Equatorial Paths Research Articles

Effects of upper mantle structure beneath Alaska on core-sensitive seismic wave absolute and differential measurements: Implications for estimates of inner core anisotropy

Inner core anisotropy is often studied using differential travel times between the inner core phase, PKPdf, and one of two outer core phases, either PKPbc or PKPab, to eliminate contamination by crust and upper mantle structure. In particular, given the similarity of the two ray paths in the shallow Earth, the PKPbc-df differential travel time is assumed to robustly reflect the structure of the inner core, and not be influenced by mantle structure. Measurements of PKPab-df and PKPbc-df differential times reveal that the inner core is anisotropic: PKPdf rays travel through the inner core ~3% faster along polar paths than along equatorial paths. Even so, measurements of both PKPbc-df and PKPab-df differential travel times on quasi-polar paths between sources in the South Sandwich Islands and stations in Alaska present greater scatter (6 s spread) than other equivalent quasi-polar paths from other parts of the globe (2 s spread). While the South Sandwich Islands to Alaska data help increase spatial sampling of the inner core, including these data in inner core models significantly increases estimates of average global inner core anisotropy strength, by more than 1%. Whether this reflects real spatial variability in the strength of inner core anisotropy or else results from complexity outside of the inner core is uncertain but is crucial for constraining the inner core composition and growth history. Using a regional tomographic model of the Alaskan upper mantle to predict upper mantle effects on PKP travel times, we show that the signature of the Alaska slab is present in trends of observed absolute PKPbc, ab, and df travel times, both as a function of distance and azimuth. Moreover, we demonstrate that the effect of the slab is not fully cancelled by differential measurements. This implies that past models of the inner core are biased towards too strong average anisotropy. In order to better constrain inner core anisotropy in future, differential measurements of core-phase travel times need to be more accurately corrected for upper mantle three-dimensional structure, which in turns requires the construction of higher resolution tomographic models.

On observation of local strong heterogeneity in the Earth’s inner core below southeastern Asia

The dimensions and nature of multi-scale structural heterogeneities in the Earth’s inner core (IC) provide important constraints on its mineralogy and formation history. Teleseismic body waves with turn points close to the inner core boundary (ICB) provide a unique tool for imaging the fine structure of the upper IC. In this study, we invoke differential travel times and amplitudes of PKPBC and PKPDF waveforms observed in crossing polar and equatorial paths to provide more constraints on the heterogeneity previously located in the quasi-eastern hemisphere of the IC (Kaazik et al., 2015; Krasnoshchekov et al., 2016). A more refined analysis of quasi-polar PKPBC/PKPDF amplitude ratios measured within the heterogeneity indicates that seismic attenuation is both frequency and depth dependent, and its relatively low Q-factor at 1Hz of approximately 118 tends to grow with depth. Outside the heterogeneity, no pronounced polar-equatorial differences are observed; the estimated Q factor is about twice as large and not directionally dependent. We also analyse new differential travel times of rays that enable sampling of the anomaly at greater depths. The analysis exhibits the polar – equatorial contrasts observed in the heterogeneity terminate at approximately 520km below the ICB, which we interpret to be its bottom. The earlier interpretation of the heterogeneity in terms of strong anisotropic volume amidst the almost isotropic eastern hemisphere of the IC can be retained, and the lower bound of anisotropy strength within the anomaly is determined to be 2%.

An anisotropic block in the inner core beneath Southeastern Asia

This work presents new experimental data on differential amplitudes and travel times tBC-tDF of the PKPDF and PKPBC seismic waves in the Earth’s core beneath Southeastern Asia. In the equatorial paths, this area has a higher (by approximately 0.3%) velocity of propagation of seismic waves than in the standard model ak135. The features of the travel time residuals in the polar path indicate the presence of a local block of 250 × 250 × 200 km in size, for which the velocity value depends on the direction of propagation of the P-wave and is higher by 1.4% than in the model ak135. Attenuation of seismic waves in this block also depends on the direction: it is two times higher for the polar direction than for the equatorial direction. These two factors indicate that this structure is characterized by features transverse isotropy, and anisotropy in the eastern hemisphere has a domain character.

