Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34
DOI 10.1186/s40645-015-0064-3

RESEARCH ARTICLE

Open AccessComplex inner core boundary from frequency
characteristics of the reflection coefficients of
PKiKP waves observed by Hi-net
Satoru Tanaka1* and Hrvoje Tkalčić2

Abstract
Frequency-dependent reflection coefficients of P waves at the inner core boundary (ICB) are estimated from thespectral ratios of PKiKP and PcP waves observed by the high-sensitivity seismograph network (Hi-net) in Japan. The
corresponding PKiKP reflection locations at the ICB are distributed beneath the western Pacific. At frequencies
where noise levels are sufficiently low, spectra of reflection coefficients show four distinct sets of characteristics: a flat
spectrum, a spectrum with a significant spectral hole at approximately 1 or 3 Hz, a spectrum with a strong peak at
approximately 2 or 3 Hz, and a spectrum containing both a sharp peak and a significant hole. The variety in observed
spectra suggests complex lateral variations in ICB properties. To explain the measured differences in frequency
characteristics of ICB reflection coefficients, we conduct 2D finite difference simulations of seismic wavefields near the
ICB. The models tested in our simulations include a liquid layer and a solid layer above the ICB, as well as sinusoidal
and spike-shaped ICB topography with varying heights and scale lengths. We find that the existence of a layer above
the ICB can be excluded as a possible explanation for the observed spectra. Furthermore, we find that an ICB
topographic model with wavelengths and heights of several kilometers is too extreme to explain our
measurements. However, restricting the ICB topography to wavelengths and heights of 1.0–1.5 km can
explain the observed frequency-related phenomena. The existence of laterally varying topography may be asign of lateral variations in inner core solidification.
Keywords: Inner core boundary; Topography; PKiKP; Finite difference modeling

Background
The inner core boundary (ICB) is one of the vital regions
for understanding the Earth’s core dynamics (Loper andRoberts 1981; Loper 1983; Bergman and Fearn 1994;
Shimizu et al. 2005; Deguen et al. 2007; Sumita andBergman 2009; Deguen 2012). Seismological studies of
the ICB and its inferred characteristics, such as thedensity jump between the inner and the outer cores, theshear-wave velocity at the top of the inner core, andscattering of seismic energy from small-scale topography
at the inner core surface, are important in elucidating
the growth mechanism of the inner core and the sourceof the geodynamo (Souriau 2007; Sumita and Bergman
2009; Deuss 2014; Tkalčić 2015).
* Correspondence: stan@jamstec.go.jp
1
Department of Deep Earth Structure and Dynamics Research, Japan Agency
for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan
Full list of author information is available at the end of the article

The hypothesis of a hemispherical structure in theupper inner core (Tanaka and Hamaguchi 1997) has
been widely accepted because it is supported by seismic
observations of body waves and free oscillations(Creager 1999; Deuss et al. 2010). Hemispherical dichotomy is recognized as a global phenomenon near the ICB(Niu and Wen 2001; Waszek et al. 2011) and possibly
near the center of the inner core (Lythgoe et al. 2014).
To explain the hemispherical structure of the inner core,
two models have been proposed: a large-scale asymmetric flow in the outer core (Sumita and Olson 1999;
Aubert et al. 2008; Gubbins et al. 2011) and translational
convection in the inner core (Alboussiere et al. 2010;
Monnereau et al. 2010). The nature of these models isthat they allow diametrically opposite scenarios of freezing and melting, i.e., one of the two hemispheres solidifies faster than the other. This has raised further
questions about whether the surface of the inner core in© 2015 Tanaka and Tkalčić. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made.

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Fig. 1 Ray paths of PcP and PKiKP seismic phases. A cross section ofEarth with ray paths of PcP and PKiKP seismic phases originating at
the source (star) and recorded by a station at the Earth’s surface

the eastern hemisphere is melting or freezing. Althoughtranslational convection models predict that the eastern
hemisphere is melting, outer-core large asymmetric flow
models disagree about which hemisphere is melting, due
to the problem setting, e.g., heat flux at the core–mantle
boundary (CMB) and outer core dynamics.
Measurements of PKiKP/PcP amplitude ratios havebeen used to infer the density jump at the ICB, as wellas to determine the shear velocity at the top of the innercore. A sketch of their ray paths is shown in Fig. 1. Studies in the twentieth century usually analyzed PKiKP recorded on short-period seismographs with apredominant frequency of 1 Hz (Engdahl et al. 1970;
Buchbinder 1972; Engdahl et al. 1974; Souriau andSouriau 1989; Shearer and Masters 1990). These pioneering studies may have been hampered by the small
number of observations and the large scatter in PKiKP/
PcP amplitude ratios due to the nature of noisy amplitude measurements (Tkalčić et al. 2009). Another factor
influencing the amplitude ratios, and possibly the anticorrelation between the two phases, is the occurrence ofnear-receiver crustal and mantle heterogeneity (Tkalčić
et al. 2010).
The new era of modern instruments, dense networks,
and improved global coverage enables observation of alarge number of PKiKP and PcP phases on the same
seismogram. For example, Koper et al. (2003) analyzed asignificant number of PKiKP phases at shorter distances
recorded by small aperture arrays of the International
Monitoring System. This study was followed by a large
number of new studies (Cao and Romanowicz 2004;
Koper et al. 2004; Koper and Pyle 2004; Poupinet and
Kennett 2004; Koper and Dombrovskaya 2005;
Krasnoshchekov et al. 2005; Leyton et al. 2005;
Kawakatsu 2006; Leyton and Koper 2007a, b; Peng
et al. 2008).

