Download Seismic low-velocity layer at the top of subducting slabs

Physics of the Earth and Planetary Interiors 149 (2005) 7–29
Seismic low-velocity layer at the top of subducting slabs:
observations, predictions, and systematics
Geoffrey A. Abers∗
Department of Earth Sciences, Boston University, 685 Commonwealth Avenue, Boston, MA 02215, USA
Received 30 May 2003; received in revised form 24 March 2004; accepted 26 August 2004
Abstract
Layered structure persists at the tops of subducting plates to depths in excess of 150 km. A low-velocity channel several km
thick produces guided seismic guided waves, which indicate that the top of the downgoing plate remains coherent and probably
has not eclogitized to >150 km depth. The surrounding medium has seismic velocities 3–6% faster than standard earth models,
as inferred from direct travel times, presumably because the waveguide lies atop cold descending lithosphere. However, guided
waves travel more slowly. Several tests with full waveform synthetics show that the guided waves can be observed only if excited
by sources that lie near or within the low-velocity channel. Thus, the frequent observation of dispersed body waves indicates
that intermediate-depth earthquakes tend to lie in waveguides. Also, receivers must be favorably placed. Observations for seven
circum-Pacific subduction zones show such signals, which can be explained as low-velocity channels 2–8 km thick. Velocity
anomalies within low-velocity channels are largest at shallowest depths, up to 14% slower than surroundings at depths less than
150 km, diminishing to <3% at greater depths. This variation in depth indicates that low-velocity channels metamorphose at
depths that can exceed 150 km to a rock closely resembling eclogite or peridotite. Metamorphism probably involves dehydration
of a layer initially abundant in hydrous minerals, although equilibration of variable fractions of metastable gabbro may explain
some observations. The size of the low-velocity anomaly correlates with slab dip, with steeply dipping slabs exhibiting the
greatest anomalies, but does not correlate with thermal parameter or convergence velocity. This correlation may reflect a greater
ability of steep slabs to funnel fluid up the slab rather than into the overlying wedge, so that slow seismic velocities integrate
effects of subduction of hydrous materials and their subsequent up-dip fluid transport. At depths exceeding 150 km, the waveguide
velocities place an upper bound on the amount of water that could be delivered to deeper mantle, to 2 wt.% or less within this
4 km thick layer.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Subduction zones; Metamorphism; Seismic low-velocity zones; Body waves; Dispersion; Dehydration
1. Introduction
∗
Tel.: +1 617 353 2616; fax: +1 617 353 3290.
E-mail address: [email protected].
0031-9201/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.pepi.2004.10.002
As oceanic plates subduct, the downgoing crust, sediments, and altered mantle undergo a sequence of phase
transformations with increasing pressure and temper-
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G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
ature (e.g., Schmidt and Poli, 1998). Many of these
reactions involve dehydration, and control the cycling
of volatiles to magmatic arcs and into the deep mantle.
However, the depths at which reactions actually occur
are poorly known in many cases, as are the extents of
dehydration, so the fluid flux to the deep mantle remains
almost completely uncertain (Williams and Hemley,
2001). Also, the metamorphism of anhydrous gabbro
may be delayed metastably (Hacker, 1996), making
the subducted crust buoyant even without water.
Fortunately, seismic measurements are beginning
to place direct constraints on the structure of sub-
ducted plates, and provide in situ bounds on dehydration. A plethora of mode-converted, reflected, and dispersed body wave phases have shown that the upper
few kilometers of subducted slabs contain sharp interfaces or layering (e.g., Gubbins et al., 1994; Helffrich, 1996; Helffrich and Stein, 1993; Yuan et al.,
2000). Such observations require that oceanic crust
remains seismically distinct from surrounding mantle, in most cases at lower seismic velocities. In
particular, high-frequency body wave distortion, described as dispersion, indicates that a 2–8 km thick
layer that is several percent slower than surrounding
Fig. 1. Ray paths sampled, from 3D ray tracing. Three-letter code is station name used, as in Table 1. Triangles: stations, circles: earthquakes.
Thick black lines: portion of ray paths inside slabs; gray lines: portion above slabs; dashed lines: contoured depths to slabs, at 50 km intervals;
barbed line: trench.
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
9
Table 1
Stations and arcs sampled, and sampling
Station
Latitude (◦ )
Longitude (◦ )
Arc
Number of P waves
Number of S waves
Ttot a (s)
ADK
COL(A)b
ERM-nc
ERM-sc
GUMO
JTS
PET
51.884
64.900
42.015
42.015
13.588
10.291
53.024
−176.684
−147.793
143.157
143.157
144.866
−84.953
158.650
Aleutians
Alaska
Hokkaido, S Kurile
N. Honshu
Mariana
Nicaragua
Kurile-Kamchatka
24
55
28
6
34
19
44
19
38
16
8
22
7
47
552
1406
990
232
985
609
811
a
b
c
Total time spent in slab for all P waves.
Station COL moved to COLA in 1996, 4 km to SW; listed coordinates for COL.
Data set from ERM split between events north of station (Hokkaido–S. Kuriles) and south (N. Honshu).
material exists atop many slabs (Abers, 2000). If these
slow zones do indeed represent hydrated rocks, then
their seismic velocities constrain the H2 O contents
of slabs (Abers et al., 2003; Hacker et al., 2003a).
Even if the slow velocities include a contribution
from metastable gabbro, the seismic velocities should
still place an upper bounds on the degree of in situ
hydration.
This paper presents a comprehensive review of the
body-wave dispersion constraints on waveguide composition (Abers, 2000), emphasizing the variability and
limitations of the dispersion data set. Several theoretical and numerical tests show the situations in which dispersion can be expected, and show the ability of current
methods to resolve the dispersion. We find that velocity measurements are sufficiently robust to allow their
variations to be measured between arcs and with depth,
for seven Pacific arc segments (Fig. 1, Table 1). The
systematics suggest that the top of oceanic plates progressively convert to eclogite as slab depth increases,
but that other effects (such as updip transport of fluids) may control the size and distribution of waveguide
anomalies.
tial low-frequency signal (Abers, 2000), although signals from Tonga earthquakes recorded in parts of New
Zealand show the opposite behavior (Ansell and Gubbins, 1986). The common dispersion can be produced
by propagation along a waveguide of constant velocity V and thickness H, surrounded by a faster medium
of velocity V0 . Other mechanisms that disperse body
waves, such as anelastic attenuation and scattering, do
not produce the large effects seen here, often produce
the incorrect sign of dispersion, and do not produce
the observed high-frequency amplification. To estimate
the velocity and thickness of the waveguide, we modify the treatment of Gubbins and Snieder (1991), who
calculated the acoustic response of a high-velocity slab
(V > V0 ). They solved the acoustic wave equation for a
uniform layer bounded by two continuous half spaces,
with continuity of vertical displacement and pressure
enforced across the two boundaries. The acoustic approximation ignores mode-converted energy, but tests
below show that it characterizes well most observations.
For a given frequency, a period equation relates frequency ω to phase velocity as:
2. Waveguide analysis
√
ωH 1/2
2 γ(1 − γ)
1/2
tan
γ
= tan Ωγ
=
V0 D
1 − 2γ
(1)
2.1. Acoustic theory
(Gubbins and Snieder, 1991). Here,
Seismic P and S body waves that travel long distances (100–1000 km) along the tops of slabs appear dispersed (Abers and Sarker, 1996; Gubbins and
Snieder, 1991). In most cases, the dispersion shows that
high frequencies are delayed with respect to the ini-
ωH
ωH
=
Ω=
V0 D
V0
V02
−1
V2
(2)
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G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
(U) as
−1
1 ∂ω
v2 dγ
U
=
=v 1−
V0
V0 ∂k
2D2 d
Fig. 2. Theoretical dispersion for a low-velocity acoustic waveguide
with wave speed 90% that of surrounding material. Thick lines: group
velocity (U/V0 ); thin lines: phase velocity (ν); both normalized to the
velocity V0 of surrounding material. Solid, dashed, and dotted lines
show solutions for the fundamental mode, first and second higher
modes, respectively.
is a nondimensional frequency, and D is a nondimensional reduced velocity of the layer:
1
=
D2
V02
V2
− 1.
