d and 8h). The location of
the deepest point of the reentrant shifts laterally away from the ridge over time. With respect to the strain
evolution, the total strain field shows shortening in the accretionary prism near the trench and slight extension
above the frontal part of the ridge (Figure 8e). Inspection of the trench-normal and trench-parallel strain
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Figure 8. (a) Location map of the Gagua Ridge, which migrates along the accretive Ryukyu margin (WNB: Western Nanao
Basin; ENB: Eastern Nanao Basin). Topographic/bathymetric data are SRTM30_PLUS [Becker et al., 2009]. Results from the
model, in which the ridge height and width as well as the plate convergence direction and velocity were adjusted to the
setting of the Gagua Ridge. Shown at 1, 2, and 3 Ma are (b) the vertical displacement, (c) the rate of vertical displacement
(averaged over 100 ka), (d) the total horizontal displacement (color coded and black arrows in the region above the ridge),
(e) the total strain, (f) the trench-normal strain, and (g) the trench-parallel strain. Positive and negative strain values indicate
shortening and extension, respectively. (h) Diagram with the depth of the reentrant (colored dashed lines in Figure 8e
indicate the position of the ridge axis at the different model times). (i) Maximum and minimum principal stresses at 1 Ma,
in which the position of the ridge corresponds to the inferred position of the already subducted bathymetric high in
prolongation of the Gagua Ridge [Dominguez et al., 1998] (see text for details). Thick white arrows indicate the plate
convergence direction, and dashed white lines denote the ridge position underneath the forearc.
components reveals that this strain pattern is primarily caused by the trench-parallel strain (Figures 8f and 8g). For
example, the trench-normal component shows some extension of the accretionary prism near the trench above
the ridge, but trench-parallel shortening attains higher values than the extensional strain. In the wake of the ridge,
zones of contractional and extensional strain develop landward of the reentrant. Again, the trench-normal strain
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component shows extension where trench-parallel component yields shortening and vice versa (Figures 8f and
8g). The principal stress field at 1 Ma of model time (our preferred position of the ridge tip; see section 5.2.3)
near the ridge shows that the maximum principal stress σ 1 is vertical close to the trench and becomes
subhorizontal toward the ridge tip (Figure 8i). The minimum principal stress σ 3 is horizontal above the ridge
and oriented approximately parallel to the trench where the ridge affects the accretionary prism but subvertical
in the other parts of the forearc wedge. Notably, both σ 1 and σ 3 are subhorizontal around the ridge tip,
indicating a stress field typical of strike-slip faulting.
5. Discussion
5.1. General Models of Ridge Subduction
Our model results with variable angles between ridge, trench, and plate convergence direction have
revealed the general patterns of forearc deformation during ridge subduction. Only if the ridge and
plate convergence direction are perpendicular to the margin is the ridge-induced deformation
symmetrically distributed above the ridge flanks (Figure 2). In contrast, a ridge oriented perpendicular to
the trench but oblique to the plate convergence direction successively affects different portions of the
forearc, with the deformation pattern being asymmetrically relative to the ridge axis (Figure 3). For
ridges oriented oblique to the margin, both stationary and migrating ridges show strong asymmetric
deformation relative to the ridge axis (Figures 2 and 4). In models with stationary ridges, uplift rates are
highest above the ridge tip and decrease to around zero above the ridge crest (Figure 2). In contrast,
migrating ridges cause a wave of uplift and subsidence of the forearc (Figures 3 and 4), which was also
reported from analogue experiments [e.g., Hampel et al., 2004b; Martinod et al., 2013] and natural
collision zones [e.g., Hsu, 1992; Macharé and Ortlieb, 1992; Gutscher et al., 1999b]. Horizontal
displacement and strain patterns also vary through space and time for both stationary and migrating
ridges. In particular, a given forearc area may experience shortening followed by extension or vice versa
during the passage of the ridge. An additional model with a larger radius (300 km) of the cylinder
representing the oceanic plate in our models shows that a lower curvature of the oceanic plate increases
the rates of vertical displacement as well as the trench-normal displacement and strain components
whereas the components parallel to the trench are nearly unaffected (Figure S3 in the supporting
information). Another experiment, in which we reduced the subduction velocity by 50% to a value of
4.5 cm/a, shows that—for the same position of the ridge underneath the forearc—the deformation
patterns are the same as in the models with a velocity of 9 cm/a except that the rates of displacement
are 50% lower (Figure S4 in the supporting information).
