Imaging the Lowermost Mantle (D ") Beneath the Pacific Ocean
with SKKS Coda Waves
by
Zhulin Yu
M.S. Geophysics, University of Science and Technology of China, 2012
B.S. Geophysics, University of Science and Technology of China, 2009
SUBMITTED TO THE DEPARTMENT OF EARTH, ATMOSPHERIC AND
PLANETARY SCIENCES IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN GEOPHYSICS
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
SEPTEMBER 2015
ARCHNES
MA5SACHUSETS INSTMUTE
OF TECHNOLOGY
SEP 28 2015
LIBRARIES
0 2015 Massachusetts Institute of Technology. All rights reserved.
Signature of A\uthor:
Signature redacted
Department of Earth, Atmospheric and Planetary Sciences
September 4, 2015
Certified by:
Signature redacted
Robert D. van der Hilst
Schlumberger Professor of Earth and Planetary Sciences
Thesis Supervisor
Accepted by:
Signature redacted
Th
rlT
Robert i. van der Hist
Schlumberger Professor of Earth and Planetary Sciences
Head, Department of Earth, Atmospheric and Planetary Sciences
2
Imaging the Lowermost Mantle (D ") Beneath the Pacific Ocean
with SKKS Coda Waves
by
Zhulin Yu
Submitted to the Department of Earth, Atmospheric and Planetary
Sciences on September 4, 2015 in Partial Fulfillment of the Requirements
for the Degree of Master of Science in Geophysics
ABSTRACT
We apply a generalized Radon transform (GRT) to SKKS data to obtain a large-scale
high-resolution image of the lowermost mantle (400 kilometers above the core-mantle
boundary) beneath the Pacific Ocean (125 0 E-750 W, 45 0 S-65 0 N in this work). More than
4,000,000 radial teleseismic traces from about 8,000 events (mb >= 5.8) between 1990
and 2015, globally recorded by one or more of a total ~27,000 receivers, were collected
from IRIS-DMC. All of the traces were automatically band-pass filtered (10s to 50s),
rotated, clustered, deconvoluted, and finally migrated to structural reflectivity profiles
using reference wavespeeds according to the iasp9l model. We compare the 2D and 3D
imaging results beneath the Pacific subduction zones and the non-subducting regions,
including the southeastern Pacific and Hawaii, focusing on the positive velocity contrast
above the CMB that might delineate the D" discontinuity. We observe broad zones of
scatter surfaces, which may indicate multiple-interface post-perovskite phase transitions
caused by compositionally differentiated subducted lithosphere. Furthermore, we observe
a sharp change in the proposed multiple-interface structure regarding the total number of
positive interfaces, the intervals, and the overall pattern of the anomalies from the
subduction zones to the non-subducting regions. Such structural complexity implies: (1)
the presence of old (at least 180 Ma) subducted material layer of either continental or
oceanic lithosphere under the whole Pacific Ocean; and (2) spatial variations in iron,
magnesium, and silica components in the subducted lithosphere. Understanding the
possible relationship between observed complexity and composition requires further
interdisciplinary research.
Thesis Supervisor: Robert D. van der Hilst
Title: Schlumberger Professor of Earth and Planetary Sciences
3
4
Acknowledgements
The three years' Master life at MIT starting from the end of August 2012 to the beginning
of September 2015 is stepping into the last hour literally, with probably the most complex
feelings in my heart through my life including happiness, gratefulness, and some regrets.
However, these feelings are all meaningful. Without any hesitation, I would like to regard
this long and tough journey as the most critical and influential experience by pushing me
to desire self-improvement, and by teaching me the mean of hardworking. No other
legacy could be more valuable than that.
I would take this opportunity to thank my advisor, Prof. Robert D. van der Hilst, for his
kindness and generosity to be completely supportive to my research and decision inside
and outside the field of seismology. His attitude in science, especially the insistence of an
honest and accurate reflection of data and results influences me a lot. I cannot appreciate
more for his modeling effect in both research and life.
The deepest gratitude goes to my family, who guided me to here at MIT. Life is a
miracle, for sure. But only with the true love from family, can the miracle come true. I
also thank my fiancee, Jiali, who saved me out from the darkest days. I love you all!
5
6
TABLE OF CONTENTS
1. IN TR O D U C TIO N ...............................................................................................................................
8
2. D A TA A N D M ET H OD O L O GY ...................................................................................................
12
2.1 G ENERALIZED RADON TRANSFORM .................................................................................................
12
2.2 D ATASET AND PRE-PROCESSING .............................................................................................................
14
2.3 A UTO-PICK M ETHOD FOR D ATA SELECTION ..................................................................................
16
2.4 POST-PROCESS TO G RT RESULTS ......................................................................................................
18
2.5 IM AGING R ESULT RELIABILITY ...............................................................................................................
20
3. RE SU LT S ...........................................................................................................................................
21
4. D ISC U SSIO N....................................................................................................................................
27
5. CONCLUSION AND FUTURE W ORK................................................................................
32
REFE RE NC E S ......................................................................................................................................
34
A PPEN D IX .............................................................................................................................................
40
A l. IM AGING RESULT RELIABILITY ..............................................................................................................
40
A 2. SAM PLING DENSITY ....................................................................................................................................
41
A 3. EXAM PLES OF Low QUALITY D ATA ................................................................................................
42
A4. R EM OVING THE M OST ISOLATED POINTS ......................................................................................
44
REFERENCES CITED IN APPENDIX INFORMATION .....................................................
45
FIGU R E S A N D C A PTION S ........................................................................................................
46
7
1. Introduction
The D" layer, typically referring to the region from the core-mantle boundary (CMB) to
several hundred kilometers above it ( Cleary, 1974), has been mostly characterized as a
thin layer with rich heterogeneities in both compressional and shear velocities. Since the
early part of the
2 0
th
century, when the existence of the anomaly at the CMB was
recognized (e.g., Dahm, 1934; Gutenberg, 1914), various types and scales of anomalies
have been discovered by different datasets and methods (Garnero, 2000; Lay & Garnero,
2011). For instance, travel time tomography showed that the large-scale pattern of the
velocity structure at the lowermost mantle, which has been validated using cluster
analysis with five different models (Lekic, Cottaar, Dziewonski, & Romanowicz, 2012),
is characterized by two Large Low Shear Velocity Provinces (LLSVPs), one beneath the
Pacific Ocean and the other beneath Africa, and the continuous circum-Pacific highshear-velocity region. On the other hand, more complicated small-scale anomalies have
been inferred from a spherical harmonics
expansion of the tomography results
(Dziewonski, Lekic, & Romanowicz, 2010; Nakagawa & Tackley, 2005) and located
with waveform modeling, travel time analysis, and migration methods applied to the
seismic waves that penetrate, bounce, or diffract at the CMB (e.g., PKP and PKIKP
precursors, teleseismic S wave, Sdiff, ScS, SKS, SmKS (m=1, 2, 3), SPdKS or SKPdS,
etc.). Of the most interest, these small-scale anomalies include ultra low velocity zones
(ULVZs) discovered beneath the African superplume (Helmberger, Ni, Wen, & Ritsema,
2000; Ni & Helmberger, 2001, 2003) and the Pacific Ocean (Cottaar & Romanowicz,
2012), pairs of positive and negative contrasts (named as perovskite lens or postperovskite lens) beneath Central America and the central Pacific (Lay, Hemlund,
8
Garnero, & Thorne, 2006; van der Hilst et al., 2007), and multiple positive interfaces
beneath areas of recent subduction (Hutko, Lay, Garnero, & Revenaugh, 2006; Shang,
Shim, de Hoop, & van der Hilst, 2014).
However, the formation of the D" layer and its structural complexity are still enigmatic.
