1
Supplementary Information:
1.1) Imaging the base of the lithosphere and other discontinuities.
The number of events included in the final image (Fig. 2) for each station are as
follows: LMN (29), HRV (123), PAL (33), LBNH (50), BINY - north (14), BINY south (20), SSPA (83). At stations LMN and PAL, only data from back-azimuths of
195-300 and 170-200, respectively, are included to avoid highly complex
waveforms on other paths. We present data from BINY in two separate back-azimuthal
bins because of the variation in the depth to which the phase from the base of the
lithosphere migrates between the events from the north, 110 km, and those from the
south, 105 km. The waveforms were migrated using station specific crustal velocity
models obtained by modelling scattered waves (Inversion methods are described in
more detail in Supplementary Information, section 2 and Supplementary Tables 1 & 2.).
For all stations, mantle velocities in the lithosphere were set to representative regional
values (see LMN values in Supplementary Table 2) while two lithosphere layers were
included for HRV (Supplementary Tables 1 & 2).
To evaluate uncertainty in discontinuity depths from lateral variation in mantle
velocity, discontinuity depths were also calculated assuming mantle shear-wave
velocities beneath each station obtained by surface-wave inversion1. At each station, the
depth of the lithospheric discontinuity in general changed by less than 1 km and in no
case changed by more than 1.6 km between the two mantle velocity models. Comparing
this analysis to the very small error bars on discontinuity depth obtained in the formal
inversions (section 2), we infer that the uncertainty in the absolute discontinuity depths
is less than 1.6 km.
When imaging discontinuities in the depth range of the base of the lithosphere,
one must be careful not to mistake reverberated crustal phases for direct converted
2
phases originating from a deeper discontinuity. We verify that the apparent phase from
the base of the lithosphere is a true direct arrival using synthetic seismograms and by
noting that variations in the arrival time of this phase between stations are not correlated
with crustal thickness. This issue is also addressed by migrating waveforms in separate
bins for different ranges of source to station distance, as is shown for station HRV
(Supplementary Fig. 1). Phases that migrate to constant depth with respect to epicentral
distance represent direct conversions, whereas reverberations manifest a false increase
in apparent depth with greater distance. At station HRV, direct converted phases image
the base of the crust (the Moho) at 30 km, a mid-lithospheric phase at 61 km, and a
discontinuity at 97 km which we interpret as the base of the lithosphere due to its
correlation with the approximate thickness of the fast velocity lid seen by surface
waves2,3. Later arrivals are well-modelled as reverberated Moho phases. The depth
predicted for the direct conversion from 97 km varies within the first three epicentral
bins (35 to 50) due to the interference with the first crustal reverberation. Yet,
interference effects in the 45-50 bin are minimal, and including these events in our data
set had no effect on the deconvolved, migrated waveform. Therefore, we omitted data at
distances less than 45 in inversions for the velocity gradient at 97 km.
Although the character of the phases varies between stations, some looking wider
(longer period) than others, the variations are consistent with variations of the entire
impulse response between stations. Therefore, variations between stations in the
character of the phases are more likely due to variable numbers of quality data included
in the bin, the noise level at a particular station, or local structure beneath a station
rather than physical differences in the nature of the discontinuity. A phase from depths
comparable to the base of the lithosphere does appear at station PAL (Fig. 2), although
the migrated waveform signal is noisier than at other stations. Stations SSPA and
LBNH manifest strong phases that are consistent with direct arrivals from depths of 102
km and 110 km, respectively (Fig. 2). Synthetic seismogram modelling shows that the
3
timing and amplitude of these phases may be slightly altered by possible interference
with smaller reverberations from discontinuities internal to the crust. However, although
the possibility of such interference leads to uncertainties in the depth and gradient
associated with a discontinuity at the base of the lithosphere, the discontinuity itself is
still required.
Another receiver function study1 which was located partially in our study region
included analysis of data from station HRV, but the study did not note the existence of a
negative phase at depths near our observed lithosphere-asthensosphere boundary. This
is to be expected given the differences between that study and our own. At HRV, which
is included in both studies, the former study included frequencies up to 1 Hz, whereas
our filters return higher frequencies, up to 2 Hz. Since the high amplitude reverberations
from the Moho arrive just after the phase from the base of the lithosphere
(Supplementary Fig. 1), our testing indicates that filtering higher frequencies from our
data would cause the phase from the lithosphere-asthenosphere boundary to interfere
with the first reverberation from the Moho, losing its appearance as a distinct and
separate phase.
