Probing Mid-Mantle Heterogeneity Using PKP Coda Waves
Michael A.H. Hedlin and Peter M. Shearer
Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics
Scripps Institution of Oceanography, University of California, San Diego
ABSTRACT
We investigate the utility of PKP coda waves for studying weak scattering from small-scale heterogeneity
in the mid-mantle. Coda waves are potentially a useful probe of heterogeneity at shallow depths because
this energy is not preferentially scattered near the CMB, as PKP precursors are, but is due to scattering
at all depths. PKP coda waves have not been used for this purpose historically because of interferencewith other late-arriving energy due to near-surface resonance and scattering. We have analyzed 3624
recordings of PKP precursors and coda made by stations in the IRIS Global Seismographic Network.
To study the range and time dependence of the scattered waves, we binned and stacked envelopes of
the recordings. PKP scattered waves increase in amplitude rapidly with range as predicted by scattering
theory. At ranges below ~125°, we predict and observe essentially no scattered energy preceding PKP.
Coda amplitudes at these ranges are independent of range and provide an estimate of energy due tonear-surface effects we can expect at all ranges. We use the average coda amplitude at ranges from 120
to 125° to correct coda amplitudes at other ranges. PKP coda waves show a strong dependence on timeand range and are clearly influenced by scattering in the lower mantle. PKP coda waves, however, do
not provide a tighter constraint on the vertical distribution of mantle heterogeneity than is provided by
precursors. This is due, in part, to relatively large scatter in coda amplitudes as revealed by a resampling
analysis. Modeling shows that PKP coda amplitudes are not highly sensitive to the vertical distributionof heterogeneity in the mantle. To illustrate this we consider single-scattering in two extreme models
of mantle heterogeneity. One allows heterogeneity just at the CMB; the other includes heterogeneity
throughout the mantle. The amplitudes of precursors are tightly constrained by our stack and support
our earlier conclusion that small-scale heterogeneity is uniformly distributed throughout the lower
mantle. The best-fit model includes 8 km scale length heterogeneity with an RMS velocity contrast
throughout the mantle of 1%.
INTRODUCTION
Since the pioneering work of Haddon and Cleary in the early 1970’s, the high-frequency energy thatprecedes the inner core phase PKP(df) has been known to result from scattering in the mantle (Haddon,
1972; Haddon and Cleary, 1974; Figure 1). These scattered waves arrive free of interference from latearriving near-surface scattered waves and thus provide a unique window into the small-scale structureof the deep Earth. Numerous studies have used recordings of these precursors to investigate the physicalproperties of small-scale heterogeneity in the mantle (e.g. Doornbos 1972; Husebye et al., 1976; Hedlin
et al., 1997). Although a recent analysis by Hedlin et al. (1997) used GSN recordings of the precursors
to study heterogeneity throughout the lower mantle, the geometry of the precursors favors studies ofthe deepest mantle as the preponderance of early arrivals come from great depth. Hedlin et al. (1997)
modeled the weak scattering that gives rise to precursors using the Born approximation and found thatthe gradual growth of the precursors with time and range favored a model that included heterogeneity
distributed with equal strength at all depths in the lower mantle. Models that include heterogeneity justat the CMB or within D’’ produce early arrivals, and thus sharper onsets than are seen in the data. Thissurprising result awaits confirmation by an independent analysis, as models involving multiple scattering
near the CMB might also be able to explain the PKP precursor observations.
PKP coda waves are due largely to near surface scattering and resonance, but also include contributions
from scattering throughout the mantle. Evidence that lower mantle scattering contributes energy to
PKP coda can be found in raw data (Figure 2). Recorded PKP coda amplitude variations with time andrange mirror those observed in the precursors. This
basic observation suggests that we might be able toput tighter constraints on the strength onheterogeneity in the mantle using coda waves
provided that we are able to correctly compensate
coda amplitudes for near surface effects. It is thisidea that we test in this paper.