(3)
The parameter γ describes a phase velocity v (normalized by V0 ) at frequency ω and wavenumber k:
2
V02
γ
1
2k
≡
V
=
− 2,
0 2
2
2
v
ω
V
D
(4)
where 0 < γ < 1 for V/V0 < v < 1. Solutions to (1) are
real and modal,
√
1/2
−1 2 γ(1 − γ)
Ωγ
= − tan
+ nπ
(5)
1 − 2γ
for n = 0, ±1, . . .. For tan−1 defined on range {−␲, 0},
the right-hand side is positive for non-negative n. Low
frequencies correspond to small Ωγ −1 in (5) and can
be only attained for n = 0 (Fig. 2). Higher modes may
be present if Ωγ 1/2 > π, interfering with fundamentalmode signals traveling slowly (γ < ∼0.35). Such signals may increase the overall frequency content of
records but do not change the difference between phase
velocities at the lowest and highest frequencies. Inversions, described below, use only the fundamental mode
(n = 0).
To calculate dispersion, Eqs. (4) and (5) are evaluated for v(Ω), which then gives the group velocity
(6)
evaluated numerically. At high frequencies (Ω 1)
and finite n (5) is satisfied if γ 1; i.e. the phase velocity approaches V. At low frequencies (5) is solved if
γ → 1 and only for n = 0, such that the phase velocity
approaches V0 . In other words, at high frequencies the
waves travel at the velocity of the waveguide, while at
low frequencies and long wavelengths the waveguide
vanishes.
For a given velocity contrast, the frequency behavior
scales as H/DV0 (Eqs. (2) and (3)). In the observations
here D ∼ 0.3–0.6, roughly 1/2. Hence, V0 /H acts as a
characteristic frequency for the waveguide, such that
signals with ω 2V0 /H travel at V0 , while signals with
ω 2V0 /H travel at V.
2.2. Measurement method
Individual body waves are extracted along with
∼5 s of pre-arrival noise and 5–15 s of signal, including all of the early-arriving signal but avoiding
any strong secondary phases. For S waves the transverse component is used to minimize effects of nearstation mode conversions. Each signal passes through
a bank of narrow-band Gaussian filters and the Hilberttransform envelope operator to generate a spectrogram (Dziewonski et al., 1969). Energy is sampled
at frequencies fi , at 0.25 Hz intervals from 0.25 to
7.5 Hz, sampled by narrow-band filters of the form
exp{−a(f − fi )2 /fin )} where f is the frequency and
a and n are constants. Setting n = 1 and a ∼ 4–8 s
gives reasonably smooth dispersion curves for the
frequencies and time windows analyzed here. Lag
times at each frequency are calculated as the arrival
time of peak energy from the dispersion curve, after time-frequency windowing (Levshin et al., 1992)
to eliminate strong late arrivals or higher modes. The
resulting lag times t(fi ) form the basic data set used
here.
2.3. Inversion
We assume a waveguide of constant thickness but
variable velocity with depth, as expected for an anomalous layer undergoing progressive metamorphism. If a
signal passes through M waveguide segments each with
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
a constant velocity, then the travel time from event j at
frequency fi is the sum of travel times through each
segment:
Tj + tj (fi ) =
M
Ljm
+ ej
V0 uim
minimizing
pred 2
wj τij − τij
11
(10)
i,j
(7)
m=1
here tj (fi ) is the measured group lag at fi , Tj the time
taken by a zero-frequency signal to traverse the slab,
Ljm the path length taken by ray j through waveguide
segment m, uim the group velocity at fi within segment
m normalized to V0 , and ej are unmodeled errors in Tj .
Equivalently,
M
1
tj (fi ) =
(8)
Tjm
− 1 + ej
uim
m=1
where Tjm is the travel time taken through each slab segment by the zero-frequency ray. Section 4.2 describes
estimation of Tjm and potential bias in assuming a planar waveguide.
The lags often show systematic shifts for each event
(ej ), because they are measured relative to a picked firstarrival onset rather than a zero-frequency group arrival
time. As a result, picks can be in error for reasons unrelated to waveguide structure. Such shifts are eliminated
by inverting differential lags τij = tj (fi ) − tj (f ) r for
some reference time based on the data; here ...r represents an average over a reference frequency band for
which signal-to-noise levels are high (3–6 Hz for measured data, fixed at 0.5 Hz for synthetic tests). With
this modification, Eq. (8) forms a potentially invertible
system of equations for differential group slowness as
a function of frequency (1/uim −1).
The number of free parameters can be decreased
from those in Eq. (8) by directly parameterizing
uim = u(fi ; pm ), where parameters become pm = (H/V0 ,
dlnVm )T , with dln Vm = (Vm − V0 )/V0 and Vm is the velocity within the mth waveguide segment. In this way,
only M + 1 parameters need be determined, with {H/V0 ,
dln V1 , dln V2 , . . ., dln Vm } describing one layer thickness and M velocities. The forward problem can then
be stated
M
1
1
pred
τij = −
. (9)
Tjm
−
u(fi ; pm )
u(f ; pm ) r
m
Eq. (9) is inverted nonlinearly for H/V0 and each
dln Vm via the simplex algorithm (Press et al., 1986),
weights wj = 1.0, 0.5, 0.25, or 0 are assigned for event
quality rankings a–d, respectively, as discussed below,
and τ i is fit between 0.25 and 6.0 Hz. Uncertainties
are determined from 1000 bootstrap substitutions of
individual dispersion measurements to the stacks, and
reported as 90% confidence limits.
3. Numerical simulations of waveguide
behavior
Several numerical tests provide insight into the behavior of the waveguides and the ability of the inversions to recover parameters. These tests simplify the
actual propagation geometry primarily by assuming
a plane-layered structure, rather than a realistic slab
shape, a geometry that allows rapid and stable calculation of responses over wide frequency bands. The
tests complement 2D finite-difference tests that have
been recently conducted for the Andean slab geometry
(Martin et al., 2003), which directly explore the effects
of slab curvature. First-order effects of slab shape on
dispersion measurements are discussed in Section 4.2.
In the tests here, full-waveform seismograms are calculated using a wavenumber integration scheme (Wang
and Herrmann, 1980). The calculated signals travel the
length of a waveguide for a distance of 200 km, sampled 32 times per second, for a parabolic source-timefunction four samples long. Seismograms are generated
for particle motion in the direction of wave propagation (R) and for the three independent double-couple
excitation functions (RDD, RSS and RDS in the terminology of Wang and Herrmann). In all simulations,
the Poisson’s ratio is 0.25 everywhere and the medium
outside the waveguide has a P wave velocity (VP ) of
8.5 km/s.
3.1. Where should waveguide effects be seen?
The first calculation examines the response of a simple waveguide of thickness 6 km and Vp = 8.0 km/s.
The source lies at the center of the layer and receivers lie at a variety of offsets normal to the
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G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
Fig. 3. Full-waveform seismograms calculated for a low-velocity waveguide embedded in a full space. Waveguide is 6 km thick (gray area) with
Vp = 8.0 km/s, surrounded by a medium of Vp = 8.5 km/s, and Vp /Vs = 1.73 in both. Source is at center of waveguide. Left: ground motion at
200 km range along the waveguide, at offset from the waveguide center as shown on vertical axis, for RDD Green’s function. Numbers (left, in
figure) show relative maximum amplitude. Dotted lines show ray-theoretical arrival times for direct and P–S converted phases. Right shows same
seismograms, filtered at a low (<1 Hz) and high (>3 Hz) frequencies (thick and thin lines, respectively). Note dispersion and high amplitudes for
sources near the waveguide only.
layer (Fig. 3). For receivers aligned along the waveguide or near it, the waveguide produces an initial
low-frequency arrival followed by high-frequency secondary arrivals. The waveguide also focuses energy
so as to amplify high-frequency signals by 10–20
times. Such amplification may explain the prevalence
of dispersed signals in otherwise complex suites of
seismograms.