To evaluate the presence of anisotropy in mantle and crustal velocities, we also
considered back-azimuthal groupings of deconvolved and migrated SV and SH
waveforms to search for azimuthal dependence in phase arrival times and amplitudes.
However, the data did not resolve any clear anisotropic signatures.
1.2) Existence of 61 km discontinuity ambiguous.
The 61 km discontinuity observed at station HRV migrates to constant depth with
respect to epicentral distance (Supplementary Fig. 1) which usually indicates that a
discontinuity exists at that depth, instead of the possibility that the phase is a
reverberation from a mid-crustal discontinuity. Although a mid-crustal discontinuity
4
which could be responsible for a reverberation at 61 km is not obvious at HRV where
the crust seems relatively simple, the 61 km phase is not observed consistently at other
stations throughout the region, leading us to question its existence. If a strong midcrustal discontinuity does exist beneath HRV, for example, an increase from 5.9 km/s to
6.7 km/s at 11.8 km depth, a negative reverberation could be produced, matching the
magnitude and the depth of the observed 61 km phase. Although such a reverberation
should migrate to increasing depth with respect to epicentral distance, the predicted
move-out is not greater than a difference of 4 km depth from 35 to 80 epicentral degrees
due to the shallow nature of the discontinuity. Therefore, move-out may be difficult to
detect for this case. We have modelled the velocity contrast at the base of the
lithosphere-asthenosphere boundary at HRV without the 61 km discontinuity to
determine the effects of our assumptions regarding the existence of the 61 km
discontinuity, and we find that the contrast at the lithosphere-asthenosphere boundary is
reduced by the absence of a discontinuity at 61 km, but not significantly, to a 3.1-4.9%
velocity contrast (Supplementary Table 2).
2) Inverting for the properties of the base of the lithosphere
Damped least-squares inversions were performed using the migrated waveforms from
our best stations, HRV and LMN, to determine the gradient of the velocity contrast at
the base of the lithosphere. However, we first modelled the structure of each layer and
discontinuity above the lithosphere-asthenosphere boundary, starting with the crust, to
ensure that their effects were appropriately accounted for when inverting for the
properties of the discontinuity at the base of the lithosphere (Supplementary Table 1).
Different observables (e.g. phase timing, amplitude, and waveform shape) were used to
constrain different discontinuities and layer velocities within the model, in order to
maximise the resolution provided by the data while minimising the number of
assumptions regarding structure. Throughout the inversion process, the number of layers
5
in depth was fixed based on observed phases to minimise the number of assumptions
regarding the internal structure of layers. The synthetic seismograms used to determine
partial derivatives were calculated using a propagator matrix method4.
The timing of the Moho Ps phase and the timing of its two, first-order
reverberations in each epicentral bin were used to invert for crustal thickness and
average crustal Vp and Vs (Step 1, Supplementary Table 1). These independent
observations provide excellent resolution of crustal thickness and average velocity.
Such single-layer models over-simplify real crustal structure, and the magnitude of the
velocity increase at the Moho is almost certainly smaller than the values implied by
these crustal velocities. Therefore, we did not include the amplitude of the Moho
conversions in these inversions. Not surprisingly, the amplitudes of the crustal phases
are the one aspect of the synthetic waveforms (red lines in Fig. 2) that do not match the
data (blue lines in Fig. 2). However, we also evaluated the impact that assuming a single
layer crust has on the inferred properties of the lithosphere-asthenosphere boundary and
found that even with very gradational crustal velocities, the velocity drop at the base of
the lithosphere varies by less than 0.5%. For the crust we calculated errors using the
formal 95% confidence limits from the inversion.
Discontinuities below the crust were modelled using waveforms migrated in a
single bin for each station. For HRV, to avoid interference between the phase from the
base of the lithosphere and crustal reverberations for small epicentral distances, we
employed only waveforms from events at distances of 45-80 (Supplementary Fig. 1).