Page 2 of 16

More specifically, Koper and Pyle (2004) measured
PKiKP/PcP amplitude ratios from seismograms filtered
between 1 and 3 Hz. Their analysis did not reveal any
differences between the eastern and western hemispheres of the inner core. Using phases from a Mariana
event observed in Japan, whose raypaths sampled the
ICB beneath the western Pacific, Kawakatsu (2006)
found little scattering energy in the PKiKP coda. However, Leyton and Koper (2007b) analyzed the coda of
PKiKP and suggested the existence of small-scale heterogeneities in the uppermost inner core. This result indicates that the strong scattering region is located beneaththe Pacific Ocean and Asia, which covers parts of theeastern and western hemispheres. On the basis of scattering properties and Q structure, Cormier (2007) inferred textural differences between the eastern andwestern hemispheres near the surface of the inner core,including vertically oriented structures in the eastern
hemisphere.
Interestingly, the existence of a high-frequency PKiKP
phase (up to 5 Hz) with steep incidence angles at the
ICB was first observed by Poupinet and Kennett (2004)
using phases recorded by narrow-aperture arrays andtemporal broadband networks on the Australian continent, whose reflection points were in the eastern hemisphere. Recently, the same class of PKiKP waves wasobserved in the eastern hemisphere on Chinese andJapanese short-period and broadband stations (J-array)(Tkalčić et al., 2009, 2010) and by the high-sensitivity
seismograph network (Hi-net) in Japan (Dai et al. 2012,
Jiang and Zhao 2012).

Fig. 2 Study area. Map view of epicenters (stars) and PKiKP bounce
points at the ICB (green circles). Event numbers are taken from Table 1

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

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Table 1 Event list
Event

Date

Time (UTC)

Lat. (°)

Lon. (°)

Depth (km)mb

Remarks

No. of used records

1

20010703

13:10:42.60

21.641142.984

290.0

6.0

DC

73

2

20021117

04:53:48.46

47.946146.419

470.2

5.8

Sm

58

3

20040725

14:35:19.06−2.427103.981

582.1

6.8

DC

83

4

20060127

16:58:53.67−5.473128.131

397.0

7.0

Sm

77

5

20070928

13:38:57.88

22.013142.668

260.0

6.7

Sm

41

6

20080322

21:24:11.27

52.176−178.716

132.0

5.8

Sm

65

7

20080705

02:12:04.48

53.882152.886

632.8

6.8

DC

49

8

20081124

09:02:58.76

54.203

154.322

492.3

6.5

DC

83

9

20090828

01:51:20.40−7.146123.427

642.4

6.3

DC

31

10

20090930

10:16:09.25−0.72099.867

81.0

7.1

DC

33

11

20100723

23:15:10.19

6.780

123.260

640.0

7.4

Sm

53

Hypocenters are taken from the Earthquake data report provided by U.S.G.S.
DC double couple, Sm smoothed radiation pattern

To contribute to a better understanding of inner core
dynamics and to constrain ICB structure in the eastern
hemisphere, here, we collect an extensive dataset of
PKiKP waves recorded by Hi-net in Japan. Our aim is to
shift focus from analyzing a single value of the PKiKP/
PcP amplitude ratio to evaluating its broad frequency
characteristics, which is philosophically similar to how
Cummins and Johnson (1988) evaluated pre-critical
PKiKP waveforms and spectra by using a hybrid fullwave-reflectivity algorithm. A dense configuration of
borehole seismograms with high SNR observations of
PKiKP waves over an unusually broad range of frequencies facilitates this new approach to estimate ICB properties. Thus, we examine data in the frequency domain
and investigate possible broader implications for Earth’s
core dynamics.