CMB

d

LM

c

b

f a
a

Time (minutes)

20

c
b

LM

f

DATA
We have analyzed 3624 recordings of PKP
precursors and coda that were made between day
151 of 1988 to the end of 1999 by stations in the
Incorporated Research Institutions for Seismology(IRIS) Global Seismographic Network (GSN).
These recordings were selected from a much larger
dataset on the basis of pre-event noise levels. We
rejected traces that exhibited noise levels that werehigh or varied sharply with time. The events in theculled dataset occurred at depths from the nearsurface to 657 km. Sixty percent of the eventsoccurred within 100 km of the free-surface. The
events were assigned body wave magnitudes
between 5.0 and 7.3. Although the GSN stations are
distributed across the globe, the tight range limits
on the recordings (120 to 145°) resulted in a rather
uneven sampling of the Earth (Hedlin and Shearer,
2000). Some areas are not sampled at all.

PRELIMINARY DATA ANALYSISThe traces in Figure 2 reveal a strong dependenceBCMdof the precursors and coda waves on range and time.
The precursors and coda increase in amplitude
120°
140°
160°
180° relative to PKP from 120 to 144°. Energetic coda isRangeseen in most traces to 60 seconds after the arrival of
Figure 1. Ray paths and travel times of the different PKP. The traces, however, also reveal variations thatbranches of PKP for a source at the surface. The are clearly not global in origin but are regional. One
retrograde ab and prograde bc branches refract notable example of this is the trace at ~ 137° which
through the outer core. The cd branch is reflected is dominated by PKP. This trace implies weakfrom the inner core boundary. The df branch refracts scattering within the small volume of the mantle itthrough the inner core. Scattering involving the samples. An earlier paper (Hedlin and Shearer, 2000)
ab or bc branch can produce precursory arrivals as examined regional variations in scattering. This
well as later arrivals that contribute to the df coda. paper is concerned with global characteristics of the
Scattering of df will not cause df precursors but will data. To constrain global average scattering strength,
also contribute to the df coda. Two hypothetical we binned each recording into the appropriate 1°
scatterers (labeled CMB and LM) produce
precursors that can arrive no earlier than the labeled bin, after correcting for event depth. Each trace wascurves in the lower panel. The deepest scatterers filtered between 0.7 to 2.5 Hz and converted to an
will give rise to the earliest precursors. Although envelope. Prior to stacking, we applied a small,
we have depicted scattering from PKP to P near downward, adjustment of the amplitude to remove
the receiver, precursors can also result from scat- pre-event noise. The binning procedure grouped
tering from P to PKP on the source side.
recordings simply on the basis of recording range
19

Range (°)

and not on the location of either the sourceor the receiver. The stacked traces thus
provide an image of the averagecharacteristics of the arrivals.

Time after PKP (s)Figure 2. Selected recordings of PKP precursors, main
phase and coda made by stations in the Incorporated
Institutions for Seismology (IRIS) Global Seismographic
Network (GSN) between 118 and 145°. The data have been
bandpassed between 0.7 and 2.5 Hz and are aligned on the
PKP(df) onset. The traces reveal a gradual increase in theamplitude of the precursors and coda waves as a functionof range. The curve indicates the minimum travel time forenergy single-scattered at the CMB.

The stacks shown in Figure 3 indicate thatcoda amplitudes at ranges from 120 to 125°are nearly independent of range. No
precursor energy is observed at theseranges. Between 125 and 144° we observea gradual increase in the amplitude of the
precursors and coda. The precursors atthese ranges increase in amplitude from theonset to PKP. After PKP, the coda
amplitudes decay gradually with time.
Scattering simulations (Hedlin et al., 1997)
indicate that most of the energy at ranges
below 125° is due to near surface effects.
To illustrate the amount by which theamplitude of the precursors and coda
increases from the low levels seen at ranges
below 145° we plotted a copy of theaverage stack from 120 to 125° at all ranges(see the dashed traces). This range
dependence is unlikely due to near surface
effects but we believe arises from scattering
within the mantle. At 145°, the traces are
dominated by PKP as the b caustic arrives
at this range. All scattered waves are smallin amplitude relative to PKP. The suites ofcurves in Figure 3 indicate the minimum
travel time for single-scattered energy
scattered at depths ranging from the CMB
to 2200 km above. This figure illustrates
that most scattered waves will follow PKP