To understand the large-scale pattern, a thermal boundary layer (TBL) must be
considered due to the high temperature contrast across the CMB and also due to the heat
flux required by the estimated heat flux balance (e.g., Lay, Garnero, & Williams, 2004;
Romanowicz & Gung, 2002; van der Hilst et al., 2007). Meanwhile, compositional
heterogeneity
was also proposed, endorsed
by heat flux
budget calculation,
thermochemical convection simulation, and wavespeeds radio analysis (compressive,
shear, and bulk sound wave) (Ishii & Tromp, 1999; Kellogg, Hager, & van der Hilst,
Trampert,
Deschamps,
Resovsky,
& Yuen,
2004).
Such
compositional
heterogeneity might be a phase transition (first proposed by Sidorin, Gurnis,
&
1999;
Helmberger, 1999), or subducted materials that were able to penetrate the transition zone
(van der Hilst, Engdahl, Spakman, & Nolet, 1991) and might reach the CMB, or both.
Later, in 2004, the discovery of the perovskit to post-perovskite phase transition (Pv to
pPv, Murakami et al., 2004) validated Sidorin and coworkers' prediction of the solid state
phase transition (though it has not been confirmed that the discontinuity is intermittent or
ubiquitous) that can generate increase in velocity and density, and further supported the
hybrid model that combined a TBL and a compositional boundary layer (CBL, e.g.,
proposed by van der Hilst & Karason, 1999). At the same time, the slab graveyard
hypothesis also developed to interpret the same observations, supported by the
correspondence of the geoid, seismic velocities (derived from tomography results),
9
calculated subducted slab accumulation (Lithgow-Bertelloni & Richards, 1998; Ricard,
Richards, Lithgow-Bertelloni, & Le Stunff, 1993), and the attenuation in the transition
zone (Dziewonski et al., 2010; Maruyama, Santosh, & Zhao, 2007); this hypothesis
believed that the slabs were cool and dense enough to sink to the CMB and piled up to
form the large-scale high-velocity region. Moving to the small-scale anomalies, the PvpPv phase transition and the conditional succeeding pPv-Pv reverse transition occurring
when a high-temperature core is buried beneath the CMB could explain for the double
crossing of the phase boundary (Nakagawa & Tackley, 2005) observed in the
aforementioned perovskite lenses. Meanwhile, partial melt in the D" layer was proposed
to generate the ULVZs (Lay et al., 2004); their TCBL model favored that the partial melt
happened in the chemical distinct heterogeneities in the D" layer, while no subducted
slabs were essential to be involved.
To conclude from the discussion above, the structure of the lowermost mantle and the
formation of the complexity are yet to be completely understood. Nevertheless, two
agreements are likely to be reached: (1) a thermal boundary layer must exist and
contribute to the large-scale heterogeneities, i.e., the two LLSVPs and the high-shearvelocity region; (2) a compositional heterogeneity (either ubiquitous or intermittent) that
could be phase transition, chemical anomaly, partial melt, or a combination of the above,
is likely to be essential to fit the observations we already have. Meanwhile, from the
perspective of geodynamics, the Pv-pPv phase transition can result in 1% denser
&
heterogeneity that can remain stable at the CMB for several billion years (Nakagawa
Tackley, 2004, 2005; Zhong & Hager, 2003); but this phase transition, as an exothermal
process, also enhances mantle convection and mantle plume formation by destabilizing
10
the D" layer, heating the ambient mantle, and inducing small-scale flows that might
trigger large-scale mantle plumes (Maruyama et al., 2007; Nakagawa & Tackley, 2004,
2005; Thorne, Garnero, Jahnke, Igel, & McNamara, 2013). Giving the direct and indirect
interdisciplinary evidences and the potential to explain some of the proposed geodynamic
processes, the Pv-pPv phase transition has been widely invoked to explain the lowermost
mantle complexity.
Recently, Shang and coworkers (Shang et al., 2014) observed two seismic reflectors
beneath Central America and East Asia in the lowermost mantle (up to 600km above the
CMB) by implementing generalized Radon transform (GRT) to SKKS and ScS data. They
interpreted the double-positive-velocity-contrast to be the consequence of multiple Pv to
pPv phase transitions in differentiated subducted slab materials (MORB, or harzburgite)
and normal pyrolite. Meanwhile, a folded unbroken subducted slab could also explain the
similar multiple-interface anomaly beneath Central America (e.g., Hutko, Lay, Garnero,
& Revenaugh, 2006). In any case, a recent subduction is likely to be vital for inducing
such a double positive velocity change feature.
In this work, we apply GRT to the lowermost mantle (up to 400 km above the CMB)
beneath the whole Pacific Ocean, and we search for multiple-positive-velocity-contrast
structures not just beneath the circum-Pacific subduction zone, below which such
anomalies were located in previous studies. We compare the lowermost mantle structures
beneath the subduction zones and the non-subducting regions in section 3, and then in
section 4 we discuss the possible formation mechanism for the observed differences.
11
2. Data and Methodology
We explore the velocity contrasts in the lowermost mantle with a 3D inverse scattering
technique, a generalized Radon transform (hereinafter GRT), which has been previously
implemented to detect weak anomalies within several hundred kilometers above the
CMB (Cao, Wang, van der Hilst, de Hoop, & Shim, 2010; Shang et al., 2014; van der
Hilst et al., 2007; Wang, de Hoop, & van der Hilst, 2008; Wang, de Hoop, van der Hilst,
Ma, & Tenorio, 2006). Compared to travel time tomography and waveform modeling,
GRT can simultaneously achieve high-resolution and large-scale imaging. We analyze
the SKKS wave and its coda wave (SKSgSKS) because they propagate partly through the
outer core, which is believed to be homogeneous; thus they are less distorted by the more
complex mantle (see Fig. 1(a) for the ray path of SKKS). An SKKS wave propagates
across the CMB, reflects at the inner side of the CMB, travels across the CMB again, and
finally reaches Earth's surface through the whole mantle, while a SKS/SKS wave
possesses an almost identical ray path except for reflecting at a possibly existing subinterface above the CMB, such as the top boundary of the D" layer.
2.1 Generalized Radon Transform
GRT is an implementation of inverse scattering based on the high frequency
approximation. Different from the conventional Common Midpoint method (CMP, or
sometimes referred as waveform stacking), which usually only uses the single specular
reflection for a specific incident ray, GRT can employ hundreds to thousands scattered
rays (Fig. 1(b)), so that richer information of the reflector can be extracted. Furthermore,
12
GRT is not limited to flat reflectors like CMP. Therefore, it is an ideal tool for our
purpose to detect the weak but probably irregular interfaces, if there does exist one or
more, with the extremely weak SKS"SKS wave. We use the Born approximation and
assume that the scatterers (mostly assumed to be interfaces) can be regarded as
perturbations relative to a reference background medium (Beylkin & Burridge, 1990; de
Hoop & Bleistein, 1997; Miller, Oristaglio, & Beylkin, 1987). For instance, the shear
wave speed c(x) can be decomposed into two parts: c(x) = co(x) + 6c(x), where 6c(x) is
the perturbation relative to the background medium co(x) (a modified iasp91 model in this
paper). The wavefield u(x) can be written in a similar manner: u(x) = uo(x) + 6u(x),
where uo(x) is the reflected wave and 6u(x) represents the scattered waves. To conclude,
inverse scattering maps (or migrates) the scattered wavefield 6u(x) back onto the change
of the wave speed 6c(x).
Unlike the usual reflected wave, the scattered wavefield 6u(x) has different slowness
vectors for the incident ray and scattered ray for the same arbitrary imaging point y (Fig.
1(b)): pS(y) and pr(y), where s stands for the source side and r stands for the receiver
side. These two vectors can then define the migration dip: v'"(y) = p'(y)/jp'(y), where
p'"(y) = ps(y) + pr(y) (Fig. 1(b)), and the dip cannot be too large (e.g., it is smaller than
100) or too small (otherwise it has no advantages over CMP). Furthermore, for multiscale analysis and avoid caustics, the recorded wavefield 6u(y; x,, Xr) (x,, xr are the
source and receiver at Earth surface) can be mapped into angle domain 6u(y; v', 0, Y) (de
Hoop & Bleistein, 1997; Wang et al., 2008, 2006) with scatter angle 0 and azimuth y.