Methods
Hi-net comprises approximately 700 short-period seismographs placed at the bottoms of individual boreholes(Okada et al. 2004). However, even for large-volumedatasets such as Hi-net, good records of PKiKP and PcP
are not frequently observed. We have detected PcP and
PKiKP waveforms from 11 earthquakes with body wave
magnitude ≥5.8 and focal depths of ≥80 km around
Japan before the 2011 Tohoku earthquake (Fig. 2,
Table 1). This covers epicentral distances from 15° to50°. The reflection points of PKiKP at the ICB are distributed beneath the western Pacific, which is part of theeastern hemisphere (Fig. 2).
After visual examination of waveforms, amplitude
spectra of PKIKP phases, and corresponding waveforms
and spectra of pre-arrival noise, we applied a zero-phase
Butterworth band-pass filter with corner frequencies of
2 and 5 Hz to 60 s record segments centered aroundtheoretical PKiKP arrival times (Fig. 3a, b). This wasdone for all records except the Mariana event (event 1),
which was examined by Kawakatsu (2006) and observed
to have large PKiKP signals around 1 Hz. Note that weuse band-pass filtering only for initial identification of
PKiKP.
After applying the band-pass filter described above
and retrieving record segments of ±10 s length around
PKiKP arrivals, seismograms were divided into subgroups comprising 70–230 stations with traces sorted byincreasing epicentral distance. We then selected subsets
of coherent waveforms by using the cross-correlation
matrix method (Tkalčić et al. 2011), which retained 46–
220 records per event. To find coherent PKiKP arrivals
in each sub-group, we empirically determined the minimum percentage (τ) of all waveform pairs that shouldcross-correlate in such a way that the average crosscorrelation coefficient equals or exceeds a threshold β.
The algorithm calculates the cross-correlation coefficients for each pair of waveforms and counts the total
percentage of pairs with cross-correlation coefficient exceeding β. For example, for β > 0.4, τ > 10 %, and 130
total waveforms, we found that 77 waveforms satisfied
these criteria and were consequently selected as “mutually coherent” (Fig. 3c). Incoherent waveforms were notused in further analyses. Subsequently, we visuallychecked the waveforms that satisfied the above criteria
to find possible PKiKP signals with high signal-to-noise
ratios, which resulted in a station list of “good” sites for
PKiKP observations.
In the next step, we prepared a spectrogram of 90 s
length from the unfiltered seismograms, with a samplinginterval of 1 s and a lapse time of 50 s from the theoretical arrival times of PcP or PKiKP (Fig. 4). Each Fourier
spectrum is calculated for a Welch tapered 10 s window(Press et al. 1988), then smoothed using a three-point
moving average. Using the station list obtained with theTanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Fig. 3 Selection of coherent waveforms. a Raw seismograms ofevent 3 recorded by Hi-net stations whose names start with letter“I.” Horizontal axis is the lapse time from the theoretical arrival timesof PKiKP. b Seismograms from a are band-pass filtered with cutoff
frequencies of 2 and 5 Hz. c The selected set of coherent waveforms
after employing the cross-correlation matrix method (Tkalčić et al.,2011) is shown by cyan lines

cross-correlation matrix method, we used both the seismograms and spectrograms of PKiKP and PcP to identify acceptable data for calculating spectral ratios of
PKiKP/PcP (Fig. 5). For each event, between 33 and 83
station records were retained (Table 1). Finally, the mean
PKiKP/PcP spectral ratio was computed at each

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frequency that exceeded the mean of the noise/PcP ratio(Fig. 5). The spectra of PcP and PKiKP contained several
peaks and holes whose central frequencies were not uniform for all events. For example, for event 3, the spectral
ratio of PKiKP/PcP exceeded the mean noise/PcP ratio
in the range 0.8 to 3.0 Hz (Fig. 5a). In the case of otherevents, however, valid frequency ranges were somewhat
different, e.g., 2–3 Hz for event 6 (Fig. 5b) and 1–4 Hz
for event 11 (Fig. 5c). Despite the above restrictions, therelatively high-frequency content of the PcP and PKiKP
waves means that these high-quality simultaneous observations over a broad frequency interval are
unprecedented.
To correct the amplitude ratios, we determined focal
mechanisms using the program of Kikuchi and
Kanamori (2003), rather than cataloged Global CMT solutions, USGS Moment tensor, and double-couple solutions. The broadband displacements of P and SH waves
in the frequency range 0.002–1 Hz were used for the inversion. Furthermore, we compared the short-period(SP) P wave amplitudes (1–5 Hz) with the radiation pattern predicted from each focal mechanism solution. Although the observed SP amplitudes showed a highdegree of scatter, we found that some events had clear
energy even near the nodal plane and null axis, suggesting a smoothed radiation pattern. This may be due toscattering near the source region, as discussed in previous studies that determined magnitudes from SP data
(e.g., (Schweitzer and Kværna 1999; Takemura et al.
2015). These results are summarized in the Remarks column of Table 1. The smoothed radiation pattern for the
short period is a likely explanation for the observation of
PcP and PKiKP in the events from Kuril (event 2) and
Mindanao (event 11), in which the take-off azimuths
and angles of PcP and PKiKP were located near thenodal plane.
Attenuation factors for the mantle and core at arbitrary frequencies were normalized to a reference frequency of 1 Hz. We then obtained the corrected
relationship between spectral and theoretical amplitude
ratios from the following relationship:APKiKP
APKiKPF PcP expð−πf 0 Δt  Þ¼
APcP corrected
APcP observed F PKiKP expð−πf Δt  Þ¼