THE DEPTH EXTENT OF MANTLE SCATTERING
Hedlin et al. (1997) considered the factors listed in the previous section and modeled a stack of 1600
PKP precursor recordings using Rayleigh-Born scattering theory (Chernov, 1960) applied to the
exponential autocorrelation function. The modeling indicated that the global average small-scale
heterogeneity has a scale length of ~8 km and is distributed uniformly throughout the lower-mantle
with an RMS velocity contrast of 1%.
We are attempting to re-examine the vertical distribution of heterogeneity in the mantle using coda
waves to check the earlier study. This requires careful consideration of the paths energy might takethrough the core before or after scattering in the mantle. Propagation through the mantle from thesurface to the CMB involves no triplications. Propagation from the CMB back to the surface after
propagation through the core is along one of four branches of PKP (Figure 1). The earliest arriving
branch at ranges between ~119 and 132° is bc which represents prograde refraction through the outercore. The ab branch lags behind by a few seconds at most. The ab and bc branches alone can yieldprecursors to PKP. These branches were considered by Hedlin et al. (1997). The other branches can beassociated only with coda arrivals. The df brancharrives first at ranges from 109 to ~119° andbeyond 132° and thus makes possible scatteredcoda arrivals across a greater range interval thanis possible from either the ab or bc branches.
Precursors and coda to PKP are due to scatteringfrom a small volume of the mantle near the sourceor the receiver.
The object of this paper is to determine if PKP
coda will allow us to place a tight constraint on
the relative importance of scattering at shallow
and great depths in the mantle. To investigate the+2000
vertical distribution of heterogeneity in the mantle
we divide the mantle into thin (20 km) layers,+1800
from the CMB to the crust, and calculate theresponse of each individual layer to the incident+1600
wavefield. The statistics of the heterogeneity areinvariant within each layer and are allowed to+1400change only in strength between layers. The+1200
calculation used in this paper is identical to the+1000
single-scattering theory used by Hedlin et al.
+800(1997) except we predict the amplitudes of PKP+600
coda as well as precursors. As a result, we also
+400
consider df refracted scattered waves. As observed
CMB+200
by Hedlin et al. (1997), the earliest and largest
contributions will come from the deepest layers.
By summing the energy of different combinations
Figure 3. Average precursor and coda amplitudes as of these kernels we can explore the effect ofa function of time and source-receiver range as
obtained from a waveform stack of 3624 scattering within different mantle depth intervals.
seismograms. Times are relative to the onset ofPKP(df). Each stacked trace is normalized to the peak To model the data using these kernels it is
PKP(df) amplitude (at about 2 seconds). The necessary to take into account the ab, bc and df
theoretical onset time from the PREM velocity model branches of PKP as well as late-arriving energy
for single-scattering at a range of depths from the that results from scattering and resonance in the
CMB to 2200 km above the CMB are shown as the near-surface. We have observed that the coda
curved lines. Note the increase in precursor and coda amplitudes are independent of range when theamplitudes with range and the gradual decay of coda recording is made at ranges below about 125°.
amplitudes with time. The dashed curve at each range The stacking procedure combines traces from
represents the average stack between 120 and 125°.
widely separated regions of the Earth. The
averaging of coda amplitudes removes regional variations and produces an estimate of the averagenear-surface energy levels we can expect at all ranges. The range independent average also includes
energy that results from scattering in the mantle and propagation through the inner core along the df
branch. Our simulations indicate that the df branch has a weak dependence on range when comparedwith the ab and bc branches which are strongly influenced by the b caustic. The simulations also
clearly show that regardless of what scattering model is used, the ab and bc branches produce essentiallyno scattered energy before or after PKP at ranges below 125°. To take into account, and remove fromconsideration, near-surface effects and the inner core refracted scattered energy, we subtract the averagecoda amplitude observed at ranges below 125° from all bins. The average stacked coda from 120 to125° possesses minor variations with time. To ensure that this structure is not introduced into thestacks by the correction procedure, we approximate the average stack using a standard coda decay+2200

