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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, B04405, doi:10.1029/2008JB006077, 2009
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Viscosity of the asthenosphere from glacial isostatic adjustment
and subduction dynamics at the northern Cascadia subduction zone,
British Columbia, Canada
Thomas S. James,1,2 Evan J. Gowan,3,4 Ikuko Wada,3,4 and Kelin Wang1,2
Received 4 September 2008; revised 23 January 2009; accepted 11 February 2009; published 15 April 2009.
[1] Late glacial sea level curves located in the Cascadia subduction zone (CSZ) fore arc in
southwestern British Columbia show that glacial isostatic adjustment (GIA) was rapid when
the Cordilleran Ice Sheet collapsed in the late Pleistocene. GIA modeling with a linear
Maxwell rheology indicates that the observations can be equally well fit across a wide range
of asthenospheric thicknesses, provided that the asthenospheric viscosity is varied from
3 1018 Pa s for a thin (140 km) asthenosphere to 4 1019 Pa s for a thick (380 km)
asthenosphere. Present-day vertical crustal motion predicted by the GIA models shows rates
of a few tenths of a millimeter per year, consistent with previous analyses. The model
viscosities largely pertain to the viscosity of the oceanic mantle beneath the subducting
Juan de Fuca slab but include a contribution from the mantle wedge above the slab.
For comparison, effective viscosities for the upper mantle due to the tectonic regime
(subduction) were computed using the strain rates and temperatures of an independent
geodynamic model of the CSZ with a wet olivine power law rheology. The effective
viscosities agree well with GIA model viscosities of 1019 Pa s or less, corresponding to an
asthenosphere of 100 or 200 km thickness. The agreement suggests a significant role for
power law flow in the GIA response. Regardless of the microphysical mechanisms
responsible for the GIA response, the viscosity values inferred from GIA can be applied to
studies of the megathrust earthquake cycle because both processes take place on comparable
time scales.
Citation: James, T. S., E. J. Gowan, I. Wada, and K. Wang (2009), Viscosity of the asthenosphere from glacial isostatic adjustment
and subduction dynamics at the northern Cascadia subduction zone, British Columbia, Canada, J. Geophys. Res., 114, B04405,
doi:10.1029/2008JB006077.
1. Introduction
[2] During the last major phase of continental glaciation,
the Cordilleran Ice Sheet (CIS) covered most of British
Columbia and parts of northern Washington State (Figure 1)
[e.g., Clague and James, 2002]. The weight of the ice sheet
caused tens to hundreds of meters of crustal depression along
coastal areas in southwestern British Columbia [Mathews
et al., 1970; Clague et al., 1982]. During this time, relative
sea level was higher than present despite global sea level
being many tens of meters lower. As the ice sheet melted, the
crust quickly rebounded and relative sea level fell owing to
glacial isostatic adjustment (GIA).
[3] Southwestern British Columbia is located above the
active Cascadia subduction zone (CSZ) where the North
1
Pacific Geoscience Center, Geological Survey of Canada, Sidney,
British Columbia, Canada.
2
Also at School of Earth and Ocean Sciences, University of Victoria,
Victoria, British Columbia, Canada.
3
School of Earth and Ocean Sciences, University of Victoria, Victoria,
British Columbia, Canada.
4
Also at Pacific Geoscience Center, Geological Survey of Canada,
Sidney, British Columbia, Canada.
Copyright 2009 by the American Geophysical Union.
0148-0227/09/2008JB006077$09.00
American plate overrides the young (6 –9 Ma) and warm
Juan de Fuca plate (Figure 1). Relative sea level and relict
lake-shoreline tilt observations indicate that the viscosity of
the shallow mantle in this tectonically active region is low
compared to cratonic areas [Mathews et al., 1970; Thorson,
1989; James et al., 2000; Clague and James, 2002], but the
uncertainty of the inferred mantle viscosity spans an order of
magnitude or greater. Relative sea level observations recently
obtained to improve the record of postglacial crustal movement in southwestern British Columbia indicate rapid sea
level fall immediately following deglaciation [James et al.,
2002; Hutchinson et al., 2004; James et al., 2005, 2009].
Preliminary analyses of the isostatic depression derived from
these sea level observations confirm the low mantle viscosity
but do not help to improve the uncertainties.
[4] Investigations are underway to observe and model the
crustal motions in the earthquake-prone CSZ [e.g., Dragert
et al., 1994; Rogers and Dragert, 2003; Mazzotti et al., 2003;
Kao et al., 2005]. Models of subduction zone dynamics,
including those of subduction zone thermal structure [e.g.,
Currie et al., 2004; Wada et al., 2008] and the great earthquake cycle of interseismic strain accumulation, coseismic
displacement, and postseismic relaxation [e.g., Wang et al.,
2003; Wang, 2007], incorporate mantle-viscosity parameters.
These parameters can be tuned, on one hand, or compared, on
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Figure 1. Location map showing the northern Cascadia subduction zone [after James et al., 2005]. The
locations of previously constructed sea level curves are from the central Strait of Georgia [Hutchinson et al.,
2004], northern Strait of Georgia [James et al., 2005], and Victoria [James et al., 2009]. Contour lines show
the depth to the top of the subducting Juan De Fuca plate [Flück et al., 1997]. The thick line shows the
maximum extent of the Cordilleran Ice Sheet [Clague, 1981].
the other hand, to viscosity values inferred from GIA modeling of sea level observations.
[5] The goal of this paper is to determine the viscosity
of the shallow mantle (‘‘asthenosphere’’) at the northern
Cascadia subduction zone. GIA modeling was carried out
to explain the newly collected, precise relative sea level
observations. The viscosity inferred from the GIA modeling
was then compared to that predicted from a model of the
tectonic regime that incorporates the dislocation creep of
olivine [Wada et al., 2008].