T PK RKK T KP GPKiKP expð−πf 0 t  PKiKP Þ;
RPP
GPcP expð−πf 0 t  PcP Þð1Þ
where the subscripts PKiKP and PcP denote the corresponding seismic phases. On the left side of the equation, A is the spectral amplitude at an arbitrary
frequency, F is the focal mechanism radiation pattern, t*
is the anelastic parameter (Lay and Wallace 1995), andΔt* is the differential anelastic parameter between PKiKPTanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Page 5 of 16

Fig. 4 Spectrograms including PcP and PKiKP. Raw seismograms and spectrograms of event 3 for a PcP and b PKiKP recorded at station IKTH.
Spectrogram scaling is in decibels (dB). The predicted arrival times of PcP and PKiKP are located at a lapse time of 50 s

and PcP. On the right side, G represents the geometricalspreading factor; f0 (=1 Hz) and f are reference and observed frequencies, respectively; TPK and TKP are thetransmission coefficients at the CMB; and RPP and RKK
denote reflection coefficients at the CMB and ICB, respectively. The reflection coefficient RKK at the ICB isestimated from the corrected spectral ratios by considering the terms of the reflection and transmission coefficients at the CMB, the geometrical spreading factor, andanelastic parameters, which are calculated using ak135(Kennett et al. 1995):ðRKK Þestimated ¼

APKiKP
APcP




 
T PK T KP GPKiKP expð−πf 0 t  PKiKP Þ
:
=

RPP
GPcP expð−πf 0 t PcP Þ
corrected

ð2Þ
We converted the spectral ratios to reflection coefficients as a function of frequency. To the first order, geometric spreading is constant with respect to frequency
under a ray-theoretical assumption. The reflection andtransmission coefficients were then calculated for planarboundaries. The correction of the attenuation factor using
t* gives a smooth exponential variation with frequency.

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

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Fig. 5 Spectra of PcP and PKiKP and spectral ratios of PKiKP/PcP. Individual PKiKP, PcP, noise spectra, and PKiKP/PcP spectral ratios for a event 3,b event 6, and c event 11 (see Fig. 2 for the event location). (Top row) Spectra of PcP (blue lines) and PKiKP (red lines), noise in the 20 s window
prior to PcP (gray lines), and noise in the 20 s window prior to PKiKP (black lines). Open circles are average spectral amplitudes for PcP, PKiKP, noise
prior to PcP, and noise prior to PKiKP at each frequency. (Bottom row) Spectral ratios of PKiKP/PcP (red lines) and noise before PKiKP/PcP (blacklines). Open circles are average values of spectral ratios at each frequency

Thus, these corrections will not result in any spectral
holes or peaks.
To reduce the unwanted effect of the CMB on the
PcP spectra, the spectral ratios of PcP/P were examined. Similar to the above procedure, we estimatedthe P wave reflection coefficients at the CMB as afunction of frequency. The obtained reflection coefficients did not always coincide with theoretical values
due to the uncertainty in focal mechanisms, large differences in P and PcP take-off angles, and other unknown causes. Thus, we corrected only thefluctuations in the reflection coefficients around theaverage values in the frequency range 1–3 Hz. The
reflection coefficients at the ICB are multiplied by thefluctuations in reflection coefficients at the CMB,
which can result in either amplifying an apparently
small PKiKP/PcP due to a large peak in the PcP
spectrum or reducing a large PKiKP/PcP due to asmall peak in the PcP.

Results
A summary of frequency-dependent ICB P wave reflection coefficients, as derived from Eqs. (1) and (2), isshown in Fig. 6. Panels are sorted by increasing incidence angle at the ICB; we refer to each panel hereafteras result n, where n stands exclusively for panel number.
Figure 7 summarizes frequency-dependent P wave reflection coefficients at the CMB derived from PcP/P
spectral ratios. In Fig. 8, these are used to correct thereflection coefficients at the ICB (Fig. 6). These corrected values are used in finite difference modelingand subsequent interpretation.
The frequency characteristics of the ICB reflection coefficients are quite complex, even in a narrow effective
signal band (Fig. 8). Roughly speaking, peaks in reflection coefficients appear around 2 Hz (results 8, 9, and
10) and 3 Hz (result 3), and holes are observed around
1 Hz (results 2, 3, and 4) and 3 Hz (result 10). Although
the discrimination is still qualitative, we recognize four
general categories of frequency-dependent characteristics: (i) a flat variation, where fluctuations in the relative
strengths of peaks and holes are between half anddouble those of the theoretical reflection coefficients (results 1, 5, 6, 7, and 11); (ii) a distinct single hole in eachreflection coefficient spectrum (results 2 and 4); (iii) astrong single peak in each spectrum (results 8 and 9);

