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Investigating the 3-D effects of mantle flow, melt production and melt
transport in the Eastern Lau Spreading Center: Slab Dominated Flow
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Electronic Signature
Investigating the 3-D effects of mantle flow, melt production and melt transport in the
Eastern Lau Spreading Center: Slab Dominated Flow?
Nicholas Harmon (R2K postdoc applicant) and Donna K Blackman (supervisor)
Project Summary
Scientific Merit. While passive flow induced by slab pull is widely considered the cause of
upwelling and broadly distributed decompression melting at mid-ocean ridges, the processes that
produce new crust at back arc spreading centers, where there is no direct pull from the
subducting slab, are poorly understood. The presence of a subducting slab influences the
formation of back arc spreading centers but its role, either by creating corner flow in the mantle
wedge or by lithospheric stresses caused by trench rollback, is not well constrained. The Eastern
Lau Spreading Center is a back arc spreading center that shows significant variations in
geochemistry, ridge morphology, crustal thickness and spreading rate over its ~400 km length,
making it an ideal place to test hypotheses of the effects of subduction induced lithospheric
stresses and mantle flow on melt migration/production at these spreading ridge systems. In a
broader context, the Tonga subduction zone also plays host to along strike variations in
convergence rate and up to a 100 mm/yr rollback rate towards the east. These variations may
lead to 3-D flow in the mantle wedge, beyond the simple corner flow created by the slab.
I propose to develop site-specific numerical models of the Lau Basin/Tongan Subduction
zone incorporating existing geodetic, marine geophysical and seismic observations to explore the
role of subduction in back arc spreading and the effects of 3-D mantle flow in the development
of the Eastern Lau spreading center. These models will predict mantle flow, melt production and
melt transport in the region. I will then use these models to generate predictions for seismic
anisotropy in the region. In addition, the models will be used to optimize the funded passive
source seismic station geometry of Wiens et al. to observe mantle flow in the region.
The goal of this research is to determine the relationship between the subducting slab and
back arc spreading. Are stresses generated by corner flow in the mantle wedge great enough to
create rifting, or is trench rollback “pull” the dominant stress? Is mantle flow in the region
controlled by the subducting slab or do the 3-D effects from trench rollback or plume influx from
Samoa control the mantle flow pattern as observed by seismic anisotropy? This work will also
help us understand the potential interaction between the arc melt generation region with the
ELSC melt generation region.
The work proposed here will directly benefit the RIDGE2000 science agenda. It will
generate models of the Eastern Lau Spreading Center ISS to test hypotheses of mantle flow,
ridge formation and development in a supra subduction zone setting. These models will also aid
in the interpretation of existing geochemical and geophysical data from the region, in addition to
planned seismic deployments in the region. Furthermore, these models will aid in site selection
for the planned seismic deployment to maximize the resolution of mantle flow.
Broader Impacts. Harmon, a new PhD, will receive training in numerical modeling and
combine this new skill with his prior experience in observational geophysics to apply results to
an oceanic spreading center environment- a new area of study for him. As a new member of the
Ridge 2000 community, Harmon will contribute insights he developed during thesis studies in
other tectonic settings and he will gain from interaction with this multi-disciplinary, national
group of researchers. Being part of the SIO community will also provide opportunities for
broader scientific growth as Harmon begins his post-graduate career.
Personal Statement- Nick Harmon
Understanding oceanic lithosphere, which spans the birth of plates at mid-ocean ridges to
their interment at subduction zones, is central to understanding plate tectonics. However, while
slab pull is generally accepted as the dominant driving force of plate tectonics, the interaction of
plates with mantle convection is poorly understood. The oceanic lithosphere provides an
excellent laboratory to test hypotheses about plate tectonics and mantle dynamics because of the
simple histories and geometries unfettered by multiple tectonic events. Yet as simple as the
oceans are, they often host a variety of small-scale anomalies such as the gravity lineations,
which I studied in my thesis. The study of ocean mantle dynamics and tectonics provides a host
of rich and interesting phenomena that I am interested in exploring.
In my career, I want to continue to expand our understanding of oceanic lithosphere,
mantle dynamics and plate tectonics on two broad fronts: observational geophysics and
geodynamics. Fortunately, during my studies at Brown University, I had the opportunity to use
both marine geophysics and marine seismology in the pursuit of my dissertation research on
intraplate volcanism. I want continue to use observational geophysical techniques to constrain
the physical parameters of the dynamics of the upper mantle such as the isotropic and anisotropic
seismic velocity structure, and relative density structure. Oceans cover ~70% of the earth’s
surface, yet seismic coverage in this broad region of the earth’s surface is extremely sparse.
Nevertheless, the development of broadband Ocean Bottom Seismometers (OBS) capable of
being deployed for over 12 months will begin to fill in the gaps in global seismic network
coverage and allow direct seismological measurements on oceanic lithosphere. These new
capabilities will illuminate a great deal of information about the nature of the upper mantle and I
want to continue to contribute to this science.
For my postdoctoral research, I would like to develop numerical models of mantle flow and
integrate these models with seismic measurements of anisotropy. Modeling provides a basis for
putting observations in context. If I want to be able to interpret the observations that I make
during my career it is imperative that I integrate geophysics with geodynamics to understand the
earth. While I do not envision myself as solely a geodynamicist, I believe that having a solid
grounding in numerical simulation of mantle flow will enhance my ability to communicate with
collaborators in that field. My graduate career included class work in numerical modeling,
scientific computing, and fluid dynamics; however, I did not apply this knowledge in a
substantial research project. I see the postdoctoral research proposed here as a way to deepen my
understanding of my graduate course work through hands on experience and expand the breadth
of my knowledge to make me more effective in my ability to interpret data and communicate
with the greater scientific community.