Finally, the structural reflectivity, that is, velocity contrast, at y can be approximated
p(y)
as I(y) = f 5u(y; vm,1O,iP)j m
3 dvm dVpdO.
13
2.2 Dataset and Pre-processing
We choose SKKS and its coda waves among the many different phases that have been
applied in the D" layer studies as discussed in section 1, because (1) anomaly in shear
velocity is usually stronger than that in compressive velocity; (2) SKKS and its coda
waves are reflected at the CMB or sub-interfaces, thus possess stronger energy caused by
the reflectors than the rays propagating only across the CMB, such as SKS; (3) they travel
comparatively less in the more heterogeneous mantle than the rays reflected at the CMB
from the top, such as ScS wave.
Global seismic recordings (over 4,000,000 radial teleseismic traces from about 8000
events with magnitude >= 5.8) were collected from IRIS-DMC. We did not include the
data before 1990 because they are negligible in volume and poor in quality.
All of the traces were pre-processed and selected using the following steps:
(1) Remove the instrument response, rotate the data to the radial and transverse
components, and have the data band-pass filtered between 10 and 50 seconds with
a 4-pole Butterworth filter. We only use the radial component (SV wave) for
SKKS data and normalize each trace with respect to its own reference phase
(SKKS here).
(2) Select the normalized radial component traces that have clear SKS or SKKS phase
around the theoretical arrival time. This selection can be done by eye or by an
auto-pick method, for instance, a multi-channel cross-correlation (Shang, 2014) or
a cluster analysis on the similarity of the waveforms (e.g., Houser, Masters,
Shearer, & Laske, 2008). We did both. First, we manually picked the recordings
14
from the events of mb = 6.0 (-270,000 traces). 34182 traces survived to be
inverted. Fig. 2 shows the stacked (with every 10 degrees in distance) waveform
of the selected traces. The theoretical travel time curves of the other phases
including SKS, S3KS, S4KS, etc., are also indicated in Fig. 2; they are matched by
the stacked seismic energy (white-and-black strips in Fig. 2). Because the ScSP
waves (blue dashed lines) have a similar slowness between 1100 and 120' of the
travelling distance, we cut off the recordings at 150 seconds after SKKS arrival
time. In spite of the fact that more than 34,000 traces are stacked, SKSSSKS phases
are still too weak to be identified by eye. To automatically select data, we applied
a k-means clustering algorithm to the similarity between each trace to every
another in the same event. The basic idea here is that a similar waveform
appearing at the theoretical SKS or SKKS arrival time in multiple recordings (>5)
would indicate an acceptable signal-to-noise ratio. Details are described in the
next sub-section.
(3) Estimate the Green's function of each trace by removing the source signature for
the selected data to enhance the imaging resolution. The source signature is
estimated with principle component analysis (Stephane, Bostock, & Fischer,
2005), and then removed with Wiener deconvolution(Chen, Huang, & PickwellMacPherson, 2010). This improved deconvolution method is based on water-level
deconvolution, but calculates the water level automatically and adaptively based
on the noise spectrum of array data.
(4) The arrival time of SKKS phase for each Green's function is adjusted with multichannel cross-correlation to align the data relative to SKKS phase. This is because
15
we were more focused on the relative positions of the CMB and the other
reflectors, if indeed they exist.
2.3 Auto-pick Method for Data Selection
The rapid increase in the number of global seismometers calls for automated data
selection algorithms that can objectively pick the seismic recordings with certain features,
such as the targeted phases (SKS or SKKS here) in many geophysical researches. Though
the criteria for "high-quality" data change from case to case, the bottom line is all of the
traces should have an acceptable signal-to-noise ratio within a certain time window.
In this work, the greatest issue in data selection is the weak energy of SKKS phase.
Meanwhile, SKKS signal is also contaminated by noise, the earlier arriving SKS phase
(between 1000 to 1100), and the closely following S3KS and S4KS (see Fig. 2). Therefore,
it is extremely hard to detect the SKKS onset as usually applied to P and S phase
detection.
Here, we applied a k-means clustering algorithm (the concept of k-means clustering
algorithms can be found in: Everitt, Landau, Leese, & Stahl, 2011) to find similarities
(measured by cross-correlation coefficient) between every trace to every other one to
classify the traces from the same seismic event based on the "shape", i.e., waveform,
within the time window of 10 and 50 seconds before and after the theoretical SKS or
SKKS arrival time. The similar method has been implemented by Houser and coworkers
with long-wavelength waveforms to obtain a tomography model of Earth mantle (Houser
et al., 2008).
16
The clustering works as follows. First, for every event, we projected each trace to a data
point by calculating the cross-correlation coefficient of every trace with every other trace
to obtain a virtual spatial distribution of all of the traces, in which the similar traces are
gathering closer. Then with a k-means clustering algorithm, one trace (e.g., point Al in
the virtual space) was grouped with the most similar other one (say, point A2), i.e., the
two points merged into one point called A', and the distances between the new point A'
and an arbitrary remaining point (e.g., C) were re-calculated by averaging the distance
between Al and C and that between A2 and C. After repeating this grouping procedure
until every trace was processed the clustering stopped and generated the so-called
"cluster tree", which recorded how the traces were grouped with the others (Fig. 3,
middle panel). Finally, a positive integer was assigned as the total number of the clusters.
This number dominates the clustering results since it controls the similarity of the points
within the same cluster; the choice relies on the understanding of the background
knowledge of the targeted problem. We set this number of the total clusters to be four,
while at most two clusters are for high-quality traces with opposite polarity in an extreme
condition, and the remaining are for noise-dominated traces. With this number, the
clusters were determined as shown in Fig. 3: the horizontal blue lines visualize which
traces have been grouped from the left to right, and the crosses between the blue lines and
the vertical black line indicate the final clusters depending on the total number of clusters
(more clusters call for a left-moving black line). The members (i.e., traces) of the same
cluster can be tracked back by following the blue lines from the crosses to the left.
The right panel of Fig. 3 is the three clusters (I, III, and IV crosses; II only includes one
trace) separated from the dataset consisting of 100 synthetics (high signal-to-noise ratio)
17
and about 20 noisy waveforms (low signal-to-noise ratio, randomly picked from real
data). We calculated the average cross-correlation coefficient and the total number of
traces for each cluster and further set up the criteria of 0.6 (for the average crosscorrelation coefficient) and 5 (for the trace number) to select the clusters that were
believed to include adequate number of similar traces.
We applied the above process to all of the about 8,000 events, and obtained more than
180,000 high-quality radial traces out of the original 4,000,000 radial traces to be
migrated with GRT. That is about 4.5% of the original dataset, and the removed 95.5%
consists of fragmentary recordings, low signal-to-noise-ratio traces, and clusters with an
average cross-correlation coefficient smaller than the empirical threshold 0.6. Examples
of these three different types of "low quality" data are shown in Appendix A3.
2.4 Post-process to GRT Results
The pre-processed Green's functions were then inverted to a 3D velocity contrast matrix
by GRT with one data point for every 1 Ox l x 10 km (latitude x longitude x height) grid.
We also estimated a reference velocity contrast matrix with synthetics (a Ricker wavelet)
and GRT to correct the influence from uneven spatial sampling distribution.