Where receivers are offset by tens of km from the
low-velocity channel, a distinct secondary phase arrives after P with moveout parallel to S. Neither P nor
this secondary phase show dispersion or amplification.
Ray tracing shows that this phase is a P-to-S converted
signal, traveling as P inside the waveguide and converting to S at the boundary. These phases have been
used to map the slab surface and estimate the velocity
beneath it (e.g., Helffrich and Abers, 1997; Matsuzawa
et al., 1986; Zhao et al., 1997).
In a complementary calculation, a receiver is placed
in the center of the waveguide and the location of
the source varies (Fig. 4). Only those sources lying
within or very close to the waveguide generate dispersion. Sources far from the waveguide produce much
smaller signals along with a secondary undispersed
phase, apparently an S–P converted phase near the
source. The observation of dispersed signals indicates
that earthquake sources lie within or very close to
waveguides.
3.2. Inversion method tests: sources and higher
modes
The inversions applied to real data (Sections 2 and
4) assume only fundamental-mode acoustic propagation. To test the validity of this approximation, the
seismograms calculated in Fig. 4 are inverted with
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
13
Fig. 4. Effect of source location on waveguide excitation for calculated P waves. Same structure and layout as Fig. 3 for geometry shown at
top. Receiver lies inside waveguide, and sources are placed at varying distances from waveguide center. Figure shows RSS Green’s function.
Amplitudes at left scaled to common level, to illustrate waveguide amplification. Sources inside waveguide (gray region) or within 0.5 times
waveguide thickness show dispersion, but sources farther do not.
the same procedure as used for actual data. If accurate, these inversions should give d ln Vp = −0.059 and
H/V0 = 0.706 s. First, signals are generated with both
source and receiver at the waveguide center (Fig. 5).
Fig. 5. Dispersion fits for numerical tests. Symbols: lags for fullwaveform calculated seismograms relative to 0.5 Hz; solid circles:
dln Vp = −0.5/8.5; triangles: dln Vp = 0. Parameters same as in Fig. 3
with both source and receiver at center of waveguide, RSS component analyzed. Lines show corresponding fits for the acoustic
fundamental-mode inversion.
The dispersion lags predicted from the inversion, based
on acoustic theory, match closely those from the fullwaveform synthetics. The fitting procedure overestimates d ln Vp slightly (−0.067) and underestimates
H/V0 (0.581 s). Next, a dispersion curve is calculated
and inverted for the same geometry but with no velocity contrast between waveguide and surroundings; as
expected, no dispersion is observed or estimated (triangles on Fig. 5).
The experiment is repeated for all three source
components (RDD, RSS, RSD) and all source locations in Figs. 4 and 6. For sources within 9 km of the
waveguide center, velocity estimates are correct usually to within 1% and always within 2%. However,
layer thicknesses are biased toward low values, on average 72% of the correct thickness, ranging from 26
to 97%. Any higher-mode excitation will distort the
fundamental-mode dispersion curve by adding highfrequency energy, leading to a thinner apparent waveguide. The mismatches are worst for the RDS excitation
14
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
more accurate inversion would require knowing accurately both the event location relative to the waveguide
and the focal mechanism, both of which are generally
unavailable. Except in the few subduction zones where
dense local images of the top of the slab have been
obtained (e.g., Ferris et al., 2003; Zhao et al., 1997),
the waveguides are only known by their effects on the
data shown here. Hence, the offset of the events from
the waveguide is not knowable. Because the events are
small (Section 4.1), global compilations of focal mechanisms such as the Harvard CMT catalog (Dziewonski
et al., 1981) include only 5% of the events studied.
3.3. Effect of a thin sediment-like layer
Fig. 6. Results from inverting full-waveform synthetic seismograms
for waveguide parameters. Parameters and data same as in Fig. 4.
Gray area shows sources inside waveguide. (A) estimated dln Vp ;
(B) estimated waveguide thickness H; (C) variance of misfit to time
lags (Eq. (10)). Symbols: double-couple excitation modes, RDD (circles), RDS (triangles) and RSS (stars). Dashed lines: correct values
within 7 km of LVZ center, dln Vp estimates show no bias but H is
underestimated.
function, with thickness estimates typically 55% of the
correct value. This excitation function has a nodal plane
parallel to the waveguide, so generates the observed P
waves only through reflection and S–P mode conversion.
For sources farther than 9 km from the waveguide
center, the inversions give a wide range of incorrect
answers and poor fits. Such results indicate that dispersion analysis cannot be conducted blindly. However, it
seems unlikely that such errors affect actual data, for
two reasons. First, these signals are small and the raw
signals do not show dispersion, but show two separate
arrivals, so would not be analyzed. Second, in these
artificial examples the dispersion is controlled by the
timing of secondary S–P phases. The phases should
not show moveout with increasing path length, but real
data do show such moveout (Section 4.4).
In summary, the dispersion inversion can recover
velocities to within ∼1–2%, but can lead to significant (∼50%) underestimates of waveguide thickness. A
A single-layer waveguide greatly simplifies subducted structure (Hacker et al., 2003a), and it has
been suggested that seismically slow metasediments
may bias the velocity anomalies estimated (Kerrick
and Connolly, 2001). In most arcs, such a layer
should be no thicker than 500 m. To estimate its
consequences, or that of any thin layer (e.g., a fluidrich channel, shear zone, talc, serpentine), seismograms are modeled for a structure which adds a
500 m thick layer of Vp = 7.0 km/s above that described
above (Fig. 7). The resulting dispersion curve shows
slightly increased group delay at frequencies above
3.5 Hz (Fig. 7), and its shape is still controlled by
the thicker layer (crust). Inversions of these dispersion curves give dln V = −0.067, similar to that obtained when a sediment layer is absent. A thin layer
alone, without underlying crust, produces a dramat-
Fig. 7. Dispersion fits for numerical tests that include a 0.5 km thick
metasediment layer (sed), either with or without 6 km of underlying
crust. Layout and parameters same as Fig. 5. Addition of sediment
to crust shows little effect.
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
ically different dispersion curve than that actually
observed.
3.4. Differences between calculated and actual
propagation geometry
Dispersed signals can be recorded at the Earth’s surface, outside the slab, so some trapped energy must be
able to leak out. Typically these signals are seen along
paths where energy travels parallel to slab strike and
along the slab surface for >100 km. Slabs are curved,
which may make it easier for dispersed signals to leak
out (Martin et al., 2003), as may rough boundaries.
Finite-difference simulations of guided waves in fault
zones support this inference (Igel et al., 1997; Li and
Vidale, 1996). The simulations show that waveguides
need not be continuous over the entire path to the observing station, just that the station must be favorably
placed with respect to where energy emerges from the
waveguide. They also show that waveguide bending
over distances much longer than waveguide thickness
has relatively little effect on propagation, but that offsets or heterogeneities that are sharp compared with
thickness can severely disrupt propagation (Igel et al.,
1997; Li and Vidale, 1996).
4. Observations
4.1. Signals and events
Several Global Seismic Network (GSN) stations
on volcanic arcs provide ray geometries that potentially sample slab waveguides, and data from such stations between 1992 and 2001 form the basis this study
(Table 1, Fig. 1). The broadband channels, used here,
sample at 20 samples-per-second and have flat response
to ground velocity from <0.01 Hz to an anti-alias corner
at ∼8 Hz, which includes the frequency band of interest (0.25–8 Hz). Both P and S waves are used, from the
vertical and tangential components, respectively.