2. Previous Regional GIA Modeling
[6] Models constrained by observed tilts of relict proglacial lake shorelines from Puget Sound and available relative
sea level data from the Strait of Georgia predicted the upper
mantle viscosity in southwestern British Columbia to be 5 1018 Pa s to 5 1019 Pa s [James et al., 2000]. A lithospheric
thickness of 35 km was assumed, which corresponds to the
depth to the top of the subducting oceanic slab in Puget
Sound. To obtain an upper bound on crustal uplift rates,
James et al. [2000] employed a mantle viscosity of 1020 Pa s
and estimated that present-day uplift rates due to ongoing
GIA are less than 0.1 mm a1.
[7] Clague and James [2002] reviewed the history of the
Cordilleran Ice Sheet (CIS), and then focused on the fit of the
model to relative sea level observations from the Strait of
Georgia. They used more realistic Earth models in which
viscosity increased with depth, and assumed a thicker 60-kmthick lithosphere, which corresponds to the depth to the top of
the subducting slab in the central Strait of Georgia. Their
model indicated that a mantle viscosity of less than 1020 Pa s
is needed to give a good fit to the data and that present-day
uplift rates on Vancouver Island are less than 1 mm a1.
[8] Clague et al. [2005] modeled sea level for the early
phases of the Fraser glaciation. Substantial ice was added to
the existing ice sheet model in the Strait of Georgia in early
times in order to match the sea level observations. The later
stages of the ice sheet model were not altered.
[9] Early global GIA models (ICE-3G [Tushingham and
Peltier, 1991] and ICE-4G [Peltier, 1994]) assumed an upper
mantle viscosity of 1021 Pa s. As a consequence of the
relatively high viscosity, model-predicted relative sea level
falls too slowly following deglaciation. The VM2 earth
model used with ICE-5G [Peltier, 2004] employs an average
upper mantle viscosity of about 4 1020 Pa s. In the
following, we will demonstrate that even this smaller value
must be further reduced in the shallow parts of the upper
mantle in order to explain sea level observations from the
northern CSZ.
3. Earth Models
[10] GIA models include a model of ice sheet growth and
decay and a model of the Earth’s response to surface loading.
The Earth models considered here are spherically symmetric
and each layer has uniform elastic properties, density, and
viscosity. The models have an elastic lithosphere, an incompressible Maxwell viscoelastic mantle divided into several
layers, and a fluid core. Density and rigidity parameters are
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Figure 2. Viscosity profile of the mantle. The gray line is
the VM2 model of Peltier [2004], and the black line is the
simplified model used in this study. The uppermost mantle
(asthenosphere) has variable viscosity and thickness.
average values from the Preliminary Reference Earth Model
[Dziewonski and Anderson, 1981]. The Earth models do not
capture the complexities of Earth structure in the CSZ but,
instead, represent average quantities.
[11] The viscosity of the mantle is averaged from the VM2
model [Peltier, 2004], except that the asthenospheric thickness and viscosity are allowed to vary (Figure 2). Asthenospheric thicknesses range from 140 to 380 km. Below the
asthenosphere and above the 670-km discontinuity, the
mantle viscosity is 4 1020 Pa s. The lower mantle has a
viscosity of 1.6 1021 Pa s above 1291 km depth and 3.2 1021 Pa s below that.
[12] Surface heat flow in the CSZ fore arc is low [Hyndman
and Lewis, 1995], suggestive of a cool, stagnant mantle
wedge [Hyndman and Wang, 1995; Wada et al., 2008]. We
assume that on the time scale of the GIA, the fore-arc material
overlying the subducting oceanic lithosphere responds elastically without a viscous component and is decoupled from
the subducting oceanic lithosphere, and we employ a 60-km
lithospheric thickness. This value corresponds to the depth to
the top of the subducting slab below the western Strait of
Georgia and is the same thickness used in earlier modeling
[Clague and James, 2002]. The response of the Earth models
to surface loading was calculated using methods described by
James and Ivins [1998].
[14] At the glacial maximum, the Cordilleran Ice Sheet
flowed smoothly over topography [Booth, 1987], which
indicates that there was significantly more ice in low-lying
areas than in areas of high elevation. The isostatic depression
was taken into account when adjusting the ice model to
produce an ice surface that gently slopes toward the Pacific
Ocean. At the CIS maximum, the model features more than
2500 m of ice in the Strait of Georgia, in contrast to less than
1500 m of ice on central Vancouver Island. This reflects the
bathymetry of the Strait of Georgia, which reaches depths
greater than 200 m, and the topography of Vancouver Island,
which has substantial regions that are higher than 1000 m.
[15] Finally, the model was refined to fit available radiocarbon constraints on deglaciation of the southwestern sector
of the Cordilleran Ice Sheet (CIS) [Gowan, 2007]. In general,
the model indicates that the ice retreat began several hundred
years before the oldest ages in an area and ice has completely
melted 100– 200 years before the oldest ages.
[16] The final ice model consists of twenty time periods
starting at 35,000 calendar years before present (cal years
B.P.). The deglaciation of Puget Sound, the Strait of Juan
de Fuca, and the Strait of Georgia is divided into eight time
periods between 15,200 and 13,900 cal years B.P. Between
13,900 and 12,900 cal years B.P., there is significant ice loss
on all grid elements. Between 12,900 and 11,500 cal years
B.P., there is an increase of ice thickness on grid elements
in mainland British Columbia to simulate readvances that
happened during this time. Since the sea level data from this
time period are of low resolution, there was no attempt to
simulate in detail the various readvances and retreats discussed by Clague et al. [1997], Kovanen and Easterbrook
[2002], and Friele and Clague [2002]. After 10,700 cal years
B.P., the ice model has no ice on any grid element, indicating
that present glacial levels have been reached.