Fortunately, the crustal reverberations at LMN arrive later than at HRV, completely
avoiding interference with the phase from the base of the lithosphere and allowing us to
model data from the full range of epicentral distances represented in the data at LMN
(35-60).
6
In all steps of the inversion where phase amplitudes were modelled (Steps 2 & 3,
Supplementary Table 1), care was taken to accurately calculate predicted migrated
waveform amplitudes and the partial derivatives of the predicted migrated waveform
with respect to discontinuity parameters. In particular, before the real waveforms were
deconvolved, each was normalised by its P-wave component amplitude, and then
weighted according to its signal-to-noise ratio. When the real waveforms were
simultaneously deconvolved and migrated, a water-level, i.e. regularisation, was applied
that in practice removes some of the higher frequency content from signal. To ensure
that the effects of these processing steps were accounted for in the predicted waveform
migration, synthetics were calculated for the P-slowness of each of the real waveforms,
the synthetics were scaled to the amplitudes of their normalised, real waveform
counterparts, and identical water-levels were applied. This procedure also ensured that
we accurately accounted for differences in phase amplitude produced by waveforms
with varying P-wave incidence angle.
When matching deconvolved, migrated waveforms in depth (Steps 2 & 3,
Supplementary Table 1), it is important that the migration model not bias the results.
Hence, we required the migration model to match our best-fitting model. To accomplish
this, the parameters that we held fixed in the inversion were held fixed at identical
values in the migration model. The parameters that varied during the inversion were
updated in the migration model once several iterations were completed and convergence
was achieved. Then the data were reprocessed using the new migration model, and the
iterative inversion was re-run. The process was repeated until subsequent inversions no
longer yielded perturbations to the best-fitting model. The number of layers in the
migration model remained constant throughout all steps of the inversion. Predicted
waveforms and partial derivatives were re-calculated for each iteration.
7
We inverted the timing and amplitude of the mid-lithospheric phase observed at
HRV to determine the depth of the potential associated discontinuity and the magnitude
of the velocity contrast (Step 2, Supplementary Table 1). Vp/Vs in the mantle
lithosphere was fixed at 1.8, and Vp in the layer above the mid-lithospheric
discontinuity was held at 8.2 km/s as determined by local refraction experiments for
depths just below the Moho5. A 5.4 ± 0.6 % shear velocity decrease with depth at 60.9 ±
0.4 km depth best fits the observed mid-lithospheric phase at HRV (Supplementary
Table 2). Errors correspond to the change in model parameter for which the migrated
synthetic waveform image hits the bounds of the two standard deviation error bars for
the depth and amplitude of the observed phase; the latter were calculated using a
bootstrap method similar to that described in Fig. Legend 2. At LMN, mantle velocity
was assumed to be constant from the Moho to the base of the lithosphere, again
matching the sub-crustal lithosphere velocity determined by refraction data5. We also
modelled HRV without the mid-lithospheric discontinuity at 61 km depth due to some
ambiguity regarding its existence (Supplementary Information, section 1.2 and
Supplemental Table 2).
At the lithosphere-asthenosphere boundary we used the complete waveform shape
to constrain not only the depth and total velocity contrast but also the thickness of the
velocity gradient assuming a linear gradient (Step 3, Supplementary Table 1).
Waveforms converted at the lithosphere-asthenosphere boundary depend on four
parameters: the velocity contrast at the discontinuity, the depth range over which the
velocity contrast occurs, the absolute depth of the discontinuity, and the dominant
period of the incident P-wave. A variety of tests including forward modelling, grid
searches, and formal inversions indicate strong trade-offs between the parameters.
Fortunately, the dominant period of the incident P-wave may be constrained
independently. Limiting the acceptable range of incident P-wave period in turn limits
the possible variation in the other parameters.
8
To determine the dominant period of the incident P-wave we simultaneously
deconvolved the P-wave signals from themselves, applying the same normalization and
water-levels that are applied to the Ps data. The result is an impulse response with a
width that represents the dominant period of the incident P-waves in the data. We then
simultaneously deconvolved synthetic P-waves that matched the p-slownesses and
amplitudes of the data and applied the same water-levels, assuming a single period for
all of the simultaneously deconvolved synthetic P-waves in a given impulse response.