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

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Fig. 6 P wave reflection coefficients at the ICB. P wave reflection coefficients at the ICB as a function of frequency, estimated from PKiKP/PcP
spectral ratios (red circles) and noise/PcP (black circles). Thin lines show the upper and lower bounds of standard errors. Thick lines are theoreticalvalues of reflection coefficients calculated using ak135 (Kennett et al., 1995). Encircled numbers are “result numbers,” arranged by ascending
incidence angle

and (iv) a strong peak and hole in the same spectrum(results 3 and 10).
The geographical distribution of these categories isplotted in Fig. 9. The diameters of the 1 and 2 Hz Fresnel zones for PKiKP are approximately 80 and 60 km at
the ICB, respectively. This is equivalent to the area of
PKiKP reflection points at the ICB that is covered by asingle event and all stations that detect PKiKP. This result suggests that our averaging within each region number is meaningful, but it is not appropriate in discussing
lateral variations in individual measurements within eachregion. Although the sampling areas are sparse, we notea tendency of frequency peaks in reflection coefficient
spectra to be most observable at low latitudes (results 8,9, and 10). Frequency holes show no such latitudinal
trend (results 2, 3, 4, and 10).

Discussion
Effects of the CMB

Regarding the effects of the CMB on PKiKP spectra during transmission through the CMB, we address this issue
in the context of the results of previous studies. Using
amplitude of precursors to PKIKP, Dai et al. (2012) and
Yao and Wen (2014) showed that several regions exhibit
weak scattering in the lowermost mantle beneath thesouthwestern Pacific. PKiKP phases from events that occurred in the Banda Sea (events 4 and 9), Sumatra(events 3 and 10), and the Philippines (event 11) enter a“normal” CMB. According to Hedlin and Shearer (2000),
there is a relatively weak scattering region in the lowermost mantle beneath the Philippine Sea, which corresponds to the CMB entry points of PKiKP for events 1
and 5 and the CMB exit points for events 1, 3, 4, 5, 9,

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

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Fig. 7 P wave reflection coefficients at the CMB. P wave reflection coefficients at the CMB as a function of frequency, estimated from PcP/P spectral
ratios (red circles) and noise/P (black circles). Thin lines show the upper and lower bounds of standard errors. Thick lines are theoretical values of thereflection coefficient calculated using ak135 (Kennett et al., 1995). Encircled numbers have the same meaning as in Fig. 610, and 11. Thus, we have reason to believe that the
CMB effects on the estimated reflection coefficients forresults 1, 2, 6, 8, 9, 10, and 11 will be negligible. However, a strong scattering area near the CMB exists beneath north Japan and the northwestern Pacific, which
includes the PKiKP CMB entry and exit points forevents 2, 6, 7, and 8. Thus, we cannot rule out the possibility that the frequency characteristics of calculated reflection coefficients for results 3, 4, 5, and 7 are CMB
effects, e.g., the high-frequency components of PKiKP
may be lost by scattering at the CMB.
Numerical simulations
Problem setup

To explain our observations, we use the 2D finite difference program e3d (Larsen and Shultz 1995; Rodgers
et al. 2006) to simulate wave propagation by solving thefull wave equation on a staggered grid. The solutions are
fourth order accurate in space and second order accurate in time. Figure 10a shows the configuration of thesimulation, for which the grid spacing is 70 m. P- and Swave velocities and densities above and below the ICB
are taken from ak135 (Kennett et al. 1995). We place asequence of point sources with 1 km spacing on astraight line 100 km long and generate a plane wave.
The incidence angle θ is a control parameter. As the input, the representative P wave waveform is taken from
the Mariana event (event 1). The calculation is valid for
frequencies up to 5 Hz. We examine the observed spectral ratios between incident and reflected waves at threepoints (triangles in Fig. 10a). To verify the configuration
and boundary conditions, and to ensure that there are
no unwanted numerical effects from the edges of thebox, we conducted a test run of a simple, flat ICB, withelastic parameters on both sides of the ICB taken fromthe ak135 model (Fig. 10b). The spectral ratios between
upgoing and downgoing waves for incidence angles of
10°, 20°, and 30° correspond to epicentral distances ofapproximately 16°, 32°, and 48°, respectively. Although
there are small frequency-dependent fluctuations (withinTanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Page 9 of 16