4.2. Sea Level Modeling
[17] Using the refined ice sheet model described above,
relative sea level was predicted for the three localities in
southwestern British Columbia that have well constrained
sea level curves. The root mean squared (RMS) error misfit of
the predicted sea level curves to the observed curves is used
to determine how well the predicted sea level matches the
constraints:
RMS ¼
4. Modeling Results
4.1. Ice Model
[13] Our ice sheet history model was modified from the
sequence originated by James et al. [2000] and revised by
Clague and James [2002] and Clague et al. [2005]. In the
vicinity of the sea level observations, the original grid
elements of the ice sheet model were divided into four equal
areas to provide increased sensitivity to the retreat history
(Figure 3). The finer grid also allows the ice thickness to
reflect the high variability of the topography. The ice sheet
model was first modified so that the predicted sea level curves
fit the magnitude of the high stands. This increased the size
of the ice load, especially in the Victoria area, a region that
previously had not been modeled. The timing of deglaciation
was then adjusted to provide rapid sea level fall at the same
time as the observations.
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rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 Xn
ðtrue SL pred SLÞ2 :
1
n
ð1Þ
Relative sea level observations have recently been collected
in the Strait of Georgia and the Victoria area to augment
the previous sparse record and facilitate more detailed GIA
modeling [James et al., 2002; Hutchinson et al., 2004; James
et al., 2005; Gowan, 2007; James et al., 2009] (Figures 1 and
4). The sea level high stand occurred between about 14,000
(Victoria) to 13,750 (northern Strait of Georgia) cal years B.P.
Sea level in Victoria fell from a high stand position of 75 m
above sea level to present-day sea level in about 800 years
[James et al., 2009]. After falling to a probable low stand
position around 30 m, sea level returned to within 4 m of
present by about 6000 cal years B.P. Direct observations in
the Victoria area only constrain the low stand to lie below
11 m and above 40 m, and this is the range shown in
Figure 4. Data from the central Strait of Georgia indicate that
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Figure 3. Ice sheet thicknesses for the final, iterated model are given for the southwestern Cordilleran Ice
Sheet (CIS) at the glacial maximum (15,400 cal years B.P.).
sea level fell rapidly from a high stand position of about 150 m
to below present sea level in 1500 –2000 years [Hutchinson
et al., 2004]. After reaching a low stand of about 15 m, sea
level returned to near present levels by about 8000 cal years
B.P. Sea level in the northern Strait of Georgia fell from a high
stand position of about 175 m to present levels in less than
3000 years [James et al., 2005].
[18] The sea level curves are well determined from 13,700
to 12,000 cal years B.P. for the northern Strait of Georgia,
13,900 to 12,300 cal years B.P. for the central Strait of
Georgia and 14,100 to 13,100 cal years B.P. for Victoria.
These time intervals are used for determining the RMS fit. An
unweighted RMS fit is appropriate because the sea level
curves are equally well constrained for these time intervals.
The uncertainty on the timing of sea level fall at each locality
is estimated to be about ±100 years.
[19] The magnitude and timing of the subsequent low
stands and recovery to present levels in the mid-Holocene
are less well determined. The mid and Late Holocene segments of the sea level curves may also include a significant
tectonic component [e.g., Hutchinson, 1992]. For these
reasons, RMS calculations were carried out only for the time
intervals indicated above and do not include the low stand
portions of the sea level curves.
[20] Predicted sea level curves are compared to observations in Figure 4 for Earth models with different asthenospheric thicknesses and the asthenospheric viscosity chosen
to optimize the fit to the observations. The predictions agree
well with the observations. They feature a very similar
rapid fall in sea level after deglaciation between 14,000 and
12,000 cal years B.P. For the central Strait of Georgia (CSG),
the Earth models with a thicker asthenosphere have a poorer
fit than the thin asthenosphere models. A slight adjustment to
an earlier time of deglaciation would improve the agreement
for the thick asthenosphere models. Overall, the models
successfully predict the rapid sea level fall observed in the
first 1000 to 1500 years after deglaciation.
[21] From 12,000 to 10,000 cal years B.P., there are slight
differences in the predicted responses that depend on the
asthenospheric thickness and viscosity. In general, however,
the features of the low stand calculation are consistent among
the model predictions. The modeled level low stand position
is about 35 m in Victoria, which is close to the maximum
low stand scenario of 40 m and slightly deeper than the
preferred low stand of 30 ± 5 m proposed by James et al.
[2009]. The predicted low stand position of about 20 m in
the central and northern Strait of Georgia is deeper than the
available observations would indicate [Hutchinson et al.,
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Figure 4. Comparison of predicted and observed sea levels in southwestern British Columbia using
the final ice model. The RMS fit (m) of the central Strait of Georgia (CSG) sea level curve is given for
each comparison. The optimal viscosity value that provides the best fit to the observations for the given
asthenospheric thickness is indicated. Two variants of the observed Victoria sea level curve are given,
corresponding to the minimum and maximum possible low stands, as discussed in the text.
2004; James et al., 2005]. By 9000 cal years B.P., the
modeled sea level at all locations approaches the same value,
indicating that the crustal response has diminished to the
same (small) level at all three locations. It is possible that
changes to the assumed VM2 viscosity structure below the
asthenosphere could produce a better fit to the low stand
portions of the sea level curves.
[22] Contour plots of the RMS misfit are given for a range
of asthenospheric thicknesses and viscosities in Figure 5.
There is no one thickness/viscosity pairing that produces the
best fit. Instead, relatively uniform, good fits are obtained
across the range of asthenospheric thicknesses that was
considered. The optimal viscosity ranges from 3 1018
(140-km-thick asthenosphere) to 4 1019 Pa s (380-kmthick asthenosphere). For a given asthenospheric thickness,
the RMS misfit rapidly increases away from the optimal
viscosity value. An RMS misfit of 16 m provides fits to the
observations that are visibly poorer than the minimum misfit
values of 8 m.
[23] Overall, the optimal misfit range is tighter for the
central and northern Strait of Georgia than for Victoria. This
is likely the result of the Strait of Georgia curves being well
constrained over a longer time period. The misfit of the
Victoria sea level curve is slightly better with a thicker
asthenosphere. This may indicate that an asthenospheric
thickness greater than 220 km is to be preferred, although
the fit for a thinner asthenosphere could be improved by
slightly revising the timing of ice sheet retreat. An asthenospheric viscosity greater than 1020 Pa s or less than 1018 Pa s
is ruled out for asthenospheric thicknesses ranging from 140
to 380 km.