To avoid complications from the upper plate, only
events deeper than 100 km are selected from standard global catalogs (or local ones, where available
in Alaska and Japan), at range (X) <750 km from the
stations. At longer distances, signals become exceedingly attenuated or otherwise complicated. Records are
selected if signal is visible throughout the 0.5–6 Hz
15
band, typically for events with magnitude >3.0 (greater
at noisy stations) but always <5.3 to avoid complex
sources. Each signal is assigned a quality rank a, b,
c, or d, with a corresponding to signals above the
noise throughout the 0.5–6 Hz band and with simple
dispersion characteristics, b corresponding to somewhat complicated signals, c corresponding to signals
with complex dispersion characteristics or obscured
signals below 1 Hz, and d being unusable. The resulting data set of quality a–c consists of 210 P waves and
156 S waves recorded at one of six stations (Table 1,
Fig. 8). Waveforms for Nicaragua were presented previously (Abers et al., 2003). At distances >200 km
most signals show dispersion effects, as high frequency energy arriving up to several seconds after the
direct P.
Paths to GSN station ERM sample more than one
arc segment, so these data have been subdivided into a
Hokkaido-S. Kurile group (ERM-n) and a N. Honshu
group (ERM-s). The S waves are highly attenuated or
otherwise obscured at JTS, perhaps due to attenuation
directly below the site, and those to GUMO show little
pattern. The Alaska station COL was relocated 4 km
to COLA in 1996, resulting in substantial increase in
resonance at 1–4 Hz even for signals that do not interact with the slab (compare records with X < 100 km,
Fig. 8C and D). This signal degradation presumably
reflects a site effect and limits the usable data at this
station. Records from several other stations were discarded for a variety of reasons, including those for
all South American sites where thick upper-plate crust
produces strong secondary phases, stations behind the
volcanic arc which did not sample the appropriate ray
paths, and stations near tectonic complexities such as
subducting ridges.
Unusual signals from Tonga earthquakes, recorded
in New Zealand, have been described extensively
in the literature and were not re-analyzed except
to confirm previous work (Ansell and Gubbins,
1986; Gubbins and Snieder, 1991; van der Hilst and
Sneider, 1996). These observations are limited to one
suite of paths, and the paths are generally longer and
deeper than those studied here. Only one record elsewhere shows high frequency preceding low frequency
arrivals (reverse dispersion). That record, from COLA
for an event on 6/09/2000 (Fig. 8C, record number 9), is
>20 km deeper than any other examined from Alaska
and is somewhat offset from the slab. It is possible
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G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
Fig. 8. Quality a and b seismograms used in dispersion analysis, for P waves traveling ray paths shown in Fig. 1. (A) Aleutians recorded at
ADK; (B) Kurile–Kamchatka recorded at PET; (C) Alaska recorded at COLA; (D) Alaska recorded at COL; (E) Kurile-Hokkaido recorded at
ERM; (F) northern Honshu recorded at ERM; (G) Marianas recorded at GUMO. For each figure pair, left panel shows broadband seismograms
(0.2–8.0 Hz) and right panel shows same data filtered at 0.75 Hz (thick lines) and 6.0 Hz (thin lines). Records are sorted from bottom to top
in order of increasing path length within slab as determined from ray tracing. Records labeled (left) by event date and quality, and (right) by
X = path length within slab (km), Z = event depth (km), and Baz = back-azimuth from station to event (◦ ). Station COLA replaced COL in 1996,
shifted 4 km. Note increasing delay of high frequencies with increasing distance. One record on (C) (6 September 2000) shows only example of
reverse dispersion.
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
17
Fig. 8. (Continued)
that reverse dispersion is generated by interaction with
eclogitized crust (Gubbins and Snieder, 1991) but that
such crust is sampled only by certain deep rays.
4.2. Ray geometry
To estimate velocities from lag times, we assume
that (1) all dispersion occurs within the subducting slab,
(2) signal path lengths in the slab are adequately represented by ray tracing through simple models, and
(3) the direct ray travels near the waveguide while
in the slab. To trace rays, the top of the subducting
plate is defined by the top of the Wadati–Benioff seismicity, contoured manually from the relocated global
hypocenter dataset (Engdahl et al., 1998), or from previously published contours of the Alaska–Aleutian sys-
18
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
tem (Plafker et al., 1994). Previous digitizations of
slabs (Gudmundsson and Sambridge, 1998) showed
significant departures from seismicity in the upper
150 km so could not be used. First-order thermal effects
are approximated by setting the velocity within the slab
to 5% faster than the surrounding mantle, which is set to
iasp91 velocities (Kennett and Engdahl, 1991). An 8%
faster slab was also tested with negligibly different final results. This geometry should approximate the path
followed by low-frequency signals. A finite-difference
Eikonal solver (Hole and Zelt, 1995; Vidale, 1990) generates a travel time field to stations from all points in
the subduction zone, which is then numerically differenced to obtain ray trajectories. Numerical experiments
showed that changes to finite-difference grid resolution
or orientation changed arrival times by less than 1%.
For most slab events, rays travel below the slab top
for tens to hundreds of km before entering the overlying mantle wedge. The ray paths (Fig. 1) travel along
slabs to a point 50–100 km distant from the stations, refracting along the slab surface, then exit into the mantle
wedge. Downgoing segments of ray paths are rare, and
never descend more than 6 km below the source depth,
except for the Marianas where some ray paths >600 km
long descend as much as 25 km into the slab below the
source. In consequence, slabs are sampled by these signals at depths near or above that of the sources and near
the top surface of the slab, with median sampling depths
near 125 km (Fig. 9).
Ray path length errors contribute only slightly to
uncertainty in velocity estimates, so the results here
are insensitive to the hypocenter catalog used. For a
signal traveling along a waveguide a distance L and
for low-frequency travel time T, the group velocity is
U0 = L/T. At high frequencies, signals arrive at T + ti
where ti is a differential time lag at frequency fi , so
that δU(fi ) = U(fi ) − U0 = L/(T + ti )−L/T. Errors in L
of dL, lead to errors in δU(fi ) of −(ti /T)(dL/L)U0 ,
to first order. Commonly L ∼ 200–500 km, and characteristic errors in path length (from event mislocation and errors in slab ray tracing) are 10–25 km, so
dL/L ∼ 5% (2–12%). Typically ti /T = 5–15% (roughly
equal to dln V; see below), so errors in differential velocities due to path length uncertainties should be of
order 0.5% (0.1–2%), a small fraction the anomalies
reported.
The interpretation of waveguide velocities (Section
3) assumes that the first-arriving, long-period arrival
Fig. 9. Distribution of rays with depth within each slab segment,
from three-dimensional ray tracing. Only portions of rays below slab
top are included. Dashed lines: 100 and 150 km depth; dotted line:
median sampling depth.
travels the same path as the guided wave, so that the
direct wave follows the slab surface. Typically, 75%
of all rays lie within 10 km of the slab surface until they exit the slab, with exceptions corresponding
to events located far from the slab surface. The velocity contrast between the high-velocity slab and the
low-velocity wedge above it guides most signals measured here, so that first-arriving signals follow the top
of slabs until rays exit slabs beneath stations (Fig. 1).
In Nicaragua, the direct rays plunge 25–50 km below the slab surface, even though earthquakes lie just
below it. Rays in Alaska plunge up to 20 km below
the surface. Rays take such plunging paths because
the Nicaragua and Alaska slabs exhibit a weak negative curvature. The effects on estimated path length
are slight; a path beneath Nicaragua that follows the
100 km depth contour (along the slab surface) would
be at most 1.5% longer than the computed ray paths.
Effects are less for paths <600 km long, and similar
path errors for Alaska are negligible. As a result, highfrequency waves that follow the slab surface will arrive
at an apparent velocity that is no more than 1.5% slower
than the direct arrival in Nicaragua, a small part of the
13% anomalies measured. Overall, ray paths can be assumed to follow the waveguide to within the uncertainties of measurement, and severe multipathing seems
unlikely.