2D and 3D images can be derived from the velocity contrast matrices. Every vertical
profile with positive (black) and negative (red) peaks is the interpolated velocity contrasts
for the corresponding location on the cross-section from 50 km below the CMB (bottom)
to 400 km above it (top). The cross-section should not be too long to reveal coherent
velocity contrasts, or too short to depict the actual reflectors due to interpolation. Usually
18
we control the interval between two vertical profiles to be around 1' (~50 km at the
CMB). For a single cross-section, we picked a potential interface when coherent positive
or negative velocity contrasts, i.e., black or red peaks, can be identified by eye. However,
it was challenging to distinguish positive contrasts from side-lobes of stronger negative
contrasts. Thus, we also obtained 3D images to more comprehensively and reliably
visualize the lowermost mantle. The 3D image was generated based on the 2D crosssections and it has a resolution of 10 x 10 x 10 km; thus no interpolation was involved.
For the whole Pacific Ocean, we manually picked the potential interfaces twice along the
cross-sections with a constant longitude from 125'E to 75'W. In the first round, we
simply looked at the current cross-section and regarded any coherent contrasts as an
interface; then in the second round, we reviewed all of the cross-sections one by one with
its adjacent three or four cross-sections simultaneously to adjust or remove an interface.
Finally, all of the double-checked interfaces, which were actually series of 3D points,
were fixed into the 3D space of our research area by their longitudes, latitudes, and
heights above the CMB, so that we can study the structure at different scales of regions
by simply extracting the associating points. However, if the 3D region is too large the
image will be too complicated and massive to find substantial patterns or features.
Therefore, we removed the "most isolated points" from the 3D point cloud (see Appendix
A4 for details) and studied sub-regions instead with the volume of about 350 x 350 x 400
km (latitude x longitude x height).
One problem in the post-processing of the velocity-contrast matrices results from the
difficulty of establishing an interface objectively. There are few presumed constraints on
how the interfaces are supposed to look like on the migrated velocity-contrast profiles, or
19
objective criteria to establish an interface, thus a quantifiable selection seems to be
challenging. However, we selected the interfaces without comparing to any previous
work and applied the second round selection to at avoid most of the subjectiveness and
improve the robustness.
2.5 Imaging Result Reliability
The trade-off between the velocity anomaly amplitude and the location of the velocity
discontinuity is always inevitable in a seismic inversion. Based on ray theory and the
iasp91 Earth model (Kennett & Engdahl, 1991), we estimated the uncertainty in the
inverted interface height caused by a velocity fluctuation: for a 100-km-high velocity
interface, a 1% constant shear velocity change between it and the CMB can only yield an
approximately 1% change in the height, i.e., 1 km, which is negligible in this work.
Therefore, we conclude that for SKKS and its coda waves, the first-order features
concerning the imaged interfaces are not sensitive to the reference velocity model.
To establish the reliability of our data processing method and imaging algorithm, the
following test was designed: we applied the identical processing sequence to different
datasets from different events but with similar total-trace numbers, and compared the
velocity contrast profiles for an arbitrary cross-section. Because GRT does not rely on a
presumed model of the target region, the sampling density and distribution dominate the
final outcome, and thus the test described above should be meaningful. We also
compared our results to previous studies conducted with different methods or datasets.
Check Appendix Al for the details and results.
20
3. Results
We select and delineate four 2D cross-sections and four 3D regions base on the estimated
accumulation of the subduction slabs at the depth of 1800 km (Fig. 4(a), calculated with
gravity anomaly, Lithgow-Bertelloni & Richards, 1998) to explore the commonality and
difference between the lowermost mantle structure beneath the circum-Pacific subduction
zone and the inside non-subducting region. We infer that a subduction takes tens of
millions of years to reach the depth of 1,800 km at the average subducting rate of less
than 10 cm/yr, thus the accumulated subducted materials at 1800 km can reflect the most
recent and vigorous subduction zone, which can also be reinforced by the match between
the blue region in Fig. 4(a) and the already known trenches along the circum-Pacific.
Accordingly, the first cross-section (colored in red, X-X'-X") is selected to be beneath
the bluest region, and the second cross-section (colored in green, Y-Y'-Y") is selected to
be beneath the comparatively yellow region (non-subducting region) and at the same time
close to the cross-section X-X'-X" to reduce the possibly existing lateral difference in
velocity structure at the lowermost mantle. For the 3D regions, we choose Central
America because multiple-interface structures have been located there in previous works
(Hutko et al., 2006; Shang et al., 2014), and the western Pacific because it is the best
sampled region along the circum-Pacific; they are both partly beneath the subduction
zone. The other two regions are completely beneath the non-subducting region inside the
circum-Pacific; we choose one beneath Hawaii of the interest of many geophysical
researches, and the last one in the southeastern Pacific since the others are all mainly in
the northern hemisphere.
21
Fig. 4(b) and (c) show the vertical velocity contrast profiles for the cross-sections (X-X'X") (red dashed line in Fig. 4(a), the background figure is from Dziewonski et al., 2010).
The most noticeable wiggles with the black peaks at the height of 0 km, which stands for
the CMB, are the positive (from top to bottom) velocity contrasts mapped from the
selected waveforms with GRT. The yellow lines in (b) (X-X') and (c) (X'-X") mark the
laterally continuous positive contrasts along the slice: here, the solid and dashed lines
represent the more and less reliable picks respectively. In (b), from left to right (X to X'),
the double-interface feature is clear and, more importantly, almost ubiquitous except for a
200-km-gap starting at about 1400 km along the CMB. This result agrees with Shang and
coworkers' work (2014) obtained with GRT as well but from SKKS and ScS data
together. Meanwhile, the interval between the two yellow-line-marked interfaces changes
from about 50 km to 100 km at the CMB distance of about 400 km. At some distances,
for instance, 300 to 350 km and 1800 to 2400 km, a weak third positive interface may
exist either at the bottom or top. Between 400 km and 900 km, at the height of about 250
km, an ambiguous interface that can be interpreted as either a negative velocity contrast
(red strong wiggles) extending from the lefts negative interface between 0 and 500 km, or
a positive one connecting with yellow-line-marked interface to the right. Therefore, the
region between 400 and 900 km seems to be a triple-interface structure with a overlying
positive or negative interface and two positive velocity changes below. As shown in (c),
the cross-section X'-X" has a similar structure as that between 400 and 900 km in (b), but
it seems to be a clear negative interface at the top (note that the x-axis scale is uneven in
(c)). From 1200 to about 2300 km along the CMB, a positive interface (dashed line) rises
sharply from 250 km to 350 km, and then suddenly disappears. Then at about 2300 km,
22
the double- or probably triple-interface structure is rapidly replaced by a simple singleinterface (at the height of ~240 km) structure.
Surprisingly, we also observe the similar double-, or even triple-positive-interface
structure beneath the non-subducting regions, which was in this case the middle Pacific
including Hawaii. Fig. 5 depicts the lowermost mantle structure in the same manner as
Fig. 4 for the cross-section Y-Y'-Y" in Fig. 5(a). In the left half of (b), a coherent, strong
and flat interface occurs at the height of about 250 km, with an underneath broken and
weaker interface from 0 to about 200 km and from 400 to about 1100 km. On the right
half, a positive interface seems to start at 1400 km along the CMB at the height of 150
km, and slightly elevates to about 180 km at the CMB distance of 1800 km; then it
declines sharply back to about 150 km within less than 200 km distance and further steps
down to about 100 km at the CMB distance of about 2300 km. Above this irregular
interface, a second interface exists at the height of about 200 km from 2000 km to at least
2800 km (the end of the cross-section). For the whole Y-Y' cross-section, a third positive
interface seems to exist from 700 to 1100 km at the height of about 320 km. A negative
(red) continuous interface is likely to cover the whole cross-section at the height larger
than 340 km, close to the upper limit (400 km) of our imaging region. Move to (c), Y'-Y"
includes the best-sampled region according to the scattering-ray-count map (check
Appendix A2 for details). We can see a comparatively simple double-interface structure
from 0 to about 1000 km along the CMB with a negative flat interface at the top (~350
km) and a bottom positive one at the height of about 130 km. Starting at 1000 km, the
structure becomes more complicated with weaker multiple-layered positive and negative
velocity contrasts almost everywhere, so that the total number of interfaces is ambiguous.