My dissertation research project, the Gravity Lineation Intraplate Melting Seismic and
Petrologic Expedition, was a large multidisciplinary experiment, combining marine geophysics,
seismology, and geochemistry. The collaborative effort between several institutions impressed
me with the power of teamwork and approaching problems from several different directions.
This style of science is one that I want to embrace in my career. To be successful I must develop
a broad range of expertise in geophysics.
The RIDGE 2000 initiative encourages the development of interdisciplinary research with
its goal of understanding “mantle to microbes” and is consistent with my own goals in many
ways. First, it encourages a broad range of scientists from geodynamicists to biologists to
collaborate to understand the fundamental processes that occur at spreading ridges. This
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interdisciplinary, integrative scientific approach has been the hallmark of my graduate education,
and by moving into the RIDGE program, I can continue with this style of science. Secondly, my
research interests are focused on understanding ocean mantle dynamics and plate tectonics.
Spreading at mid ocean ridges, which generates new oceanic lithosphere, is a fundamental
process in plate tectonics which I have not had the opportunity to study extensively. This
postdoctoral fellowship will greatly improve my understanding of this process in a collaborative
scientific atmosphere.
In addition to broadening my own background, I believe a large part of the mandate of
scientific research is education. During my undergraduate career, I worked as a literacy tutor in
an inner city public school in Roxbury, MA, and during graduate school, I have been active in a
science outreach program at a primary school in Providence, RI. At Brown, I have been a
teaching assistant for two courses and have thoroughly enjoyed my teaching experience to date. I
would like to continue doing science outreach programs through my postdoctoral work because
nothing motivates a child to become interested in science more than seeing someone who is
pursuing science actively and enthusiastically.
Scripps Institute of Oceanography, because of its emphasis on oceanic research and broad
range of expertise, is the ideal place to develop my career goals. The potential for collaboration
at the institution is very good and the resources, in terms of research facilities and infrastructure,
are outstanding. Donna Blackman, my prospective advisor, has expertise in developing
numerical models and observational geophysics, and perhaps more importantly in integrating
models with seismic observations. I believe that working with her at Scripps will provide an
excellent opportunity to develop along the career trajectory I see for myself.
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Dissertation Overview- Nick Harmon
My current research interests are focused on understanding mantle dynamic processes
through observational geophysics in marine settings. The bulk of my dissertation work to date
has been focused on understanding the origin of a series of non-hotspot intraplate volcanic ridge
systems in the Pacific Ocean that are not associated with a spreading ridge or subduction zone.
These ridge systems are coincident with lineated gravity anomalies that trend parallel to the
spreading direction of the Pacific Plate. In fact, these seamounts represent a volcanic process not
explained by plate tectonics and therefore might provide insight into the finer scale dynamics of
mantle flow and lithospheric interaction. In the pursuit of this investigation, I have employed
standard marine geophysical techniques including gravity and topography analysis, as well as
seismic analysis from the Ocean Bottom Seismometer (OBS) deployment of the Gravity
Lineations Intraplate Melting Seismic and Petrologic Expedition (GLIMPSE) experiment.
Using Gravity and Topography Data to Test Hypotheses
Central to understanding the origin of these seamounts is determining whether it is a
lithospheric process, such as thermal cracking of the lithosphere and subsequent tapping of
ambient asthenospheric melt, or if the cause of these features is a dynamic asthenospheric
process, such as small-scale convection or Richter rolls. Fortunately, the predictions for the
various processes that have been suggested for the formation of the volcanic edifices diverge
enough to allow us to test the models. With gravity and topography analysis, I have been able to
show that there is a mantle dynamic component required to produce these features and that
simple cracking of the lithosphere cannot explain all of the observations, effectively eliminating
this suite of models as the origin of these features.
Harmon, N; Forsyth, D W; Scheirer, D; Holmes, C. Analysis of Gravity and Topography in the
GLIMPSE Study Region: Isostatic Compensation and Uplift of the Sojourn and Hotu
Matua Ridge Systems. Submitted to J. Geophys. Res. 2005.
Forsyth, D W; Harmon, N; Scheirer, D; Duncan, R. The Distribution of Recent Volcanism and
the Morphology of Seamounts and Ridges in the GLIMPSE Study Area: Implications for
the Lithospheric Cracking Hypothesis for the Origin of Intraplate, Non-Hotspot Volcanic
Chains. Submitted to J. Geophys. Res. 2005.
Teleseismic Body Wave Analysis of the GLIMPSE Experiment
The geometry of the GLIMPSE long-term OBS deployment was designed to optimize ray
path coverage for surface wave tomography, limiting the potential for body wave tomography.
However, SKS splitting analysis and average body wave delay times can be used to determine
broad scale heterogeneities of the anisotropic and compressional and shear wave velocity
structure for the region. I have observed a trend with increasing seafloor age in both the strength
of anisotropy and average body wave delays. On older seafloor, P and S waves arrive earlier
relative to stations closer to the spreading axis, likely reflecting the increasing thickness of the
seismically fast lithosphere, while the strength of anisotropy appears to decrease with increasing
seafloor age. On seafloor of roughly the same age, I observe that the latest arrivals correlate with
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low-density mantle material as determined from the gravity anomalies. These observations are
consistent with a dynamic mantle process.