One-dimensional modeling of multiple scattering in the upper inner core: Depth extent of a scattering region in the Eastern Hemisphere

Attenuation of PKP(DF) in the Eastern Hemisphere is examined in terms of multiple scattering to simultaneously explain a puzzling relationship, a relatively fast velocity anomaly corresponding to strong attenuation. Reflectivity synthetics with one-dimensional random velocity fluctuations are compared with observations of PKP(DF)/PKP(Cdiff) amplitude ratios and differential travel times of PKP(Cdiff)-PKP(DF) for the equatorial paths. A Gaussian distribution of P-wave velocity fluctuations with the standard deviations of 5%, 6%, and 7% in the uppermost 200 km of the inner core is superimposed on the velocity structure that is slightly faster than the typical structure in the Eastern Hemisphere, which is likely to explain both the travel time and amplitude data as far as only the one-dimensional structure is considered. Further examinations of the statistic characteristic of scatterer distribution in two and three-dimensions are required to obtain a realistic conclusion.

Depth extent of hemispherical inner core from PKP(DF) and PKP(Cdiff) for equatorial paths

Differential travel times and amplitude ratios of PKP(DF) and PKP(Cdiff) (partly including PKP(BC)) for equatorial paths at epicentral distances from 150° to 160° are examined to discuss the radial structure of the uppermost 500km of the inner core. By using seismograms with a predominant frequency of approximately 0.5Hz, 649 measurements are successfully collected, including 295 and 354 readings for the Eastern and Western hemispheres, respectively. Forward modeling with the reflectivity method suggests that the best-fit velocity structures in the Eastern and Western hemispheres are 0.5% faster and 0.9% slower, respectively, than an average structure at the inner core boundary (ICB), and that the velocity perturbations become linearly closer to the average with depth, finally coinciding with the average at 400km and 250km below the ICB, respectively, if ak135 is adopted for the structure above the ICB. In the Eastern hemisphere, the Q values in the uppermost 250km of the inner core and that in the range from 300 to 450km below the ICB are approximately 180 and 1000, respectively. In contrast, the Q value in the Western hemisphere is almost constant at approximately 300–400 in the uppermost 450km of the inner core.

Predictive mechanism for anisotropy development in the Earth's inner core

We present a model for the grain growth and deformation of the Earth's inner core that explains the dominant features of seismic velocity and attenuation anisotropy. At the surface of the inner core, the dominant deformation mechanism is diffusion creep. Grain growth continues via grain-boundary migration recrystallization such that, depending upon the magnitude of stress and grain size, dislocation-controlled creep dominates in as little as 1–2 m or as much as ~ 100 km below the crystallization horizon. Subsequent dislocation link climb leads to the development and maintenance of lattice-preferred orientation (LPO) increasing seismic velocity anisotropy with depth. The model predicts an inner core viscosity of 10 20–22 Pa-s deforming in a regime with a deviatoric stress of 10 3–4 Pa, consistent with an inner core anisotropic growth model. We provide explanations for the development of shape-preferred orientation of grains elongated in the equatorial direction in the context of the fast direction of seismic waves correlating to the direction with the greatest attenuation. We predict high attenuation at the top of the inner core, decreasing with depth, with an attenuation that is 30% greater along polar paths than for equatorial paths through the center of the Earth.

Inner core structure: Constraints from frequency dependent seismic anisotropy

Seismic waves sampling the inner core have revealed that it is anisotropic, propagation being faster and attenuation stronger for waves travelling parallel to the Earth's rotation axis, relative to those parallel to the equatorial plane. Here, the anisotropy in attenuation is investigated in the frequency range 0.2–2 Hz, in a region of the uppermost inner core sampled by rays of various orientations. A spectacular amplitude decay with frequency is observed for polar paths whereas it is very mild for equatorial paths, leading to a much stronger anisotropy at high frequency than at low frequency. A velocity dispersion is also observed for polar paths, with a propagation faster at high frequency than at low frequency. These observations may provide important constraints on the texture of the inner core, and help to better understand its growth mechanism.