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
19
4.3. Regional velocity V0
In some cases, the arrival times of the first-arriving
(low-frequency) signal can place bounds on absolute velocities. These velocities constrain the composition and temperature of the region sampled by the
low-frequency signals, inferred to be that surrounding
the waveguide (see above). Where station coverage is
sparse, hypocenter errors can exceed the residuals, so
single-station measurements of arrival time provide little constraint on velocities. Also the locations trade off
with the velocities, because the stations used to measure dispersion can be critical to locating the earthquake. As a result, only two arc segments studied here,
Alaska and Hokkaido, have hypocenters good enough
to avoid these effects, as is evident from the correlation between arrival time residuals and ray path length
in the slab (Fig. 10). Residuals are calculated relative
to the (USGS or Alaska network) catalog location and
the iasp91 travel time curves (Kennett and Engdahl,
1991).
The paths in Alaska and Hokkaido sample P velocities 2.8–5.3% and 0.3–7.1% faster, respectively,
and S velocities 4.5–6.0% and 3.8–6.6% faster, respectively, than iasp91. These estimates are derived
from the moveout of residuals in Fig. 10, so should
be unaffected by uniform biases between iasp91 and
the travel-time curves used to calculate origin times
(Kennett and Engdahl, 1991). At 75–150 km depth, the
requisite velocities would then be 8.3–8.6 km/s for Vp
and 4.7–4.8 km/s for Vs , or roughly 3–6% faster than
iasp91. Because some tradeoff may still exist between
hypocenter and velocities, these are likely underestimates. This observation is consistent with propagation
through a mantle that is overall colder than average, at
velocities consistent with those inferred for the interior
of slabs globally (Lay, 1997).
4.4. High-frequency lags and waveguide velocities
As a rough estimate of velocities within waveguides,
the lags of 3–6 Hz energy relative to the first arrival are
measured as a function of ray path length (Fig. 11). For
all stations, the lags increase with increasing range,
as expected from a dispersion effect that scales with
path length within the slab. These lag times include
a delay between the high-frequency pulse onset and
the peak of the Hilbert-transform envelope. Within nar-
Fig. 10. Arrival time residuals for first-arriving (low-frequency) signals at two stations as a function of predicted ray path length in slab,
relative to the iasp91 travel times (Kennett and Engdahl, 1991) and
the U.S.G.S. catalog hypocenters. Solid circles: P waves; open circles: S waves. Lines show best-fit robust regressions. Negative slopes
indicate fast paths, as expected for propagation in cold anhydrous
slabs.
row frequency bands this delay should not change with
distance, however, so the slope of the curves should
scale to the relative velocity within each slab (Table 2).
Hence, most waveguides are 3–8% slower than their
surroundings.
Table 2
P velocities inferred from moveout of 3–6 Hz signal relative to onset
Station
dT/dX (s/km)
dln Vp a
ADK
COL(A)
ERM
GUMO
JTS
PET
0.003119
0.002743
0.005399
0.008898
–
0.006264
−0.027
−0.023
−0.046
−0.076
−0.145b
−0.053
a
b
For reference Vp0 = 8.5 km/s.
From Abers et al. (2003), events <150 km deep.
20
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
Fig. 12. Results from fitting dispersion curves at several arcs
(Table 1). Each LVZ is assumed to have a constant thickness but differing velocities in three regimes: 0–100 km depth (dark gray bars and
circles), 100–150 km depth (light gray bars and triangles; Table 4),
and >150 km depth (open bars and inverted triangles).
Fig. 11. Lag of high-frequency energy (3–6 Hz) from first arrival
as a function of path length within slab, for P waves. Each symbol
corresponds to a different arc segment (Table 1); lower-left corner
of station name lies at 0 s lag. Trend shows progressive lag of high
frequencies, and slope gives velocity anomaly seen by high frequencies. Lines show trend (Table 2) from robust slope estimation. Lags
for JTS shown elsewhere (Abers et al., 2003).
5. Inversions for North Pacific Arcs
For each arc, all measured dispersion curves are inverted for waveguide structure in the manner described
in Section 3, jointly inverting all dispersion curves for
each phase (P or S). Several inversions are done for each
slab, varying the number of parameters that describe the
waveguide. In the simplest inversions, the waveguide is
treated as a single homogeneous layer. The dln Vp range
from 3 to 8% slow, with dln Vs /dln Vp ∼ 1 (Table 3).
These velocities overlap with the 5–8% slow range reported previously (Abers, 2000) although the size of
the data set has more than doubled. They also correlate closely with velocities inferred from moveout of
high-frequency energy (Table 2; Section 4.4), as expected. Normalized waveguide thicknesses lie in the
range H/V0 = 0.22−0.65 s for P or 0.43−0.78 s for S,
with 15–40% uncertainties at 90% confidence. These
estimates correspond to H = 2–4.5 km for both P and
S measurements. The P and S data sets give sim-
ilar thickness estimates even though the actual frequency content of the signals differ, supporting the
inference that waveguide effects produce the dispersion. Again, the thickness estimates probably underestimate true thickness by up to a factor of two (Section
3.2); a more realistic bounds on layer thickness may
be 2–8 km.
In a final set of inversions, the waveguide at each
arc is divided into three segments, one spanning depths
0–100 km, a second at 100–150 km, and a third at
>150 km depth (Table 4, Fig. 12). This inversion
isolates rays at a common depth range for all arcs
(100–150 km), to overcome potential biases in sampling with depth (Fig. 9). The parameter estimates
(Fig. 12) and dispersion curves (Fig. 13) show greater
dispersion at shallower depths. In other words, the
waveguide effect decays as the slab descends. The
deepest segments all show layer velocity anomalies of
less than 8% in absolute amplitude, averaging 3.5%
slow, while at <150 km depth the waveguides average 7% slow and can be as much as 13 ± 3% slower
than surrounding mantle. This effect was first documented for Nicaragua (Abers et al., 2003), and is consistent with observations in Japan that show ∼15%
slow layers at 50 km depth (Hori et al., 1985) and
6% slow layers at >100 km depth (Matsuzawa et al.,
1986).
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
21
Table 3
Results from inversion assuming constant waveguide velocitya
Station
Phase
nVarb
H/V0 (s)
dln V
ADK
COL
ERM-n
ERM-s
GUMO
JTS
PET
ADK
COL(A)
ERM-n
ERM-s
GUMO
JTS
PET
P
P
P
P
P
P
P
S
S
S
S
S
S
S
0.590
0.726
0.533
0.481
0.457
0.371
0.546
0.451
0.390
0.613
0.491
0.581
0.583
0.504
0.44 [0.21, 0.58]
0.65 [0.49, 1.06]
0.49 [0.39, 0.62]
0.37 [0.14, 0.49]
0.22 [0.16, 0.28]
0.41 [0.35, 0.46]
0.35 [0.21, 0.49]
0.5 [0.35, 0.66]
0.47 [0.38, 0.56]
0.75 [0.52, 1.1]
0.56 [0.21, 0.72]
0.43 [0.29, 0.56]
0.78 [0.45, 1.19]
0.49 [0.33, 0.54]
−0.036 [−0.05, −0.028]
−0.027 [−0.036, −0.018]
−0.045 [−0.058, −0.035]
−0.037 [−0.057, −0.031]
−0.083 [−0.095, −0.075]
−0.084 [−0.112, −0.067]
−0.046 [−0.055, −0.039]
−0.054 [−0.071, −0.038]
−0.049 [−0.057, −0.042]
−0.028 [−0.044, −0.017]
−0.03 [−0.054, −0.024]
−0.063 [−0.082, −0.049]
−0.048 [−0.066, −0.04]
−0.041 [−0.047, −0.034]
a
b
Brackets show 90% confidence range from bootstrap.
Variance of residual time lags normalized to variance of data.