We created synthetic auto-deconvolved impulse responses for a variety of incident Pwave periods until we found the auto-deconvolved impulse response that fit the data
best. The 95% confidence limits for the best-fitting incident P-wave period at each
station were established using an F-test. The dominant periods that fall within the 95%
confidence limits for HRV are 1.5-2.0 s, and those for LMN are 2.9-3.7 s.
Because parameter trade-offs are strong, and to avoid the exclusion of viable
models, we fixed gradient thickness at a variety of values and inverted for the bestfitting period, depth, and velocity contrast. Supplementary Fig. 2 shows the best-fitting
velocity drops and P-wave periods that correspond to the fixed gradient thicknesses.
The misfits between the data and the deconvolved, migrated Ps waveforms for these
parameter combinations are approximately equal, increasing slightly for the 12 km thick
gradient at LMN. However, we accept only those models for which the incident P-wave
periods fall within the 95% confidence limit for the best-fitting incident P-wave period
(Supplementary Fig. 2b). At HRV a 3.3-5.7% shear velocity drop over 5 km or less at
96.6-96.8 km depth is acceptable at 95% confidence, assuming the existence of the midlithospheric discontinuity. Without the mid-lithospheric discontinuity, the velocity drop
is 3.1-4.9%. At LMN a 6.8-7.4% velocity contrast that occurs over 5 km or less at 90.690.7 km depth gives the best fit to the dominant period of the incident waveform. Yet, a
velocity contrast that occurs over 10 km requiring a 10.7% contrast cannot be excluded
by the 95% confidence limit on the dominant period of the incident P-wave at LMN.
9
The error bars on the absolute depth of the discontinuity reported here are the formal
error bars from the inversion. However, we prefer to use the broader 1.6 km error bars
inferred by comparing the absolute depths obtained with this approach to those obtained
assuming surface wave velocity structure beneath each station2 (Supplementary
Information, section 1.1).
During the inversions for the parameters above, density and Vp/Vs were assumed
to be constant across the lithosphere-asthenosphere boundary, at 3.32 g/cm3 and 1.8
respectively. However, we also performed inversions in which the density decreased by
10% with depth and Vp/Vs ratio rose from 1.80 to 1.85 with depth over the gradient of
the discontinuity. Reducing the density at the base of the lithosphere by 10% has only a
small effect on the velocity contrast, decreasing it by ~0.25%. Increasing Vp/Vs by 0.05
affects the P-wave velocity contrast dramatically, reducing it by ~2.75% relative to the
value determined for fixed Vp/Vs; however, the necessary S-wave velocity contrast
remains unaffected. Overall, our assumptions concerning density and Vp/Vs do not
significantly affect our conclusions regarding S-wave velocity properties at the
discontinuity.
We assumed a linear velocity gradient at the lithosphere-asthenosphere boundary.
However, we did experiment with exponential gradients, and for gradients over the
same depth range, the magnitude of the velocity contrasts required are nearly identical
for the two cases. Hence, we cannot significantly modify our results by changing the
shape of the velocity gradient.
3) Expected velocity gradients due to variations in temperature, hydration, grain
size, and melt.
10
If the observed velocity contrast is caused by purely thermal gradients, olivine
deformation experiments6 suggest that it can be described according to the following
equations:
∂lnVS/∂T = ∂lnVSU/∂T - F(α) [Q-1(ω,T)/π] (E+PV)/RT2
where
Q-1=Ad-mToαexp(-α(E+PV)/RT)
F(α)=(πα/2)cot(πα/2)
and the change in the unrelaxed shear wave speed with respect to temperature,
∂lnVSU/∂T = -8.6x10-5 K-1; activation energy, E=424,000 J/mol; A=730 s-αµmm; grain
size, d=1mm; the frequency (ω) dependence of attenuation, α=.26; the grain size
sensitivity of attenuation, m=.26; and activation volume, V=6x10-6 m3/mol (refs 6, 7) .