Complex seismic anisotropy in the top of the Earth's inner core beneath Africa

We report complex seismic anisotropy in the top 80 km of the Earth's inner core beneath Africa. The anisotropy in the top 80 km of the inner core is constrained using differential travel times, amplitude ratios, and waveforms of the PKiKP‐PKIKP phases sampling Africa along various directions. The differential PKiKP‐PKIKP time residuals (relative to the Preliminary Reference Earth Model [PREM]) along the polar paths are larger than those along the equatorial paths by 0–1.4 s, indicating the presence of seismic anisotropy in the top 80 km of the inner core. Furthermore, the observations along the polar paths show complex regional variations beneath Africa: the differential PKiKP‐PKIKP travel time residuals vary from 1.2 s beneath eastern Africa, to −0.1 s beneath central Africa, and to −0.2 to 0.8 s beneath western Africa. A correlation between small PKIKP/PKiKP amplitude ratios and large differential PKiKP‐PKIKP travel time residuals is observed. The waveform data are spatially binned into six groups to constrain the regional dependence of velocity and attenuation anisotropy in the top 80 km of the inner core. Overall, the seismic data can be explained by an isotropic upper inner core (UIC) overlying an anisotropic lower inner core (LIC) in the top 80 km of the inner core across Africa. The thickness of the isotropic UIC varies from 0 to 50 km, and the P velocity transition from the isotropic UIC to the anisotropic LIC is sharp, with velocity increases laterally varying from 1.6% to 2.2%. The attenuation structure along the polar paths has a Q value of 600 for the isotropic UIC and Q values varying from 150 to 400 for the anisotropic LIC. The complex seismic anisotropy in the top of the inner core is found in a region where a rapid change of the inner core boundary (ICB) between 1993 and 2003 was discovered (Wen, 2006) and may be explained by complex alignments of iron crystals, resulting from a localized anomalous solidification of the inner core.

Seismic velocity and attenuation structures in the top 400 km of the Earth's inner core along equatorial paths

We study seismic velocity and attenuation structures in the top 400 km of the Earth's inner core based on modeling of differential traveltimes, amplitude ratios, and waveforms of the PKiKP‐PKIKP phases observed at the epicentral distance range of 120°–141° and the PKPbc‐PKIKP phases observed at the distance range of 146°–160° along equatorial paths. Our data are selected from the seismograms recorded in the Global Seismographic Network from 1990 to 2001 and many regional seismic networks. The observed PKiKP‐PKIKP and PKPbc‐PKIKP phases exhibit distinctive “east‐west” hemispheric patterns: (1) At the distance ranges of 131°–141° and 146°–151°, PKIKP phases arrive about 0.3 s earlier than the theoretical arrivals based on the Preliminary Reference Earth Model (PREM) for the PKIKP phases sampling the “eastern hemisphere” (40°E–180°E) of the inner core and about 0.4 s later for those sampling the “western hemisphere” (180°W–40°E). At the distance range of 151°–160°, PKIKP phases arrive about 0.7 s earlier than the predicted arrivals based on PREM for those sampling the eastern hemisphere and about 0.1 s later for those sampling the western hemisphere. (2) Amplitude ratios of the PKIKP/PKiKP phases at the distance range of 131°–141° and of the PKIKP/PKPbc phases at the distance range of 146°–151° are, in general, smaller for the PKIKP phases sampling the eastern hemisphere than for those sampling the western hemisphere. At distances greater than 151°, the PKIKP/PKPbc amplitude ratios become indistinguishable for the two hemispheres. These observations can be best explained by two different types of seismic velocity and attenuation models along equatorial paths, one for each hemisphere, in the top 400 km of the inner core. For the eastern hemisphere, the velocity structure has a velocity increase of 0.748 km/s across the inner core boundary (ICB), a small velocity gradient of 0.0042 (km/s)/100 km in the top 235 km, followed by a steeper velocity gradient of 0.1 (km/s)/100 km extending from 235 km to 375 km, and a velocity gradient of 0.01 (km/s)/100 km in the deeper portion of the inner core; the attenuation structure has an average Q value of 300 in the top 300 km and an average Q value of 600 in the deeper portion of the inner core. For the western hemisphere, the velocity structure has a velocity increase of 0.645 km/s across the ICB and a velocity gradient of 0.049 (km/s)/100 km in the top 375 km; the attenuation structure has an average Q value of 600 in the top 375 km of the inner core. Our results suggest that the inner core hemispheric variations in velocity extend deeper than 375 km below the ICB and the top 235 km of the inner core in the eastern hemisphere is anomalous compared to the rest of the inner core in having a small velocity gradient, high velocity, and high attenuation.