23
After all, since about 1800 kin, two strong and coherent negative velocity contrasts occur
at the height of about 150 and 300 kin, and both of them rise slightly by less than 50 km
through to the end of the cross-section.
We want to point out that, as seen as the dotted yellow lines, some interfaces are
ambiguous and can be alternatively interpreted as the side-lobe of a stronger negative
contrast. Therefore, a more comprehensive visualization of the 3D velocity contrast was
implemented to reduce this type of uncertainty based on an assumption that each
interface should belong to a certain surface with considerable surface area so that they
can be detected. We implemented a second-round picking as described above. Thus we
obtained coherent positive and negative interfaces for each cross-section along a
longitude based on not only the current cross-section but also the adjacent three or four,
so that the interpretation in terms of continuous surfaces is more robust. Then, gathering
all cross-sections, the most possibly existing interfaces throughout the whole Pacific
Ocean were recorded in the form of a series of 3D points. Consequently, an arbitrary
region can be visualized in a 3D way without interpolation, which may cause artifacts
and bias as well. Finally, we removed the "most isolated" points to clean the final images
(see Appendix A4 for details).
Fig. 6 shows the 3D results for the four different regions beneath the Pacific Ocean:
Central America (a), the western Pacific (b), Hawaii (c), and the southeastern Pacific (d).
The small black cubes are the picked positive contrasts, while the negative contrasts
(similar red cubes, not shown in Fig. 6) are not shown to highlight the positive contrasts
structure. The overlapping transparent colored rectangle plates sketch the simplified (with
no surface deformation) surfaces that the black cubes seem to form; we rotate the 3D
24
images to choose these plates by eye. The attaching black numbers next to the plates
indicate the approximate heights above the CMB. Note that the bottom is 50 km instead
of 0 km (the CMB), and the top height changes between 400 and 350 km. The red oval at
the bottom of (c) between latitude 15' and 300 represents the location of the recently
detected ULVZ (Cottaar & Romanowicz, 2012). The projections of the four regions at
the earth's surface are marked as shadow rectangles in Fig. 1(c). Comparing to the
"subducting map" (Fig. 4(a)), as we can see, the first two regions (Central America (a)
and the western Pacific (b)) simultaneously encompass the subduction zones and nonsubducting regions, while the latter two (Hawaii (c) and the southeastern Pacific (d)) have
no noticeable subduction zone above. The light blue plates are for the positive-velocitycontrast surfaces beneath the non-subducting regions, and the green are for the
subduction zones. We use orange ovals to mark the positive anomalies that seem to
connect two surfaces at different heights and thus lead to spatially complex and
continuous positive contrast structures. The double-headed arrows indicate the average
intervals between two surfaces.
Fig. 6(a) and (b) both show a strong and sudden lateral change in terms of the total
number of positive interfaces, the intervals, and the overall pattern of the anomalies from
non-subducting regions to subduction zones. Beneath Central America (a), two parallel
interfaces (marked as transparent light blue plates) at the height of about 150 and 340 km
above the CMB exist to the east of longitude 270', while three different interfaces
(marked as transparent light green plates) distributed at the height of about 100, 140, and
230 km above the CMB to the west of the two blue plates with a couple of chunks of
converging black cubes between the green plates. A few small-area surfaces seem to
25
occur randomly away from the plates. Beneath the western Pacific (b), the image
possesses a similar pattern: two blue plates at the height of about 90 and 230 km to the
east of three green plates located at the height of 100, 150, and 200 km, and the latters are
complicated by two chunks of black cubes dipping between the bottom and the next
shallower interfaces. To summarize, from left to right (higher longitude to lower
longitude), the double-layer structure beneath non-subducting regions (parallel light blue
plates) changes into a triple-layer structure beneath subduction zones (separated light
green plates), and the interval between the bottom and the next above interface decreases
from about 140~190 km (light blue double-headed arrows) to less than 50 km (the lower
light green double-headed arrows); meanwhile, smaller anomalies that seem to connect
two or more interfaces (hereinafter connecting anomaly) appear (marked as orange ovals),
while the structure between the two light blue plates seems to be relatively free of
surface-like scatterers.
In Fig. 6(c) and (d), which are entirely beneath the non-subducting regions, we can see
three almost horizontal light blue interfaces at the height of about 70 (or 90 km at the
southwestern corner, which is probably separated by the ULVZ), 170 and 250 km
beneath Hawaii (c), and two interfaces that seem to bend downwards in the middle at the
height of about 120-140 km and 210-230km beneath the southeastern Pacific. Some
small-scale isolated anomalies also exist in both images, but in (d), they seem to form a
surface above the two blue plates with one vague connecting anomaly (orange oval, if a
top third layer interface exists) extending from the upper blue plate in (d). To conclude,
the intervals between the bottom and the next upper plate are more coherent, slightly
change from about 80 to 100 km, whereas that between the bottom and the top in (c) is
26
almost constant, about 180 km. For the other places except the orange oval in (d), a
connecting anomaly can hardly be found; in the other words, the interfaces are usually
completely separated similar to the light blue plates in (a) and (b) beneath non-subducting
regions.
Considering the 2D and 3D renditions of the imaging results together, two features are
common:
(1) Structures beneath the subduction zones are more complex than that beneath nonsubduction regions, with multiple-positive-velocity-contrast interfaces distributed
at different depth but also connected at some places by the connecting anomalies.
Topography observed in the 2D imaging might be the mixture of the main
interfaces and the connecting anomalies;
(2) The intervals between interfaces beneath the non-subducting regions are, on
average, more constant and larger (compare those between the bottom and the
next above interface) than those beneath subduction zones; and the interfaces are
usually completely separated at the spatial scale of 300 x 350 (latitude x longitude,
at the CMB, it is about 1500 km x 1800 km varying with latitude), without the
connecting anomalies between them.
4. Discussion
The consistent observation of the widespread occurrence of multiple-positive-shearvelocity-contrast discontinuities beneath the Pacific Ocean may have interesting
27
implications for our understanding of the interaction between the subducted slabs and the
lowermost mantle and the history of lithospheric subduction.
Two hypotheses were proposed to explain multiple-positive-velocity-contrast interfaces
assuming a positive velocity change at the CMB results from Pv-pPv phase transition(s).
First, a folded subducted slab that has descended deeply to the CMB could lead to
multiple scattering interfaces, as well as a strong scatterer inverted in a seismological
exploration (Hutko et al., 2006); then a complex lowermost mantle structure can be
imaged depending on the deformation of the slab. Second, multiple Pv-pPv phase
transitions occurring in differentiated chemical compositions among subducted MORB,
harzburgite, and normal lowermost pyrolite can also induce separated inverted velocity
discontinuities at different heights above the CMB (Shang et al., 2014); the interval
between a pyrolite transition and a harzburgite trasnsition is about 200 km or larger. To
conclude, subducted slab material was required in both cases. This does not, however,
readily explain the observations of structure beneath the central Pacific.
Assuming the interfaces are the result of phase transition, the implication out of the
commonalities between our 2D and 3D visualizations will be that such differentiated
phase transitions also happen beneath the non-subducting regions, and thus the bottom
400 km mantle seems to embrace subducted lithosphere that must have similar chemical
components to the subducted oceanic lithosphere beneath the circum-Pacific. The four
3D images also imply a gradual changing in the distribution of the connecting anomalies:
the younger subduction zone, Central America (~50 Ma), has the more volume of such
anomaly compared to the western Pacific region (-150 Ma); the southeastern Pacific and
Hawaii cannot possess subducted slabs that accumulated at the CMB, if they did, later
28
than the two other regions; in the other words, they have older (and probably much older)
subducted martials, and correspondingly have the completely separated interfaces with
almost no connecting anomaly according to the 3D images.
