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Supplementary information
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“Seismic Evidence for the Depression of the D” Discontinuity beneath the Caribbean:
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Implication for Slab Heating from the Earth’s Core”
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Justin Yen-Ting Koa, b, Shu-Huei Hunga,*, Ban-Yuan Kuoc, and Li Zhaoc
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This file includes:
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1. Data Processing
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2. Data Measurement and Correction
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3. Synthetic Experiments on Data Sensitivity to Model Variables
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4. Synthetic Example to Illustrate the Waveform Modeling Procedure
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5. Data Misfits and Lateral Variation of the Resulting 1-D Models
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6. Modelled 1-D Structure for Waveform with no SdS Arrival
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7. Detectability of the D” Discontinuity
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8. Large SdS Amplitudes Observed in the Central North American Continent
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Supplementary References
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Supplementary Table 1
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Supplementary Figures S1-S11
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1. Data Processing
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For each earthquake we align all the selected waveforms along the SH phase
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arrivals by an adaptive stacking method [Rawlinson and Kennett, 2004]. This process
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would correct the arrival time moveout with epicentral distances and suppress as much
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of the traveltime perturbation as possible resulting from local velocity heterogeneity
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beneath individual stations and difference in station elevations. Finally, to remove the
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difference in waveform shapes from the variability of finite-source processes, we
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determine a common source wavelet for each event by stacking the aligned S arrivals
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at the stations at 70 degrees or less which have little contribution of seismic energy from
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later triplication arrivals. An iterative time-domain deconvolution with a Gaussian
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width factor of 0.4 (equivalent to a low-pass filter with the cutoff frequency of 0.2 Hz)
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[Ligorría and Ammon, 1999] is then applied to removal of the obtained source wavelet
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from individual aligned traces. An example of data processing is summarized in Figure
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S1.
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2. Data Measurement and Correction
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As the differential traveltime and relative amplitude measurements are less
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influenced by event mislocation and upper mantle heterogeneity and provide strong
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constraints on lowermost mantle structure (Fig. 1c), we construct our dataset that
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comprises the observed differential ScS-S and SdS-S traveltimes (∆𝑇𝑆𝑐𝑆−𝑆 and ∆𝑇𝑆𝑑𝑆−𝑆 )
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and ScS/S and SdS/S amplitude ratios ( ∆𝐴𝑆𝑐𝑆/𝑆 and ∆𝐴𝑆𝑑𝑆/𝑆 ). Overall waveform
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similarities between observed and synthetic traces in the modeled time window are also
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included as part of the measures of optimization criteria in the search of the best-fit
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model. Prior to data modeling, the measured differential traveltimes are corrected for
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contributions from mantle velocity heterogeneity based on a global tomography model
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[Ritsema et al., 2002].
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Additionally, certain types of focal mechanisms for available events may be
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unfavorable for excitation of shear wave energy toward our stations which have a very
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limited distance and azimuthal coverage. It can cause fluctuations in waveform
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amplitudes between nearby stations and introduce large uncertainties in modeling the
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changes of amplitude ratios and overall waveform shapes genuinely associated with the
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D” structure. We thus exclude those data observed at station azimuths that would yield
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large fluctuations of amplitude ratios estimated based on theoretically-predicted
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radiation patterns [Lay and Wallance, 1995],
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𝑅𝑆𝐻=𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝛿𝑐𝑜𝑠𝑖ℎ𝑠𝑖𝑛𝜙+𝑐𝑜𝑠𝜆𝑠𝑖𝑛𝛿𝑠𝑖𝑛𝑖ℎ𝑐𝑜𝑠2𝜙
1
+𝑠𝑖𝑛𝜆𝑐𝑜𝑠2𝛿𝑐𝑜𝑠𝑖ℎ𝑐𝑜𝑠𝜙− 2𝑠𝑖𝑛𝜆𝑠𝑖𝑛2𝛿𝑠𝑖𝑛𝑖ℎ𝑠𝑖𝑛2𝜙,
(S.1)
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where 𝜙=𝜙𝑓−𝜙𝑠, is the difference between the strike azimuth of the fault plane, 𝜙𝑓, and
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the source-to-station azimuth, 𝜙𝑠, 𝛿 is the dip of the fault plane, 𝜆 is the slip rake angle,
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and 𝑖ℎ is the takeoff angle for a given shear wave. We select 7 representative focal
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mechanisms and calculate the theoretical amplitude ratios at the epicentral distances
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from 75o to 80o and azimuthal range between 310o and 360o most available in our data
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(Fig. S2). Only the stations with the predicted values that fall within the standard
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deviation of all the calculated amplitude ratios for each event are used for the following
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data measurement and grid search modeling.