In the process of determining the S wave delay times, I developed a method for correcting
the delay times for ubiquitous ultra-slow, shear velocity sediment layer using converted phases.
I determine up to .4 s corrections for S delays that ranged from ±1 s, implying that without this
type of correction up to 20% of the travel time delays due to sediment could be mapped into
mantle anomalies in body wave tomography experiments.
Harmon, Nicholas, Forsyth, Donald W.; Lamm, Rosalee; Webb, Spahr C. P and S Wave Delays
Beneath Intraplate Volcanic Ridges and Gravity Lineations Near the East Pacific Rise,
Manuscript in Preparation to be Submitted to J. Geophys. Res., 2006
Harmon, Nicholas; Forsyth, Donald W.; Fischer, Karen M.; Webb, Spahr C.Variations in shearwave splitting in young Pacific seafloor, Geophys. Res. Lett., Vol. 31, No. 15, L15609
10.1029/2004GL020495, 2004
Crustal Structure from Ambient Seismic Noise
Another project that I am currently involved in is focused on adapting the method of
Shapiro and Campillo [2004] to OBS data using ambient seismic noise to determine the shallow
structure of the oceanic crust in the GLIMPSE experiment. The method entails determining the
seismic velocities from stacked cross-correlated noise signals between station pairs. Then using
these velocity estimates I can invert for the shallow seismic structure of the crust. Additionally,
knowledge of crustal structure can improve the accuracy of deeper earth analysis such as body
wave tomography and receiver function analysis. Initial results are very promising and show
there are a strong signals in the ambient noise recorded during the 11-month deployment of the
experiment. There is a phase that appears to have crustal velocities and there appears to be a very
strong signal in the microseism frequency range traveling with the velocity of sound in water.
This second phase might have interesting applications for the physical oceanographic community
as well as for seismologists. I will also apply this technique to help constrain crustal structure for
the currently deployed TUCAN seismic experiment in Nicaragua and Costa Rica.
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Introduction
Understanding the formation of the earth’s crust at mid ocean ridges is fundamental to
discerning the thermal and chemical evolution of the earth and perhaps the evolution of life.
Spreading ridges are active in deep ocean basins and in back arc basins above subduction zones
but the mechanisms that drive these divergent plate boundaries are different. In large mid-ocean
ridge systems slab pull is generally considered the dominant driving force of plate spreading,
generating melting at mid ocean ridges by
passive upwelling of the mantle in response
to entrainment of material by the moving
plates.
Figure 1 Schematic of slab influences on back
arc spreading from Turcotte and Schubert
[2002] showing mantle wedge corner flow (a)
and trench rollback (b) controlled spreading.
Geophysical observations at fast spreading centers like the East Pacific Rise support this
hypothesis [Forsyth et al., 1998]. In contrast, at back arc basins there is no direct “pull” from the
slab, because subduction is occurring beneath the spreading ridge. Nevertheless, there may be a
strong contribution to plate motions by suction forces due to the sinking of the slab [Conrad and
Lithgow-Bertelloni, 2002]. One hypothesis suggests that corner flow due to the subducting slab
creates a stagnation point beneath the proto-back arc spreading center where mantle flow
diverges [Turcotte and Schubert, 2002]. This diverging flow beneath the lithosphere then creates
rifting and ultimately a back arc spreading center (Figure 1a). In another hypothesis, trench roll
back creates a lithospheric force similar to slab pull, while the foundering of the subducted slab
stimulates upward mantle flow [Turcotte and Schubert, 2002]. The combination of mantle flow
and extensional stresses create back arc spreading (Figure 1b). Essential to differentiating
between these two hypotheses and others for the development of back arc spreading centers is
comprehending the function of the subducting slab.
Figure 2 Variation along strike of the
ELSC and CLSC from Martinez and
Taylor 2002. Panel a shows bathymetry
of the region, hashed black lines
indicate limit of arc volcanics white line
indicates spreading center axis, Panel b
shows axial depth and ridge arc
distance. Panel c shows spreading rate
and axial area. Panel d shows the along
axis free air and the mantle Bouguer
anomaly adjusted for effects of the
trench. Panel e is the plan form of the
adjusted mantle Bouguer anomaly.
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The Eastern Lau Spreading Center (ELSC), one of the RIDGE 2000 Integrated Study Sites,
is a back arc spreading center that provides a unique opportunity to understand the role of
subduction in back arc ridge processes. The ridge shows significant along strike variations in
geochemistry, petrology, ridge morphology, and spreading rate (figure 1). Going from the
southern Valu Fa Ridge to the northern extent of the ELSC the spreading rate increases from 40
mm/yr to 95 mm/yr [Zellmer and Taylor, 2001], while the ridge goes from a rise-like ridge to an
axial valley type spreading center [Martinez and Taylor, 2002]. This is opposite what is normally
observed at mid ocean ridges; slower spreading ridges, like the mid Atlantic Ridge, have axial
valley structures and faster spreading ridges have broad rises with narrow axial peaks similar to
the EPR. The petrology and geochemistry of the region provides some clue to the along axis
variations. The distance between the arc and the ELSC increases northward from 40 km to 100
km and the erupting magmas go from andesitic to more tholeitic [Vallier et al., 1991].