[24] The viscosity of the asthenospheric channel can be
estimated for a thinner asthenosphere. For the case where viscous flow is confined to a thin layer, a diffusion constant (D)
for channel flow is given by
5 of 13
D¼
rgH 3
3h
ð2Þ
JAMES ET AL.: CASCADIA SUBDUCTION ZONE VISCOSITY
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Relation (3) suggests a linear relationship between the logarithms of asthenospheric viscosity and thickness. Figure 6
shows that the expected linear relationship starts to break
down above 300-km thickness, suggesting that the assumption of channel flow is less valid at larger thicknesses. A
linear regression through the other points provides an extrapolation to a thinner asthenosphere. A 50-km-thick asthenosphere would require a viscosity of about 2 1017 Pa s and a
10-km-thick asthenosphere would need a viscosity substantially less than 1016 Pa s in order to explain the sea level
observations.
4.3. Current Crustal Uplift Rates
[25] The model-predicted crustal uplift rates due to GIA for
the ice load history are given in Figure 7a for an asthenospheric thickness and viscosity of 300 km and 2.5 1019 Pa
s, respectively. The present-day uplift rate on Vancouver
Island is predicted to be about 0.1 mm a1. The uplift
predicted by a variant of the ICE-3G deglaciation model
[Tushingham and Peltier, 1991], without the southwestern
British Columbia ice history included, generates uplift rates
of 0.3 to 0.35 mm a1 on Vancouver Island for the same
viscosity structure (Figure 7b). The sum of the two predictions, which includes the effect of distant ice sheets as well as
the local Cascadia model, is given in Figure 7c and features
uplift rates on Vancouver Island of 0.4 to 0.45 mm a1.
[26] These predictions are consistent with recent analyses
of the postglacial isostatic depression at Victoria [James et al.,
2009] and the northern Strait of Georgia [James et al., 2005],
in which the present-day rate of crustal uplift was estimated to
be 0.12 and 0.25 mm a1, respectively. Although the model
predictions (Figure 7c) given here are larger by factors of two
to four, the magnitude of all the predictions is only a few
tenths of a millimeter per year and is below the resolution of
GPS observations. This is in contrast to other regions where
current postglacial uplift rates reach magnitudes of many
millimeters per year (e.g., Churchill, Manitoba, 10 mm a1
[Lambert et al., 2006]) and, in circumstances that feature
recent ice mass wastage and low mantle viscosity, a few
centimeters per year (e.g., Glacier Bay, Alaska, 30 mm a1
[Larsen et al., 2005]).
Figure 5. Contours of the RMS fit (m) of the predicted sea
level curves to the observations are depicted for a range of
asthenospheric thicknesses and viscosities for (a) Victoria,
(b) the central Strait of Georgia, and (c) the northern Strait
of Georgia. The predictions were generated using the final ice
model depicted in Figure 3.
where r is density, g is the acceleration due to gravity, H is
the thickness of the channel, and h is the channel viscosity
[Cathles, 1975]. The rate of crustal response is determined by
the diffusion constant. Solving for viscosity h, we have
h¼
rgH 3
3D
ð3Þ
Figure 6. A logarithmic plot of optimal asthenospheric
viscosity and thickness pairs and their extrapolation to thinner values. Also given is the effective viscosity of serpentine
using the flow law parameters of Hilairet et al. [2007] and
assuming GIA strain rates, as discussed in section 5.4.
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[27] Measured present-day crustal uplift rates from Global
Positioning System (GPS) observations along the west coast
of North America (from northern California to the southern
Alaska panhandle) range from about 2 to 4 mm a1
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[Mazzotti et al., 2008]. The GPS observations have substantial scatter that may reflect inherent uncertainties in the GPS
time series or local site effects, but spatially coherent patterns
of vertical crustal motion suggest that there are real regional
variations at the level of a few millimeters per year. The small
GIA rates predicted here from the late Pleistocene deglaciation of the CIS indicate that other processes, such as active
tectonics, must be largely responsible for the variations in
current vertical crustal motion.
5. Implications for Upper Mantle Viscosity
in the Cascadia Subduction Zone
[28] Are the asthenospheric viscosities inferred from GIA
modeling with linear Maxwell viscoelastic Earth models consistent with laboratory-constrained, nonlinear, temperaturedependent flow properties of mantle minerals? The sea level
observations are located in the CSZ fore arc where crustal
heat flow is low [Hyndman and Lewis, 1995] and the subducting oceanic lithosphere is 40 to 70 km deep (Figure 1).
[29] Geodynamic modeling of the CSZ that explains
features of the observed heat flow, depth of crustal seismicity,
and the relative paucity of arc volcanism shows that the sea
level sites are underlain by a stagnant mantle wedge that
reaches about 600°C at 70 km depth [Wada et al., 2008]
(Figure 8a). Beneath the fore-arc mantle wedge lies the
subducting oceanic lithosphere, which reaches temperatures
of 1000°C at about 100 km depth. A few tens of kilometers
further landward of the sea level observations, temperatures
of 1000°C are reached at shallower depths of about 60 km
in the arc and back-arc regions of the subduction zone.
[30] The sea level sites are located in the boundary zone
between the oceanic and continental plates. It is likely that the
observed rapid sea level response is primarily a consequence
of the viscosity of the oceanic mantle that lies directly
beneath the sites, but the ice sheet extended east over continental mantle, and the observed response must also have a
contribution from the continental mantle wedge. Thus, in the
following we consider the viscosity of the subducting oceanic
mantle, as well as the hot, circulating arc and back-arc continental mantle wedge.