Consequently, the difference among the four regions, along with the broad existence of
the multiple-interfaces velocity structure, may lead to two interpretations:
(1) Differentiated phase transitions caused by compositional heterogeneities in the
subducted oceanic lithosphere is a pervasive feature beneath the Pacific Ocean;
the slow motion of the subduction zones during the opening and closing of ocean
basins (Wilson cycles) throughout Earth's history could account for the wide
distribution of the subducted materials;
(2) Though with similar features, the different structures at the lowermost mantle
beneath the subduction zones and non-subducting regions may have different
origins. Beneath the non-subducting regions, the oceanic subducted materials
were accumulated earlier, at least earlier than about 180 Ma, since when no
vigorous subduction has happened inside the circum-Pacific; and thus they have
been mostly stratified in a high-pressure and -temperature environment. This
process might start when old subductions initiated oceanic slabs with various
chemical components and contents to sink deeply to the lowermost mantle, where
Pv-pPv transition occurred in different compositions at different depths. This
transition yielded heat that was able to increase the ambient mantle temperature
(Nakagawa & Tackley, 2004) and induced small-scale mantle flows. As a result,
this region surrounding the subducted slab became relatively hot and unstable,
and this environment, possibly aided by the background mantle convection and
29
small-scale mantle dynamics (Russell, Lay, & Garnero, 1998), helped the
different chemical compositions to stir and then fix to a certain depth depending
on density. Finally, the long-time mixture left a hundreds-of-kilometers-thick
layer with multiple horizontal velocity discontinuities at certain depths. On the
other hand, under a subudtion zone, the recently sank oceanic slabs reached the
CMB as a relatively rigid body, intruding the existing old-subducted-material
layer discussed above, and it thus generated the dipping connecting anomalies
seen in our imaged results over the multiple-interface background structure. We
use a diagram to show these two processes in Fig. 7.
Following the two premises, now we take a close look at the heights of the interfaces and
the intervals between them.
The Pv-pPv transition height is influenced by the chemical composition and content of
the subducted slab or materials, such as aluminum, magnesium, iron, silica, etc., but the
&
relationship is still subtle and complex (Caracas & Cohen, 2005; Catalli, Shim,
Prakapenka, 2009; Grocholski, Shim, & Prakapenka, 2013). Generally, iron component
decreases the transition pressure (i.e., elevates the height above CMB, Mao et al., 2004;
Ono & Oganov, 2005), while silica and aluminum has the opposite effect. Grocholski and
his group (2012) proposed that aluminum may play a critical role in the detectability of
the Pv-pPv phase transition, but the effect can be remarkably mitigated by the other
phases that can participate in Al partitioning with the Mg-silicate phases, such as the
calcium-ferrite-type aluminous (CF) phase. Therefore, we will not discuss the aluminum
effect here. Meanwhile, the velocity contrast in terms of the amplitude and the sign
&
(positive or negative) across these transitions is also controversial (e.g., Caracas
30
Cohen, 2005; Kiefer, Stixrude, & Wentzcovitch, 2002; Tsuchiya & Tsuchiya, 2006).
Therefore, a reliable identification to each of the imaged interfaces with respect to a
certain compositional heterogeneity is challenging. However, the bottom interface is
likely to be related to the transition in normal pyrolite for its significantly lower height,
and the upper interface(s) could be transitions in subducted MORB, harzburgite, or any
lithospheric material richer in iron than the lowermost pyrolite that is believed to be
radially homogeneous and low in iron at that depth (Badro et al., 2003; Irifune et al.,
2010).
At the same time, subducted materials of different ages have been fused and
homogenized at different levels, and thus have varying iron contents because the lighter
elements (e.g., Si, Al, Mg, Ca) may have been depleted during the mixture, while iron
still remains and elevates the phase transition boundary as discussed. This process
explains the height variation of the positive velocity discontinuitiy.
Continental lithosphere may also contribute to the complexity of the lowermost mantle
structure beneath the Pacific Ocean. During an oceanic lithosphere subductiion,
continental lithospheric pieces can be dragged downwards attached to the oceanic slab to
the deep mantle, if not being blocked at the transition zone, and thus lead to local
anomalies. A testable prediction then would be small-scale anomalies (continental
materials) surrounding a large-scale one (oceanic materials). On the other hand, since
there is no straightforward evidence that shows continental lithosphere can subduct to the
lower mantle (e.g., Burtman & Molnar, 1993; Fan, Ni, & Wallace, 1994; Negredo,
Replumaz, Villaseflor, & Guillot, 2007), we do not think the old subducted materials are
from continental lithosphere.
31
5. Conclusion and Future Work
Two meaningful remarks can be inferred from this work.
First, the combination of cluster analysis, GRT, and SKKS coda waves brings substantial
benefits to high-resolution and large-scale lowermost mantle imaging. Reliability test and
the comparison to previous studies with different methods and datasets both establish the
robustness and the credibility of cluster analysis, as an automatic data quality control
process, and GRT as an imaging method. As a result, we can see a promising future of
applying the same processing sequence to more data to obtain a comprehensive global
model of the lowermost mantle.
Second, an unknown or incompletely understood mechanism should exist to account for
the widespread multiple-positive-shear-velocity-contrast interfaces within the bottom 400
km at the CMB. This mechanism should have led to, or is still inducing large-scale lateral
-
compositional heterogeneities to the pyrolite mantle in the high-temperature and
pressure environment. Following the current understanding of the genesis of velocity
discontinuity at the lowermost mantle, we consider the Pv-pPv phase transition as the
fundamental mechanism in this work due to its nature to generate broad and weak shear
velocity contrasts within hundreds of kilometers above the CMB and its previous success
in explaining various types of anomalies. More importantly, the differentiated phase
transitions in subducted materials (for example, MORB and harzburgite) and mantle
pyrolite, along with the influence of different chemical components and contents
(especially iron) on the transition height, can match the most significant feature in our
observations, the multiple-positive-shear-velocity-contrast interfaces, and at the same
32
time fit the height of the interfaces. We propose that deep subducted materials are
involved because the structure beneath non-subducting regions shows similar pattern as
that beneath subduction zones; therefore it is reasonable to infer that they have similar, if
not same, origins, which are oceanic lithosphsere subductions probably from different
ages. This difference in the time, for which the subducted materials have remained at the
mantle bottom, explains the difference between the structures beneath subduction zones
and non-subducting regions in a straightforward way.
To move forward, a comprehensive evaluation of the lowermost mantle structure around
the whole Earth should be promising to bring new insights to our understanding of what
has happened or what is happening at the CMB. This evaluation aims at revealing the
change in the structural pattern of the lowermost mantle with regard to temperature,
tectonic history, upper mantle velocity, subduction zones, bulk wavespeed anomaly, etc.,
and thus calls for a novel data processing (e.g., graphic processing) algorithm to organize
the massive scattering points we picked. Alternatively, a multiple-scale 3D scattering
density map that depicts the possibility of the existence of a scattering point or surface
may lead to the same destination.
33
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39
Appendix
Al. Imaging Result Reliability
GRT does not rely on a presumed model of the target region, so the sampling density and
distribution dominate the final outcome. Therefore, we applied the identical processing
sequence (described in Methodology and Data) to different datasets from different events
but with similar total-trace numbers, and compared the velocity contrast profiles for an
arbitrary cross-section. We also compared our results to previous studies conducted with
different methods or datasets.
Fig. A1.L shows the reliability test results. The cross-section starts at 1S, 105'W and
ends at 30'N, 77'W, beneath Central America. The upper and lower panel shows the
velocity contrast profiles inverted with the dataset from the events of magnitude (mb) 6.3,
and 6.4 to 6.5 respectively. The total number of the traces for each dataset is about
20,000. Though not perfectly, the overall features agree with each other: the left part of
both pictures has a negative-positive-negative velocity contrast from top to bottom; the
middle part seems to be chaotic for both; the right part has a similar pattern to the left.