Apparently, Valu Fa crustal formation is pirating magma from the volcanic arc, while towards
the north the ELSC has an increasingly arc-independent melt production regime [Martinez and
Taylor, 2002]. These observations indicate that the melt production in the back arc is influenced
volcanic arc magma production in the mantle wedge, not by simple spreading-induced upwelling
decompression melting like that observed at mid ocean ridges.
Figure 3. Cartoon of potential 3-D flow influences from Turner and Hawkesworth [1998]. This
cartoon shows the geochemical influences from the Samoan plume and Indian Ocean, but does not
indicate effects from underneath the slab due to trench roll back.
Outside of the spreading system, the region around ELSC is tectonically rich. The
convergence rate of the Tonga subduction zone also positively correlates with the back arc
spreading rates, with a maximum convergence rate of 240 mm/yr in the north grading down to
160 mm/yr in the south [Bevis et al., 1995], while the trench is rolling back at a rate of up to 100
mm/yr [Hall et al., 2000]. Fluids experiments suggest that trench rollback can induce return flow
around the sides and beneath the slab [Buttles and Olson, 1998; Kincaid and Griffiths, 2003]. In
fact, geochemical tracers point toward 3-D flow in the mantle wedge. Mantle flow rates into the
Lau Basin of 40 mm/yr from the north, subduction downwelling of 20-40 mm/yr, and 45-65
mm/yr from the west are inferred using isotopic and minor element inputs from the Samoan
Plume, the subducted Louisville seamount chain, and Indian/Pacific ocean mantle, respectively
[Turner and Hawkesworth, 1998]. Further corroborating 3-D flow, shear wave splitting analyses
from the LABATTS seismic deployment show a rotation of seismic fast directions from trench
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perpendicular west of the Central Lau Spreading center to trench parallel at the Tonga Volcanic
arc [Smith et al., 2001]. The change in fast direction suggests a change from plate spreading
dominated mantle flow to along strike flow beneath the arc in the northern Lau Basin [Smith et
al., 2001] but could also indicate a change in the dominant slip system due to water enrichment
in the mantle wedge [Jung and Karato,2001].
The motivation for this study is to understand the role of the subducting slab in the
formation and development of back arc spreading centers. Working from a broad tectonic scale
to variation along ELSC I am driven by the following questions:
• Does corner flow or lithospheric stresses applied by trench rollback control upwelling
and melting at the spreading ridge; i.e., what is the role of the subducting slab in back
arc spreading?
• How does the proximity to the volcanic arc affect the ridge morphology, spreading
rate, and geochemistry, i.e. is it the addition of water that allows for large degrees of
melting without significant increase in spreading?
• What are the effects of three-dimensional flow on melt production/transport, ridge
morphology and chemistry/petrology?
•
One way to examine these questions is through numerical modeling of the Tongan
Subduction Zone/Lau Basin. Previous attempts to model numerically the Tongan Back Arc using
2-D approximations or symmetrical 3-D simulations [Ribe, 1989; Hall et al., 2000, Conder et al.,
2002] have been successful in explaining some of the observations. Specifically, Ribe [1989]
showed that as a back arc spreading ridge migrated away from the arc the source regions for the
two types of volcanism became more distinct, while Conder et al. [2002] showed that slab
induced corner flow may cause asymmetric melting at the back-arc ridge preferentially drawing
material from the Indian ocean. Hall et al. [2000] looked that the potential for 3-D flow in the
mantle due to subduction normal plate motions and found that these motions could reproduce
some but not all the observations of seismic anisotropy. These modeling efforts have not
addressed all of the issues; for example, what is the effect of a variable viscosity on the results of
Ribe [1989]. To fully understand the region, the three-dimensional effects due to rollback,
differential plate motion and potential plume flux, must be accounted for in quantitative models.
When combined with geophysical and geochemical observations, 3-D numerical modeling will
provide powerful constraints on the effects of mantle flow and melt transport in the region.
Proposed Research
The research I propose for the R2K Postdoctoral Fellowship will occur in three phases:
1. Run a series of numerical experiments to assess possible patterns of mantle
flow and melt transport/production of the Tonga Subduction Zone/Lau Back
Arc Basin. Search the parameter space of these experiments to find the range
of models that fit existing geophysical and geochemical observations.
2. Determine for each of these models the predicted seismic anisotropy structure
due to lattice-preferred orientation of mantle minerals from the predicted
mantle flow.
3. Use the predicted seismic anisotropy from the numerical modeling to optimize
the station geometry of the scheduled long term ocean bottom seismometer
deployment in the ELSC ISS to observe the regional mantle flow pattern.
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The purpose of this research is twofold: generate predictions for different mantle flow
fields to examine melt generation and transport in the ELSC and facilitate interpretation of
seismic observations from the scheduled seismic deployment to the ELSC in 2009.
Using numerical experiments to understand 2-D and 3-D effects on mantle flow, melt
generation, and melt transport
The first phase of the proposed research is the numerical modeling of the Lau Basin back
arc spreading system and will be the most substantial portion of the work of the postdoctoral
fellowship. With this research, I will explore the motivating questions of the study. To
accomplish this there will be three families of models. One family of models will explore the
relative importance of trench rollback versus slab induced corner flow on evolution of rifting.