Since some of these parameters were determined by matching data at experimental
conditions, we subtract the 200 MPa pressure at which the experiments were performed6
from the pressure at 100 km depth, 3.36 GPa, and use the result as pressure, P. For the
period, To, we use the dominant incident P-wave periods which fall within our
confidence limits, 1.5 and 2 s at HRV, corresponding to 5.7 and 3.3% velocity contrasts
respectively, and 2.9 and 3.7 s at LMN, corresponding to 10.7 and 6.8% velocity
contrasts respectively. Since an increased absolute background temperature, T,
decreases the thermal contrast required to explain a given velocity contrast, we have
chosen a relatively high asthenospheric temperature to be conservative. We find that at
1375° C we require at least a 119-210° C thermal contrast to explain the 3.3-5.7%
velocity contrast at HRV and a 222-374° C thermal contrast to explain the 6.8-10.7%
velocity contrast at LMN. Other parameter choices are also conservative. For example,
the value of 6x10-6 m3/mol for activation volume is at the low end of experimentally
determined values8, and larger activation volumes would increase the required
11
temperature contrast. Similarly, 1 mm is small for olivine grain size at temperatures and
stresses appropriate for ~100 km depth9, and a greater mantle grain size (say 10 mm)
would also require a larger temperature jump (173-315° C at HRV and 331-552° C at
LMN). Alternative physical models10 have been proposed to explain the experimental
data6 we employ; however, these alternative interpretations would not significantly
affect the thermal gradients we calculate.
In numerical models of mantle flow and temperature that allow for small-scale
convection at the transition from thick cratonic lithosphere to thinner lithosphere in
which viscosity is dependent solely on temperature and pressure11,12, the thermal
gradients at the base of the lithosphere are typically smaller than 2-5° C/km. Even
allowing for untested combinations of model parameters, 10° C/km is a generous upper
bound on the thermal gradient possible at the base of a ~100 km thick lithosphere12. A
gradient of 5° C/km would predict at most 55° C over 11 km at LMN and 25° C over 5
km at HRV. Using the parameter values described in the previous paragraph, a 55° C
thermal contrast results in a 1.7% maximum velocity contrast for the dominant periods
at stations LMN, and a 25° C thermal contrast results in a 0.7% maximum velocity
contrast for the dominant periods at HRV. Such velocity contrasts are far too small to
explain the 3.1-10.7% velocity drop required by our data. A gradient of 10° C/km would
produce a 3.3% maximum velocity contrast for the dominant periods at stations LMN,
and a 1.3% velocity contrast for the dominant periods at HRV. These predictions still
fail to match the minimum velocity drop required at LMN (6.8%) and HRV (3.1%).
Additionally, these mantle flow models allow significant small-scale convection
to develop only in situations where the upper plate is relatively stationary with respect
to the asthenosphere12. If shearing due to the motion of the North American continental
lithosphere over the asthenosphere is allowed, the thermal gradient at the base of the
12
lithosphere will be reduced12, thus reinforcing the statement that thermal contrasts alone
are insufficient to explain the velocity contrast observed in our data.
The magnitude of a shear-wave velocity drop due to a dehydration front at the
lithosphere-asthenosphere boundary is difficult to estimate due to a lack of direct
experimental measurements of the effects of water on olivine and other upper mantle
minerals. However, water may be assumed to reduce velocity primarily by enhancing
seismic attenuation13 using the following relationship14:
V (ω, T, P, C) =V0 (T, P) [1-1/2cot (πα/2) Q-1(ω, T, P, C)]
where V0(T,P) is the anharmonic seismic wave velocity, ω is frequency, T is
temperature, P is pressure, and C is composition. Given that the shear-wave velocity
drop at the lithosphere-asthenosphere boundary and the asthenospheric velocities we
observe are comparable to the values for old Pacific Ocean regions15, we used values of
shear-wave Q (inverse attenuation) for the lithosphere (150) and the asthenosphere (50)
from this study15 to estimate the effects of weakly frequency dependent attenuation on
velocity. Assuming values of α, a parameter that describes the frequency dependence of
attenuation, of 0.1-0.3, water would reduce shear-wave velocity by 1.3- 4.3%. Thus, the
velocity drop that can be attributed to the presence of water overlaps the minimum
velocity contrast at HRV (3.1%) but does not attain the minimum value at LMN (6.8%).