Such variations in the displacement field in the forearc have also been reported from 3-D analogue models
but for a limited number of angles between ridge, trench, and plate convergence direction [e.g., Dominguez
et al., 1998; Hampel et al., 2004b; Martinod et al., 2013]. Our numerical models, which cover a larger variety of
angles, show that the strain maxima are typically located around and above the frontal part of the ridge but
tend to shift from the ridge tip to its flanks for lower angles between ridge axis and margin. Note that the
modeled displacement and strain patterns apply to the offshore and coastal forearc region, as our models
do not include the arc and back arc and neglect possible buoyancy effects of the subducting ridge, which
may become particularly important in the context of flat-slab subduction. Concerning the landward extent
of the region, over which the influence of the ridge may be recognizable, different notions exist. For
example, two-dimensional numerical models indicate that as soon as a ridge reaches asthenospheric
depths, the uplift signal starts to decay and finally disappears 200–300 km landward from the trench
[Gerya et al., 2009]. In contrast, Espurt et al. [2007] showed that the position of the subducted portion of
the Nazca Ridge correlates with the Fitzcarrald Arch, which is located 750 km landward of the Peruvian
trench at the western boundary of the Amazonian basin, and that the subducting ridge probably caused
the uplift of this dome-shaped area.
A comparison between models with erosive and accretive forearcs shows that although the principal
symmetric or asymmetric deformation patterns occur in both types of models, considerable differences
exist in the horizontal displacements and strain fields. The presence of an accretionary prism with
mechanically weak sediments leads to a localization of strain in the frontal part of the wedge. For example,
an elongated, trench-parallel zone primarily characterized by shortening develops ~50 km away from the
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Figure 9. Diagrams showing the indentation of the model forearc in landward direction (i.e., the reentrant created by the
subducting ridge) at 1.5 Ma of model time in the experiments with erosive and accretive forearcs. Shown are reentrants
caused by (a) stationary ridges, (b) trench-normal ridges, (c) ridges oriented at an angle of 60° with respect to the trench,
and (d) ridges oriented at an angle of 30° with respect to the trench. Colored dots indicate the intersection between ridge axis
and trench.
trench, which is less pronounced or absent in experiments with erosive forearcs (compare, for example,
Figures 2a and 2b with Figures 5a and 5b). With respect to the depth of the reentrant, accretive model
forearcs generally show somewhat deeper reentrants than erosive forearcs (Figure 9). Both accretive and
erosive forearcs show maximum indentation (~600 m and ~420 m, respectively) if the ridge and plate
convergence direction are perpendicular to the trench (Figure 9a). For oblique orientations of ridge and/or
plate convergence direction, the reentrant becomes asymmetric and its depth decreases (Figure 9). Note
that the deepest point of the reentrant and the ridge axis generally do not coincide, which was also
observed in analogue experiments [Martinod et al., 2013]. The width of the reentrant increases over time
and exceeds the ridge width by a factor of about 1.5–2 times when the ridge tip has reached a position
~100 km away from the trench. As the results from our models for the Cocos, Nazca, and Gagua Ridges
(section 5.2) suggest, the geometry of the reentrant also depends on the ridge height and ridge width,
with high and narrow ridges causing deeper reentrants than broader ridges. The relationship between
these parameters and the reentrant depth has been explored in another study (S. Zeumann and A.
Hampel, Three-dimensional finite element models on the deformation of forearcs caused by aseismic
ridge subduction: The role of ridge shape, friction coefficient of the plate interface and mechanical
properties of the forearc, submitted to Tectonophysics, 2015).
5.2. Comparison of Model Results With Geological Data From Case Studies
5.2.1. Cocos Ridge
The topographic map of Central America reveals several striking geomorphological features in the
landward prolongation of the Cocos Ridge (Figure 6a). Among them are the Osa und Burica Peninsulas,
which are located about 20–30 km away from the Central American Trench, a thrust belt called Fila
Costeña and—separated from the Fila Costeña by a valley—the Talamanca Range, which shows the
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largest width and highest peaks inboard of the Cocos Ridge (Figure 6a). The Burica Peninsula coincides
with the prolongation of the southeastern edge of the Cocos Ridge as well as with the northern end of
the Panama Fracture Zone [e.g., Gardner et al., 1992; Morell et al., 2011; Spikings and Simpson, 2014]. A wealth
of data exists on the uplift history of the peninsulas and the exhumation history of the Talamanca Range,
which many authors attribute at least partly to the subduction of the Cocos Ridge [e.g., Corrigan et al., 1990;
Sitchler et al., 2007; Morell et al., 2012; Gardner et al., 2013], although the onset of ridge subduction is still
under debate. In the following, we will discuss—based on our model results—two alternative scenarios for
the onset of ridge subduction against the background of the available geological data.