Fig. 8 Corrected P wave reflection coefficients at the ICB. P wave reflection coefficients at the ICB as a function of frequency, estimated from
PKiKP/PcP spectral ratios (red circles) and noise/PcP (black circles). Ratios are corrected for fluctuations estimated from the P wave reflection
coefficients at the CMB, obtained from the PcP/P ratios in Fig. 7. Thin lines are upper and lower bounds by standard errors. Thick lines aretheoretical values of the reflection coefficient calculated using ak135 (Kennett et al., 1995). Horizontal arrows indicate the effective frequency
ranges. Encircled numbers are explained in Fig. 6

a factor of 2, at most), their average values coincide wellwith the theoretical reflection coefficients at the ICB.
Simulations for a thin layer above the ICB

As discussed in the “Background” section, there are
multiple conceptual models that can explain freezing
and melting of the quasi-eastern hemisphere. To investigate the possibility of a thin layer above the
ICB, we run a series of simulations with layer thicknesses of 0.1, 0.25, 0.5, 0.75, 1.0, 3.0, and 5.0 km.
For a solid layer above the ICB with finite shearwave velocity and slight variations in compressional
wave velocity and density (Vp = 10.6–10.9 km/s, Vs =1–3 km/s, ρ = 12.4–12.5 g/cm3), all the resultant
reflected wave amplitudes are small. However, a lightor heavy liquid layer (Vp = 9.6–10.3 km/s, ρ = 12.5 g/

cm3 for heavy liquid, ρ = 11.5 g/cm3 for light liquid)
results in large amplitudes. In particular, we findthat the amplitudes of seismograms filtered withcentral frequencies of 1 and 2 Hz become large
when we insert a heavy liquid layer above the ICB
with Vp = 9.6 km/s, ρ = 12.5 g/cm3, and a thicknessesof 0.75 or 1 km (Fig. 11a, b). This finding is qualitatively consistent with the results of Krasnoshchekov
et al. (2005). However, we also find that spectral ratios continuously increase as a function of frequency
for any incidence angle (Fig. 11c), without distinct
peaks or holes in the frequency range 0.5 to 3 Hz.
Since this does not explain our observations, we reject the model of a thin layer above the ICB as apossible explanation for the observed frequencydomain characteristics of PKiKP.

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Fig. 9 Summary map of frequency characteristics of P wave
reflection coefficients at the ICB. Distribution of the reflection
points of PKiKP waves at ICB (green dots), and “result numbers”
indicating their frequency characteristics by colors. White: almost
flat spectrum; blue: spectrum with a spectral hole; red: spectrumwith a spectral peak; half red and blue: both a hole and a peak.
Yellow dots indicate the exit and entrance points of PKiKP at the
CMB. Double black and red circles are Fresnel zones at the ICB
and CMB, respectively. Inner and outer circles are Fresnel zone
estimates for 2 and 1 Hz, respectively

Simulations for topography at the ICB

Earlier PKiKP and PcP amplitude ratio analyses madesporadic seismological observations of a lower density
contrast at the ICB than predicted values for spherically symmetric Earth models, as low as 200–300
g/m3(Koper and Pyle 2004; Tkalčić et al. 2009). In
addition, Gubbins et al. (2008) inferred a low density
contrast from geodynamical considerations. These results indirectly support the existence of a dense layer
at the top of the inner core (F-layer) to explain thesmaller density differences between the outer andinner cores. However, there is no proof from seismology that such a layer is a global feature. Masters
and Gubbins (2003) noted that even the relatively
large density jump inferred from free oscillation analyses is consistent with an F-layer having a strong
density gradient: the free oscillation data would average over thick layers below and above the ICB, while
the body wave would be sensitive to variations
across the ICB. A lower density contrast across the
ICB would permit larger topography (Buffett 1997).
Of particular interest is the possibility of sharp edges
between the solidification and melting areas. Recent
waveform modeling suggests significant topography