Since the sampling coverage for the two datasets is different, it is possible that one has a
better imaging for a certain area.
In Fig. A1.2, we compare our velocity contrast profiles to previous results. (a) shows the
cross-section beneath Central America in which a perovskite lens was discovered (van
der Hilst et al., 2007) also with GRT, but ScS precursors and coda waves. The red dotted
rectangles in the upper panel indicate the lower interface of the perovskite lens that is
40
interpreted as the post-perovskite to perovskite (pPv-Pv) phase transition. The higher
interface, which is marked as B 1, LI, B2, and B3 in the lower panel, can also be clearly
noticed in the upper panel with similar location and shape, as indicated with yellow solid
lines. The gap between Li and B2 in the lower panel is more noticeable in the upper
panel, which may imply two lenses (left and right) possibility. In (b), we show our
imaged cross-section to the southeast of Hawaiian Islands beneath where another
perovskite lens was detected with waveform modeling and S+ScS waves (Lay et al.,
2006). A steep change in the positive velocity contrasts, marked with the yellow line,
may result from different Pv-pPv phase transition depths. This result matches the
significant decline in the height of the proposed Pv-pPv phase transition from Bini to
Bin3 (see the lower panel) in Lay and coworkers' result. The ULVZs proposed in their
work is unfortunately undetectable due to the strong side-lobe of the CMB.
A2. Sampling Density
Seismic inversion always relies on the sampling density of the ray paths, which in this
case are the scattering points within the bottom 400 km at the CMB beneath the Pacific
Ocean. Different from CMP, the GRT method employs the scattered rays and thus
possesses hundreds to thousands times denser sampling points than only using the
specular reflected rays. To estimate the sampling density distribution, we calculated the
total number of the specular reflected points and scattering points; the former depicts the
first-order sampling density and provides a comparison between the sampling densities of
the two types of sampling points. Fig. A2 includes the distribution map for both. The
upper-left panel, which is for specular reflected points, was generated by counting the
41
total number of rays reflected just at the CMB. On the other hand, the bottom-right panel
is for the scattering points, and it was generated by summarizing the numbers of the rays
scattered at any point between the CMB and 400 km above it for each 10
x 10
area.
As expected, the two maps show similar sampling distribution with the best-sampled area
extending from the northwestern Pacific to the southeastern. The densest sampling rate
for specular reflected rays is about
reaches about
2 ^14 . 5
2A7
= 128 points, while for scattered rays, the number
= 23,170 points per 1 x 10 area. This approximate 180 times
increase in the sampling density contributes to advantage of GRT in terms of imaging
weak interfaces.
A3. Examples of Low Quality Data
There are three types of low-quality data: (1) fragmentary recordings, which are not
continuous or complete within the time window we are interested in; (2) low signal-tonoise-ratio traces, which are so contaminated by long- or short-wavelength noise that no
meaningful seismic signals can be easily extracted; and (3) the traces in the clusters that
do not possess an average cross-correlation coefficient larger than 0.6 in this work, and
this part of data does include some meaningful information, but at the same time contains
strong noises that could distort the final imaging results.
We use an arbitrary event happened on Jan.
2 8 th,
2015 near Tanga (mb = 6.2) to show the
examples for each type of low-quality data in Fig. A3. The total number of radial traces is
355.
The first two types of low-quality data possess almost no SKKS signal, thus they can be
removed with confidence. In Fig. A3 (a), we plot 40 examples from the total number of
42
168 fragmentary recordings. The x-axis is the time from 0 to 800 second. As we can see,
the recordings have different length from 0 to 800 seconds, and the waveforms are more
like noise. Fig. A3 (b) shows the 46 traces with low signal-to-noise-ratio. Most of them
are contaminated by high-frequency noises, and the waveform will be almost flat after
being filtered from 10 to 50 second, which may imply that the targeted signal (SKKS
wave) is too weak. A few of them (#22, #34-36, #38, #39) are dominated by lowfrequency noises, and they might be caused by instrument faults.
The third type, on the other hand, is influenced by the empirical threshold choice of the
average cross-correlation coefficient, which means a trade-off between the quality of the
data and the total volume of the selected data is inevitable. In Fig. A3 (c), we plot the
cluster (including 109 traces) with the average cross-correlation coefficient of 0.52 as an
example. Almost all of the traces seem to have a signal-to-noise ratio of no larger than 1,
as we can see that the energy close to the time 0 second is not noticeably stronger than
the other segments of the same trace. Therefore, it is difficult to tell if the fluctuation is
seismic energy or just noise. The other three clusters are similar to this one.
Consequently, no data survived in the auto-pick process with the threshold of average
cross-correlation coefficient at 0.6.
For the whole 4,000,000 radial traces dataset, most of the data were removed due to the
0.6 threshold. The relative volume of the first-type low-quality data (fragmentary
recordings) decreases with the time from the year of 1990 to 2015, but still composes a
considerable portion of the removed data. The second-type low-quality data mainly
consists of the traces with weak or even no seismic energy of either SKKS or other
43
phases. Each type of low-quality data should be considered and removed due to their
considerable volume in the original dataset.
A4. Removing the Most Isolated Points
Our attempt to generate a comprehensive 3D image for the lowermost mantle beneath the
whole Pacific Ocean leads to a significant challenge: how to organize the massive, dense,
and sometimes chaotic picked points, which represent the positive and negative velocity
contrasts, in an objective way to yield the most possibly existing interfaces.
Theoretically, a graphic processing algorithm that can identify curved surfaces from a
point cloud should be ideal to overcome this challenge. But to apply such an algorithm to
our work is not easy, obviously. Therefore, we leave this task to the next stage.
So far, we cleaned the 3D image by removing the most "isolated" points defined as those
not belonging to any surface larger than 2'x2'. Here is how we did it:
1. For each point, we searched its adjacent cube (defined as 20 x20 x20km, centered
at the target point) to tell if it belongs to a surface boundary (henceforth, boundary
points) or the inside area (henceforth, inner points).
2. We removed all of the "boundaries" by removing the boundary points, twice, so
.
the remaining points must belong to a surface larger than 2 0 x20
3. We recovered the removed points if they were the boundaries of the remaining
surfaces.
44
References Cited in Appendix Information
Lay, T., Hernlund, J., Garnero, E. J., & Thorne, M. S. (2006). A post-perovskite lens and
D" heat flux beneath the central Pacific. Science, 314(5803), 1272-1276.
doi:10.1 126/science.1133280
Van der Hilst, R. D., de Hoop, M. V, Wang, P., Shim, S.-H., Ma, P., & Tenorio, L.
(2007). Seismostratigraphy and thermal structure of Earth's core-mantle boundary
region. Science, 315(5820), 1813-7. doi:10.1 126/science. 1137867
45
Figures and Captions
-e
Cfc ocean
(b)
(a)
150
ISO-
*
-150-
specUWrelcedon
-
-
--
scatcredrays
-12
C
x
'W
30-
r4
-O-
.
-Wo-
Y
d
-30*
I.
t-AM)
V
I10-
I!
ANE
Ieo
-Iwo-
-120-
-- 0-
Fig. 1. (a) the diagram of the ray path of SKKS and SKSdSKS waves. (b) the generalized Radon
transform mechanism for SKKS waves. For the incident ray (in blue), the green ray stands for
the single specular reflected ray, while the blue dashed lines are all of the scattered rays. Details
and the notions are introduced in the Section 3. (c) shows the imaged area, the Pacific Ocean
(65 0 E-750 W, 45 0 S-65 0 N), and the discussed cross-sections and regions in this paper. Red dashed
lines indicate the cross-sections X-X'-X" beneath the circum-Pacific subdution zone, while the
green Y-Y'-Y" are beneath the non-subducting regions. The four shadow rectangles are the
regions we analyzed with 3D visualization.
