Supplementary information

“Seismic Evidence for the Depression of the D” Discontinuity beneath the Caribbean:

Implication for Slab Heating from the Earth’s Core”

Justin Yen-Ting Koa, b, Shu-Huei Hunga,*, Ban-Yuan Kuoc, and Li Zhaoc

This file includes:

1. Data Processing

2. Data Measurement and Correction

3. Synthetic Experiments on Data Sensitivity to Model Variables

4. Synthetic Example to Illustrate the Waveform Modeling Procedure

5. Data Misfits and Lateral Variation of the Resulting 1-D Models

6. Modelled 1-D Structure for Waveform with no SdS Arrival

7. Detectability of the D” Discontinuity

8. Large SdS Amplitudes Observed in the Central North American Continent

Supplementary References

Supplementary Table 1

Supplementary Figures S1-S11

1. Data Processing

For each earthquake we align all the selected waveforms along the SH phase

arrivals by an adaptive stacking method [Rawlinson and Kennett, 2004]. This process

would correct the arrival time moveout with epicentral distances and suppress as

much of the traveltime perturbation as possible resulting from local velocity

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heterogeneity beneath individual stations and difference in station elevations. Finally,

to remove the difference in waveform shapes from the variability of finite-source

processes, we determine a common source wavelet for each event by stacking the

aligned S arrivals at the stations at 70 degrees or less which have little contribution of

seismic energy from later triplication arrivals. An iterative time-domain

deconvolution with a Gaussian width factor of 0.4 (equivalent to a low-pass filter with

the cutoff frequency of 0.2 Hz) [Ligorría and Ammon, 1999] is then applied to

removal of the obtained source wavelet from individual aligned traces. An example of

data processing is summarized in Figure S1.

2. Data Measurement and Correction

As the differential traveltime and relative amplitude measurements are less

influenced by event mislocation and upper mantle heterogeneity and provide strong

constraints on lowermost mantle structure (Fig. 1c), we construct our dataset that

comprises the observed differential ScS-S and SdS-S traveltimes (∆ T ScS−S and ∆ T SdS−S

) and ScS/S and SdS/S amplitude ratios (∆ AScS /S and ∆ ASdS/S). Overall waveform

similarities between observed and synthetic traces in the modeled time window are

also included as part of the measures of optimization criteria in the search of the best-

fit model. Prior to data modeling, the measured differential traveltimes are corrected

for contributions from mantle velocity heterogeneity based on a global tomography

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model [Ritsema et al., 2002].

Additionally, certain types of focal mechanisms for available events may be

unfavorable for excitation of shear wave energy toward our stations which have a very

limited distance and azimuthal coverage. It can cause fluctuations in waveform

amplitudes between nearby stations and introduce large uncertainties in modeling the

changes of amplitude ratios and overall waveform shapes genuinely associated with

the D” structure. We thus exclude those data observed at station azimuths that would

yield large fluctuations of amplitude ratios estimated based on theoretically-predicted

radiation patterns [Lay and Wallance, 1995],

𝑅𝑆𝐻=𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝛿𝑐𝑜𝑠𝑖ℎ𝑠𝑖𝑛𝜙+𝑐𝑜𝑠𝜆𝑠𝑖𝑛𝛿𝑠𝑖𝑛𝑖ℎ𝑐𝑜𝑠2𝜙+𝑠𝑖𝑛𝜆𝑐𝑜𝑠2𝛿𝑐𝑜𝑠𝑖ℎ𝑐𝑜𝑠𝜙−1

2 𝑠𝑖𝑛𝜆𝑠𝑖𝑛2𝛿𝑠𝑖𝑛𝑖ℎ𝑠𝑖𝑛2𝜙, (S.1)

where 𝜙=𝜙𝑓−𝜙𝑠, is the difference between the strike azimuth of the fault plane, 𝜙𝑓,

and the source-to-station azimuth, 𝜙𝑠, 𝛿 is the dip of the fault plane, 𝜆 is the slip rake

angle, and 𝑖ℎ is the takeoff angle for a given shear wave. We select 7 representative

focal mechanisms and calculate the theoretical amplitude ratios at the epicentral

distances from 75o to 80o and azimuthal range between 310o and 360o most available

in our data (Fig. S2). Only the stations with the predicted values that fall within the

standard deviation of all the calculated amplitude ratios for each event are used for the

following data measurement and grid search modeling.

