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High‐Frequency (6 Hz) PKPab Precursors and Their Sensitivity to Deep Earth Heterogeneity

We present observations on a new precursory phase of seismic waves scattered in the deep Earth. This phase arrives prior to the PKPab wave at epicentral distances larger than 155°, and we call it PKPab precursor. We show that the presence of the PKPab precursor is a necessary consequence of scattering in D″, which is the commonly accepted cause of the PKPdf precursor at distances smaller than 145°. PKPdf waves that propagate through the inner core should arrive before the PKPab precursor but those, are strongly attenuated in the inner core at frequencies between 4 Hz and 8 Hz used here, making the PKPab precursor the earliest teleseismic signal at distances larger than 155°. Calculated PKPab precursor sensitivity kernel shows that this phase is mostly sensitive to scattering along the closest PKPbc path between source and receiver. It can thus help to constrain the lateral distribution of heterogeneity along D″.

shows the increase of scattered intensity due to a 50-km-thick scattering layer above the CMB calculated with differential radiative transfer simulations as detailed in the supporting information Text S1, which contains additional references to Takeuchi (2016) and Trabant et al. (2012). The random velocity fluctuations in this heterogeneous layer are described by an exponential autocorrelation function with fluctuation strength of 10% and a correlation length of 0.1 km. A number of timedistance windows of the global wavefield that have been investigated for waves scattered in the deep Earth are shown in Figure 1(a). ScP and PcP top side reflections at the CMB can show precursors that originate by reflections above the CMB as well as coda waves from reverberations in the heterogeneous layer or off great-circle reflections (Gassner et al., 2015;Shen et al., 2016;Wu et al., 2014). Short distance PKKP precursors (Chang & Cleary, 1978, 1981 also originate from off great-circle bottom side reflections at the CMB (cf., Figure 1(a)). PKP precursors probe the D″ layer in near-vertical transmission.
Paths corresponding to the PK*Pbc onset are shown in the inset of Figure 1(b). Figure S1 shows paths and corresponding onset times for source and receiver side D″ scattering of the PKPab and PKPbc branches. Scattering of PKP waves at D″ can divert energy into the distance range below 145° which would otherwise not be accessible to PKP (Haddon & Cleary, 1974;Hedlin et al., 1997). These waves form the PKPdf precursor which arrives before the PKPdf phase (cf., Figure S1(e)) that travels through the inner core (PKIKP) and is the earliest ballistic phase in the core shadow. This situation provides exceptional conditions for the observation of PKPdf precursors (cf., Figure 1(b)). Opportunities to probe the lower mantle by transmission in a near-horizontal direction are provided by P diff coda (cf., Figure 1). While diffraction along the CMB vanishes with increasing frequency, at short period, P diff coda waves in the core shadow zone have been interpreted as a sign of scattering along the CMB (Bataille & Lund, 1996) or, as a signature of scattering throughout the mantle (Earle & Shearer, 2001). An overview of the travel time-distance windows in which scattered waves from the deep Earth can be observed is given in Shearer (2015).
The time window between PKPdf and PKPab at distances beyond the PKPbc window (Δ > 155°) has rarely been investigated for the arrival of scattered energy as it is affected by the coda of PKPdf which can be generated locally in the crust below the receiver. Still, arrivals in a continuation of PKPbc at the c-cusp have been identified by Nakanishi (1990), Tanaka (2005), and Zou et al. (2008) and have been interpreted as compressional waves diffracted along the inner core boundary (ICB). While ICB diffraction is a likely scenario at low frequencies, Nakanishi (1990) and Tanaka (2005) note that CMB scattering might become important at higher frequencies. Adam and Romanowicz (2015) reported the arrival of a 0.5-2-Hz scattered signal in the same time-distance window and interpreted it as energy being scattered at the ICB.
Understanding the origin of such faint signals arriving from the deep Earth provides a powerful tool to investigate the small-scale structure of the deep mantle in terms of its statistical properties, that is, the strength of elastic parameter fluctuations and their size distribution. It can yield valuable information about the distribution of chemical or thermal heterogeneity without the blurring effect of the tomographic filter. It also may help to constrain the depth extent and lateral distribution of features like plume clusters (Mc-Namara, 2019) or accumulations of heterogeneous material in the basal mélange formed from subducted slabs (Tackley, 2012).
10.1029/2020GL089203 2 of 9 Figure 1. Increase of seismic energy due to scattering in a 50-km-thick layer above the CMB. Simulations used a 600-km-deep P wave source in the velocity and attenuation model ak135-f (Kennett et al., 1995;Montagner & Kennett, 1996). (a) Arrival times of seismic phases and relevant regions of the time-distance domain that have been investigated for scattering in the deep Earth are indicated. (b) A zoom into the timedistance window of PKP waves (dashed box, panel a). Theoretical onset times for waves scattered at the CMB are indicated and labeled with "*" indicating the scattering event. The frequently discussed PKPdf precursor and the PKPab precursor discussed below are labeled. Inset in (b) shows a cross section of the Earth with the paths of the fastest PK*Pbc waves. CMB and ICB are indicated. The blue bar at the surface shows that distance range of PKPbc. CMB, core-mantle boundary; ICB, inner core boundary.