The dispersion curves (Fig. 13) and inferred waveguide velocities (Table 4; Fig. 12) also show variations of a factor of 2 and 3 from arc to arc in the
100–150 km depth range. This variation exceeds that
in the homogeneous-layer inversion, suggesting that
some real variation had been masked by depth averaging. The slab segments sampled at GUMO and JTS
show some of the slowest waveguide velocities. At JTS,
velocities for 100–150 km depth (13 + 6/−5% slow)
match those determined previously with a somewhat
simpler approach (Abers et al., 2003).
6. Discussion
6.1. V0 and low slab temperatures
Absolute velocities, where they can be measured,
show that the low-frequency signals travel 3–6% faster
than predicted from global models (Fig. 10). Presumably, these signals represent the slab mantle beneath
the waveguide. Fig. 14 compares the estimated lowfrequency velocities to predictions for a range of ultramafic compositions, using the elasticity data base of
Table 4
Inversion results assuming velocity changes at 100, 150 km depth
Station
Phase
nVara
H/Vo (s)
dln V (100–150 km depth)
ADK
COL(A)
ERM-n
ERM-s
GUMO
JTS
PET
ADK
COL
ERM-n
ERM-s
GUMO
JTS
PET
P
P
P
P
P
P
P
S
S
S
S
S
S
S
0.581
0.688
0.528
0.470
0.448
0.301
0.514
0.438
0.382
0.589
0.413
0.542
0.518
0.495
0.35 [0.16, 0.49]
0.47 [0.39, 0.69]
0.46 [0.27, 0.54]
0.31 [0.05, 0.43]
0.21 [0.14, 0.27]
0.35 [0.26, 0.38]
0.29 [0.16, 0.39]
0.40 [0.24, 0.52]
0.45 [0.35, 0.53]
0.50 [0.44, 0.74]
0.30 [0.17, 0.45]
0.32 [0.19, 0.52]
0.55 [0.26, 0.62]
0.41 [0.30, 0.53]
−0.01 [−0.06, 0]
−0.02 [−0.04, 0]
−0.03 [−0.06, −0.01]
−0.02 [−0.08, 0]
−0.10 [−0.13, −0.08]
−0.13 [−0.19, −0.08]
−0.05 [−0.08, −0.04]
−0.03 [−0.11, 0]
−0.05 [−0.07, −0.03]
−0.01 [−0.03, 0.]
0.00 [−0.07, 0.]
−0.10 [−0.13, −0.08]
−0.08 [−0.11, 0]
−0.03 [−0.06, −0.02]
a
Variance of residual time lags normalized to variance of data.
22
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
Fig. 13. Observed P wave dispersion curves for each arc and depth segment, and corresponding fit from inversion (Fig. 12). Vertical axis shows
dln U, fractional change in group velocity, corrected to zero at 0.25 Hz. Results shown only for depth ranges sampled by >5% of ray path lengths.
Shallower depths generally produce greater waveguide anomalies, and high frequencies are usually 5–15% slower than low frequencies.
Hacker and Abers (2004), and shows that the fast observed velocities can be explained only by propagation
in cold and largely anhydrous mantle. The ultramafic
compositions plotted represent the range of probable
anhydrous slab compositions from enriched lherzolite
to harzburgite (Hacker et al., 2003a). The velocity estimates assume a fixed Mg number of 0.9 and ignore
effects of anelastic dispersion on velocities (Karato,
1993), which should be negligible at these low temper-
atures. The iasp91 velocities indicate temperatures of
1200–1350 ◦ C at these compositions, while the higher
velocities sampled by low-frequency ray paths indicate temperatures of 400–900 ◦ C. For comparison, the
weakly hydrated peridotites would have significantly
lower velocities, lower than those observed unless temperatures are below 400 ◦ C. The weakly hydrated case
assumes 1.3 wt.% H2 O, calculated by mechanically
mixing the appropriate hydrous with anhydrous high-P
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
23
Fig. 15. Predicted relations between water content and seismic P
velocities, after Abers et al. (2003). Circles: predictions calculated
for lithologies as labeled at 3 GPa and 400 ◦ C following Hacker
et al. (2003a,b), referenced to pyrolite. Thin lines: predictions for
free fluid in isolated pores (spheres; dotted), interconnected tubes
(dashed), or penny-shaped cracks (solid) for H2 O in pyrolite, as
described previously (Abers, 2000). Thick gray lines: regression
relation on rocks, dln Vp /d (wt.% H2 O) = −2.0 ± 0.2 (% per%), or
gabbro-eclogite mixing trend.
Fig. 14. Calculated velocities for peridotites at 4 GPa compared
with seismic constraints. Bulk compositions are lherzolite (l hz), depleted lherzolite/enriched harzburgite (dl hz) and harzburgite (harz)
of Hacker et al. (2003a,b), calculated for high-pressure garnet peridotite facies (dry), both dry and mixed with hydrated facies for a bulk
1.3 wt.% H2 O (hyd). Hydrous facies are serpentinite below 600 ◦ C or
chlorite-peridotite at 600–800 ◦ C, their approximate stability limits.
Dotted lines: velocities at 120 km depth from iasp91 (Kennett and
Engdahl, 1991). Gray boxes: velocity constraints from arrival times
of low-frequency arrivals (Fig. 10).
endmembers of identical bulk composition (Hacker et
al., 2003a). Thus, the arrival times require propagation
through a cold and largely anhydrous slab, and limit
H2 O content over large parts of the downgoing plate.
They also probably rule out the possibility that any region below the low-velocity zone is hot enough to allow
partial melt.
6.2. Causes of the low velocity layer: fluids and
temperature
Eclogite has Vp similar to or exceeding that of anhydrous peridotite (Gubbins et al., 1994), so the low-
velocity layer cannot be eclogite. Eclogite should be the
stable mafic phase at these pressures for temperatures
above c. 500–650 ◦ C (e.g., Hacker et al., 2003a; Peacock, 1993; Schmidt and Poli, 1998). This leaves
four classes of potential explanations for the lowvelocity layer: gabbroic crust persists metastably, a
serpentinized layer lies above or below the subducting crust, hydrated oceanic crust (with H2 O bound in
hydrous minerals) persists to great depth at low temperatures, or abundant free fluid exists in pores. The
first three cases require low temperature in or near
the subducted crust, and the last three indicate that
slow wave speeds correlate with the extent of hydration
(Fig. 15).
If sufficiently cold and hydrated, mafic crust can
contain several wt.% H2 O to 6 GPa, which would cause
seismic velocities to be 5–15% slower than surrounding
mantle (e.g., Connolly and Kerrick, 2002; Hacker et al.,
2003a). Similarly, serpentinized upper mantle within
the descending plate could form a potentially major
reservoir for additional fluids (Peacock, 2001; Rüpke
et al., 2002), as could hydrated mantle immediately
above the downgoing crust (Davies and Stevenson,
1992). Free H2 O must exist in at least trace quantities,
as it is transported out of the slab, and forms a poten-
24
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
tially significant reservoir at depth. In all mineralogical cases the relationship between H2 O content and
dln Vp is similar: a 2 wt.% increase in H2 O produces
a 1% decrease in dln Vp (Fig. 15). Free fluid shows a
similar relationship, provided that the pores are interconnected.
Anhydrous gabbro could persist metastably to considerable depth in slabs (Ahrens and Schubert, 1975;
Hacker, 1996), and would form a 10–15% slow layer
that is either the thickness of the entire oceanic crust
(6–8 km) or the thickness of the lower crust (2.5–4 km).