Seismic velocity structure in the Earth's outer core

We constrain seismic velocity structure in the Earth's outer core by analyzing differential travel times, waveforms, and amplitude ratios of several pairs of core phases. We use differential travel times and waveforms of PKPbc‐PKIKP at 144°–148°, PKiKP‐PKIKP at 120°–141°, PKiKP‐PKPBdiff at the PKP caustics distance range (141°–145°), and differential travel times and amplitude ratios of PKPab‐PKPbc at 146°–159°. To avoid the influence of the inner core anisotropy in velocity, we only use the PKiKP‐PKIKP and the PKPbc‐PKIKP observations whose PKIKP phases sample the inner core along the equatorial paths (paths with their ray angles being larger than 35° from the Earth's rotation axis). These observations show the following characteristics: (1) both the observed PKPbc‐PKIKP and PKiKP‐PKIKP differential travel times show a distinct “east‐west” hemispheric pattern. PKIKP phases arrive about 0.7 s earlier for those sampling the “eastern” hemisphere (40°E–180°E) than those sampling the “western” hemisphere (180°W–40°E); (2) the observed differential PKiKP‐PKPBdiff travel time residuals also exhibit a hemispheric difference. PKiKP‐PKPBdiff differential travel times are about 0.9 s larger for those sampling the western hemisphere than those sampling the eastern hemisphere; and (3) both the observed PKPab‐PKPbc differential travel times and PKPbc/PKPab amplitude ratios show scatter. Overall, these observations can be best explained by two one‐dimensional P velocity models, one for each hemisphere, at the bottom of the outer core. The seismic data sampling the eastern hemisphere can be explained by PREM at the bottom of the outer core, while those sampling the western hemisphere can be explained by a lower velocity gradient at the bottom of the outer core, which has reduced velocities relative to PREM linearly increasing from 0% at 200 km above the inner core boundary (ICB) to −0.35% at the ICB. Different velocity gradients at the bottom of the outer core indicate that there may exist a compositional difference and/or a large‐scale temperature difference there and that inner core formation processes may be different between the two hemispheres. Different inner core formation processes may produce different geometric inclusions of melt in the top of the inner core, and thus may provide an explanation to the hemispheric variation of seismic velocity and attenuation in the top of the inner core. The seismic data also suggest that the variation of seismic velocity in the tangential cylinder of the outer core, if it exists, is less than 0.1%. We use a compressional wave tomographic model to study the travel time delays caused by the seismic heterogeneities in the mantle. The tomographic model is unable to explain the scatter of the travel time data, suggesting the existence of unknown strong small‐scale seismic heterogeneities in the mantle.

Frequency‐dependent seismic attenuation in the inner core 2. A scattering and fabric interpretation

Broadband velocity waveforms of PKIKP in the distance range 150–180° are inverted for a model of inner core attenuation due to forward scattering by a three‐dimensional heterogeneous fabric. A mean velocity perturbation of 8.4 ± 1.8% and a scale length of heterogeneity of 9.8 ± 2.4 km are determined from 262 available PKIKP ray paths. The velocity perturbations are larger for polar than for equatorial paths, decrease with depth, and show anisotropy in both global and regional data. For paths beneath North America, the smallest scale lengths (1–5 km) tend to lie in either the upper 200 km of the inner core or along paths close to the rotational axis. The depth dependence of attenuation is roughly similar to that obtained assuming a viscoelastic origin, except a more abrupt transition is seen between higher attenuation in the upper inner core and lower attenuation in the lower inner core. This transition may be sharp enough to produce either a first‐ or second‐order discontinuity with depth in the long‐wavelength (composite) elastic moduli. A fabric that satisfies the observed depth dependence and anisotropy of attenuation requires solidification of iron crystals having high (>10%) intrinsic anisotropy, which are preferentially aligned in time and depth. Since weak velocity dispersion, elastic anisotropy, attenuation anisotropy, and their depth dependence agree with that predicted by such a fabric, we suggest that scattering attenuation is not a small fraction but, rather, the predominant mechanism of attenuation in the inner core in the 0.02–2‐Hz frequency band.