Observation of the PKPab Precursors
Additionally to the PKPdf precursor at Δ < 145°, Figure 1(b) shows a further arrival of scattered energy at distances Δ > 155°. For reasons discussed later, we term this phase PKPab precursor. This phase has been discussed sporadically in the literature, and there is no consensus about its origin. Waves propagating through the inner core arrive earlier in this distance range, and it is not clear whether the scattered energy that arrives between the PKPdf and PKPab should be regarded as a coda of PK-Pdf or as a precursory signal to PKPab. In contrast to the PKPdf precursor at Δ < 145°, the PKPab precursor at Δ > 155° in Figure 1 might thus be hidden in the PKPdf coda depending on the relative strength of both signals at the given frequency.
A possibility to observe the PKPab precursor unambiguously is to show its spatial coherency over an extended distance range. To avoid the effect of source-side crustal scattering, we use large deep earthquakes. Since lateral variability of D″ scattering could disturb the spatial coherency when records from different areas are combined, we try to use records from compact regions. Deep sources in South America recorded by the dense Japanese HiNet seismic stations (NIED, 2019;Obara et al., 2005;Okada et al., 2004) offer a perfect source-receiver configuration to observe the desired signals. Figure 2 shows HiNet vertical seismogram envelopes from two events stacked in 1° distance bins. The first is a 570-km-deep event with Mw 6.8 from January 1, 2011, in Argentina that covers 151° < Δ < 167° while the 592-km-deep Mw 7.5 Peru event from November 24, 2015, covers 135° < Δ < 152°. Data processing for Figure 2 is described in the supporting information Text S2. Two frequency bands are shown in Figure 2. The low-frequency band between 0.35 Hz and 0.7 Hz shows energetic arrivals following the PKPdf and PKPab travel time curves and some energy arriving prior to the PKPdf below 145°-the known PKPdf precursor.

Figures 2(b) and 2(c) and Figures S2 and S3 (supporting information)
show the same data filtered in the 4-8 Hz frequency band and differ significantly from the low-frequency panel.
Three main observations can be made. (a) A significant amount of energy travels through the entire Earth in the 4-8 Hz band. (b) The PKPdf phase is strongly attenuated on the path from Peru to Japan at these high frequencies compared to the PKPab phase. There is no indication of energy propagating through the inner core in the 4-8 Hz band. (c) For distances Δ > 155°, a distinct increase of energy follows the PK*Pbc line of the earliest possible arrival of D″ scattered PKPbc energy in Figure 2(b). This is the PKPab precursor that is predicted by the simulations in Figure 1. The slowness of the PKPab precursor, derived from the onset of arriving energy, transitions from the slowness of the PKPbc phase at the c-cusp (Δ = 155°) to a slowness close to that of PKPab for Δ > 165°. This curvature of the hodochron is diagnostic for the origin of the PKPab precursor. For increasing distances, the onset of energy is significantly delayed with respect to the arrival time of the inner core-diffracted wave PKP − C diff . The PKPdf precursor for Δ < 145° follows the PK*Pab and PK*Pbc lines at Δ < 145°.
We would like to emphasize that the presence of the PKPab precursor is not due to a local effect at the source of the event (Argentina) or local disturbances within the HiNet. Figure