Our first and preferred scenario is based on the modeled spatial distribution of ridge-induced uplift, which
shows two areas with maximum values above the ridge tip and near the trench, respectively (Figure 6b). If
we correlate these two areas of maximum uplift with the location of the peninsulas and the highest part of
the Talamanca Range, the distance between them (approximately 80–100 km in nature) can be tentatively
used to infer the position of the ridge beneath the forearc from the model. Our preferred position is a
location of the ridge tip ~150 km away from the trench (Figure 6b). With the applied plate convergence
velocity of 92 mm/a, this implies that the Cocos Ridge started to subduct ~2 Ma ago, in agreement with
studies favoring an onset of ridge subduction during the Late Pliocene to Quaternary [Lonsdale and Klitgord,
1978; Gardner et al., 1992, 2013; MacMillan et al., 2004; Morell et al., 2012]. The maximum uplift rate in the
model averaged over 2 Ma is 1 mm/a at the location of the two peninsulas, which agrees well with the
average Quaternary uplift rate of ~1 mm/a derived from Pliocene marine sediments exposed on the Burica
Peninsula [Corrigan et al., 1990]. Above the northwestern flank of the Cocos Ridge, where an average
Quaternary uplift rate of ~0.4 mm/a was derived from sediment cores recovered at an Integrated Ocean
Drilling Program drilling site on the shelf northwest of the Osa Peninsula [Vannucchi et al., 2013], we obtain
average uplift rates around 0.5 mm/a since 2 Ma. Our preferred scenario also supports the findings by Morell
et al. [2012] who argue, based on thermochronological data, that only the Late Pliocene/Quaternary
exhumation history of the Talamanca Range can be linked to the subduction of the Cocos Ridge.
Our first scenario cannot explain the high uplift rates during the Late Quaternary that were derived from
marine terraces, incised river terraces, and young marine deposits raised above sea level. For example,
Morell et al. [2011] obtained uplift rates of 2–19 mm/a from 14C and optically stimulated luminescence
(OSL) ages from exposed marine deposits and soil chronosequences on the Burica Peninsula. Gardner et al.
[1992] derived an uplift rate of ~5 mm/a for late Holocene terrace on the Burica Peninsula. Radiocarbon
and OSL ages obtained from marine deposits across the Osa Peninsula also show high Late Quaternary
uplift rates between 2 and >6 mm/a [Gardner et al., 1992, 2013; Sak et al., 2004]. The latter authors argue
that the Cocos Ridge has a steep frontal part dipping 18°, which was positioned beneath the Osa
Peninsula ≤0.5 Ma ago, although the initial contact between ridge and forearc may have been established
as early as 1.5–3 Ma [Gardner et al., 1992, 2013; Sak et al., 2004]. Our modeled distribution of uplift rates at
0.5 Ma shows that such a late onset of ridge subduction can explain the high Late Quaternary uplift rates,
which is our second scenario, in which the Cocos Ridge has not yet reached a position beneath the
Talamanca Range. However, neither of the two scenarios (i.e., onset of ridge subduction at ~2 Ma or
≤0.5 Ma, respectively) can explain the high but spatially variable uplift rates of the Osa and Burica
Peninsulas during the Late Pleistocene/Holocene, which may be caused by seamounts and elongated
ridges on top of the Cocos Ridge [Sak et al., 2004; Gardner et al., 2013]. This also is indicated by the
observation that the reentrant of the Cocos Ridge is irregular and locally (i.e., opposite to the Osa and
Burica Peninsulas) 30–40 km deep in nature, while our model results indicate that a ridge with a smooth
surface should create a broad (~350 km) but only ~3 km deep reentrant (Figure 6d). Holocene uplift rates
may also be affected by site-dependent sea level changes [Woodroffe and Horton, 2005] and by the
vertical displacements during the seismic cycle.