5.1. Effective Viscosity of the Mantle Derived
From Nonlinear Flow Laws
[31] Karato and Wu [1993] synthesized laboratory studies
and geological and geophysical observations and found that
the upper mantle is likely to deform by power law (dislocation) creep. Nonlinear, temperature-dependent plastic flow
arising from dislocation creep is given by
Q þ PV
e_ ¼ Asn exp RT
ð4Þ
Figure 7. Uplift rates (mm a1) calculated for (a) the ice
sheet model developed here loading an Earth model with a
lithosphere thickness of 60 km, asthenosphere thickness of
300 km, and asthenosphere viscosity of 2.5 1019 Pa s,
(b) the ICE-3G model with southwestern British Columbia
masked, using the same Earth model as Figures 7a, and (c) the
sum of Figures 7a and 7b.
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With values of n typically in the range of 3 to 3.5, the exponent of the strain rate e_ takes on values of 0.67 to 0.71.
Thus, a larger strain rate delivers a smaller effective viscosity,
if other factors are held constant.
[32] If two processes, such as GIA and subduction, are
both occurring, then the determination of the effective viscosity requires additional attention [e.g., Schmeling, 1987;
Ranalli, 1995]. Assuming that the two processes are occurring with a subduction strain rate e_ S and GIA strain rate e_ G,
then the effective viscosity depends on the total strain rate e_ =
e_ S + e_ G. With reference to equation (5), if one strain rate
is much larger than the other, then the effective viscosity is
determined by the larger strain rate. In this case, the process
occurring at slower strain rates does not influence the
effective viscosity greatly, and the slower process will proceed as though operating under a linear flow law. On the other
hand, if the two strain rates are similar in magnitude, then the
effective viscosity is scaled by a factor of 2(1n)/n (= 0.6 for
n = 3.5) relative to the effective viscosity that would be
determined if only one of the processes were active.
[33] In the following, we first determine the effective
viscosities for subduction and GIA separately, and then we
discuss the effective viscosity when GIA and subduction are
considered jointly.
Figure 8. (a) Temperatures (°C), (b) strain rates (s1), and
(c) effective viscosities (Pa s) for the preferred Cascadia
subduction model of Wada et al. [2008, Figure 6c]. For the
oceanic mantle, effective viscosities were obtained assuming a tectonic strain rate of 5 1015 s1, as discussed in
section 5.2. Labeled sites (arrows) 1, 2, and 3 correspond
to the approximate location of the Victoria, central Strait of
Georgia, and northern Strait of Georgia sea level curves,
respectively. The location of arc volcanism is given by the
triangle. The gray shading in the overriding and subducting
mantle corresponds to the stability zone of the serpentine
mineral antigorite.
where e_ is the flow strain rate, A is a material parameter, s is
the stress, n is the power law exponent (n = 3 – 3.5 for the
materials considered here), Q is the activation energy, R is the
gas constant, and T is temperature [e.g., Evans and Kohlstedt,
1995]. The dependence on the pressure P and activation
volume V is relatively small and is neglected here. We also
ignore the tensorial nature of stress and strain, as the focus of
the discussion is on the magnitudes. Defining an effective
viscosity heff = s/2_e, we have
1
Q
heff ¼ e_ ð1nÞ=n A1=n exp
2
nRT
ð5Þ
5.2. Effective Viscosity of the Upper Mantle
From Tectonic Processes
[34] For the preferred Cascadia model of Wada et al.
[2008, Figure 6c] (and their associated discussion), strain
rates in the convecting mantle wedge due to subduction reach
1014 s1 at depths of 70 to 90 km and are above 1015 s1
below about 60 km depth (Figure 8b). Above the subducting
slab, at depths greater than 70 km, effective viscosities are
mostly in the range of 1018 Pa s to 1019 Pa s (Figure 8c). These
values are attained to the east (landward) of the sea level
observations.
[35] The model of Wada et al. [2008] predicts the thermal
structure of the subducting oceanic lithosphere but does not
consider its deformation. To calculate the effective viscosity
of the oceanic mantle from equation (5) with the predicted
temperature requires an estimate of the strain rate at which the
oceanic mantle undergoes strain. We derive the estimate in
two different ways:
[36] 1. Assuming the mantle beneath the subducting Juan
de Fuca plate is moving with the oceanic plate, its strain rate
can be derived by noting that beneath the study region the
subducting slab sinks 40 km as it travels 100 km eastward in
about 2.4 Ma (assuming a convergence rate of 4.5 cm a1).
This gives a strain rate of 40 km/100 km/2.4 Ma = 5 1015 s1 for the oceanic mantle in the vicinity of the CSZ.
[37] 2. Regionally, the Juan de Fuca plate is a few hundred
kilometers wide (ranging from about 350 to 650 km from the
Juan de Fuca ridge to where it reaches about 100 km depth in
the CSZ). The Juan de Fuca ridge is spreading at about 6 cm
a1, while the Juan de Fuca plate is subducting at about
4.5 cm a1. Assuming an average width of 500 km and
assuming similar upwelling and downwelling rates in the
upper mantle of 5 cm a1 gives a strain rate of 10 cm a1/
500 km = 6 1015 s1. The regional oceanic mantle strain
rate is essentially identical to the strain rate estimated for the
oceanic mantle at the CSZ.
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Table 1. Flow Law Parameters
Material
A (s1 Pan)
n
E (kJ mol1)
Dry Olivinea
Wet Olivinea
Serpentineb
4.85 1017
4.89 1015
4.47 1038
3.5
3.5
3.8
535
515
8.9
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and would also relate to the reduced rate of response some
time after the load was removed. Deep oceanic mantle viscosities are less than about 3 1019 Pa s, and the mantle
wedge viscosity is less than about 5 1019 Pa s at depths
greater than about 80 km.
a
Hirth and Kohlstedt [1996].
Hilairet et al. [2007].
[38] In discussing the generation of mid-ocean ridge
basalts and the evolution of the oceanic lithosphere and
mantle, Hirth and Kohlstedt [1996] considered the oceanic
mantle to be composed of dry olivine (dunite) above about
60 km depth and wet olivine below. Using their flow law
parameters for the two materials (Table 1) and temperatures
given in Figure 8a and assuming a uniform strain rate 5 1015 s1 gives effective viscosities for the subducting
oceanic mantle (Figure 8c). If oceanic mantle deformation
is localized in a thin, low-viscosity layer, perhaps arising
from the slab sliding over a layer containing partial melt, then
strain rates in this part of the oceanic mantle could be larger
than assumed here and the effective viscosities would be
smaller. Thus, the oceanic mantle effective viscosities shown
in Figure 8c are a probable upper bound.