The large variations in spreading rate and convergence rate in the ELSC make it an ideal place to
test these two hypotheses because of the presence of both strong rollback up to 100 mm/yr and
the correlation between spreading rate and convergence rate. By exploring the parameter space
of rollback rate and subduction rate we can determine the rates where these two mechanisms are
capable of rifting the lithosphere and sustaining spreading, which can be compared to
observations in the Lau basin. The second family of models will explore the effects of trench and
arc proximity on the production and migration of melt beneath the ELSC. These models will use
the arc/trench to ridge distances observed in the ELSC and will compare degrees and extents of
predicted melting with existing petrological and geochemical data (Turner and Hawkesworth,
1998; Bezos et al., 2005). The other family of models will be focused on using the spreading,
rollback and convergence velocities to examine patterns of broad-scale, 3-D flow in the mantle
in the Lau Basin. This work will be focused on determining limits on the magnitude and depth
extent of possible along strike flow and examining how this might affect melt patterns along the
ELSC. I expect there to be some non-uniqueness in the modeling, so my goal is to determine
what families of models satisfy the observations and what the successful parameter space is for
these families.
Investigating trench rollback vs. slab induced corner flow
The yield strength envelope (YSE) of a peridotite/basaltic lithosphere provides a means for
determining if the flow stresses are enough to initiate rifting [Kohlstedt et al., 1995]. By
constructing 2-D models of subduction zone corner flow, I can determine the stresses at the base
of the lithosphere created by viscous flow beneath the overriding plate and the thermal structure
at the base of the lithosphere that can provide information about changes in the strength of the
lithosphere due to thermal erosion. Even without an overriding plate velocity and no trench
rollback subduction zone type corner flow creates a zone of upwelling and diverging flow
beneath sites that could ultimately become spreading centers. In the first part of this exploration,
we will only look at the effects of slab dip and velocity on the corner flow velocities beneath the
overriding lithosphere, and compare it with the thresholds necessary to begin extension in the
lithosphere. In the second part of this modeling, we will add various rollback rates to the models
(rollback can be simulated by replacing the stress free condition at the base of the model with a
velocity boundary condition. In this manner, we can explore the subduction slab dip, slab
velocity, and rollback velocity space. Finally, we can compare the results from the numerical
modeling parameter exploration with the ELSC and other subduction zones to determine how
much trench rollback is required to generate a back arc basin.
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Global models of the lithospheric stress field indicate that stresses rarely exceed 100 MPa
at wavelengths > 200 km, and I do not expect that stresses induced by rollback alone will be able
to generate rifting [Lithgow-Bertelloni and Guynn, 2004]. The YSE requires several hundred
MPa stresses for the mid lithosphere near the brittle ductile transition to fail [Kohlstedt et al.,
1995]. I envision a two-stage process, heating from below from upwelling mantle to weaken the
lithosphere and then combined viscous flow and rollback stresses to create rifting and ridge
formation. Alternately, thinning might be enhanced by small-scale convection aided by water
weakening in the hydrated mantle wedge and might allow rollback stresses to rift the lithosphere
[Arcay et al., 2006]. Even then, a weakened zone may be required for rifting to occur, such as the
arc where magma is injected into hot crust.
Testing ridge magma piracy from arcs
The work proposed here is similar to previous work [Ribe, 1989; Conder et al., 2002] but it
will extend that work and also build on the rollback/cornerflow models I propose here.
Specifically, this modeling effort will quantitatively test the magma piracy hypothesis of Taylor
and Martinez [2003]. In the conceptual model of Taylor and Martinez [2003], initial corner flow
above the subducting slab causes hotter mantle to advect up into weakened arc lithosphere
causing arc volcanism that gradually gives way to rifting and spreading. As the spreading center
migrates away from the arc, the melt supply region for the ridge gradually separates from the arc.
By examining the actual geometry of the ELSC and the arc, I can examine the distances where
the separation between the arc and ridge sources occurs and determine if a ridge/arc separation
ranging from 40-100 km is significant.
Similar to the previous rollback/corner flow models, I will develop a series of twodimensional transects across the ridge and trench from north to south to investigate the effects of
moving the arc closer to the ridge on melt production and the source region in the mantle.
Determining the distance along axis between model transects is important because I want to
observe changes in the interaction between the arc and the ridge melt supply regions. If I assume
that the width of the melt source region for the ELSC is constant at 100 km, then the arc axis
overlaps this source region for approximately 100 km from the southern tip of Valu Fa up to ~22
ºS. To capture changes on the 100 km length scale of this overlap we should model transects at
least half that distance or every 50 km along the ELSC axis.
With the thermal and flow structure, I can determine melt production in a region assuming
a mantle composition, temperature, pressure, and upwelling rate. Initially, I will use a linear
relationship to determine the amount of melt generated in the region assuming a certain amount
of melting for a given pressure change. In regions where we expect dry depleted mantle and little
interaction with the hydrated mantle wedge I will use a dry harzburgite solidus. For the hydrated
mantle wedge I will use a wet mantle solidus. More complicated melting models such as MELTS
or pHMELTS can be applied in advanced stages of the modeling to track the changes in
mineralogy, trace elements and mineral water content [Asimow and Ghiorso, 1998; Asimow et
al., 2001; Asimow et al., 2004] and test the potential for buoyant flow due to depletion of the
matrix. To account for the transport of fluids from the dewatering of the slab and their effect on
melting I will apply a method similar to Cagnioncle et al. [2004]. This method tracks depletion
through time using the tracer ratio method [Tackley and King, 2003] to avoid numerical
dispersion common in grid techniques due to advection [Cagnioncle et al., 2004]. They use a
table lookup of the P,T, water content and composition based on the output of pMELTS
[Hirschmann et al., 1999] for increasing degrees of partial melting to determine the melting and
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depletion in a solid element [Cagnioncle et al., 2004]. These models will allow us to examine the
depth of melting, lateral distribution of melt production and melt production rate.