Not only does 3D structural heterogeneity have a significant influence on

observed amplitude anomalies, but different radiation patterns of the earthquakes can

also produce intrinsic fluctuations in amplitude for seismic phases arriving at different

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azimuths and takeoff angles. We thus correct the source-related amplitude-ratio

deviations from the raw measurements using eq. (S.1). It is worth mentioning that

amplitude information can provide critical constraints particularly on the sharpness of

the seismic discontinuity superior to differential traveltime data but they should be

treated with caution owing to numerous factors as discussed here which can

substantially alter the amplitudes of arriving phases. Further detailed investigation of

3D wave propagation effect on amplitude fluctuations is necessary for future studies.

3. Synthetic Experiments on Data Sensitivity to Model Variables

Rather than using numerous free variables to parameterize a radial velocity

model for the D” layer and fit every detail in the observed data with suspected

resolvability, we aim primarily at investigating the overall characteristics of the

discontinuity undulation and shear velocity structure of the underlying D” layer linked

to the “slab graveyard” feature as inferred from seismic tomography [Grand et al.,

1997]. We choose three model parameters including and impedance contrast (VD”) on

the D” discontinuity and radial velocity gradient (GD”) within the D” layer to depict

the first-order feature of D” in our study region.

It is well noted that there exist severe trade-offs between the constraining

discontinuity topography and neighboring velocity structure particularly relying on

differential traveltime observations. As each type of the datasets provide different

effective levels of constraints on a finite number of model variables used to

characterize the D” structure, we first construct a large set of ground-truth synthetic

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seismograms for a thorough combination of different model parameters computed

with the DSM [Kawai et al., 2006] to elucidate the sensitivity of the observed

waveforms and measured data to the perturbation of each model parameter which

guides for the following search of optimal D” models.

Figs. S3-S5 show the testing ranges of the perturbations for individual model

parameters and corresponding shear wave velocity variations with depth in the

lowermost 600 km mantle. The figures also exemplify the comparison of DSM-

computed synthetic SH triplication waveforms and predicted differential traveltimes (

∆ T ScS−S and ∆ T SdS−S) and amplitude ratios (∆ AScS /S and ∆ ASdS/S) between the testing

models at epicentral distances of 70 and 75 degrees. In Fig. S3, starting with the

PREM model, we fix the thickness of the D” layer to be 264 km and vary the velocity

jump across the D” discontinuity from 1% to 3%. It is clear that the SdS arrival times

are barely changed but their amplitudes increase significantly with the magnitude of

the velocity contrast. On the other hand, both the ScS-S times and ScS/S amplitudes

decrease gradually with the velocity contrast. In Fig. S4, we instead fix the velocity

contrast of 3% across the D” discontinuity and vary the velocity gradient from -6% to

+3% within a 264-km thick D” layer. Similar to those shown in Fig. S3, the decrease

of the velocity gradient in the D” layer has a negligible influence on the SdS arrival

times but substantially reduces the ScS-S differential times. Moreover, it has distance-

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dependent but reverse influence on SdS/S and ScS/S amplitude ratios being enlarged

and reduced, respectively. In Fig. S5, we vary the thickness of the D” layer from 150

km to 350 km and implement a fixed velocity jump of +3% across the discontinuity in

PREM model with the uniform velocity in the D” layer. The results show the SdS-S

differential times are most sensitive to the topographic variation of the D”

discontinuity.

According to the above synthetic experiments, we find that all three model

parameters exert strong effects on amplitude ratios, ∆ ASdS/S but differential

traveltimes, ∆ T SdS−S, are only affected by the thickness of the D” layer. That is, we

are capable of mapping the topography of D” discontinuity based on ∆ T SdS−S alone.