model (Pechmann et al., 2000). We
assume the coda envelope amplitude as afunction of time, A(t), can be describedas follows:
log[A(t)] = log[Ao] - α log (t - tp),
where tp is the time of the PKP onset, Ao
is the onset amplitude, α is a free fitting
parameter. We deduct the best fit
exponential decay function from the binsat all ranges. The correction applies only
to the data points at times after the onsetof PKP.
The result is given in Figure 4. We haveshown the bins between 130 and 141°. The
bins at greater ranges are difficult tointerpret due to proximity to the b caustic.
The bins at ranges below 130° provide
little insight as there is very little energy
before PKP or after PKP once thecorrection for df and the near-surface
effects is made. At each range we show
the stacked, and corrected, data and thestandard errors from a resampling analysis(Efron and Tibshirani, 1991). The standard
errors increase after the arrival of PKP.
This is expected as coda amplitudes arelargely due to near surface effects. These
effects depend on the depth of the event.
Most events were located within 100 km
Figure 4. Observed PKP(df) precursor and adjusted coda of the surface. Some events were > 600
amplitudes compared to theoretical predictions of twomodels of mantle heterogeneity. The whole-mantle km in depth. While we have observed
simulations are shown by the solid curve, the CMB only robust range independent estimates ofsimulations are represented by the dashed curves. The data coda amplitudes at ranges below 125°, andand their standard errors are indicated by the grey shaded have inferred similar behavior at greater
regions. Coda decay is explained equally well by these two ranges, wide variability in the amplitudes
extreme models of mantle heterogeneity.
that are present in individual traces isrevealed by the resampling analysis.
Despite the scatter in the corrected PKP coda amplitudes shown in Figure 4, it is clear that the coda
energy remains well above zero even after corrections for near-surface scattering are applied. Thisimplies that scattering from the CMB and/or deep mantle is a significant contributor to PKP coda
energy at these ranges. This result could have been anticipated from Figure 3, given the observed
increase in PKP coda amplitude for those ranges where such deep scattering could occur. One goal ofthis paper is to test whether these PKP coda observations can place new constraints on the depth extent
of lower mantle scattering.
Predicted results from two different models are shown in Figure 4. One model (represented by thedashed curves) allows 8-km scale length heterogeneity within a 20-km-thick mantle layer immediately

above the CMB and models the effect of scattering at or very close to the CMB (short-wavelength
topography on the CMB would produce similar effects). The second model (solid curves) allows 8-km
heterogeneity to be uniformly distributed throughout the mantle. For each model, we adjusted the
RMS amplitude of the velocity variations to obtain the best fit to the PKP precursors. Our simulations
reveal that coda decay rates are nearly independent of the vertical distribution of heterogeneity in the
mantle. The CMB-only model predicts slightly more rapid decay of coda amplitudes after PKP. Thisdifference is seen at all ranges. Taking into account uncertainty about the coda amplitudes as determinedfrom a resampling analysis, our stacks indicate that both models are in nearly equal agreement with thedata. Both predict an increase in energy before PKP and then a gradual decay.
However, as noted in Hedlin et al. (1997), the two models do not produce equal fits to the PKP precursors.
The model that includes heterogeneity just at the CMB produces onsets that are more rapid than observed.
In addition, the CMB scattering model requires much larger velocity perturbations to achieve the same
amplitude of scattering. The whole mantle model requires RMS velocity perturbations between 1 and
2% whereas the CMB scattering model requires perturbations of 5.5 to 7.5% within the deepest 20 kmof the mantle.
CONCLUSIONS
Our analysis of 3624 teleseismic recordings of PKP precursors and coda indicates that coda arrivals do
not provide a useful constraint on the vertical distribution of heterogeneity within the mantle. There are
two reasons for this. While the onset of scattered energy depends strongly on the vertical distributionof heterogeneity, the coda decay rates are nearly insensitive to this. The second reason is that thestatistical variability of coda amplitudes is high. The standard errors of the stacked data are greaterthan the difference between the coda amplitudes predicted by the two models.
Our analysis of simulated and recorded data indicates that PKP precursors remain the most effective
probe of small-scale heterogeneity in the mantle. Specifically, the increase in the amplitude of the
precursors with time and increasing range appears to be a diagnostic indicator of the vertical distributionof the heterogeneity. Our analysis of 3624 high-quality teleseismic recordings confirms the conclusionsof Hedlin et al. (1997). PKP precursors are consistent with scattering uniformly distributed throughout
the lower mantle and not with scattering confined to the CMB. The preferred model requires ~ 1%
RMS heterogeneity with a scale length of 8 km at all depths..
ACKNOWLEDGEMENTS
This research was made possible by high-quality data in the FARM archive at the IRIS DMC. This
research was funded by National Science Foundation EAR99-093370.
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