Melt transport can be determined by assuming a porous flow model and solid state
transport. for example assuming isotropic permeability after Phipps Morgan [1987]:
r &
r # r
& k #&
*#
r
!!$$ ),g ( *' 2U + $ + + !' ' • U !! + U
u = ($$
3"
%
"
% µ- "%
where u is the melt velocity, k is the permeability, µ is melt viscosity, φ is melt fraction, η is the
solid bulk viscosity, ζ is shear viscosity, U is the solid velocity, g is the acceleration of gravity
and Δρ is the density contrast between the melt and the solid. Thus, I can probe the relationships
between melt production and mantle flow. More complicated melt transport schemes can be
explored by introducing anisotropic or heterogeneous permeability and a variable matrix
viscosity into the model.
The geochemistry of the ELSC is a complicated function of the magmatic source material,
melt mixing, fractionation and crustal assimilation. Completely modeling these processes is
beyond the scope of the research proposed here; however, I do want to be able to compare our
models with existing geochemical data. One way to determine composition of the parent magmas
of the ELSC ridge in these models would be a weighted average of the melts that have coalesced
from the production region beneath the ridge. For comparison with the observed geochemical
data, I must normalize the unfractionated model bulk composition to low pressure fractionation
values of Fe8.0, Na8.0, Mg8.0, etc. To do this I can use pHMELTS [Asimow et al., 2004] to
fractionate the model melt to MgO=8% at low pressure, which can then be compared directly to
the published geochemical data along the ELSC axis of Taylor and Martinez [2003] (and
upcoming results of Langmuir and co-workers from the Lau ISS). I do not expect to match the
exact values in the geochemistry along axis because there is no way to determine the amount of
magma mixing and crustal assimilation that has taken place in a numerical model. I do expect to
match the relative changes along axis. To do this I will explore the effect of mantle source
starting composition. By varying the starting depletion in the region beneath the spreading ridge,
with more depletion where the ridge has spread further from the arc, I believe I will be able to
match the trends in the observed geochemistry with the numerical simulations.
Initial results of this work will be discussed with petrologists and geochemists in detail,
taking advantage of R2K and InterRidge sponsored workshops, both for Lau in particular and for
more general meetings that emphasize ridge processes.
(
)
Broad-scale flow in the Lau Basin, Initial 3-D models
After studying the series of 2-D numerical experiments, I will construct simplified 3-D
models with the aim to determine the kinematic effect of the along-strike changes of plate
boundary geometry on mantle flow. This phase of the project is envisioned as an initial step
toward development of more complete models which can eventually address: the effect of 3-D
flow on melt production and transport; whether trench rollback edge flow can passively entrain
enough material from the Samoan Plume to match the geochemical observations or whether
active plume flux required? The broad scale models are expected to be able to allow an
assessment of the amount of material that could be added from the Indian Ocean asthenosphere
due to slab foundering. Models of this type have never been constructed for the Lau Basin and
will provide insights into previously hypothesized mantle flow patterns.
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Figure 3 View of Lau Basin and slab seismicity beneath the Tonga subduction zone. This seismicity can be
used to determine the geometry of the subducting slab as a constraint for 3-D modeling. The seismicity
reveals the tear in the slab that may allow material from the Samoan Plume to enter from the north.
There are a few 3-D codes available for calculating fluid flow and heat transfer.
Commercial codes such as Femlab provide ease of use, ability to handle 2 and 3 dimensions and
coupled differential equations for heat transfer and fluid dynamics. The only draw back to this
type of solver is the lack of parallelization; however Femlab has been used to run fairly
computationally intense models in a few days [Montessi, personal communication]. Codes
developed by Blackman and co-workers are currently running at IGPP (Boundary Element
(Blackman, 1991; Blackman and Forsyth, 1992; Blackman, 1997; and a modification of Tekton
to 3D with coupled finite
difference thermal calculation
(Van Wijk and Blackman, 2004;
2005)). Each of the approaches
mentioned thus far could provide
moderate resolution models of
overall flow in a mantle wedge
with backarc spreading whose
proximity to the trench varies
monotonitcally along strike.
More detailed 3D models are
beyond the scope of this project.
Figure 4 Illustration of box model to be used for broad scale 3-D flow modeling. The velocities are prescribed
at the top, bottom, and slab side of the box and normal stress is zero everywhere else. To simulate trench roll
back, we could prescribe velocities in the gray region of the slab and allow a zero normal stress condition
everywhere else on the slab.
The boundary conditions of the model will be extremely important for this modeling work.