With respect to the horizontal deformation patterns, our model results are consistent with GPS
measurements in Central America, which show NE-SW trending velocity vectors inboard of the highest
part of the Cocos Ridge and diverging vectors above the prolongation of the southeastern and
northwestern ridge flanks [LaFemina et al., 2009]. From the Osa and Burica Peninsulas, Corrigan et al.
[1990] report subhorizontal shortening perpendicular to the margin and margin-parallel extension derived
from faults and folds in Pliocene-Pleistocene sediments. In our model, a similar strain pattern is indicated
by the total displacement vectors, whose length decreases landward. As the vectors near the ridge axis
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slightly point away from the ridge crest, minor margin-parallel extension occurs close to the trench,
consistent with the observed pattern of faulting. Further landward, the NW-SE-striking, 20–30 km wide Fila
Costeña thrust belt has developed in former forearc basin sediments [Fisher et al., 2004; Sitchler et al.,
2007]. As noted by Sitchler et al. [2007], the number of thrust sheets increases from three above the flanks
of the Cocos Ridge to five above the ridge axis. From a balanced cross section located above the ridge
axis, Sitchler et al. [2007] derived a minimum amount of shortening of ~36 km (~58 %) at a rate of
~40 mm/a during the last ~1 Ma. The amount of shortening decreases toward the northwest and
southeast (i.e., above the ridge flanks) [Fisher et al., 2004; Sitchler et al., 2007]. The geologically derived
location and timing of active horizontal shortening inboard of the Cocos Ridge agrees well with our
preferred first scenario (onset of ridge subduction 2 Ma ago), in which a broad zone of marginperpendicular shortening develops during the last 1 Ma of model time where the Fila Costeña thrust belt
formed in nature. The amount of shortening in our model is about an order of magnitude lower than the
amount observed in the thrust belt, presumably because our model cannot capture the formation of the
thrust belt and the additional shortening caused by subducting seamounts. Alternatively, our model may
suggest that part of the shortening results from the plate convergence and/or underplating of tectonically
eroded forearc material and is only locally (i.e., above the ridge axis) enhanced by the subduction of the
Cocos Ridge [cf. Sitchler et al., 2007].
5.2.2. Nazca Ridge
At the modern collision zone between Nazca Ridge and the Peruvian margin, shoaling of the water depth by
~1.5 km along the sediment-starved trench from south of the Nazca Ridge to its crest documents the uplift of
the steep toe of the wedge by the underthrusting ridge [Hagen and Moberly, 1994; Hampel et al., 2004a]. Side
scan sonar and bathymetric images showed that the indentation of the forearc by Nazca Ridge is negligible
and that laterally continuous ridges indicative of thrust faulting are absent [Hagen and Moberly, 1994; Li and
Clark, 1994; Hampel et al., 2004a]. A similarly small reentrant and only minor shortening near the trench are
also predicted by our Nazca Ridge model (Figure 7). Rather than enhanced shortening as onboard of the
Cocos Ridge, the most pronounced effect of the subduction of the migrating Nazca Ridge is a propagating
wave of forearc uplift and subsidence, which is documented both in the geological record and as
observed in our numerical model. At the Peruvian coast between 13.5°S and 16°S, a series of marine
terraces located between modern sea level and an elevation of 900 m provides evidence for considerable
uplift of the forearc caused by the ridge [Hsu et al., 1989; Hsu, 1992; Saillard et al., 2011]. Uplift is
distributed asymmetrically with respect to the ridge axis, with the uplift maximum of ~900 m indicated by
the highest preserved terrace being located above its leading southern flank [Hsu et al., 1989; Hsu, 1992;
Macharé and Ortlieb, 1992]. In contrast, the forearc experiences net subsidence above the trailing ridge
flank [Macharé and Ortlieb, 1992; Le Roux et al., 2000]. Rates of uplift have been obtained by dating of the
marine terraces as well as the correlation with sea level highstands. Based on electron spin resonance and
amino acid racemization analyses, the lower terraces up to an elevation of 320 m were assigned ages
between 40 ka and >880 ka [Hsu et al., 1989; Hsu, 1992]. From the elevation of the terrace assumed to
have formed during the last interglacial at 125 ka, the same authors derived an uplift rate of ~0.5 m/ka.