Page 10 of 16(Dai et al. 2012); however, determination of the amplitude is a more difficult problem than determinationof the wavelength.
One possibility of most simplified geometry is that asinusoidal topographic structure might develop at thelargest scales (λ = 10–100 km) (Buffett 1997). At theselength scales, there is an inverse relationship between relaxation time scale and wavelength (Turcotte andSchubert 2002). In addition, the time scale required for
topography to relax varies inversely with density contrast
and linearly with viscosity. As the viscosity of the outer
core is effectively zero (de Wijs et al. 1998), the rate ofrelaxation is thus entirely controlled by deformation in
the inner core.
On the other hand, spike-shaped topographic structures might develop as a result of dendritic growth,
likely at smaller scales (λ = 10–several 100 m) (Bruce
Buffett, pers. comm.). Such topography could be relaxedthrough melting and freezing (thermal relaxation). As
the temperature gradients are steeper at short wavelengths, this can drive the heat flow needed to melt or
freeze.
Given the above, we test two different classes of topography at the ICB. In the first scenario, we test a regularsinusoidal topography with wavelength λ and height H(Fig. 12a). The values of (λ, H) tested, in kilometers, are(0.1, 0.1), (0.2, 0.2), (0.5, 0.5), (1.0, 1.0), (1.5, 1.5), (2.5,
2.5), (2.5, 2.6), (2.5, 2.7), (5.0, 2.5), and (10.0, 5.0).
Figure 13 shows the results of selected combinations of
λ and H. The topographies with λ = 0.1 and 0.2 km and
H = 0.1 and 0.2 km did not reproduce any spectral peaks
and holes and yielded spectra similar to those obtained
from a simple discontinuity model (Fig. 10b). However,for a slightly more prominent topography of λ = 0.5 km
and H = 0.5 km, we find a clear peak in spectral ratios
around 1.2 Hz (Fig. 13a). The ICB topography with λ = 1.0
and H = 1.0 km results in an increased number of spectral
peaks (Fig. 13b). The topographic model with λ = 1.5 andH = 1.5 km produces distinct peaks around 2 Hz for incidence angles of 20° and 30° and remarkable holes around
1.2 Hz for incidence angles of 10° and 30° (Fig. 13c). The
best results are obtained for the topography characterizedby λ = 1.5 and H = 1.5 km. The simulated spectra containsimilar characteristics to those observed in the reflection
coefficient profiles of results 8, 9, and 10. However, when
the longer λ and larger H are used in simulations (e.g., λ =5 and H = 2.5 km; λ = 10 and H = 5 km), the reflection coefficients overall become smaller than those for the flat
ICB. The spectra are devoid of peaks at higher frequencies(Fig. 13d, e).
Finally, we introduce “spiky” topography to address
the possibility of dendritic growth of the inner core
(Sumita and Bergman 2009), which is mathematically
expressed in our simulations by a reversed cycloid with

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Page 11 of 16

Fig. 10 Configuration of 2D finite difference simulations and a test run. a Configuration of 2D finite difference simulations using e3d (Larsen andShultz 1995). Small red circles represent multiple sources used to simulate a plane wave. Triangles mark the locations of virtual receivers used torecord the reflected waves. Incidence angles θ are a control parameter. b Spectral ratios between upward and downward waves using a flat
discontinuity in simulations for incidence angles of 10°, 20°, and 30°. Thick lines are theoretical values of the reflection coefficient calculated using
ak135 (Kennett et al. 1995)

upward sharp tips (Fig. 12b). We tested several (λ, H)
combinations for this conceptual model: (0.1, 0.1), (0.2,0.2), (0.5, 0.2), (0.5, 0.1), (0.5, 0.2), (1.0, 0.2), (1.0, 0.5),(1.0, 1.0), (1.0, 2.0), (1.2, 1.7), (1.5, 1.5), (1.5, 2.0), (2.0,
1.0), (2.0, 1.5), (2.0, 2.0), and (5.0, 2.0). The overall characteristics of the spectral ratios for spiky topography,
with λ ≤ 2 km and H ≤ 2 km (Fig. 14a–d), can be summarized as a gradual decrease in spectral ratio as frequency
increases from 0.5 to 5 Hz. This topographic model
can explain several peaks or holes for incidence angles of θ = 10° and 20° and many peaks at frequencies
around 2, 3, and 4 Hz for θ = 30°. The topography with
λ = 5 km and H = 2 km results in relatively flat and small
spectral ratios in the frequency range 0.7–5 Hz. Such amodel can explain many holes at frequencies larger than
2.5 Hz for θ = 10°–20° and peaks for θ = 30°. However,these results cannot adequately explain our observations
because the overall reflection coefficients are too small.

The resultant characteristics are slightly different fromthose produced by the sinusoidal topographies, eventhough their structural dimensions are the same. The
frequencies of the distinct spectral peaks decrease withincreasing wavelength and height (Fig. 14b–d), whereas
no distinct peaks are observed for the topography with
λ = H = 0.5 km. The spiky topography with λ = H =1.0 km results in a distinct peak around 1.7 Hz for θ =10°–20° and a large hole around 1.5 Hz for θ = 30°(Fig. 14b). The topography with λ = 1.5 and H = 1.5 km
yields a distinct single peak at roughly f = 1.2 Hz. There
are several spectral holes for θ = 10°–20° and peaksfor θ = 30° at f > 2 Hz (Fig. 14c). Of all the test caseswith spiky topography, the case with λ = H = 1.0 km
most closely matches the observed spectral ratios.
In summary, our observations and numerical simulations suggest that the inner core boundary is a sharpboundary without transitional layers. The hypothesis of