5.4. Stagnant Mantle Wedge
[43] We also considered whether the cold, stagnant forearc mantle wedge could have a viscous response on GIA time
scales. Tectonic strain rates here are much smaller and GIA
strain rates dominate. If the stagnant mantle wedge were to
contribute significantly to the sea level response, viscosities
appropriate to a channel with a thickness in the range of 10
to 40 km would be required. As discussed in section 4.2,
this would imply effective viscosities in the range of 1015 to
1017 Pa s (Figure 6).
[44] Petrological considerations and seismic observations
suggest the fore-arc mantle is heavily serpentinized [Bostock
et al., 2002; Hyndman and Peacock, 2003; Brocher et al.,
2003; Ramachandran et al., 2005]. Using flow law parameters for antigorite serpentine [Hilairet et al., 2007] (Table 1),
which is at least 1 order of magnitude weaker than any other
major mantle mineral, the effective viscosity of the stagnant
mantle wedge ranges from 1020 Pa s to 6 1020 Pa s for
5.3. Effective Viscosity of the Upper Mantle From GIA
[39] A representative GIA strain rate during the time of the
fastest response can be derived by noting that following
deglaciation, the central Strait of Georgia rose about 35 m
relative to Victoria in 1000 years [James et al., 2009]. The
sites are 140 km distant so the strain rate is about 1014 s1.
This is the peak rate, and it applies to the mantle near the
changing surface load during the time of fastest rebound. At
greater distances (or depths) from the changing load, or at
later times, GIA strain rates were lower.
[40] Effective viscosities were computed for uniform strain
rates of 1014 and 1015 s1 (Figures 9a and 9b) using
equation (5), the temperatures given in Figure 8a, and the
parameters appropriate to wet and dry olivine (dunite) [Hirth
and Kohlstedt, 1996]. For the hot, actively convecting mantle
wedge, a wet dunite rheology was assumed. For the oceanic
mantle we have adopted the structure that was assumed in
section 5.2.
[41] For a strain rate of 1014 s1, the effective viscosity of
the continental mantle wedge is less than 1020 Pa s below
about 60 km depth and less than 1019 Pa s below about 80 km
depth (Figure 9a). In the oceanic mantle, the dry dunite
rheology leads to viscosities larger than about 1021 Pa s for
distances less than about 40 km from the slab top. At 50 km,
the increasing temperatures cause the viscosity to drop to
about 5 1019 Pa s. The assumed transition to a wet dunite
rheology at greater depths then leads to a sharp reduction in
viscosity to values of 5 1018 Pa s and lower. Overall, the
viscosity of the oceanic mantle is about a factor of 2 less than
that predicted for the arc and back-arc mantle wedge. The
presence of volatiles and melt in the arc and back-arc mantle
wedge would be expected to reduce effective viscosity and
the values shown in Figure 9 are a probable upper bound.
[42] The effective viscosity is a factor of 5 larger when
the strain rate is decreased by a factor of 10 to 1015 s1
(Figure 9b). A smaller strain rate may be more representative
of conditions further away from the imposed surface load,
Figure 9. Contours of effective viscosity are shown for
uniform strain rates of (a) 1014 s1 and (b) 1015 s1, corresponding to peak and reduced GIA strain rates. Temperatures from Figure 8a were employed in the calculations, and a
wet olivine (dunite) rheology is assumed for the continental
mantle wedge and for the oceanic mantle at depths greater
than about 50 km below the top of the subducting slab. A dry
olivine rheology is assumed for shallower parts of the oceanic
mantle. Flow law parameters are from Hirth and Kohlstedt
[1996]. Other labeling is the same as Figure 8.
b
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[46] At greater distances and depths from the shrinking ice
mass, GIA strain rates were lower and GIA effective viscosities were higher. For this case, the tectonic effective viscosities would dominate, and the sea level observations would
sample effective viscosities of 1019 Pa s and lower.
[47] The effective tectonic viscosities are the same as the
lower end of the viscosity range determined from the GIA
modeling. The sea level observations could be fit well with
an asthenosphere having a viscosity of 3 1018 Pa s and
thickness of 140 km, 1019 Pa s at 220 km, and 4 1019 Pa s
at 380 km. Thus, an asthenosphere of 100- or 200-km thickness and a viscosity between 1018 and 1019 Pa s fits the sea
level observations well and is consistent with experimentally determined nonlinear dislocation flow laws for wet
olivine deforming at rates consistent with the subduction of
the Juan de Fuca oceanic plate. Below this layer lies higherviscosity upper mantle.
Figure 10. Summary of model and effective viscosities for
GIA and tectonics. ‘‘Model’’ is the GIA modeling reported
here using a linear Maxwell rheology. Asthenospheric thicknesses (km) are given for selected viscosity values. ‘‘Oceanic
mantle’’ refers to the effective viscosity below about 60 km
depth (wet olivine rheology), and ‘‘cont. mantle’’ refers to the
actively circulating arc and back-arc mantle wedge. Effective
viscosities for glacial isostatic adjustment (GIA) are computed using a peak GIA strain rate of 1014 s1 and a reduced
strain rate one tenth of that (Figure 9; section 5.3). Effective
viscosities due to tectonics were computed from the model of
Wada et al. [2008] for the continental mantle wedge (Figure 8;
section 5.2).
GIA strain rates ranging from 1014 s1 to 1015 s1 and for
temperatures given in Figure 8a (Figure 6). The degree of
serpentinization of the fore-arc mantle is uncertain, but
estimates range from about 20% to 60%. Consequently, the
effective viscosity may be somewhat higher than estimated
here assuming a pure antigorite rheology, although the
probable presence of free water would act to reduce viscosity.