Using an alternative correlation between the multiple terraces and the peaks of the oxygen-isotope curve,
Macharé and Ortlieb [1992] determined a maximum uplift rate of ~0.7 m/ka. Recent cosmogenic 10Be
exposure dating of the terraces showed that cumulative uplift rates have progressively increased since
~400 ka from ~0.4 to ~0.9 m/ka [Saillard et al., 2011]. Our modeled distribution of the finite vertical
displacements and uplift rates agree with these data. Notably, however, the modeled amount of uplift
along a profile ~60 km away from the trench is higher (~1.5 km; Figure 7c) than the elevation of the
highest preserved terrace and reflects the height of the ridge. Similarly high values of 1.2 km were
obtained by Hsu, [1992] based on a geometric model and by Hampel et al. [2004b] from 3-D analogue
models. Although one may argue that the discrepancy between observed and modeled maximum uplift
may be attributed to the neglect of isostatic effects in these models, numerical models of subduction zone
scale designed to analyze the link between Nazca Ridge and the Peruvian flat slab (and hence including
buoyancy) showed that forearc uplift is equal to or higher than the ridge relief [Gerya et al., 2009]. Therefore,
it seems more probable that marine terraces once existed at higher elevations but were subsequently
destroyed by erosion [Hsu 1992; Wipf et al., 2008]. Uplift of the forearc by more than 900 m is also supported
by the observation that strata found in the submarine part of the forearc at 12°S (i.e., north of the Nazca
Ridge) are exposed onshore where the Nazca Ridge subducts [Hsu, 1992; Macharé and Ortlieb, 1992].
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In the coastal region of South Peru, Quaternary normal faulting documents horizontal extension above the
subducted part of the Nazca Ridge [Sébrier et al., 1985, 1988]. The extension direction varies from
predominantly N-S above the leading ridge flank to NE-SW above the toe of the northern flank [Sébrier
et al., 1985, 1988; Mercier et al., 1992]. Some of these faults offset Pleistocene marine terraces and hence
postdate them in age [Sébrier et al., 1985; Saillard et al., 2011]. In our model, we obtain extensional strain
above the ridge, compatible with the observed normal faulting at the Peruvian coast. Also, the orientation
of the minimum principal stress axes and their rotation from the leading to the trailing ridge flank
(Figure 7j) agree well with the stress axes derived from normal faults [Sébrier et al., 1985; Saillard et al., 2011].
5.2.3. Gagua Ridge
High-resolution bathymetric data from the collision zone between Gagua Ridge and Ryukyu margin show
that the ~60 km wide accretionary prism is indented by ~20 km where the northern end of the Gagua
ridge intersects the trench [Dominguez et al., 1998; Schnürle et al., 1998; Lallemand et al., 1999]. The
reentrant is ~20 km wide and highly asymmetric with respect to the ridge axis, with the ridge being
located close to the western boundary of the reentrant. Despite the steep slope (~20°) of the reentrant
walls, there are no signs of slumping. The actual contact between the ridge and the accretionary prism is
obscured by a ~2 km thick pile of turbidites delivered from the west [Lallemand et al., 1999]. The region
north of the reentrant, in prolongation of the Gagua ridge, is uplifted and characterized by conjugate
strike-slip faults that diverge to the NW and NE, respectively [Dominguez et al., 1998; Lallemand et al.,
1999]. The orientation of the conjugate faults indicates a horizontal compression and implies that the
maximum and minimum principal stress axes are rotated at the collision zone compared to the adjacent
unaffected by ridge subduction [Wu et al., 2010]. North of the area, where the Gagua Ridge enters the
trench, a pronounced topographic high is located, which separates the Nanao and East Nanao Basins
(Figure 8) [Dominguez et al., 1998; Lallemand et al., 1999]. In 2001, this area was ruptured by an Mw 6.8
oblique normal fault earthquake, which occurred at a depth of ~12 km [Konstantinou et al., 2011].