Such slow velocities are observed in the slowest waveguides, in the Marianas and Nicaragua, but most waveguides show layers <10% slow, too fast to be pure
metastable gabbro (Fig. 12). The intermediate velocities could reflect varying degrees of eclogitization,
provided that some mechanism exists that could regulate the gabbro → eclogite transformation to different
rates in different subduction zones. Also, the resulting gabbro-eclogite mixture would need to be well
mixed at a scale comparable to the waveguide thickness, in order to trap signals effectively. Increased
temperature, decreased grain size, increased availability of fluids, higher strain rates, and increased iron
content all enhance the gabbro → eclogite transformation (Ahrens and Schubert, 1975; Hacker, 1996;
Rubie, 1990). Gabbros in subducting oceanic crust
have limited compositional variation and most strain
is likely occurring in the overlying wedge, so the
main controls should be fluid abundance and temperature. Observations of natural rocks show that coarsegrained dry gabbros can persist untransformed far
into the eclogite stability field (up to 800 ◦ C), but in
the presence of fluids they transform near equilibrium (Hacker, 1996). Beyond those constraints, though,
the conditions for metastability remain poorly understood.
Are the waveguides slow because of hydrous phases
within them, or because they contain metastable gabbro
that is too dry to react? On the basis of seismic velocities
alone it is difficult to tell, although the two hypotheses
predict opposite relationships between seismic velocities and fluid content. Some systematics (Section 6.5)
indicate that slower velocities are seen where H2 O can
be expected to be more abundant, near seismicity and
where slabs dip steeply, favoring the first hypothesis.
All of these scenarios indicate low temperatures inside the waveguide. At 3–5 GPa, hydrated mafic assem-
blages are stable at temperatures below either 450 ◦ C
(Hacker et al., 2003a) or 650 ◦ C (Connolly and Kerrick,
2002; Schmidt and Poli, 1998), while serpentine will be
stable at temperatures up to 650 ◦ C (Schmidt and Poli,
1998; Ulmer and Trommsdorf, 1995), and chlorite may
persist in peridotites up to 800 ◦ C (Hacker et al., 2003a).
The temperature requirements for gabbro metastability
are less clear. Using a calibration of crustal metamorphic reaction rates (Baxter, 2003), we calculate that
the gabbro → eclogite reaction should take place in
4–100 Ma at temperatures varying from 600 to 800 ◦ C,
for mm to cm grain sizes. This calculation has reported
uncertainty of one order of magnitude, and assumes that
the rate-limiting processes are similar to those involved
in regional crustal metamorphism. In summary, temperatures within the waveguide appear to be less than
600–800 ◦ C for either the metastability or hydration
hypotheses, although the conditions for metastability
remain poorly understood. By contrast, geochemical
tracers in arc magmas indicate that sediment routinely
melts, requiring temperatures at the top of the slab (but
at unknown depth) to be in excess of 800 ◦ C (Johnson
and Plank, 1999). It may be that both observations can
be accommodated by a very steep thermal gradient at
the top of the slab, as predicted by thermal models
that incorporate temperature-dependent viscosity (van
Keken et al., 2002).
6.3. Variations in depth
The results (Tables 3 and 4, Fig. 12) modify the
conclusions reported previously (Abers, 2000) in that
the waveguide velocities vary widely between different
arcs and with vary with depth. Although waveguides
are on average 5–8% slower than the surrounding mantle, they are even slower in roughly half the cases
at depths less than 150 km. At greater depth, the
waveguides are less apparent. Such a trend is consistent
with petrologic phase equilibria; increasing pressures
and temperatures trigger a sequence of progressive
dehydration reactions in mafic and ultramafic rock
(Schmidt and Poli, 1998). As dehydration progresses,
seismic velocities approach those of anhydrous eclogite
(in mafic rocks) or peridotite (in ultramafic rocks). Delayed eclogite formation in anhydrous gabbros could
exhibit a similar trend, although it is unclear why the reaction would consistently take place near 150 km depth.
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
25
earthquake abundance with increasing depth may then
reflect a gradual decrease in the rate of devolatilization as eclogite formation progresses. This scenario is
consistent with receiver-function images of waveguide
disappearance and correlative seismicity variations in
the Alaska slab (Ferris et al., 2003).
6.4. Waveguides and intermediate-depth
earthquakes
The forward modeling results indicate that earthquakes must be located within or very close to the
waveguide in order to generate dispersed signals
(Fig. 4), similar to the conclusion reached by 2D finite
difference modeling (Martin et al., 2003). Receiverfunction images of slab low velocity channels also
show that many intraslab earthquakes lie within the
channel, at least at depths less than 150 km (Ferris et
al., 2003; Yuan et al., 2000). The most obvious explanation is that the conditions for intermediate-depth
seismogenesis occur within the waveguide but not necessarily outside it. In some situations earthquakes must
be able to nucleate in the deeper slab mantle, because
double seismic zones exist. However, the vast majority
of earthquakes lie in single planes or the upper plane
of double seismic zones, near subducting crust, so it
seems reasonable that the conditions for seismogenesis
are most commonly found within the waveguides imaged here. Elsewhere, we have argued that low-velocity
waveguides and intermediate-depth earthquakes both
exist as a consequence of dehydration (Hacker et al.,
2003b), so that earthquakes lie in or near low-velocity
channels because they are triggered by the release of
volatiles during metamorphism. The gradual decay in
6.5. Variations among arcs: updip fluid flow?
The waveguide velocities at 100–150 km depth vary
considerably between arcs (Fig. 12, Table 4). In order to
understand this variation, the velocities are compared
with a variety subduction parameters (Table 5; Fig. 16).
The waveguide velocities (dln Vp ) may be influenced
by parameters such as slab dip (δ), convergence rate (V),
plate age (A), and the thermal parameter Φ = AV sin ␦
(Kirby et al., 1996; Molnar and Gray, 1979). The latter
three, related to variations in temperature of the slab
interior, correlate poorly with dln Vp (Table 5). The
poor correlations with Φ, V, and A indicate that temperature within the slab does not control velocities in the
waveguide. The slab descent rate, a potential control
on the temperature at the slab surface (England et al.,
2004), also correlates poorly with dln Vp (|R| < 0.1),
further suggesting that temperature does not play a
major role in waveguide velocities. The dln Vp also
correlate poorly with mean depth of sampling (correla-
Table 5
Arc parametersa and correlation with velocities
Arc
Zray (km)
Aleutian
Alaska
Hokkaido
N. Honshu
Mariana
Nicaragua
N. Kurile
131
108
122
128
161
114
138
±
±
±
±
±
±
±
35
20
24
35
26
37
38
DipV (◦ )
49
37
43
36
58
68
47
±
±
±
±
±
±
±
6
2
5
3
7
3
4
Correlationc with dln V (100–150 km)
R (P)
−0.241
−0.911
R (S)
−0.358
−0.752
a
DipE (◦ )
42
25
29
29
60
62
45
±
±
±
±
±
±
±
3
4
3
1
2
1
3
−0.892
−0.777
Incoming plate
age (Ma)
60
50
104
98
118
28
73
±
±
±
±
±
±
±
0.181
0.152
7
3
3
8
5
1
3
Convergence rate
(mm/year)
70
57
90
91
38
68
76
±
±
±
±
±
±
±
0.495
0.901
2
2
0
1
1
2
1
Φ (102 km)
23
12
43
44
38
17
39
±
±
±
±
±
±
±
0.163
0.391
1
1
3
3
3
3
6
Grabensb
2
1
1
3
3
3
3
−0.527
−0.328
Zray = range of sampling depth for rays; DipV = slab dip from contoured surface to slab seismicity calculated below volcanic arc; DipE = slab
dip averaged from trench to deepest earthquake in convergence direction (Gorbatov and Kostoglodov, 1997); Φ = thermal parameter (see text);
DipE, incoming plate age, convergence rate, and Φ from profiles of Gorbatov and Kostoglodov (1997) except for Nicaragua, for which their
methodology was replicated. Uncertainties are 1 − σ variations between profiles, except Φ which is their averaged reported uncertainty, and Zray
and DipV which are calculated here.
b Grabens seaward of trench wall classified by Hilde (1983) as (3) “well-developed”, (2) “variously developed”, or (1) “less obvious”; Nicaragua
classified as (3).
c R = correlation coefficient between each parameter and dln V at 100–150 km depth from Table 4; R(P) for P waves; R(P) for S waves.