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Not only does 3D structural heterogeneity have a significant influence on observed
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amplitude anomalies, but different radiation patterns of the earthquakes can also
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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
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deviations from the raw measurements using eq. (S.1). It is worth mentioning that
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amplitude information can provide critical constraints particularly on the sharpness of
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the seismic discontinuity superior to differential traveltime data but they should be
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treated with caution owing to numerous factors as discussed here which can
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substantially alter the amplitudes of arriving phases. Further detailed investigation of
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3D wave propagation effect on amplitude fluctuations is necessary for future studies.
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3. Synthetic Experiments on Data Sensitivity to Model Variables
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Rather than using numerous free variables to parameterize a radial velocity model
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for the D” layer and fit every detail in the observed data with suspected resolvability,
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we aim primarily at investigating the overall characteristics of the discontinuity
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undulation and shear velocity structure of the underlying D” layer linked to the “slab
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graveyard” feature as inferred from seismic tomography [Grand et al., 1997]. We
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choose three model parameters including and impedance contrast (VD”) on the D”
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discontinuity and radial velocity gradient (GD”) within the D” layer to depict the first-
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order feature of D” in our study region.
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It is well noted that there exist severe trade-offs between the constraining
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discontinuity topography and neighboring velocity structure particularly relying on
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differential traveltime observations. As each type of the datasets provide different
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effective levels of constraints on a finite number of model variables used to characterize
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the D” structure, we first construct a large set of ground-truth synthetic seismograms
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for a thorough combination of different model parameters computed with the DSM
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[Kawai et al., 2006] to elucidate the sensitivity of the observed waveforms and
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measured data to the perturbation of each model parameter which guides for the
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following search of optimal D” models.
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Figs. S3-S5 show the testing ranges of the perturbations for individual model
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parameters and corresponding shear wave velocity variations with depth in the
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lowermost 600 km mantle. The figures also exemplify the comparison of DSM-
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computed synthetic SH triplication waveforms and predicted differential traveltimes
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(∆𝑇𝑆𝑐𝑆−𝑆 and ∆𝑇𝑆𝑑𝑆−𝑆 ) and amplitude ratios (∆𝐴𝑆𝑐𝑆/𝑆 and ∆𝐴𝑆𝑑𝑆/𝑆 ) between the
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testing models at epicentral distances of 70 and 75 degrees. In Fig. S3, starting with the
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PREM model, we fix the thickness of the D” layer to be 264 km and vary the velocity
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jump across the D” discontinuity from 1% to 3%. It is clear that the SdS arrival times
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are barely changed but their amplitudes increase significantly with the magnitude of the
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velocity contrast. On the other hand, both the ScS-S times and ScS/S amplitudes
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decrease gradually with the velocity contrast. In Fig. S4, we instead fix the velocity
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contrast of 3% across the D” discontinuity and vary the velocity gradient from -6% to
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+3% within a 264-km thick D” layer. Similar to those shown in Fig. S3, the decrease
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of the velocity gradient in the D” layer has a negligible influence on the SdS arrival
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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
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and reduced, respectively. In Fig. S5, we vary the thickness of the D” layer from 150
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km to 350 km and implement a fixed velocity jump of +3% across the discontinuity in
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PREM model with the uniform velocity in the D” layer. The results show the SdS-S
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differential times are most sensitive to the topographic variation of the D” discontinuity.