For mantle flow, the plate velocities in the region are well constrained by geodetic observations
and marine geophysical observations [Bevis et al., 1995; Zellmer and Taylor, 2001] providing
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boundary conditions for the spreading ridge and subducting slab. The geometry of the ridge
system is known, and the shape of the subducting slab can be determined by mapping the
seismicity of the slab (Figure 4). Thus the geometry and boundary conditions for half the model
are known (Figure 5). At the base of the model the two boundary conditions are possible. If the
depth of the model is sufficient, the velocities can be set to zero and flow in the upper part of the
model (simulating the dislocation creep regime) will reasonably approximate corner flow models
allowing corner flow to develop in the mantle wedge [Hall et al.,2000]. If I want to simulate
trench rollback then a velocity equal to the rollback velocity can be employed to create flow
around the slab [Hall et al., 2000]. On the sides of the box model I want to allow material to flow
in and out of the box so I will use a neutral boundary condition or zero normal stress. In the north
where the Samoan plume is hypothesized to be injecting material into the system, in some
models I can impose a pressure condition equivalent to the plume flux. The thermal boundary
conditions will be fixed temperatures at the top and bottom boundaries, allowing the slab itself to
advect and conductively cool to steady state. I will impose insulating conditions at the side of the
model, with a heat flux imposed from the Samoan Plume in some models.
Within the domain of the model, initially I will assume the isoviscous case for the solid
flow. For the 2-D models I will include a thermal, water and pressure dependent viscosity. If it is
feasible computationally for the 3-D case, I will try to incorporate the P, T, H20 dependent
viscosity. In the isoviscous cases however, the viscosity will be one of the parameters that I will
search over to find the best fit to the observations.
Translating Mantle Flow to Lattice Preferred Orientation and Seismic Anisotropy
Translating mantle flow to seismic anisotropy is predicated on a few principles. The upper
mantle is comprised of peridotite, whose main constituent is olivine with some orthopyroxene,
which are both seismically anisotropic. These mantle peridotites deform by dislocation creep in
response to stresses in the upper mantle due to plate tectonics and mantle convection. At several
percent strain the mantle peridotites develop a lattice preferred orientation (LPO) of olivine
grains in which the seismically fast crystallographic axis of the minerals are aligned, over
sufficient length scales to be detectable by seismic waves. The strain rate that develops LPO is
related to stress predicted by the flow model through empirically determined flow laws that are
extrapolated from laboratory to mantle conditions. These principles are born out by field
observations of peridotite mantle xenoliths and ophiolites in which the majority of specimens
exhibit LPO of olivine due to slip on the (010)[100] system or type A [Ben Ismail and
Mainprice, 1998]. While observations of seismic azimuthal anisotropy in ocean basins show fast
directions parallel to absolute plate motion in a hot spot reference frame, indicating that seismic
anisotropy fast directions and mantle flow lines are roughly parallel [e.g. Raitt et al. 1969].
In practice, to calculate LPO from mantle flow, the mantle is discretized and the strain of a
mineral aggregate is determined from the local stresses in each unit [Chastel et al., 1993;
Blackman et al., 1996; Hall et al., 2000; Tommasi et al., 2000; Kaminski and Ribe, 2001;
Blackman and Kendall, 2002]. The effective anisotropic elastic constants of the predicted
mineral orientation distribution in a given mantle parcel can be computed. Then to determine
seismic signatures that would be observed on the surface, the varying elastic properties along a
given seismic ray path are integrated [Hall et al., 2000; Blackman and Kendall, 2002]. The
differences in these procedures arise from the particular model used for determining LPO. The
models ranging in complexity from assuming that olivine a axes alignment is parallel and
proportional to the finite strain ellipse along the streamline [Hall et al., 2000], to lower bound
C-12
methods in which grains are allowed to deform heterogeneously as long as the stress in the
aggregate is homogenous [Blackman and Kendall, 2001], to viscoplastic self consistent models
where the stress and strain are in equilibrium in the aggregate [Wenk et al., 1991]. For these
studies, I will employ a lower bound method approach for estimating LPO along stream lines
[Blackman and Kendall, 2002]. To account for the potential of other deformation mechanisms
occurring such as dynamic recrystallization, I may also employ the method of Kaminsky and
Ribe [2000].
The methods described above assume slip on the (010)[100] and (001)[100] systems
dominate. However, recent laboratory work suggests that under high flow stresses and water
contents the dominant slip system of olivine changes from type A (010)[100] to type b
(010)[001], rotating the seismically fast crystallographic a axis 90º to the flow direction and in
the plane [Jung and Karato, 2001]. Field work in the Higashi-Akaishi peridotite body, formed in
a supra subduction zone setting like ELSC, shows evidence for thin dunite veins with type B
LPO [Mizukami et al., 2004]. Furthermore, numerical experiments incorporating new olivine
flow laws indicate that it may be possible to form B type LPO over the thickness of the wet cold
nose of the mantle wedge [Kneller et al., 2005]. These studies indicate that this change in slip
system could occur, drastically altering the interpretation of the observed seismic anisotropy and
mantle flow in the region. To explore the possibility of B type fabric forming in the Lau Basin, I
propose to develop a modified lower bound method that allows a change in the dominant slip
system from type A to type B in regions expected to have high stress (i.e. high viscosity) and
high water content. An ad hoc method to do this would be to modify the activation stresses of
the slip systems in the high stress wet regions so that slip on the B type (010)[001] system was
the lowest, this approach may be an effective way to model this behavior in lieu of laboratory
data.