Origin of the PKPab Precursor
The onset of PKPab precursor emerges at the c-cusp of the hodochron that connects the PKPbc and PKiKP (inner core reflection) branches with a common slowness. Thus, it seems reasonable to assume a relation of the PKPab precursor to one of these two phases. Possible mechanisms could be (a) diffraction of PKiKP waves along the ICB or the propagation through a heterogeneous waveguide above the ICB, or (b) deviation of PKPbc waves into the shadow of the inner core by scattering in the mantle or outer core. Feasibility to differentiate between these two possibilities is provided by the slowness-distance relation of the earliest energy arrival. For mechanism (a), the energy diffracted along the ICB or propagated around the inner core by any other process that perturbs the ray parameter close to the ICB should arrive with constant slowness for all distances. This should be the slowness of PKiKP waves at the c-cusp or a somewhat higher or lower but constant slowness if a low-velocity layer is invoked at the ICB or the head wave propagates with the inner core velocity (PKP diff travel time in Figure 2). Observations in Figures 2(b) and 3 do not favor the ICB-diffraction mechanism (a).
Mechanism (b), that is, the deviation of PKPbc wave direction, would mean that part of the PKPbc wave energy that travels just atop the inner core gets scattered on its path through the Earth. Depending on the depth distribution of the heterogeneity that causes the scattering, different onset times are possible. However, from the PKPdf precursor at distances Δ < 145°, it is known that especially the D″ layer above the CMB scatters wave energy and is thus a right candidate.
As shown in Figure S1, a deviation of the propagation direction of PKP waves at the CMB on the source (or receiver) side to create P*KP (PK*P) waves explains the onset time of the PKPdf precursor energy for Δ < 145° (Figure 2). Scattering of both the PKPab and PKPbc branches contributes to the PKPdf precursor. Source and receiver side scattering of core phases at D″ have very similar effects and we will not differentiate between those in the following.
At distances Δ > 155°, there is no ballistic PKPbc arrival and scattered PK*Pab energy arrives after the ballistic PKPab. However, energy can be shed into this distance range by deviating PKPbc energy at D″. This energy arrives after the PKPdf phase, but prior to PKPab-the reason for calling it PKPab precursor. We emphasize that the predicted onset of PK*Pbc is curved, transitioning from the PKPbc slowness at short distances, to a higher slowness that is similar to the PKPab slowness, at larger distances, just as it is observed in Figures 2(b) and 3. Since the earlier PKPdf arrival is strongly attenuated in the high frequency, as shown in Figure 2, the scattered PK*Pbc energy forms the first notable arrival.
We summarize that (a) scattering of core phases in the lower mantle is a commonly accepted process as confirmed for example by the PKPdf precursor at Δ < 145°. (b) Diffraction at the ICB is an unlikely mechanism because of the high frequencies used here (c) in simulations of energy propagation considering scattering in the lower mantle predict the arrival of energy that is in qualitative agreement with the observation of the PKPab precursor (cf., Figures 1-3). Furthermore (d) the curvature of the onset time curve of the PKPab precursor makes an origin at the ICB unlikely. These ideas strongly support the hypothesis that the observed PKPab precursor at Δ > 155° is a consequence of the same process that causes the well-known PKP precursor at Δ < 145°-the scattering in the heterogeneous lower mantle.