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According to the above synthetic experiments, we find that all three model
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parameters exert strong effects on amplitude ratios, ∆A𝑆𝑑𝑆/𝑆 but differential
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traveltimes, ∆𝑇𝑆𝑑𝑆−𝑆 , are only affected by the thickness of the D” layer. That is, we are
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capable of mapping the topography of D” discontinuity based on ∆𝑇𝑆𝑑𝑆−𝑆 alone.
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Furthermore, for the ScS related data measurements, only the change of the velocity
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near the CMB can induce noticeable variations in differential traveltimes and amplitude
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ratios, providing a critical constraint on the gradient within the D” layer. See Table S1
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for a brief summary of the extent of influence of each model variable on observed
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differential traveltime and amplitude ratio data.
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4. Synthetic Example to Illustrate the Waveform Modeling Procedure
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In Fig. S6, we present a synthetic example to illustrate our modeling procedure.
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First, we construct DSM-computed, SH-component seismograms for a presumed 1-D
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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
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observed waveforms with signal-to-noise ratios (SNR) on the order of 16 and 5. The
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procedure applied to real data measures is then employed to generate synthetic datasets
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which comprise differential traveltimes, amplitude ratios and waveform decorrelation
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coefficients measured directly from the simulated waveforms. Finally, we determine
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the topographic height of the D” discontinuity based on the measured SdS-S differential
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times and then search for the optimal solutions of the other two model variables, VD”
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and GD”, by minimizing the defined cost function.
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Fig. S6(b) illustrates how the changes of VD” and GD” would affect the fitting of
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different types or combinations of data measures and how severe the tradeoff between
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them would be provided that only specific datasets are included as constraints. It also
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demonstrates that the model solution, if considering only the phase information, i.e.,
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differential traveltime and waveform decorrelation, in the cost function, is possibly
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trapped into multiple local minima, especially for the low S/N data. Further including
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the amplitude-ratio misfits in the cost function, on the other hand, can largely eliminate
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the tradeoff between VD” and GD” and drive the search toward the global minimum of
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the model space.
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5. Data Misfits and Lateral Variation of the Resulting 1-D Models
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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
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topographic height of the D” discontinuity (HD”) for all the resulting 1-D models. As
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the 3D structural variations have more pronounced effects on waveform amplitudes,
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the amplitude-ratio data account for a larger proportion of the errors of about 50%.
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In Fig. S8(a), we show the lateral variations in the topographic height of the D”
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discontinuity (HD”) and shear velocity perturbation (lnVs) at 2800 km depth from the
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individual, unaveraged 1-D models. They in general display similar E-W variations as
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those shown in Fig. 3(b), which have the lowest topographic relief and strongest shear
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velocity reduction in the central part of our study region. Fig. S8(b) displays the
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standard deviations HD” and lnVs within each cap, while Fig. 8(c) shows the cap size
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used for lateral averaging of HD” and lnVs shown in Fig. 3(b). The larger standard
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deviations may roughly indicate the abrupt, unphysical structural variations between
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the nearby 1-D models within the cap resulting from the unmodelled 3D effects. They
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are usually much smaller in the densely-sampled region compared to the variational
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ranges of HD” (over 150 km) and lnVs (~5%) for the large-scale structure over 600 km
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along the E-W direction.