Apparently, the effective viscosity of the stagnant mantle
wedge is about 2.5 orders of magnitude too large to have
yielded viscously and contributed to the observed sea level
response.
5.5. Combined Effective Viscosity
[45] The effective viscosities and viscosity range inferred
from the GIA modeling are summarized in Figure 10. The
effective viscosities due to tectonics are similar for the
oceanic and back-arc mantle and have values of 1019 Pa s
and less. During deglaciation, when peak GIA rates of about
1014 s1 were experienced, the effective viscosity in both
regions due to GIA was very similar to the effective viscosities due to tectonic processes. Thus, combining the two
processes may have led to a reduction in effective viscosity of
a factor of 0.6, as discussed in section 6.1, and could have
shifted effective viscosities from 1019 Pa s and lower to 6 1018 Pa s and lower.
5.6. GIA Model Viscosity: Oceanic or Continental
Mantle?
[48] Both the effective viscosity of the oceanic mantle and
the hot, circulating arc and back-arc mantle wedge agree with
the viscosity range obtained from the GIA modeling. This is
consistent with both regions contributing to the observed
response, although the oceanic mantle directly underlying
the observations would respond directly to changes in surface
load brought about by deglaciation, and thus would be
expected to contribute the majority of the response.
[49] The Strait of Georgia sea level sites are located about
70 km from where surface heat flow rises sharply near the
volcanic arc [Hyndman and Lewis, 1995] and low-viscosity
continental mantle is expected. Spatial wavelengths of the
Earth’s response to the ice load that are longer than 50–
100 km would be sensitive to the viscosity of the back-arc
(continental) mantle. As well, relative to the sea level sites,
the ice sheet extended a much greater distance eastward past
the subduction arc into the back-arc region than it extended
westward. Thus, long spatial wavelengths would sample
continental mantle more than oceanic mantle, although they
also sample deeper into the mantle and the effect of a shallow,
thin, low-viscosity layer is thus reduced. These considerations suggest that the GIA model viscosities are a blend of
oceanic and continental mantle viscosity, but that the oceanic
mantle contributed most of the response.
5.7. GIA and a Transient Mantle Rheology
[50] Instead of GIA sampling a power law medium whose
viscosity is conditioned or determined by subduction-related
processes, it is possible that GIA is sampling a transient
rheology that is independent of the long-term deformation.
Karato [1998] has suggested that because dislocation density
is proportional to stress, a power law medium undergoing
deformation from two processes will not simply respond as
the sum of the deformation rates as described in section 5.1
(equation (5)). Instead, deformation by the more ephemeral
process (GIA) will proceed by a transient creep mechanism.
Ranalli [1998] also put forward arguments suggesting that
dislocation creep (power law) and diffusion creep (linear)
almost balance. He introduced the concept of a transition
stress marking the boundary between predominantly linear
creep (low stress) and power law creep (high stress).
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[51] We do not rule out the possibility that GIA occurs
primarily through a transient creep mechanism at the CSZ.
It is possible that the correspondence of the GIA model
viscosities, GIA effective viscosity, and tectonic effective
viscosity is accidental. Nevertheless, the agreement suggests
to us that power law creep plays an important role in the
deformation induced by GIA. Karato’s [1998] argument
depends on a uniform population of dislocations, all of which
are participating in the deformation related to the background
stress. But the mantle is heterogeneous on many spatial
scales. It is possible that the imposition of an additional stress
from GIA could lead to the activation of additional dislocations and a power law response as described in section 5.1.
We also note that a power law rheology explains features of
short-term transient deformation following large earthquakes
[e.g., Freed and Bürgmann, 2004; Freed et al., 2006],
although postseismic observations can be explained using
a transient rheology [e.g., Pollitz, 2003; Pollitz et al., 2006]
and other processes (poroelasticity, after slip) may also be at
play.
[52] Although transient creep may be at work for monthly
to decadal-scale postseismic deformation following large
earthquakes, its importance in the postglacial response at
the time scale of hundreds to thousands of years is presently
unclear. Given the agreement between effective viscosities
inferred from GIA and long-term subduction processes,
we think there is good reason to believe that a power law
rheology is important on the GIA time scale. A complete
resolution of this issue is beyond the scope of the paper.
Explicit GIA modeling at the CSZ with a power law rheology
and including subduction zone processes would be a useful
next step.
5.8. Implications for Models of the Megathrust
Earthquake Cycle
[53] As reviewed by Wang [2007], models are being
actively developed to explain deformation features of the
megathrust earthquake cycle. One observed feature is that the
location of the largest coseismic subsidence, which tends to
occur approximately above the landward termination of the
locked part of the subduction interface, is also where the
largest postseismic uplift occurs [e.g., Thatcher, 1984; Cohen
and Freymueller, 2001]. This feature can be replicated in
megathrust earthquake cycle models by assuming, below the
strong oceanic lithospheric lid a few tens of kilometers thick,
an oceanic mantle with long-term effective viscosity around
1020 Pa s. Immediately after the earthquake, loading of the
locked zone recommences and for this choice of oceanic
mantle viscosity, postseismic uplift occurs. For a smaller
oceanic mantle viscosity (e.g., 1019 Pa s), however, subsidence occurs because the weaker oceanic mantle yields
quickly to the increased load of the overriding continental
lithosphere caused by coseismic slip along the subduction
interface. In this case, to generate uplift, it is necessary to also
assume that significant after slip occurs on deeper portions of
the subduction fault.
[54] Our GIA modeling of sea level observations from the
northern CSZ indicates that the (shallow) oceanic mantle has
a viscosity less than 4 1019 Pa s. Smaller values below
about 1019 Pa s are required if the deformation is proceeding
through power law creep. Models developed to explain the
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great earthquake cycle at subduction zones with young
oceanic lithosphere will need to incorporate a low-viscosity
oceanic mantle. This may require significant deep after slip in
the megathrust earthquake cycle to explain the nature of
postseismic deformation.