Seismic anisotropy in the top 400 km of the inner core beneath the “eastern” hemisphere

Depth variation in seismic anisotropy at the top 400 km of the inner core beneath the “eastern” hemisphere is investigated by comparing the differential travel times of PKP phases recorded at distances from 127° to 160°. At distances less than about 150°, there is no noticeable difference in differential travel times for PKP phases sampling both the polar and the equatorial paths. At greater distances, however, PKIKP phases arrive systematically earlier (about 0 ∼ 0.5 second) in the polar path than in the equatorial path. These observations suggest that, in the “eastern” hemisphere, seismic anisotropy exists only in depths greater than about 200 km below the inner core boundary (ICB) with seismic velocities along the polar paths (an average of 27.6° from the earth's spin axis) being 0.4% faster than those along the equatorial paths.

PKP travel times at near antipodal distances: implications for inner core anisotropy and lowermost mantle structure

Previous studies from PKP(AB–DF) differential travel times at large distances suggest that the central part of the inner core is very anisotropic. These differential times, however, can be affected greatly by strong heterogeneity in the lowermost mantle. Here we examine a unique data set of PKP travel times from global digital and analog stations at near antipodal distances, where the effects of both inner core anisotropy and mantle heterogeneity are the greatest. Our results show that the AB–DF residuals for the polar paths are consistently larger than those of the equatorial paths by over 3–4 standard deviations. We also measured DF and AB absolute times, and found that the DF residuals are negatively correlated with the AB–DF residuals while the AB residuals have a much weaker correlation with the AB–DF residuals. We compare several mantle models with the data. Our results suggest that the mantle structure can explain part of the residuals of the equatorials paths, but cannot explain the polar path anomalies. These results strongly suggest that most of the AB–DF anomalies for the polar paths are likely from the inner core anisotropy and not from mantle heterogeneity. Assuming a uniform cylindrical anisotropy model, the average inner core anisotropy amplitude is about 2.5%. On the other hand, equatorial paths from events in the west Pacific and recorded at South America show a steep azimuthal change in AB–DF times (about 4 s over a 60° azimuthal range). The sharp change is well predicted by existing P and S tomographic models: the azimuthal change occurs as the AB paths sweep across the great slow anomaly in the central Pacific. The high correlation between the P and S velocities suggests that the central Pacific slow anomaly may be of thermal origin.

Inner core anisotropy and heterogeneity level

An analysis of core phase travel times is performed in order to estimate the relative contributions of heterogeneities and anisotropy and their distribution inside the inner core. A stochastic analysis performed on the equatorial paths, which are poorly sensitive to anisotropy, indicates that the inner core exhibits a heterogeneity level smaller than 0.3% at all depths on scale lengths larger than 200 km. This result, extended to all path orientations, suggests a predominant effect of the anisotropy on travel times anomalies. A simultaneous inversion of absolute and differential core phase travel times for any path orientation favours a simple inner core model in which a large, homogeneous structure with 3% uniform anisotropy is asymmetrically surrounded by a homogeneous isotropic layer with a thickness of 100–200 km on the western hemisphere, increasing to 400 km over a large part of the eastern hemisphere.

Seismic attenuation of the inner core: Viscoelastic or stratigraphic?

Broadband velocity waveforms of PKIKP in the distance range 150° to 180° are inverted for inner core attenuation. A mean Qα of 244 is determined at 1 Hz from 8 polar and 9 equatorial paths. The scatter in measured Q−1 exceeds individual error estimates, suggesting significant variation in attenuation with path. These results are interpreted by (1) viscoelasticity, in which the relaxation spectrum has a low‐frequency corner near or slightly above the frequency band of short‐period body waves, and by (2) stratigraphic (scattering) attenuation, in which attenuation and pulse broadening are caused by the interference of scattered multiples in a velocity structure having rapid fluctuations along a PKIKP path. In the scattering interpretation, PKIKP attenuation is only weakly affected by the intrinsic shear attenuation measured in the free‐oscillation band. Instead, its frequency dependence, path variations, and fluctuations are all explained by scattering attenuation in a heterogeneous fabric resulting from solidification texturing of intrinsically anisotropic iron. The requisite fabric may consist of either single or ordered groups of crystals with P velocity differences of at least 5% and as much as 12% between two crystallographic axes at scale lengths of 0.5 to 2 km in the direction parallel to the axis of rotation and longer in the cylindrically radial direction, perpendicular to the axis of rotation.