Furthermore, for the ScS related data measurements, only the change of the velocity

near the CMB can induce noticeable variations in differential traveltimes and

amplitude ratios, providing a critical constraint on the gradient within the D” layer.

See Table S1 for a brief summary of the extent of influence of each model variable on

observed differential traveltime and amplitude ratio data.

4. Synthetic Example to Illustrate the Waveform Modeling Procedure

In Fig. S6, we present a synthetic example to illustrate our modeling procedure.

First, we construct DSM-computed, SH-component seismograms for a presumed 1-D

model in D” using the same source-receiver geometry as that of real data (right panel

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of Fig. S6(a)). Second, various levels of Gaussian random noise are added to mimic

the observed waveforms with signal-to-noise ratios (SNR) on the order of 16 and 5.

The procedure applied to real data measures is then employed to generate synthetic

datasets which comprise differential traveltimes, amplitude ratios and waveform

decorrelation coefficients measured directly from the simulated waveforms. Finally,

we determine the topographic height of the D” discontinuity based on the measured

SdS-S differential times and then search for the optimal solutions of the other two

model variables, VD” and GD”, by minimizing the defined cost function.

Fig. S6(b) illustrates how the changes of VD” and GD” would affect the fitting of

different types or combinations of data measures and how severe the tradeoff between

them would be provided that only specific datasets are included as constraints. It also

demonstrates that the model solution, if considering only the phase information, i.e.,

differential traveltime and waveform decorrelation, in the cost function, is possibly

trapped into multiple local minima, especially for the low S/N data. Further including

the amplitude-ratio misfits in the cost function, on the other hand, can largely

eliminate the tradeoff between VD” and GD” and drive the search toward the global

minimum of the model space.

5. Data Misfits and Lateral Variation of the Resulting 1-D Models

In Fig. S7, we plot a histogram showing the distribution of the total misfit errors

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and proportions of three misfit terms in the defined cost function as a function of the

topographic height of the D” discontinuity (HD”) for all the resulting 1-D models. As

the 3D structural variations have more pronounced effects on waveform amplitudes,

the amplitude-ratio data account for a larger proportion of the errors of about 50%.

In Fig. S8(a), we show the lateral variations in the topographic height of the D”

discontinuity (HD”) and shear velocity perturbation (lnVs) at 2800 km depth from the

individual, unaveraged 1-D models. They in general display similar E-W variations as

those shown in Fig. 3(b), which have the lowest topographic relief and strongest shear

velocity reduction in the central part of our study region. Fig. S8(b) displays the

standard deviations HD” and lnVs within each cap, while Fig. 8(c) shows the cap size

used for lateral averaging of HD” and lnVs shown in Fig. 3(b). The larger standard

deviations may roughly indicate the abrupt, unphysical structural variations between

the nearby 1-D models within the cap resulting from the unmodelled 3D effects. They

are usually much smaller in the densely-sampled region compared to the variational

ranges of HD” (over 150 km) and lnVs (~5%) for the large-scale structure over 600

km along the E-W direction.

6. Modelled 1-D Structure for Waveform with no SdS Arrival

The synthetic experiments shown above indicate the differential SdS-S times

provide robust constraints on HD”. However, many shear wave traces particularly

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traversing D” in the south-central part of our study region as shown in Fig. 3(b) do not

have noticeable SdS arrivals for HD” estimates (Fig. S9). We thus assume 150 km for

HD” in the waveform modeling, which essentially results in a 1-D structure with very

small and negligible velocity contrast on the D” discontinuity (Fig. S9)

7. Detectability of the D” Discontinuity

In Fig. S10, we show 1-D DSM synthetics for the D” models with a 0.2 km/s

shear velocity increase within a transition zone whose thickness (W) varies from 0 to

120 km near 300 km above the CMB. The results show the SdS amplitudes decrease

with increasing W more drastically at shorter distances but still are visible at >78o

distances for W=120 km. The peak arrival times of SdS relative to S used to estimate

HD” are almost unchanged.