Optimizing the ELSC passive-source OBS deployment
The passive source broadband OBS deployment for the ELSC is tentatively planned for
2008 and will deploy 50-60 instruments for approximately 10 months to study the seismic
structure of the mantle. The geometry of the array is designed to be flexible enough for both
surface wave tomography and body wave tomography using local and teleseismic events. To do
this the instruments will be deployed in two long transects crossing the ELSC and one transect
along the ELSC ideal for body wave tomography, with intervening instruments to maximize
azimuthal ray coverage for surface waves. While the aperture and geometry of the array are set
by the requirements of the study, i.e. investigating the crustal and upper mantle structure of the
spreading system, the individual placement of instruments can be tweaked to improve resolution
locally if modeling predicts the possible occurence of detailed mantle flow patterns that could be
discerned. For example, if modeling indicates changes in mantle flow direction over short
distances such as transitioning from 2-D corner flow to 3-D along strike, station spacing can be
decreased to capture/characterize that change. The tradeoff in the optimization problem laid out
here is the balance in the resolution requirements for the tomography studies and the shear wave
splitting studies. The modeling work I propose to do here will predict the upper mantle
anisotropic structure for different flow regimes and suggestions for station geometry
optimization can be made so that testing between hypotheses is enhanced.
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Figure 5 Illustration of planned passive
seismic array seafloor (black circles) and land
(white squares) stations are overlain on colorcoded bathymetry (red-shallow, blue-deep).
A systematic way to optimize the OBS
deployment would be to cast it as an inverse
problem, with station locations being the
parameters solved for and the earth structure
recovered by the data to be minimized. Abt
et al. [2005] have developed a method for
shear wave splitting tomography to recover
the strength of anisotropy and fast direction
in the earth, precisely the quantities
determined the modeling efforts proposed
here. By assuming a distribution of
earthquakes from the subducting slab and
station geometries, I can generate a series of
resolution tests using this method to find
which station geometries recovered the most
accurate mantle structure. The station
locations for the transects along and across
the ridge will be considered fixed, but the distribution of the “random” stations can be adjusted.
The most efficient approach for this type of inversion would be a Monte Carlo inversion, which
will allow for exploration of potential distributions. With this type of inversion and several
different predicted earth models, I expect there to be several geometry solutions that achieve
similar model recovery, which will provide options for tradeoffs with tomography resolutions.
Ultimately, optimal station locations will be determined through this study, tomography
resolution requirements, and site-specific factors such as sediment cover which allows for better
coupling of the instruments to seafloor than bedrock. This approach will greatly enhance the
OBS deployment by designing it with expected earth structure in mind.
Scientific Impacts
The work proposed here would further the RIDGE 2000 scientific agenda in several ways
in addition to broadening my expertise in geophysics and my understanding of mid ocean ridge
processes. By generating 3-D site-specific numerical mantle flow models of the Lau Basin, I will
be able to test fundamental hypothesis about the relationship between subduction, tectonics,
mantle flow, and melt migration at back arc spreading centers. This work will contribute
significantly to our understanding of the formation of a significant fraction of the earths crust at
this type of spreading center. In addition, the modeling work that I propose to do here will
directly benefit the funded and scheduled seismic deployment to the Eastern Lau Spreading
Center by creating preliminary models of mantle flow and melt transport that can be tested by the
seismic observations. This work will also help in implementing that seismic deployment by
optimizing station locations for endmember models.
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Donna Blackman
12 February 2006
I am writing in support of Nick Harmon's application for a Ridge 2000 postdoctoral
fellowship. Nick first contacted me before Fall AGU, this past December, expressing
interest in working with me when he completed his degree at Brown University. We met
to discuss the possibilities at AGU and it very quickly became clear that there was work
that could further his development as a geophysicist that would ideally complement an
upcoming Ridge 2000 project- the crust and mantle imaging experiment in the Lau Basin
by Wiens and co-PIs. Since the OBS deployment for that experiment must wait until
about 2008, there is time to explore an initial series of numerical models of mantle flow
and melt production. These models would form a more complete basis for understanding
the physical and dynamical system that the seismic experiments will image. Thus, when
those data are eventually in hand, progression to more complete models can be designed
much more readily- first order parameter dependencies of model results already having
been explored to a reasonable extent. In light of the fact that ultimately full 3-D
dynamical models will be required to do justice to the R2K Lau OBS experiment, Nick's
interest in developing some expertise in numerical modeling of mantle flow seems an
ideal opportunity to take advantage of. We are already in touch with Conder to coordinate
the proposed initial work with the planned more complete modeling that will accompany
the OBS data interpretation.
The 2-D finite element program that will be a key part of the proposed first series of
numerical runs is one that I have used extensively. It was developed over the years by a
series of Brown University researchers and includes a flexible set of subroutines within
which to explore assumptions about viscosity, melting curve, retention of melt, and
depletion of the residual. This is the mantle flow code with which my prior modeling of
seismic anisotropy was done so coupling between this and the LPO and anisotropic
elasticity codes is fully operational. The main new coding work will be to generate the set
of initial/boundary conditions that are appropriate for the subduction/back arc setting.
The proposed initial set of 3-D kinematic models will also use programs that are currently
in use by a current post doc, Jolante Van Wijk, and/or I. Again, the main new
programming that Nick will need to do is model input development and I can certainly
work with him on this aspect as well as mentoring his general learning in the use of
numerical models to test hypotheses of the effects of a suite of physical parameters on the
predicted style and pattern of mantle flow.
Donna Blackman