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Page 12 of 16

Fig. 11 Results of numerical simulations for a liquid thin layer above the ICB. Maximum amplitudes of the reflected waves measured onseismograms filtered around 1 and 2 Hz as a function of increasing angular distance at the ICB. Synthetic seismograms are calculated byincluding a heavy liquid layer (Vp = 9.6 km/s, ρ = 12.5 g/cm3) overlying the ICB with varying thicknesses: a 0, 1000, 3000, and 5000 m andb 100, 250, 500, and 750 m. c Spectral ratios for the 1000 m-thick heavy liquid layer for incidence angles of 10°, 20°, and 30°

Fig. 12 Diagram of ICB topography. Diagram of ICB topography used in numerical simulations with wavelength and height defined as λ and H,
respectively. a Sinusoidal topography; b “spiky” topography. The meaning of each topographic model is explained in the text

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Page 13 of 16

Fig. 13 Results for sinusoidal topographies. Representative results, characterized by height H and length λ, for incidence angle 10 degrees (left),
20 degrees (middle) and 30 degrees (right). The values of H and lambda are as follows: a) λ = 0.5, H = 0.5, b) λ = 1.0, H = 1.0, c) λ = 1.5, H = 1.5,d) λ = 5, H = 2.5, e) λ = 10 H = 5

melt at the surface of the inner core in the quasi-eastern
hemisphere is not supported by our simulations. The
most likely scenario to explain some of the observed
spectral characteristics is the existence of topography at

the ICB; however, more than one class of topography
must be invoked to explain all observations. We therefore conclude that the topography characteristics of the
ICB vary laterally. These variations may result from

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

Page 14 of 16

Fig. 14 Results for spiky topographies. Same as Fig. 13, but “spiky” topography was used in simulations. The values of H and λ are as follows:a) λ = 0.5, H = 0.5, b) λ = 1, H=1, c) λ = 1.5, H = 1.5, d) λ = 2, H = 2, e) λ = 5 H = 2lateral variations of inner core solidification. If solidification is dynamically driven from top to bottom, its geographical pattern will be controlled by the pattern ofouter core convection (Bergman et al. 2002; Aubert etal. 2008; Gubbins et al. 2011). If the solidification isinstead driven from the bottom up, the pattern will beaffected by variations in inner core convection (Deguen
and Cardin 2011). Furthermore, small-scale variations in
topographic characteristics suggest small-scale convection in a mushy zone at the ICB (Bergman and Fearn

Tanaka and Tkalčić Progress in Earth and Planetary Science (2015):34

1994; Deguen et al. 2007). While we cannot distinguishbetween these hypotheses in the present study, largely
due to the fact that we sample only sparse and limitedareas of the ICB, further observations of PKiKP and PcP
will improve our understanding of large-scale ICB structure and dynamics.

Conclusions
Frequency characteristics of ICB reflection coefficientswere investigated for the area around Japan using Hi-net
vertical component seismograms. We found four patterns in the frequency-dependent behavior of reflection
coefficients: (a) a nearly flat spectrum (little variation),(b) a significant hole at a frequency of approximately 1
or 3 Hz, (c) a peak at a frequency of approximately 2 or
3 Hz, and (d) the existence of a hole and a peak. The
variety in observed spectra reflects the complex natureof the ICB. To interpret these observations, we conducted 2D finite difference simulations. Since we tested
only limited cases with planar geometry, further simulations are required. Our modeling results suggest that
holes and peaks in the spectra of reflection coefficientscan be qualitatively explained by a sinusoidal or spikelike topography at the ICB, with wavelengths and heights~1–1.5 km, whereas a liquid or solid layer overlying the
ICB does not reproduce any of the observed spectralfeatures.
Abbreviations
CMB: core–mantle boundary; ICB: inner core boundary.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
ST analyzed waveform data. HT performed finite difference simulations. The
manuscript was written by ST and HT. Both authors read and approved thefinal manuscript.
Authors’ information
ST is Deputy Director and Senior Scientist at the Department of Deep Earth
Structure and Dynamics Research, Japan Agency for Marine-Earth
Science and Technology.
HT is Associate Professor and Senior Fellow at Seismology andMathematical Geophysics, Research School of Earth Sciences, The
Australian National University.
Acknowledgements
The authors are grateful to the National Research Institute for Earth
Science and Disaster Prevention (NIED), Japan, for providing high-quality
seismograms recorded by the high-sensitivity seismograph network(Hi-net). The authors thank two anonymous reviewers who give valuablecomments. S.T. was supported in part by MEXT KAKENHI grant number
15H05832. H.T. was supported by the Japan Society for the Promotionof Science and the Research School of Earth Science, The Australian
National University during his stay in Japan. Most of the figures weredrawn using GMT (Wessel and Smith 1998).
Author details
1
Department of Deep Earth Structure and Dynamics Research, Japan Agency
for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan.
2
Research School of Earth Sciences, The Australian National University,
Canberra ACT 2601, Australia.

Page 15 of 16

Received: 21 April 2015 Accepted: 8 October 2015

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