8. Large SdS Amplitudes Observed in the Central North American Continent

Fig. S11 shows the anomalously large SdS amplitudes recorded at the stations

located in the central part of the USArray and the distance of ~80o away from the

event. These triplication arrivals traverse the middle of our study D” region with the

depressed D” topography and large negative shear velocity gradients in the D” layer

as constrained by the observed shear wave data. The resulting models properly predict

the observed ScS/S amplitude ratios but apparently underestimate the SdS/S amplitude

ratios.

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Supplementary Reference

Grand, S.P., van der Hilst, R.D., Widiyantoro, S., 1997. Global seismic tomography: a

snapshot of convection in the Earth, GSA Today 7(4), 1–7.

Kawai, K., Takeuchi, N., Geller, R.J., 2006. Complete synthetic seismograms up to 2

Hz for transversely isotropic spherically symmetric media, Geophys. J. Int. 164,

411-424. 

Lay, T., Wallace, T.C., 1995. Modern Global Seismology, Academic Press, San Diego,

521.

Ligorría, J.P., Ammon, C.J., 1999. Iterative deconvolution and receiver function

estimation, Bull. Seismol. Soc. Am. 89, 1395-1400.

Rawlinson, N., Kennett, B.L.N, 2004. Rapid estimation of relative and absolute delay

times across a network by adaptive stacking, Geophys. J. Int. 157: 332–340.

Ritsema, J., Deuss, A., van Heijst, H.J., Woodhouse, J.H., 2011. S40RTS: a degree-40

shear-velocity model for the mantle from new Rayleigh wave dispersion,

teleseismic traveltime and normal-mode splitting function measurements.

Geophys. J. Int. 184, 1223–1236.

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Supplementary Table

Table S1. A brief summary of the results of data sensitivity tests.

Data Increase in Impedance Contrast (VD”)

Increase in Velocity Gradient (GD”)

Increase in D” Thickness (H)

SdS/S amp increase increase increaseSdS-S time unchanged unchanged decreaseScS/S amp decrease decrease unchangedScS-S time decrease decrease unchanged

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Supplementary Figures

Figure S1. Illustration of processing of triplication shear waves recorded by the

USArray. (a) SH-component displacement traces first aligned along predicted S

arrival times based on PREM. (b) Further alignment of the S phase arrivals through

10 iterations of the adaptive stacking procedure [Rawlinson and Kennett, 2004]. The

top red trace is considered as a reference wavelet or source wavelet obtained from the

linear stack of the waveforms recorded at distance less than 70o. (c) Impulsive-like S-

wave signals after the source wavelet being removed from the traces in (b) through an

iterative deconvolution [Ligorría and Ammon, 1999]. For the following data measure

and waveform modeling, we restrict our attention only to S and ScS phases and

triplication arrivals in between them at the distance range of about 65o-85o (blue

traces), where these waves all traverse the D" layer within the region of our primary

interest.

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Fig. S2. The investigation of the influence of earthquake radiation patterns on

relative waveform amplitudes. Theoretical amplitude ratios of ScS/S (top) and SdS/S

(bottom) plotted as a function of azimuth at the epicentral distances of 75o and 80o for

seven earthquakes used in our study. The corresponding double-couple focal

mechanisms are shown in the upper-right corner of each panel. The dashed lines

indicate the azimuths at which the predicted amplitude ratios are larger than the

standard deviation of those at the azimuths between 310o and 360o and excluded from

the cost function estimation in the waveform modeling.

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Fig. S3. Data sensitivity to the velocity contrast (VD”) across the D” discontinuity.

Synthetic experiments illustrating how the sudden velocity increase across the D”

discontinuity affects shear wave triplication waveforms and measured differential

ScS-S and SdS-S traveltimes (∆ T ScS−S and ∆ T SdS−S) and ScS/S and SdS/S amplitude

ratios (∆ AScS /S and ∆ ASdS/S), shown on the middle and right of the figure,

respectively. The synthetic SH waveforms are calculated by the DSM [Kawai et al.,

2006] in PREM and five trial models with VD” ranging from +1 to +3% shown on the

left.

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Fig. S4. Data sensitivity to the shear velocity gradient (GD”) in the D” layer.

