Comment on “Inner Core Rotation Captured by Earthquake Doublets and Twin Stations” by Yang and Song

Yang & Song (2022, https://doi.org/10.1029/2022GL098393) first claimed existence of Earth's inner core differential rotation based on the waveform similarity of two neighboring stations AAK and KZA across an earthquake doublet and then postulated a local velocity gradient at the top of the inner core based on the difference of PKiKP‐PKIKP differential times between the stations and inferred inner core differential rotation rate. In this comment, we collectively analyze the seismic data in the region and add the data of another nearby station HORS into analysis. HORS and KZA, located in an opposite direction away from AAK, consistently exhibit high waveform similarity. Collective analysis of seismic data demonstrates the invalidity of both their logic of claiming existence of inner core differential rotation and their postulation of “a local inner core gradient” to infer differential rotation. Localized and episodic inner core surface change provides a physically consistent explanation to the seismic data.

Abstract Yang & Song (2022, https://doi.org/10.1029/2022GL098393) first claimed existence of Earth's inner core differential rotation based on the waveform similarity of two neighboring stations AAK and KZA across an earthquake doublet and then postulated a local velocity gradient at the top of the inner core based on the difference of PKiKP-PKIKP differential times between the stations and inferred inner core differential rotation rate. In this comment, we collectively analyze the seismic data in the region and add the data of another nearby station HORS into analysis. HORS and KZA, located in an opposite direction away from AAK, consistently exhibit high waveform similarity. Collective analysis of seismic data demonstrates the invalidity of both their logic of claiming existence of inner core differential rotation and their postulation of "a local inner core gradient" to infer differential rotation. Localized and episodic inner core surface change provides a physically consistent explanation to the seismic data.
Plain Language Summary Whether Earth's inner core differentially rotates with respect to the rest of Earth or it experiences localized episodic change of its surface has been vigorously debated. While both mechanisms are derived based on temporal changes of compressional seismic waves that touch the inner core, the hypothesis of inner core differential rotation is criticized for its lack of direct supporting seismic evidence and existence of many inconsistencies in explaining the seismic data. Yang & Song (2022, https://doi. org/10.1029/2022GL098393) claimed existence of inner core differential rotation based on waveform similarity of two neighboring stations AAK and KZA across an earthquake doublet. They further postulated a local inner core velocity gradient and inferred inner core differential rotation rate. Here, we collectively analyze the seismic data in the region and add the seismic data of another nearby station HORS into analysis. Collective analysis of seismic data demonstrates the invalidity of both their logic of claiming existence of inner core differential rotation and their postulation of "a local inner core gradient" to infer inner core differential rotation. Seismic evidence is contradictory to the hypothesis of inner core differential rotation. Instead, a localized and episodic inner core surface change provides a physically consistent explanation to the seismic data. • Yang and Song (2022)'s logic of claiming existence of inner core differential rotation is invalid • Yang and Song (2022)'s postulation of "a local inner core gradient" and inference of inner core differential rotation are invalid • Localized and episodic inner core surface change provides a physically consistent explanation to the seismic data

Invalid Logic of Claiming Existence of Inner Core Differential Rotation
The core evidence of their claiming inner core differential rotation relied on the waveform similarity between the recording of AAK in the earlier event of the doublet (99 AAK) and the recording of KZA in the later event of the doublet (07 KZA) (Figure 2c in Yang and Song (2022)). Because of the similarity, they concluded "This is clear evidence that the KZA path samples the vicinity of the patch of the IC that was sampled by the AAK path earlier for the corresponding pair." There is nothing surprising that the AAK-KZA station pair in similar epicentral distances could exhibit similar waveforms of the inner core phases, as the waveforms of the inner core phases in the neighboring stations are in first order controlled by the epicentral distance. Therefore, waveform similarity between the neighboring stations of similar epicentral distances does not in anywhere imply or require that their sampling inner core patches have moved. The unique aspect of the AAK and KZA data is that they sample an inner core region that exhibits temporal changes of the inner core surface and their PKiKP (CD) phases change over time (Wen, 2006;Yao et al., 2015Yao et al., , 2019Yao et al., , 2021. The localized and episodic nature of the inner core surface change (Wen, 2006;Yao et al., 2015Yao et al., , 2019Yao et al., , 2021 would change a station's PKIKP-PKiKP waveforms between the doublets; it could also possibly make neighboring stations coincidently exhibit more similar waveform with the other station than themselves across the doublet in some doublets. Inner core differential rotation is not required to explain the similarity of waveforms between AAK and KZA across a doublet. In fact, if we adopt the logic of Yang and Song (2022), that is, waveform similarity between the data in a station in the earlier event of a doublet and the data in a nearby station in the later event of the doublet would indicate an inner core differential rotation, we will reach a contradictory conclusion when we also consider the seismic data recorded in another nearby station in the region, HORS (Figure 1a). In comparison with KZA, HORS also has a similar epicentral distance as AAK, but is located in an opposite direction (NW48°) away from AAK to the direction (SE45°) KZA is away from AAK ( Figure 1a). 07 KZA and 07 HORS waveforms are almost identical to each other with a cross-correlation coefficient of 0.995 between them (top panel in Figure 1b). Note that the AAK-KZA waveform comparison in their core evidence (middle panel in Figure 1b; same as Figure 2 in Yang and Song (2022)) is nearly identical to the AAK-HORS waveform comparison (bottom panel in Figure 1b). Thus, 07 HORS waveform can be used to replace 07 KZA waveform in the core evidence of Yang and Song (2022). If we follow the logic of Yang and Song (2022) that waveform similarity between the neighboring stations across the doublet indicates an inner core shift, the inner core patch sampled by 99 AAK data would have simultaneously shifted eastward (in more exact, SE45°) to the position sampled by 07 KZA data (as Yang and Song (2022) claimed) and westward (in more exact, NW48°) to the position sampled by 07 HORS data! This contradictory conclusion indicates that there is no validity of the logic presented in Yang and Song (2022) in concluding the existence of inner core differential rotation based on waveform similarity between neighboring stations across a doublet.

