Understanding the Earth's inner core (IC) is crucial for comprehending planetary formation and evolution. The IC, less than 1% of Earth's volume, acts as a time capsule of our planet's history, its growth driving outer core convection and maintaining the geodynamo. Changes in the IC's structure could reflect shifts in the geomagnetic field, profoundly impacting Earth's evolution. Early seismological investigations focused on the IC's isotropic structure and its boundary with the liquid outer core. However, since the 1980s, research has increasingly focused on its anisotropic properties, initially modeled as depth-independent cylindrical anisotropy. Subsequent discoveries revealed hemispherical dichotomy and radial variations in anisotropy, prompting increasingly complex models incorporating variations in P-wave anisotropy, attenuation, and even S-wave anisotropy. Despite these advances, the innermost part of the IC remains enigmatic due to limitations in volumetric sampling by existing seismological probes. Travel times and amplitudes of PKIKP waves have been primary tools, but probing the centermost ball requires near-antipodal earthquake-station positioning, which is challenging. Normal modes offer limited resolution near the Earth's center. Coda correlation studies, exploiting correlated features in long earthquake recordings, have emerged as promising tools, but challenges remain in interpreting their complex correlation features. The hypothesis of a distinct innermost inner core (IMIC) with distinctive anisotropic properties from the outer shell has been proposed and corroborated by various studies but with significant unknowns regarding its radius, the nature of the transition to the outer IC, and its precise anisotropic properties.

Previous studies on the Earth's inner core have explored its isotropic and anisotropic structures. Early research focused on isotropic models, but the discovery of travel time anomalies led to the development of anisotropic models. Initial models proposed depth-independent cylindrical anisotropy, explaining compressional wave travel times (PKIKP waves) and normal-mode splitting functions. However, further research revealed hemispherical dichotomy and radial variations in anisotropy. Recent studies propose even more complex structures, including variations in P-wave anisotropy and attenuation, as well as observations of S-wave anisotropy. The challenge of probing the innermost inner core (IMIC) has led to the use of various techniques, including analysis of PKIKP waves, normal modes, and coda correlation studies. While these studies have provided valuable insights, significant unknowns remain about the IMIC's radius, transition to the outer inner core, and precise anisotropic properties.

This study utilizes the growing global seismograph network to create global stacks of seismic waveforms from significant seismic events (Mw ≥ 6.0). Waveforms are retrieved from international data centers, bandpass filtered (10–100 s for global stacks, 7–13 s for regional analysis), and grouped into 1-degree distance bins. A median filter removes traces with anomalous amplitudes. The remaining traces are linearly stacked without amplitude normalization. To enhance visibility of arrivals at significant lapse times, a time-dependent polynomial multiplier is applied. The study identifies and analyzes multiple body-wave reverberations through the Earth's inner core, termed PKIKP multiples (PKIKP, PKIKP2, PKIKP3, PKIKP4, PKIKP5), where the number indicates the number of passages through the Earth's diameter. These reverberations, previously unreported for more than two passages, are used to constrain IMIC properties. Residual travel times for pairs of exotic arrivals (e.g., PKIKP4-PKIKP2 and PKIKP3-PKIKP) are measured on stacked waveforms over dense regional networks, correcting for source location errors, Earth's ellipticity, and mantle heterogeneities using models like DETOX-P3. Finite-frequency numerical experiments validate the methodology's sensitivity. A cylindrically anisotropic model of the Earth's inner core is used to fit the residual travel times. The anisotropic model is parameterized using a function of the sampling angle (ξ), incorporating parameters for anisotropy strength (ε, γ, α). Orthogonal distance regression accounts for uncertainties in both explanatory and response variables. The study compares models with and without an IMIC, focusing on the centermost-sensitive observations to infer the IMIC's distinctive anisotropic pattern. The methodology leverages dense seismic arrays like USArray and AlpArray to improve spatial sampling of the Earth's center, mitigating uncertainties associated with earthquake location errors by using differential travel times. Bootstrap methods estimate uncertainties in travel time measurements. Data from the Alaskan branch of the USArray and the 2018 Anchorage earthquake are particularly important for sampling the Earth's center due to the podal geometry of the observed waves.

The study reports the first observations of up to fivefold reverberating P-waves (PKIKP multiples) traversing the Earth's diameter, significantly extending the capability to probe the Earth's deepest interior. These observations, primarily derived from the stacking of seismic waveforms from multiple seismic stations, enhance weak signals while suppressing incoherent noise. The study's key finding is the confirmation of an anisotropically distinctive innermost inner core (IMIC) within the Earth's inner core. The IMIC is characterized by a ~650 km radius. Analysis of the differential travel times of these PKIKP multiples indicates that P-wave speeds in the IMIC are approximately 4% slower at angles around 50° from the Earth's rotation axis compared to the P-wave speeds along the polar direction or the equatorial plane. The outer shell of the inner core displays much weaker anisotropy, with the slowest direction located in the equatorial plane. The study also reveals that the uncertainties due to earthquake location errors are substantially mitigated by measuring the differential travel times of a pair of exotic phases. The consistent observations across multiple earthquakes and seismic networks bolster the confidence in the results. The findings support a model where the IMIC's anisotropic properties contrast sharply with those of the outer inner core. The use of dense regional seismic arrays (such as USArray and AlpArray) significantly improves the spatial resolution of the data, providing detailed insights into the inner core's structure near the Earth's center. The study utilizes orthogonal distance regression to account for measurement uncertainties in both explanatory and response variables, enhancing the robustness of the anisotropic model parameters.

The direct observation of PKIKP multiples using regional seismic arrays offers significant advantages in sampling the Earth's inner core. The unique sampling of the IC along the north-south direction, particularly near the Earth's center, helps clarify the anisotropic structure of the IMIC. The methodology effectively mitigates uncertainties from earthquake location errors by focusing on differential travel times. The findings corroborate previous research suggesting the existence of an IMIC, adding significant detail to its anisotropic properties and providing a contrasting picture with the outer inner core. The observed differences in anisotropy between the IMIC and the outer shell could point to a significant change in the growth regime of the Earth's inner core during its history, which can be explored with advanced geodynamic models and further research. These observations strengthen the understanding of the Earth's inner core's complex structure and dynamics, and the potential to use these observations for better understanding Earth’s long-term evolution. The results contribute to a more comprehensive understanding of the Earth's deep interior and its evolution, offering crucial constraints for geodynamic models.

This study provides robust evidence for a distinctly anisotropic innermost inner core (IMIC) using novel observations of multiple body-wave reverberations through the Earth's core. The methodology successfully leverages the ever-growing global seismic network to reveal previously inaccessible details of the Earth's deep interior. Future work should focus on characterizing the IMIC-outer inner core transition and exploring the geodynamic implications of the observed anisotropic structure.

The study's reliance on specific types of earthquakes and the availability of dense seismic arrays limits the generalizability of the findings to some extent. While the methodology effectively mitigates some sources of uncertainty, other factors, such as incomplete understanding of mantle heterogeneities, could potentially influence the results. Further research is needed to completely quantify these uncertainties and to test the robustness of the findings using broader datasets.