Synthetic experiments illustrating how GD” influences shear wave triplication

waveforms and measured differential ScS-S and SdS-S traveltimes (∆ T ScS−S and

∆ T SdS−S) and ScS/S and SdS/S amplitude ratios (∆ AScS /S and ∆ ASdS/S) in PREM and

six trial models with GD” varying from -6% to +3%. The figure layout remains the

same as Fig. S3.

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Fig. S5. Data sensitivity to the topographic height of (HD”) of the D”

discontinuity. Synthetic experiments illustrating how HD” or the thickness of the D”

layer influences shear wave triplication waveforms and measured differential ScS-S

and SdS-S traveltimes (∆ T ScS−S and ∆ T SdS−S) and ScS/S and SdS/S amplitude ratios (

∆ AScS /S and ∆ ASdS/S) in PREM and five trial models with HD” varying from 150 km to

350 km above the CMB. The figure layout remains the same as Fig. S3.

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Fig. S6. A synthetic test to illustrate and verify our waveform modeling

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procedure. (a) (Left) Presumed 1-D model with a 260-km thick D” layer (red line)

used to generate synthetic shear waveforms shown on the right. Black lines represent

trial models in grid search. (Right) The top trace shows a synthetic SH waveform at

75∘for the presumed model computed by the DSM [Kawai et al., 2006]. The middle

and bottom traces simulate the observed waveforms by adding Gaussian noise to the

top trace with high and low signal-to-noise ratios (SNR) of 16 and 5, respectively.

The numbers next to the three synthetics are the thickness of the D” layer determined

from the observed SdS-S times marked by the dashed vertical lines. (b) Image maps

with contours showing the cost function estimated over a wide range of model

variables, VD” (velocity contrast on the D” discontinuity) and GD” (velocity gradient in

D”). Each column shows the grid search results constrained by the combined dataset

of differential traveltimes and waveform decorrelation coefficients (left), amplitude-

ratio data only (middle), and all of them simultaneously (right). The rows from top to

bottom correspond to the results obtained with noise-free, high and low SNR

waveforms shown in (a). The presumed “true” model and optimal solutions of VD” and

GD” at the global minima of the cost function are marked by magenta circles and

yellow stars, respectively.

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Fig. S7. Histogram showing the total misfit error and proportion of the errors from

each type of data varying with the determined topographic height (HD”) of the D”

discontinuity for all the resulting 1-D models. There is no obvious correlation for the

depressed topography which yields a larger total misfit error and amplitude error.

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Fig S8. (a) Relative shear velocity perturbations (δlnVs) with their mean removed at

2800 km depth (top) and topographic heights (HD”) of the D” discontinuity (bottom)

plotted at the ScS bounce points, obtained from the individual resulting 1-D models.

(b) The standard deviations of the δlnVs and HD” for the resulting 1-D models within

each cap. (c) The cap size used for lateral averaging of δlnVs and HD”.

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Figure S9. Example of a shear waveform showing no noticeable SdS arrival and

the resulting best-fit 1D structure. For the trace with no available Scd-S differential

time to estimate the topographic height of the D” discontinuity, we assume 150 km in

grid search modeling of the 1-D velocity structure. The resulting best-fit model yields

a negligible impedance contrast on the presumed D” discontinuity.

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Fig. S10. 1-D DSM synthetics for the D” discontinuity occurring over a depth

interval (W) from 0 to 120 km. (Left) 1-D shear wave velocity models in D” used in

the calculation of synthetic waveforms. (Middle) The resulting triplication shear

waveforms plotted as a function of distance between 66-87o. (Right) The differential

SdS-S and ScS-S times measured from the synthetic records. Color dots shown on the

left side of the plot indicate the minimum distance for each W at which the SdS starts

to be detectable.

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Fig. S11. Abnormally large amplitudes of SdS phases observed in the central

North American continent. The optimal 1-D models for individual station-event

pairs indicate that the densely sampled region beneath northern South America has a

thinner D” layer with relatively slow shear velocities. The observed SdS amplitudes

are clearly underpredicted by the synthetics, particularly at the distance of ~80o.

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