A 1993/2003 earthquake doublet recorded at the Yellowknife seismic array showed that the amplitude of PKiKP — the compressional seismic phase reflected from the inner-core boundary (ICB) — changed by roughly a factor of three in a decade while the phase traversing the inner core changed little. This was interpreted as kilometer-scale corrugations of the ICB with horizontal wavelength of about 10 km and relief between a few hundred meters and a few kilometers. Whether such corrugations are quasi-fixed bumps advected past the reflection points by differential rotation of the inner core, or a genuinely time-dependent boundary signal of freezing, melting, and deformation at the top of the core, remains unresolved after two decades: published relief estimates span roughly 0.3 to 14 km, no global map or spectrum of the short-wavelength topography exists, no dynamical model has demonstrably sustained such corrugations over decades, and inner-core rotation rates and viscosities remain contested. The problem is to determine the physical origin of decadal inner-core waveform changes, the amplitude, wavelength spectrum, and global distribution of short-wavelength ICB structure, and the mechanism and material properties — top-inner-core viscosity and differential rotation rate — that support it.

Background

Earth's solid inner core, an iron-alloy sphere of radius about 1221 km, crystallizes from the liquid outer core at the inner-core boundary (ICB); the freezing expels light elements that help drive convection of the outer core and, with it, the geodynamo — the self-sustaining dynamo process in the liquid core that generates Earth's magnetic field. Seismology probes the ICB with compressional waves: PKiKP is reflected at the ICB, PKIKP (also called PKP(DF)) passes through the inner core, and PcP is reflected at the core-mantle boundary above. At epicentral distances beyond about 140 degrees PKiKP is reflected 'postcritically', which strongly amplifies its sensitivity to conditions at the boundary. An earthquake doublet is a pair of earthquakes that rupture essentially the same fault patch at different times; because the source and the ray path are nearly identical, differences between the two seismograms isolate time-dependent changes in Earth's deep structure.

Since the mid-1990s, such data revealed that the inner core rotates slightly faster than the mantle and crust ('differential rotation' or 'super-rotation'; Song and Richards 1996), later confirmed and quantified with waveform doublets (Zhang et al. 2005), with estimated rates falling from the order of one degree per year toward a few tenths of a degree per year as data improved. Independently, short-period array observations showed that PKiKP amplitudes and codas (the wavetrains trailing the main arrival, produced by scattering) vary erratically from place to place, hinting that the ICB is not the smooth, sharp discontinuity of reference Earth models.

Cao, Masson and Romanowicz (2007) combined these threads. For an exceptionally clean 1993/2003 doublet in the South Sandwich Islands recorded postcritically at the Yellowknife array in northern Canada, the PKiKP amplitude of the 1993 event was about three times smaller than that of the 2003 event, while the PKIKP and PP amplitudes barely changed; reference models cap the PKIKP/PKiKP ratio at 1.9 even with no inner-core attenuation, so the 1993 PKiKP was anomalous. They attributed this to topographic corrugations of the ICB with horizontal wavelength near 10 km, with a conservative upper bound of 3-5 km on the relief and a plausible value as small as 300-500 m. Two interpretations were offered. In the first, the corrugations are quasi-fixed features of the boundary, and the decadal amplitude change is caused by inner-core super-rotation advecting them past the fixed reflection points, at roughly 0.1-0.15 degrees per year. In the second, the topography itself changes on decadal scales through inner-core growth (local freezing and melting), which requires the viscosity at the top of the inner core to be below about 101610^{16} Pa·s so the boundary can deform that fast. Because long-wavelength ICB topography is rapidly relaxed away gravitationally and viscously, kilometer-scale bumps can persist for decades only if the near-boundary viscosity is large enough, or if small-scale convection in the top of the inner core continually regenerates them. The paper thus posed four interlinked open issues: the advection-versus-time-dependence question; the true amplitude and geometry of the corrugations; the sustaining mechanism; and tighter constraints on the rotation rate and top-inner-core viscosity that would discriminate the scenarios. It also claimed generality — that ICB corrugations would explain not only its Yellowknife observations but also previously observed PKP(DF) coda variability, PKiKP codas, amplitude variability at subcritical distances, and decadal PKIKP envelope changes — which raises the further question of the global extent and lateral coherence of such structure.

Subsequent work fractured along exactly these lines. Reflection studies inferred ICB relief from a few hundred meters to 14 km depending on method and region; temporal-change studies split between groups attributing decadal waveform changes to a rotating heterogeneous inner core and groups attributing them to localized, episodic boundary change; and geodynamic, nutation-based, and atomistic estimates of inner-core viscosity disagree by orders of magnitude. A 'mushy zone' — a mixed solid-liquid transition layer of the kind produced when a multicomponent alloy freezes — has been invoked and locally imaged at the ICB, but its relationship to the short-wavelength corrugations is not established. The result is a well-posed but unresolved problem at the interface of deep-Earth seismology and core dynamics.

Problem Statement

Determine the nature, geometry, and dynamics of short-wavelength (kilometer-scale wavelength) topography on Earth's inner-core boundary, as one jointly consistent seismological and geodynamical characterization. Specifically: (1) establish whether the observed decadal changes in inner-core-reflected and inner-core-grazing seismic phases — PKiKP amplitude and coda changes, and PKIKP waveform changes — are produced by advection of quasi-stationary short-wavelength ICB corrugations past the reflection points under inner-core differential rotation, by genuine time-dependent change of the boundary and shallow inner core (freezing and melting, convection, viscous deformation), or by a combination of both, and quantify the relative contributions; (2) determine the vertical amplitude, lateral wavelength spectrum, and lateral coherence of the corrugations, and establish how widely such features occur around the ICB, reconciling current relief estimates that span roughly 0.3-14 km; and (3) identify a geodynamical mechanism that can generate and sustain corrugations of the inferred scale and amplitude over decades against diffusive relaxation — such as small-scale convection in the top of the inner core, a mushy or slurry boundary layer (a mixed solid-liquid layer near the boundary, the slurry variant containing solid crystals suspended in liquid iron), or sufficiently high near-boundary viscosity — and derive from it self-consistent quantitative constraints on the viscosity at the top of the inner core and on the inner-core differential rotation rate. The three parts are physically interlinked: the advection-versus-time-dependence question is constrained by the corrugation amplitude, wavelength spectrum and sustaining mechanism, and constrains them in turn. The inferred topography and its time dependence must jointly explain the seismic observations (PKiKP amplitude and coda, and PKIKP/PKP(DF) waveform, coda and envelope constraints), and the proposed mechanism must be able to support the inferred topography under admissible core conditions.

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