26
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
Fig. 16. Correlations between waveguide P velocity and subduction
zone parameters, for (A) dip measured on slab surface beneath volcanic arc; (B) dip averaged between trench and deepest earthquakes
(Gorbatov and Kostoglodov, 1997); and (C) thermal parameter Φ,
a measure of expected maximum depth of cold temperatures within
slab. R is correlation coefficient.
tion coefficient |R| < 0.24), indicating that the variation
does not represent a depth bias or a bias related to path
geometry.
Convergence rate correlates well with dln Vs but not
dln Vp . It is not clear why this should be the case, but
the S dispersion measurements are less accurate than
P. S wave dispersion is contaminated by P coda, high
frequencies can be significantly attenuated, and S wave
excitation of waveguides is more sensitive than P to the
source mechanism. Hence, correlations in the S data but
not the P are viewed with skepticism.
The waveguide velocities correlate best with slab
dip (Table 5). Dip is measured in two independent
ways. One, DipV, measures the dip of digitized slab
surfaces (used for ray tracing, Section 2.3) directly beneath each arc volcano, averaged along each slab segment. A second measure (DipE in Table 5) takes dips
from Gorbatov and Kostoglodov (1997), which are averaged from trench to deepest earthquake in each slab
segment. Nicaragua was not included in that study, so
its parameters are estimated following the method described by the authors. The DipE measurements are derived from independent data, so constitute a check on
the DipV results, but DipV probably reflects better the
local slab geometry where waveguides are observed.
Both dip measures give strong correlations (R = −0.89
versus −0.91 for dln Vp ) although DipV exceeds DipE
by 5–10◦ . R will be significant at the 95% confidence
interval if |R| > 0.829, provided the seven data have
approximately Gaussian errors. The S-wave velocities do not show correlations that are as high, presumably reflecting greater noise for reasons discussed
above.
Some process probably unrelated to temperature
must link dip to dln V. The correlations indicate greater
hydration in steeper slabs, or slower gabbro → eclogite
reaction rates. One possibility is that additional H2 O is
delivered to slabs at 100–150 km depth, from dehydration at greater depths (Fig. 17). As hydrous phases
break down and release volatiles within the slab, buoyancy should drive upward fluid flow. The permeability
structure through which fluids pass is unlikely to be homogeneous, and permeability fabric are probably oriented parallel to the slab surface. As a consequence, a
significant fraction of aqueous fluids may travel up dip
rather than vertically; other paths may exist as well to
drive fluids into deeper portions of the downgoing plate
(Hacker et al., 2003b). Any dip-parallel anisotropy in
permeability could create such a pathway, so it seems
reasonable that up-dip flow will be favored in slabs that
dip more steeply. Hence, in steeply dipping slabs the
metamorphic fluids may tend to migrate preferentially
up dip. It is less clear how steep dips (but not faster
descent rates) would suppress eclogite formation in anhydrous gabbro.
Fluids migrating up the slab may decrease dln V
in two ways. First, a free fluid fraction directly reduces seismic velocities (Fig. 15). Second, the addition
of fluid allows hydrous phases to form in rock oth-
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
27
6.6. Fluid transport to deeper mantle
While these variations indicate significantly differing fluid pathways and metamorphic histories in
steeply-dipping slabs than shallow ones, there may
be little difference in the amount of H2 O delivered to
greater depths. At all slabs, the waveguide anomalies
below 150 km depth do not exceed 8% slow and are
on average 3.5% slow, indicating that the enhanced hydration seen at <150 km depth has disappeared. These
measurements allow somewhat less than 2 wt.% H2 O
on average past 150 km depth over a layer 4 ± 3 km
thick, a substantial fraction of the fluid likely delivered to the trench. However, 1–3% velocity anomalies
lie within measurement error, and velocities in anhydrous eclogites or peridotites can vary by this much depending upon bulk composition (Gubbins et al., 1994;
Hacker et al., 2003a). As a result, no H2 O need be
present below 150 km depth to explain the observations, although up to 2 wt.% is allowed. Equivalently,
H2 O flux to the deep mantle in these layers must be
less than 0.7 × 1012 kg/year, perhaps much less.
Fig. 17. Cartoon illustrating how flow of metamorphic fluids might
be affected by slab dip and permeability structure, for: (A) low dips.
(B) high dips. Greater dips may favor up-dip fluid transport (black
arrows), adding fluid beyond that delivered from the trench (open
arrow).
erwise undersaturated in H2 O. Undersaturation may
be common; mafic rocks at 2–5 GPa can hold up to
5.4 wt.% H2 O and serpentinized harzburgites can contain over 13 wt.% H2 O (e.g., Hacker et al., 2003a), but
the subducting oceanic crust likely does not contain
more than 1–3 wt.% H2 O at trenches (e.g., Alt et al.,
1996; Kerrick and Connolly, 2001; Peacock, 1990).
The low seismic velocities seen in steeply dipping
slabs (dln V ∼ −10–15%) indicate up to 5 wt.% H2 O
(Fig. 15), so an additional source of fluids may be required, such as from deeper dehydration reactions. This
scenario requires temperatures low enough for hydrous
phases to be stable, which may be the case in the lower
crust away from the plate interface (van Keken et al.,
2002). One important consequence is that the hydration
inferred from seismic velocities does not represent the
total flux from oceans into the deep mantle, but the sum
of downward flux from subduction and up-dip transport
associated with deeper devolatilization.
7. Conclusions
Low velocity waveguides several kilometers thick
are a common if not ubiquitous feature of subducting
plates. They manifest themselves as mode-converted
signals and dispersion of body waves. A series of numerical experiments illustrate the range of conditions in
which such phases can be observed. Waveguides produce body-wave dispersion only for a favorable raypath geometry, one that requires sources to lie inside
or very close to the waveguides. In most cases, dispersion indicates waveguide thicknesses of 2–8 km, with
large uncertainties because of the difficulty in resolving
higher-mode excitation.
The waveguides show substantial variations in velocity both with depth and between arcs. Waveguides
show the lowest velocities at the shallowest depths
where they reach velocity anomalies of dln VP ∼ −14%
in some slabs. Such low velocities can be explained by
either metastable gabbro or fully hydrated mafic rocks
at low temperatures. Deeper than 150 km, most slabs
show |dln VP | < 4%, indicating that the anomalous layer
has largely equilibrated with the surrounding mantle.
Between different subduction zones, dln V varies by a
factor of 2–3 at depths less than 150 km. These varia-
28
G.A. Abers / Physics of the Earth and Planetary Interiors 149 (2005) 7–29
tions correlate with slab dip but do not correlate with
convergence velocity, plate age, thermal parameter, or
sampling depth. One explanation is that steeply dipping slabs (Nicaragua, Marianas) create conditions that
favor up-dip transport of fluids from deep dehydration reactions. In gently dipping slabs, the buoyancy
of the fluids more readily drives them into the overlying mantle wedge. Presumably a steady state fluid flux
is achieved, with fluids ascending up the slab, into the
mantle wedge, and into the deep mantle at fixed rates.
These observations and their correlations with slab
parameters support the inference that low-velocity slab
waveguides reflect the presence of fluids or hydrous
minerals, rather than variable metastability of anhydrous gabbros, although that possibility cannot be
ruled out. This inference could be tested with careful
observations of Poisson’s ratio, and additional measurements of absolute velocity. Magnetotelluric measurements have the potential to resolve this issue, by
distinguishing interconnected fluid from dry rock along
the top of the slab (Evans et al., 2002).
Acknowledgments
The GSN data have been provided by the IRIS
Data Management Center. Some figures are made using GMT (Wessel and Smith, 1991). The work benefited substantially from detailed comments by B.
Hacker on an early draft, by reviews from E.R. Engdahl
and G. Helffrich, and by the volume editor S. King.
This work supported by NSF Grants EAR0096027,
EAR0096028, and EAR 0215577.
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