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6. Modelled 1-D Structure for Waveform with no SdS Arrival
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The synthetic experiments shown above indicate the differential SdS-S times
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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
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have noticeable SdS arrivals for HD” estimates (Fig. S9). We thus assume 150 km for
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HD” in the waveform modeling, which essentially results in a 1-D structure with very
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small and negligible velocity contrast on the D” discontinuity (Fig. S9)
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7. Detectability of the D” Discontinuity
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In Fig. S10, we show 1-D DSM synthetics for the D” models with a 0.2 km/s shear
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velocity increase within a transition zone whose thickness (W) varies from 0 to 120 km
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near 300 km above the CMB. The results show the SdS amplitudes decrease with
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increasing W more drastically at shorter distances but still are visible at >78o distances
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for W=120 km. The peak arrival times of SdS relative to S used to estimate HD” are
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almost unchanged.
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8. Large SdS Amplitudes Observed in the Central North American Continent
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Fig. S11 shows the anomalously large SdS amplitudes recorded at the stations
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located in the central part of the USArray and the distance of ~80o away from the event.
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These triplication arrivals traverse the middle of our study D” region with the depressed
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D” topography and large negative shear velocity gradients in the D” layer as constrained
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by the observed shear wave data. The resulting models properly predict the observed
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ScS/S amplitude ratios but apparently underestimate the SdS/S amplitude ratios.
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Supplementary Reference
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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.
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Kawai, K., Takeuchi, N., Geller, R.J., 2006. Complete synthetic seismograms up to 2
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Hz for transversely isotropic spherically symmetric media, Geophys. J. Int. 164,
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411-424.
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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
192
times across a network by adaptive stacking, Geophys. J. Int. 157: 332–340.
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Ritsema, J., Deuss, A., van Heijst, H.J., Woodhouse, J.H., 2011. S40RTS: a degree-40
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shear-velocity model for the mantle from new Rayleigh wave dispersion,
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teleseismic traveltime and normal-mode splitting function measurements.
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Geophys. J. Int. 184, 1223–1236.
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Supplementary Table
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Table S1. A brief summary of the results of data sensitivity tests.
Data
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Increase in Impedance Increase in Velocity
Contrast (VD”)
Gradient (GD”)
Increase in D”
Thickness (H)
SdS/S amp
increase
increase
increase
SdS-S time
unchanged
unchanged
decrease
ScS/S amp
decrease
decrease
unchanged
ScS-S time
decrease
decrease
unchanged
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Supplementary Figures
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Figure S1. Illustration of processing of triplication shear waves recorded by the
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USArray. (a) SH-component displacement traces first aligned along predicted S arrival
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times based on PREM. (b) Further alignment of the S phase arrivals through 10
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iterations of the adaptive stacking procedure [Rawlinson and Kennett, 2004]. The top
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red trace is considered as a reference wavelet or source wavelet obtained from the linear
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stack of the waveforms recorded at distance less than 70o. (c) Impulsive-like S-wave
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signals after the source wavelet being removed from the traces in (b) through an
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iterative deconvolution [Ligorría and Ammon, 1999]. For the following data measure
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and waveform modeling, we restrict our attention only to S and ScS phases and
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triplication arrivals in between them at the distance range of about 65o-85o (blue traces),
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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
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relative waveform amplitudes. Theoretical amplitude ratios of ScS/S (top) and SdS/S
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(bottom) plotted as a function of azimuth at the epicentral distances of 75o and 80o for
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seven earthquakes used in our study. The corresponding double-couple focal
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mechanisms are shown in the upper-right corner of each panel. The dashed lines
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indicate the azimuths at which the predicted amplitude ratios are larger than the
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standard deviation of those at the azimuths between 310o and 360o and excluded from
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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.
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Synthetic experiments illustrating how the sudden velocity increase across the D”
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discontinuity affects shear wave triplication waveforms and measured differential ScS-
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S and SdS-S traveltimes (∆𝑇𝑆𝑐𝑆−𝑆 and ∆𝑇𝑆𝑑𝑆−𝑆 ) and ScS/S and SdS/S amplitude ratios
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(∆𝐴𝑆𝑐𝑆/𝑆 and ∆𝐴𝑆𝑑𝑆/𝑆 ), shown on the middle and right of the figure, respectively. The
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synthetic SH waveforms are calculated by the DSM [Kawai et al., 2006] in PREM and
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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.