Anisotropy in inner core attenuation: A new type of data to constrain the nature of the solid core

During the last decade, the presence of velocity anisotropy inside the inner core, with a fast axis parallel to the Earth's rotation axis, has been well established. The quantitative analysis of the amplitudes of waves which sample a particular region of the inner core, under Africa, but exhibit various orientations allows us to document and characterize the presence of anisotropy in attenuation. The analysis is based on a comparison of both amplitudes and travel times of the PKP(DF) wave, which samples the inner core, and the PKP(BC) wave, which has nearly the same path but bottoms inside the liquid core. The data reveal that the direction of strong attenuation correlates with that of fast velocity. When referred to the same epicentral distance and focal depth, the PKP(DF)/PKP(BC) amplitude ratio are about five times lower for paths tilted by 25° with respect to the Earth rotation axis, than for nearly equatorial paths. A clear negative correlation is observed between travel time and amplitude residuals, when the angle to Earth rotation axis varies. This first quantitative analysis, combined with experimental results on oriented crystals and mushy media, may bring important constraints on the mechanism responsible for anisotropy in the inner core.

Anisotropy in the center of the inner core

We have assembled a collection of PKP data from broadband records of the Geoscope network. This collection is unique because, for the first time, it includes polar paths at epicentral distances between 172° and 177°, for which PKPDF samples the central part of the inner core. After Hilbert transforming the DF branch, the waveforms of PKPAB and PKPDF usually become very similar, and we measure differential travel times with an accuracy of a fraction of a second. The differential (AB‐DF) times for equatorial paths are close to those predicted by PREM, whereas for the polar paths, they are larger by 3 to 6 sec. Absolute DF times confirm that the effect is primarily in the inner core. These observations are compatible with a model of cylindrical anisotropy in the inner core with the axis of symmetry aligned with the Earth's spin axis and an amplitude of 3.5%. They require that the anisotropy extend to the central part of the inner core, confirming extrapolations made by Creager (1992) and ruling out models where anisotropy is confined to the outer 300 km of the inner core (Tromp, 1993).

Anisotropy of Earth's inner core

In an effort to confirm inner core anisotropy, we conducted a systematic search for PKP ray paths with various angles from the Earth's spin axis. In particular, we studied paths nearly parallel to the spin axis (polar paths) and those nearly parallel to the equatorial plane (equatorial paths). Data for earthquakes and explosions were collected from Worldwide Standardized Seismograph Network (WWSSN), Long Range Seismic Measurements (LRSM), and Global Digital Seismograph Network (GDSN). Absolute times (DF, BC) and differential times (BC‐DF, AB‐DF) as well as waveform data were examined. For all polar paths, differential times of BC‐DF consistently yield residuals of 1.5 to 3.5s larger than equatorial paths. Absolute DF time residuals exhibit anomalies of the same magnitude (1 to 4s) with DF being early along polar paths while BC residuals have no obvious correlation with the differential time anomalies. DF phases appear multi‐pathed for polar paths and are relatively simple for equatorial paths. These results coupled with previous studies suggest an axisymmetric anisotropy at the top of the inner core.

Hydrogen trajectories in alkene-to-carbene rearrangements. Unequal deuterium isotope effects for the axial and equatorial paths

The rearrangement of alkenes to carbenes yields deuterium isotope effects upon irradiation for the axial and equatorial paths. This study has focused on the migration trajectory that accompanies the rearrangement. 15 refs.

Splitting of normal modes and travel time anomalies due to the magnetic field of the Earth

We examine the effects of a toroidal magnetic field on two types of seismic data: first, on splitting of normal modes and, second, on body wave travel times. The main contribution of this paper is the derivation of formulas for these problems. Comparison between data and theory indicates that the magnitude of the toroidal magnetic field (T20) has to be as large as 250 T (tesla) to explain the data. There are, however, some inconsistencies among the fit to the data set. For example, some modes require a strong magnetic field near the core mantle boundary, while other modes require a weak field. Also the travel time difference between polar and equatorial paths is not explained by the T10 or T20 field. A field with odd angular degree 𝓁 (T𝓁0 or S𝓁0) is needed to produce the travel time difference between the polar and equatorial paths. We also point out that ohmic dissipation due to a strong magnetic field with 100 T is about 4–5 orders of magnitude larger than the present heat flow output of the Earth. The analysis suggests that the magnetic field in the outer core is not the cause of seismic anomalies.