The obvious coincidence between the northern end of the Gagua Ridge, the deep reentrant, and the
topographic high in prolongation of the ridge has led to a discussion how far the Gagua Ridge extends
beneath the Ryukyu margin and when its subduction started. While some authors argue that the ridge
extends beneath the Ryukyu margin and has been subducted since at least the Pliocene [e.g., Schnürle
et al., 1998; Sibuet et al., 2002], others relate the deep reentrant, the network of conjugate strike-slip faults,
and the topographic high between the East and West Nanao Basins to an already subducted feature
(seamount or smaller ridge) in front of the Gagua Ridge [Dominguez et al., 1998]. According to plate
reconstructions by Dominguez et al. [1998], this feature began to subduct ~1 Ma ago, whereas the
northern end of the main Gagua Ridge presently located in the trench had not yet started to subduct. The
same authors also argue that the accretionary prism east of the Gagua Ridge does not show signs of uplift
or deformation indicative of a westward sweeping of the ridge. Our model results support this
argumentation as they indicate that a broad (but not deep) reentrant should develop in the wake of the
migrating ridge if ridge subduction continued for 1 Ma or longer (Figure 8h). Also, our model results
suggest that the principal stress and strain axes should vary along strike of the forearc as a result of ridge
migration, which is not recognizable at the Ryukyu margin east of the Gagua Ridge [Wu et al., 2010]. A
position of the subducted feature beneath the topographic high as indicated by analogue experiments
and plate reconstructions [Dominguez et al., 1998] as well as seismic and seismological data [Konstantinou
et al., 2011] agrees well with the displacement and strain fields at 1 Ma (Figure 8). Notably, the orientation
of the strike-slip faults above the leading seamount flank, the corresponding direction of horizontal
compression, and the rotation of the stress axes compare well with our modeled stress field, which shows
subhorizontal orientations of both σ 1 and σ 3 around the ridge tip (Figure 8i). The deep reentrant as well as
the scar caused by slumping on the rear flank of the subducted seamount can, however, not be captured
by our model due to the elongated shape of the model ridge.
6. Conclusions
Using a series of numerical models, we have analyzed how the subduction of aseismic ridges affects the
forearc wedge. In all experiments, the forearc is uplifted and moves away from the advancing ridge.
Most important for the style and distribution of deformation above the subducting ridge are the angles
between the ridge, the plate convergence direction, and the margin, while the contrast in the mechanical
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strength between erosive and accretive forearcs plays a lesser role. The distribution of the rates of vertical
displacement as well as the horizontal displacements and strains are generally asymmetric along strike of the
forearc and relative to the ridge axis. This includes the cases in which plate convergence direction and ridge
are parallel but oblique to the margin. Only if ridge and plate convergence direction are oriented
perpendicular to the trench is the deformation symmetric relative to the ridge axis and along strike of the
margin. For stationary ridges, the highest uplift rates occur in front of the ridge and above its tip. In contrast,
migrating ridges cause a wave of uplift above the leading flank followed by subsidence above the trailing
flank. The magnitude of the modeled uplift rates agrees well with uplift rates derived, for instance, from
marine terraces and supports the results from studies that concluded that subduction of aseismic ridges may
enhance uplift and exhumation of rocks in the upper plate. Similar to the vertical displacements, horizontal
displacement and strain pattern change through space and time during the passage of a subducting ridge.
Our experiments further indicate that the differences in the deformation patterns developing in accretive
and erosive forearcs are most pronounced in the frontal part of the wedge, where the presence or absence
of an accretionary prism controls the mechanical strength of the forearc. Reentrants are generally larger for
accretive forearcs than for erosive forearcs, but their size also increases with increasing height of the ridge, as
shown by the models adjusted to the case studies. The results from the models adjusted to the Cocos,
Nazca, and Gagua Ridges show an overall good agreement with deformation patterns reported from these
margins and provide constraints on the onset of subduction of the Cocos and Gagua Ridges. The case
studies also indicate that the ridge height and width as well as the presence of seamounts on the ridge
may also play an important role. In future experiments, we will investigate the effect of the ridge
geometry, the mechanical strength of the forearc, and the friction coefficient along the plate interface
on the forearc deformation.
Acknowledgments
We thank the Associate Editor J. van
Hunen, V. C. Manea, and an anonymous
reviewer for their constructive comments. Funding by the Deutsche
Forschungsgemeinschaft (DFG) is
gratefully acknowledged (grant
HA3473/7-1). Some of the figures were
created using the Generic Mapping
Tools (GMT) [Wessel and Smith, 1998].
The data for this paper are available by
contacting the corresponding author.
ZEUMANN AND HAMPEL
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