What is the role of grain size? Grain size, like water, affects the attenuation
component of velocity6. Therefore, the total effect of water and grain size on velocity is
also limited by observed values of attenuation to be < 4.3%. Could grain size variation
contribute to sharpening the velocity contrasts predicted from purely thermal models?
This scenario is very unlikely. Since grain size is inversely proportional to stress16-18, a
sharp increase in shear stress with depth would be required for grain size to be
responsible for the observed velocity contrast. However, in models in which viscosity
13
depends only on temperature and pressure12, shear stress generally decreases gradually
with depth.
Alternatively, if asthenospheric temperatures are above the damp-solidus, melt
fractions of 1.4-1.8% (ref. 19) or 3.6-5.7% (ref. 20) in the asthenosphere could easily
produce the roughly 7% velocity drop inferred for the best-fitting LMN models and
even the 11% velocity drop associated with the largest gradient thickness permitted by
the LMN data. In scenarios involving melt, the base of the lithosphere would be defined
by the damp-solidus, thus prohibiting melt from rising into the lithosphere. For
peridotite solidi corresponding to 800-1000 H/106 Si (ref. 21), a range of reasonable
mantle temperatures will be above the solidus at asthenospheric depths, and will cross to
temperatures below the solidus at the 90-110 km depths we infer for the lithosphereasthenosphere boundary. One possible model for generating melt in the asthenosphere
beneath eastern North America would be upward flow and decompression of mildly
hydrated asthenospheric material along the contours of the more rigid, shallowing
lithosphere. This type of flow occurs in mantle flow models that incorporate the WSW
absolute motion of the North American plate12,22 (Fig. 1). Alternatively, mantle
temperatures may exceed the solidus within the asthenosphere without the need for
decompression21. In general, if melt leaves the region, drawing the water that has
partitioned into it away, a mechanism to rehydrate stationary mantle or bring in new
hydrated mantle is required. Such re-supply of hydrated mantle is provided by the
upward flow beneath the continental interior described above. In any model involving
wet melting, and in the earlier hypothesis that involves a sub-solidus hydrated
asthenosphere, a reasonable question is how the diffusion of hydrogen into the
postulated dry sub-solidus lithosphere would affect lithospheric properties. The
presence of hydrogen would effectively hydrate and locally reduce velocities, but the
maximum length scale for this diffusion over the 300-450 My since emplacement of the
14
lithosphere is 6-7 km (ref. 21), consistent with the sharp lithosphere-asthenosphere
boundary imaged in this study.
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Supplementary Fig. 1
SV waveforms from HRV deconvolved and migrated in epicentral distance bins.
Red signifies positive polarity, or a velocity increase with depth, while blue
indicates a negative amplitude corresponding to a velocity decrease with depth.
Black lines indicate the migrated depths of synthetic phases predicted from our
preferred HRV model, including direct conversions from the Moho (30 km), 61
km, and 97 km depth. Later arrivals show greater apparent depth with distance
and correspond to crustal reverberations.
Supplementary Fig. 2
Parameter trade-offs and model constraints. Blue lines represent LMN models,
while green lines show HRV results. Red stars indicate models that fit the Ps
conversion from the base of the lithosphere, and whose dominant incident Pwave periods fall within the 95% confidence limits from the auto-deconvolution
test. Black stars are models that fit the Ps conversion from the base of the
lithosphere, but require P-wave periods outside the 95% confidence limits. a)
16
The best-fitting models for several gradient thicknesses show that the observed
Ps conversion from the base of the lithosphere can be fit with a variety of
models at HRV and LMN. However, each model corresponds to a single
dominant incident P-wave period, and the dominant period may be constrained
independently. b) RMS misfit of the auto-deconvolved P-wave synthetics to the
auto-deconvolved P-wave data for the dominant periods used with the models
in Supplementary Fig. 2-a. The numbers next to the stars indicate the gradient
thickness that corresponds to that P-wave period. The red dashed lines show
the 95% confidence limits on the dominant period at HRV and LMN, indicating
that models with gradients as thick as roughly 5 km are acceptable at HRV,
while at LMN the gradient may occur over 11 km or less.