46
300
250
200
100
50
0
-50
100
110
120
150
140
130
Distance (degree)
160
170
Fig. 2. Stack of the 34,182 manually picked high-quality traces aligned along the SKKS
theoretical arrival time (0 second on the y-axis). Each waggle (strong black-white contrast)
indicates the arrival time of an arriving phase at a certain distance, thus a series of coherent
waggles compose the practical travel time curve. The overlapping dashed lines are the theoretical
travel time curves corresponding to the marked phases (SKS, S3KS, S4KS, PS, SKSP, etc.). The
practical travel time matches the theoretical prediction perfectly. Most of the other phases close
to SKKS have a noticeable difference in slowness, except ScSP (marked in blue) between the
distance of 1100 and 120'. Therefore, we cut the data at 150 seconds (orange horizontal line)
after the SKKS arrival time to circumvent the difficulty in depressing ScSP signals.
47
Synthetics test: synthetics + LQ traces randomly picked
evdp: 300km
gcarc: 100-180
100
80
E
-150
100
-0
0
so
100
150
0
50
100
150
20
_150
-150
-100
-50
Time /s
0
50
100
150
0
0.1
0.2
0.3
0.4
0.5
_100
_10
0.
Fig. 3. K-means clustering algorithm. The left panel includes 100 synthetics calculated by normal
mode and 20 low-quality traces randomly picked from the global data we collected. The middle
panel shows the cluster tree, which demonstrates how each trace is grouped with the most similar
other one(s). The total number of the clusters (N) serves as the vertical black line in the middle
panel that determines when to stop the clustering. In our case, N=4. When the clustering stops,
i.e., the traces are grouped from left to right until stop at the cross of the vertical black line and
the blue horizontal lines (I, II, III, IV in the middle panel), we can find back the grouped traces
with the cluster tree. In the right panel, we plot the clustered traces belonging to the same groups
(I, III, and IV. II is not shown because there is only one trace). Compare the left and right panel,
the k-means clustering algorithm successfully selects most of the synthetics as expected.
48
(b) X
I tip
400
0
(C)
160D
1200
Boo
2000
X"
X'
0
200
o
40
1200
1600
2000
2400
F ig. 4. (a) the calculated gravity anomaly caused by subducted materials at the depth of
1800 km; the background figure is from Dziewonski, Lekic, & Romanowicz, 2010. The
red dashed line marks the cross-sections X-X'-X" in (b) and (c). The shadow polygons are
the four regions in Fig. I (c) with different projecting method here. (b) (X-X') and (c) (X'X") are both vertical velocity contrast profiles along the cross-section (red dashed line in
(a)). Black is positive velocity contrast, and red is negative. Yellow lines depict coherent
contrasts that likely to compose an interface, and a dashed line means the picks arc less
confident. Note the distance interval along the CMB is not constant in (c).
49
2
(b) y
iII~~~~l~~4(:I4 4
4444114~
0
(c)
Y'
400
00
1200
160W
120
IEOO
2000
2400
2800
,IP
0
400
800
2000
2400
Dim=nc at the CMB (kmn)
Fig. 5. Same as Fig. 4. The cross-sections Y-Y'-Y" are marked as the green dashed lines in
(a). The two cross-sections (b) and (c) are both beneath non-subducting regions.
50
2800
(a) Central America
400
.- M
-340 kmn
3S0
a300
250
M
0rA5
Akm
200
4-0
100
-100 km
'10 5
so
255
260
265
270
275
280
28S
Longitude ()
(b)
Western Pacific
350
E wJ
8
250
2w)
-S
903O km
20
-Akm
xw
so
05
135
4
145
ISO
155
so
Longitude ()16
51
Hawaii
(c)
4W
E
3W
U250
2W
M k
oow
Latlttde (d
(*
eSoutheastern Pacific
ea
10~~21
(d)
T
ksm02
M
-230 k
0
.020
.00
50
s-30
-25
-20
415
0
.10
10257
.260
LAtitude(*
Fig. 6. 3D imaging of the selected regions marked as the shadow rectangles in Fig. 1(b): (a)
Central America; (b) Western Pacific; (c) Hawaii; (d) Southeastern Pacific. (a) and (b) are
partly beneath a subduction zone, while (c) and (d) are entirely beneath non-subducting
regions. The overlapping transparent rectangle plates sketch the simplified (ignore the
deformation) surfaces that the positive contrasts could likely to form. Light blue plates are
beneath non-subducting regions, and the green ones are beneath subduction zones. Orange ovals
are the connecting anomalies. In (c), a ULVZ may exist according to the negative contrasts that
are not shown in this paper.
52
Ocean
Continent
Fig. 7. Diagram of the lowermost mantle structure beneath subduction zones and non-subducting
regions. The light blue and dark yellow layers are post-perovskite phase oceanic lithosphere rich
in iron and post-perovskite phase pyrolite respectively. The heights of the two interfaces (dashed
lines) change probably due to iron content. The oceanic lithospheric material in the light blue
layer subducted older than the normal blue subduction slab on the right, it has formed a
background structural layer at the bottom mantle at least for part of the Pacific Ocean. The blue
irregular chunk of subducted slab reached the CMB recently and leads to complexity in the
imaged velocity structure.
53
-400
300
100
0
-50
-100
custaltriocP 0
35 0
000
0
160
50
-100
--- oO
-0
I
1 IJ~.iIJI
c~AO ~4.t~r~cQ (kin)
Fig. Al.1. Comparison between the imaging results from different datasets. The upper panel
shows the result from the recordings for all of the events of magnitude (mb) 6.3, while the lower
panel is for the events of magnitude (mb) 6.4 to 6.5. The cross-section is beneath Central
America. The two blue vertical lines separate the cross-sections into three sub-sections.
54
I&
(a)MO
10
-
*
0
-00
-100
-in,
.3-
~-
LS~
-
40083AU
300r
20
100
cam
4
IMn VA
A
400
100
CM
(b)
I10
-moo
Woo
I
~F"7
0010
1
-0
qvr-I 3
U7
IWO
40
=Toe,*WA tP0MWoVVeiM
2M 272-1270
i1O
Ions 0-4Wh O
st bue~fh V"m GiWit
PMMQfi
&
Fig. A1.2. Comparison between our results and some of the previous studies. The upper panel
shows the results for a cross-section beneath Central America (van der Hilst et al., 2007). The
bottom panel is for a cross-section to the southeast of Hawaii (Lay, Hernlund, Garnero,
Thorne, 2006). Our results are the top half of both panels. The yellow lines indicate the matches
between our results and the aforementioned works.
55
an_
"V.
WJ
8rM W# i O
riInm
b
ok
7
.~i
U01
odf
40
20
I-~.
4
/
I
a
3
2
LI
-401
0
-0
20
200
150
100
3W0
136
135
a
126
11-
IIt
106
4
ISO
Io
120
W00
M0
-
(0.)
140
Logud /*
Fig. A2. Sampling density map. The upper figure shows the specular reflection points
distribution at the CMB. The bottom figure is for the scattering points distribution calculated by
summarizing the scattered rays from the CMB to 400 km above it for every 10 x 1 area. The
color represents the natural logarithm of the count number for both.
56
(a)
(c)
V"A'O
~
~
-
~
~Y
-~
~
to
<~
J~.
,-~
I
~
I
~*1
/i ~
*
a,
$0
im / OOMW
tow
'
1
1,
Fig. A3. Examples of the three types of low-quality data. The x-axes are all time in second. (a) is
for the fragmentary recordings, and the x-axis is from 0 to 800 second. (b) shows the traces with
low signal-to-noise ratios. (c) is a cluster with the average cross-correlation coefficient of 0.52,
which is lower than the threshod 0.6. The blue vertical dashed line in (b) and (c) indicates the
theoretical arrive time of SKKS wave.
57