6. Discussion and Summary
[55] GIA modeling of new relative sea level data has
determined a close relationship between assumed asthenospheric thickness and inferred viscosity. The optimal value of
the asthenospheric viscosity ranges from 3 1018 Pa s to 4 1019 Pa s for asthenospheric thicknesses ranging from 140 km
to 380 km. The viscosity values are similar to the 5 1018 to
5 1019 Pa s range originally estimated by James et al.
[2000] and Clague and James [2002], but the earlier estimates
were not based on a confined asthenospheric thicknesses.
[56] We have also calculated effective viscosities of both
the subducting oceanic mantle below the assumed dry ‘lid’
and the continental arc and back-arc mantle wedge assuming
power law creep and using temperatures from a geodynamic
model of the Cascadia subduction zone. Values thus determined are consistent with the lower range of asthenospheric
viscosities derived here from GIA modeling. A 100- or
200-km-thick layer with a viscosity of 1018 Pa s to 1019 Pa s
reproduces the sea level observations and is consistent with
the effective viscosities expected at this plate boundary,
which features subduction of a young oceanic plate. An alternative interpretation of the GIA modeling results in terms of
transient deformation is possible but the agreement between
the GIA model viscosities and the GIA and tectonic effective
viscosities is consistent with a substantial role for power law
deformation in the GIA response.
[57] Regardless of the microphysical mechanisms at work
to generate the GIA response, the viscosity values inferred
from the GIA modeling can be applied to studies of the
megathrust earthquake cycle because there is substantial
overlap between the timescales of both processes. The GIA
response in northern Cascadia was rapid, featuring an exponential decay time of about 500 years [James et al., 2005],
and sea level fell rapidly in 1000 to 2000 years (Figure 4).
This time range is comparable to the 500 –600 year average
repeat time of great megathrust earthquakes at the CSZ
[Atwater and Hemphill-Haley, 1997; Goldfinger et al., 2003].
[58] If strain is localized in the oceanic mantle just below
the moving lithosphere, perhaps because of the nonlinear
rheology, then the effective viscosities for the oceanic mantle
based on thermal modeling results may require careful
interpretation, because viscous deformation takes place in
both the ‘‘layer’’ of higher strain rate and thus lower viscosity
and the underlying mantle of lower strain rate and thus higher
viscosity. However, the GIA modeling still gives constraints
on the viscosity of the asthenosphere. Extrapolation of
the viscosities inferred from the GIA modeling (Figure 6)
indicates that viscosities around 1018 Pa s are needed for a
100-km-thick asthenosphere and 1017 Pa s for a 40-km-thick
asthenosphere.
[59] Good fits to GIA observations using linear rheology
Earth models have been obtained for many regions. This
could indicate the prevalence of a transient linear rheology on
GIA time scales, which for many parts of the world is a few
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thousand years. Two related studies of the Laurentide postglacial uplift which compared a composite linear and nonlinear rheology to a purely linear rheology found a slight
preference for the composite rheology to explain relative sea
level [Gasperini et al., 2004; Dal Forno et al., 2005]. For the
composite rheology, the majority of the GIA deformation
took place through the nonlinear mechanism.
[60] It could also be that GIA samples linear effective viscosities that are determined by tectonic and mantle convection processes acting on power law materials, as we suggest
for the CSZ. This is also suggested by the results of Wu
[2001], who found a good fit to relative sea level data in
North America with a power law rheology, provided an
ambient tectonic stress of 10 MPa was assumed in the mantle.
Other studies have reported variable success in explaining
GIA observables with a purely nonlinear rheology and no
viscosity conditioning by tectonic processes [e.g., Wu, 1998,
2002; Wu and Wang, 2008]. These studies illustrate some of
the approaches for the treatment of Earth deformation that
have been taken to explain GIA observations.
[61] It would be valuable to determine if linear viscosity
models developed to explain GIA observations are also
consistent with constraints on heat flow, experimentally
determined flow laws, and inferred tectonic and mantle
convection strain rates, as described here for the northern
CSZ. For example, GIA modeling of the response to Little
Ice Age retreat derived an optimal viscosity around 3– 4 1018 Pa s for a 110-km-thick asthenosphere at Glacier Bay
(GB), southeast Alaska [Larsen et al., 2005]. The GB
viscosity is only a factor of 3 – 4 larger than the value extrapolated from our modeling for a 110-km-thick asthenosphere
(Figure 6). The relatively close correspondence suggests
the GB value could be explained in terms of the tectonic
preconditioning of a power law medium, but this needs to
be explored.
[ 62 ] The sea level observations modeled here were
obtained from sites located above the stagnant mantle wedge
but relatively close to the actively circulating continental
mantle wedge. The observed rapid sea level fall is likely
predominantly due to the low viscosity of the oceanic mantle
that directly underlies the sites, but a contribution from the
low-viscosity arc and back-arc mantle wedge located landward of the observations is also possible. Modeling with a
laterally variable CSZ structure would be needed to quantify
the relative contributions.
[63] Efforts to collect precise relative sea level observations
from further seaward (e.g., the west coast of Vancouver Island)
and landward (the mainland coast of British Columbia and
Washington State east of the Strait of Georgia and Puget
Sound) would be well warranted, as they could be related
more directly to the rheology of the oceanic mantle and
continental arc and back-arc mantle wedge, respectively. This
could give further insight to geodynamic processes at this
subduction zone.
[64] Acknowledgments. Kevin Fleming, Stephane Mazzotti, Roy
Hyndman, and an anonymous reviewer are thanked for reviews and
discussions that helped to substantially improve the manuscript. Evan
Gowan was supported by a Graduate Fellowship from the University of
Victoria, the Natural Sciences and Engineering Research Council (NSERC)
of Canada, and the Geomatics for Informed Decision Making Network of
Centres of Excellence (GEOIDE NCE). Ikuko Wada was supported by
NSERC and the USGS National Earthquake Hazards Reduction program.
This is Earth Sciences Sector contribution 20080407.
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E. J. Gowan, T. S. James, I. Wada, and K. Wang, Pacific Geoscience
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