Invalid Postulation of "a Local Velocity Gradient" at the Top of the Inner Core
It has become a standard practice in most inner core differential rotation studies to first postulate a local velocity gradient at the top of the inner core and an inner core differential rotation as the interpretation, and then use the gradient to infer the differential rotation rate. If the seismic data did not exhibit temporal change and were in contradiction with observed temporal changes in other geographic locations or in other time periods, a seismically "silent" differential rotation was argued by postulating existence of a laterally homogeneous structure (i.e., a zero gradient) at the top of the inner core specifically for those contradictory data, similar to the discussion presented in Yang and Song (2022) on the two doublets that do not exhibit temporal changes: "Interestingly, the temporal changes are also very small even with dT of 8.0 and 9.5 years. The observation is also consistent with IC rotation as a rotation of a uniform structure does not produce a temporal change." It should be pointed out that those postulations of a gradient or a zero gradient were made without any physical justification. Nor was there any independent supporting evidence for the existence of such a "local gradient" or a zero gradient. In Yang and Song (2022), the "local gradient in the inner core" can be rejected when we collectively consider the data recorded in AAK, KZA, and HORS. In their study, the "local gradient" was postulated and derived from the "spatial ddt" between the AAK-KZA station pair, which was defined as the difference of the differential PKiKP-PKIKP (CD-DF) times measured in the two stations. Besides the near identical waveform to KZA in Figure 1b, HORS has also consistently exhibited high waveform similarity with KZA for the other earthquakes occurring near the doublet 99-07 during the lifetime of its operation (Figures 1c and 1d), indicating that the temporal changes of the seismic data in these two stations are nearly identical. If we follow the same postulation of Yang and Song (2022), but use the data of the AAK-HORS station pair to derive the "local velocity gradient," we will obtain "a local velocity gradient" that is in a totally reversed direction to the one derived by Yang and Song (2022) based on the data of the AAK-KZA station pair, as stations HORS and KZA are located in opposite directions from AAK (Figure 1a). Such a contradiction clearly illustrates the invalid postulations of existence/nonexistence of a local velocity gradient in the studies of inner core differential rotation and inconsistency of the hypothesis of inner core differential rotation.

Origin and a Consistent Explanation of the Temporal Changes of Seismic Signal
There is a simple physically consistent explanation for the apparent correlation of the "spatial ddt" with the annual temporal change measured from AAK and the observed waveform similarity between HORS and KZA. AAK is noted to exhibit temporal changes of PKiKP travel time (Wen, 2006;Yao et al., 2015Yao et al., , 2019Yao et al., , 2021. The temporal change of PKiKP phase indicates that the inner core surface experiences temporal change. The close proximity of the AAK and KZA data sampling paths in the inner core surface and the Fresnel zone (bottom-right inset, Figure 1a) effects would suggest that the inner core phases observed at these two stations will exhibit similar manners of temporal change, albeit in different magnitudes depending on the details of the inner core surface change. The "spatial ddt" in Yang and Song (2022), or the difference of the differential PKiKP-PKIKP (CD-DF) times measured in the neighboring stations, is simply the difference of the individual temporal PKiKP changes observed in the two stations. Since two neighboring stations would exhibit similar patterns of temporal change of inner core phases, but possibly in different magnitudes, it is not surprising that the temporal change rate (i.e., annual temporal change) observed at one station (AAK) correlates with the difference of temporal changes observed at the two neighboring stations. Judged from that the differential PKiKP-PKIKP times are always shorter in AAK observations than KZA observations (Figure 3, Yang and Song (2022)) and the temporal change is in the trend of shorting the differential travel time (Figure 3a, Yang and Song (2022)) or PKiKP arrives progressively earlier over time, the largest temporal change is observed at AAK and the inner core surface of AAK data sampling is closer to the center of the temporal change. As the sampling regions of the inner core surface for HORS and KZA data have a similar distance away from the major region of temporal change of the inner core surface, these two stations experience similar waveform changes from the temporal change of the inner core surface.
In conclusion, Yang and Song (2022) presented no seismic evidence that would require an inner core differential rotation with respect to the mantle. On the contrary, it adds another example of invalid logic of claiming existence of inner core differential rotation and faulty postulations of inner core differential rotation and "a local velocity gradient" at the top of the inner core to a pile of seismic evidence in the literature that are contradictory to the hypothesis of inner core differential rotation (Yao et al., 2015(Yao et al., , 2019(Yao et al., , 2021.