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Synthetic experiments illustrating how GD” influences shear wave triplication
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waveforms and measured differential ScS-S and SdS-S traveltimes ( ∆𝑇𝑆𝑐𝑆−𝑆 and
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∆𝑇𝑆𝑑𝑆−𝑆 ) and ScS/S and SdS/S amplitude ratios (∆𝐴𝑆𝑐𝑆/𝑆 and ∆𝐴𝑆𝑑𝑆/𝑆 ) in PREM and
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six trial models with GD” varying from -6% to +3%. The figure layout remains the same
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as Fig. S3.
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Fig. S5. Data sensitivity to the topographic height of (HD”) of the D” discontinuity.
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Synthetic experiments illustrating how HD” or the thickness of the D” layer influences
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shear wave triplication waveforms and measured differential ScS-S and SdS-S
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traveltimes (∆𝑇𝑆𝑐𝑆−𝑆 and ∆𝑇𝑆𝑑𝑆−𝑆 ) and ScS/S and SdS/S amplitude ratios (∆𝐴𝑆𝑐𝑆/𝑆 and
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∆𝐴𝑆𝑑𝑆/𝑆 ) in PREM and five trial models with HD” varying from 150 km to 350 km above
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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 procedure.
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(a) (Left) Presumed 1-D model with a 260-km thick D” layer (red line) used to generate
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synthetic shear waveforms shown on the right. Black lines represent trial models in grid
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search. (Right) The top trace shows a synthetic SH waveform at 75∘for the presumed
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model computed by the DSM [Kawai et al., 2006]. The middle and bottom traces
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simulate the observed waveforms by adding Gaussian noise to the top trace with high
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and low signal-to-noise ratios (SNR) of 16 and 5, respectively. The numbers next to the
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three synthetics are the thickness of the D” layer determined from the observed SdS-S
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times marked by the dashed vertical lines. (b) Image maps with contours showing the
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cost function estimated over a wide range of model variables, VD” (velocity contrast on
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the D” discontinuity) and GD” (velocity gradient in D”). Each column shows the grid
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search results constrained by the combined dataset of differential traveltimes and
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waveform decorrelation coefficients (left), amplitude-ratio data only (middle), and all
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of them simultaneously (right). The rows from top to bottom correspond to the results
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obtained with noise-free, high and low SNR waveforms shown in (a). The presumed
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“true” model and optimal solutions of VD” and GD” at the global minima of the cost
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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
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type of data varying with the determined topographic height (HD”) of the D”
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discontinuity for all the resulting 1-D models. There is no obvious correlation for the
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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
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2800 km depth (top) and topographic heights (HD”) of the D” discontinuity (bottom)
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plotted at the ScS bounce points, obtained from the individual resulting 1-D models. (b)
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The standard deviations of the δlnVs and HD” for the resulting 1-D models within each
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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
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the resulting best-fit 1D structure. For the trace with no available Scd-S differential
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time to estimate the topographic height of the D” discontinuity, we assume 150 km in
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grid search modeling of the 1-D velocity structure. The resulting best-fit model yields
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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
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interval (W) from 0 to 120 km. (Left) 1-D shear wave velocity models in D” used in
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the calculation of synthetic waveforms. (Middle) The resulting triplication shear
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waveforms plotted as a function of distance between 66-87o. (Right) The differential
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SdS-S and ScS-S times measured from the synthetic records. Color dots shown on the
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left side of the plot indicate the minimum distance for each W at which the SdS starts
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to be detectable.
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Fig. S11. Abnormally large amplitudes of SdS phases observed in the central North
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American continent. The optimal 1-D models for individual station-event pairs
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indicate that the densely sampled region beneath northern South America has a thinner
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D” layer with relatively slow shear velocities. The observed SdS amplitudes are clearly
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underpredicted by the synthetics, particularly at the distance of ~80o.
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