Local Sensitivity of the PKPab Precursor to Scattering
Waves scattered in the deep Earth provide means to investigate the structure of the lower mantle at a spatial scale below the resolution limits of seismic tomography. The PKPab precursor offers a new opportunity for this. Here, we investigate the spatial sensitivity of this signal. We use the theory of Margerin et al. (2016) to derive an intensity sensitivity kernel, which describes the sensitivity of the seismogram envelope to a local SENS-SCHÖNFELDER ET AL.  increase of scattering strength. We simplify the treatment in three ways. (a) Wave propagation through the inner core is blocked. Since we observe that PKPdf waves vanish in the 4-8 Hz frequency range (cf., Figures 2b, 3, S2, and S3), waves that propagate through the inner core cannot contribute to the scattered arrival either. Scattering within the inner core would generate PKPdf coda rather than a separate phase that is disconnected from the PKPdf arrival. (b) We assume that scattering leading to the PKPab precursor is isotropic, which simplifies the treatment of scattering angles. Increased probability of forward scattering would reduce the probability of scattering close to either source or receiver. (c) The scattering process is restricted to a single scattering of P waves because S wave propagation is highly unlikely for the short travel time of the PKPab precursor.
Under the assumptions made, we can calculate the volume in which scattering can contribute to the observed PKPab precursor by convolution of the forward and backward P wave intensity. These intensities can be obtained by radiative transfer simulations, as described in Text S1 for excitation at the location of the earthquake (forward simulation) and the location of the receiver (backward simulation). The sensitivity finally describes the probability of a wave packet that arrives in a particular time-distance window to have traveled from the source to a particular location in space where scattering occurred, and then continued to the receiver location. Figure 4(a) shows a cross section through the sensitivity kernel in the great-circle plane for an epicentral distance of Δ = 160° and a lapse time of 1,155 s, which is within the time-distance window of the PKPab precursor. It describes the influence of heterogeneity (i.e., the possibility for wave scattering) on the amplitude of the PKPab precursor. Regions, where this probability is high, have a strong influence on the precursor amplitude. If this probability is low at some location, the influence is weak because it is unlikely that a wave arriving in the time-distance window was scattered there. Zero influence means that it is impossible for wave energy to arrive in the time-distance window of the PKPab precursor even if it is scattered there.
High sensitivity is located along the PKPbc path through the outer core and lower mantle. In this narrow volume, waves are scattered mostly in the forward direction meaning that small perturbations of the propagation direction of PKPbc waves can generate the PKPab precursor at 1,155 s at 160° distance. Due to the high amplitude of the PKP phase, the influence of this region on the PKPab precursor amplitude is high as indicated by the color in Figure 4(a). Another patch of sensitivity is located in the midmantle. It indicates that scattering of P waves in the midmantle allows waves to travel around the slow outer core and still carry energy to a receiver in the time-distance window of the PKPab precursor. However, considering the smaller SENS-SCHÖNFELDER ET AL.  representation of the volume of sensitivity with color indicating distance to the equatorial plane. Two distinct regions of sensitivity exist. One is draped on the inner core along the PKPbc path. Due to the high PKP amplitudes, heterogeneity in this volume has a strong influence on amplitudes of the precursor. Another sickle-shaped region of sensitivity that allows for large deviations form the great circle is formed by scattering of P waves in the mantle. Heterogeneity in this region, however, has less influence on the amplitude of the PKPab precursor than in the elongated region that extends through the deep Earth (cf., Figure 4(a)). CMB, core-mantle boundary; ICB, inner core boundary.
amplitudes of the participating waves, there is a low probability that the scattering in this region contributes to the observed signal-resulting in a weak influence of this region on the precursor.
Since scattering allows for off great-circle path propagation, the sensitivity has a significant 3D component, as illustrated in Figure 4(b). The volume with the strong influence on the PKPab precursor that extends through the deep Earth is draped on the inner core and shows small deviations from the great-circle plane. The region of P wave scattering in the midmantle forms a sickle-shaped volume of sensitivity, perpendicular to the great-circle plane. Energy in the PKPab precursor window that was scattered in the mantle can, therefore, arrive with significant deviations from the great-circle direction.

Discussion
Using numerical simulations, we show that scattering in the lower mantle results in the arrival of scattered energy before the PKPab phase at Δ > 155°. This energy arrives after PKPdf. In the high-frequency band between 4 Hz and 8 Hz, waves do not propagate through the inner core on the path between South America and Japan due to high intrinsic or scattering attenuation in the inner core. This vanishing of the PKPdf energy makes the PKPab precursor the first notable arrival on seismograms recorded in this distance range, which can be readily observed in individual records of deep earthquakes. We speculate that the PKPab precursory signal is also present at lower frequencies where it is masked by the earlier PKPdf arrival and its coda. For the outer core and the mantle, our observations of 6 Hz core phases imply the need for high Q at this frequency range.
The origin of the PKPab precursor has been discussed earlier. A number of articles discussed the PKP − C diff phase that should result from the diffraction of compressional waves around the inner core along the ICB. Nakanishi (1990) present observations of 2.5-3.3 Hz PKP − C diff waves in the distance range 152° < Δ < 157°. From the complex, long-lasting waveforms, their earliest arrival, and their high slowness, Nakanishi (1990) concluded that scattering at the base of the upper mantle around 660 km depth is more likely to generate these arrivals than ICB diffraction. Tanaka (2005) investigated PKP − C diff coda using short-period seismic arrays and found slowness ranging between 1 s/° and 5 s/° extending through the whole range covered by PKPab and PKPbc waves. Scattering at the CMB was invoked as an alternative origin of the PKP − C diff coda signal, since the slowness of waves scattered close to the c-cusp is too close to that of PKP − C diff waves to be separated by the arrays. These early works are thus in agreement with our interpretation of the PKPab precursor as scattered PKPbc with a likely location of the scattering close to the CMB. Adam and Romanowicz (2015) report on a scattered phase that arrives 5-20 s after the PKPbc or PKP − C diff phases which they call M-phase. Adam and Romanowicz (2015) use coherent stacking of 1 Hz signals within distance ranges up to 10° and conclude that the scattered M-phase originates at the ICB. Scattering at the CMB was ruled out because the M-phase appears as an isolated phase in the phase weighted stack with a slowness between 0.7 s/° and 1.6 s/°. This slowness is too low for PKPbc waves scattered at the CMB beyond 160° distance. This finding appears to contradict our interpretation. However, first the 1 Hz frequency range differs from our observation and second the argument that Adam and Romanowicz (2015) use to rule out the possibility of PKPbc scattering close to the CMB is strongly based on the limitation of the slowness range to 1.6 s/° maximum. This constraint is derived under the assumption of distance independent slowness even though it is not shown that the M-phase at Δ > 160° has a slowness below 1.6 s/°. The fact that the M-phase appears as an isolated phase is enforced by the phase weighted stacking and does not exclude the actual presence of an extended wave train originating from waves with a significant spread of slowness and back azimuth.
Thus, we think that our interpretation of the PKPab precursor, as scattered PKPbc waves are compatible with earlier studies. Other effects like diffraction or propagation in thin heterogeneous low-velocity layers at ICB and CMB might additionally affect high-frequency PKP waves and cannot be ruled out. But they are not required to explain the present observations. The discussed PKP − C diff coda, as well as the M-phase, may be interpreted as a signal with the same origin as the PKPab precursor. Since the heterogeneity at D″ is widely accepted, it should be taken into account in any interpretation of signals that might have passed through D″. This concerns all investigations of the inner core. The difference in coda decay between PcP and PKiKP coda at small distances, for example, should not be interpreted without considering the effect of the twofold PKiKP transmissions through D″ which can significantly alter the shape of the coda.
The possibility to observe the PKPab precursor at Δ > 155° requires strong attenuation of the earlier arriving PKPdf waves that pass through the inner core. Longitudinal variations of PKiKP versus PKPdf travel time and amplitude differences indicate hemispherical asymmetry of inner core attenuation (Monnereau et al., 2010). This will likely influence the observability of the PKPab precursor. The PKPab precursor in locations where it can be observed can increase the lateral resolution of PKP-based CMB studies. Combined with observations of the PKPdf precursor, it allows using earthquakes from a much wider distance range. The observation of scattered waves at the exceptionally high frequencies used here provides means for the investigation of heterogeneity in the deep Earth at a length scale of the order of a kilometer or below.
As indicated by the elongated shape of the sensitivity kernel in Figure 4, the vertical resolution of the scattering location is relatively poor. Since the required deviation of the propagation direction (scattering angle) is small, the scattering can happen almost anywhere between the source and receiver. However, it is known from array analysis of the PKPdf precursor (e.g., Thomas et al., 1999) that the most likely location of scattering is D″. Considering that scattering cannot occur in the outer core the PK*Pbc onset time is the earliest possible time for the arrival of scattered energy and Figures 2 and 3 clearly show that there is no earlier arrival. As heterogeneity shallower in the mantle causes later arrivals, the emergent increase of PK-Pab precursor energy might thus indicate that scattering is not confined to the CMB but might occur in a larger part of the lower mantle.
The theoretical possibility of propagating seismic energy in the time-distance window of the PKPab precursor by P*P scattering in the midmantle (cf., Figure 4) is challenging to test because of the much stronger PKP phases. However, for scattering deeper in the mantle, the P*P scattered waves can arrive prior to any scattered core phase and could be used to investigate scattering above D″.

Conclusion
We show that the frequency range for investigation of the deep Earth with teleseismic waves can be extended toward frequencies of several Hertz. The attenuation of high-frequency waves in the inner core allows for the observation of scattered PKPbc waves as PKPab precursor in the shadow of the inner core. Without this attenuation, the PKPab precursor would be masked by the PKPdf coda (which is likely the case at lower frequencies). This situation is similar to the PKPdf precursor that can only be so clearly observed as the first arriving phase because the low-velocity core deviates the P phase-thereby creating the (outer) core shadow.
We calculate the sensitivity kernels of the PKPab precursor for heterogeneity using elastic radiative transfer simulations. The kernels describe the Earth's region in which scattering would contribute to seismic energy's arrival in a given time-distance window. Scattering in D″ that causes the PKPdf precursor at Δ < 145° is also the most likely mechanism causing the PKPab precursor at Δ > 155°. Combining these sensitivities kernels with observations of scattered energy from PKPab and PKPdf precursors will improve the imaging and characterization of heterogeneity in the deep Earth.

Data Availability Statement
Data from Japan (NIED, 2019) were kindly provided by the National Research Institute for Earth Science and Disaster Resilience and are available at www.hinet.bosai.go.jp. Data from Brazil were kindly provided by the Brazilian seismographic network (RSBR) and the participating institutions. They are available from www.rsbr.gov.br with details about access given in Bianchi et al. (2018).