Inner Core Research Articles

Topography of Earth's inner core boundary from high-quality waveform doublets

Precise determination of the topography of a major internal boundary of the Earth is difficult because of the trade-off with the unknown velocity structure above it. However, the discoveries of the inner core (IC) rotation and high-quality teleseismic waveform doublets make the precise mapping of the topography of the inner core boundary (ICB) possible. Here we examine IC refracted (PKP-DF) and reflected (PKP-CD) waves recorded at the Yellowknife Array and other global stations from 14 high-quality doublets, among a large collection of doublets in S. Sandwich Islands that are recently discovered. Our results show clear evidence for spatial and temporal variations of IC reflections in traveltimes and in waveforms. If the time separation (dT) between the two members of the doublet is less than 3 yr, the IC arrivals show little temporal change in traveltimes or waveforms. If dT is greater than about 6 yr, some doublets show large variations but some others do not. The ICB regions beneath Atlantic and Indian Oceans show little temporal change. The regions that show large variations are beneath Africa and the Central America, which coincide with large seismic anomalies at the core–mantle boundary (CMB). Inside these two ICB regions, there are fine-scale (km scale) variations. The largest temporal changes of IC reflections are about 0.10 to 0.14 s, corresponding to a topographic variation of up to about 3.7 to 5.2 km. The results suggest ICB topography of a few kilometres on fine to regional scales. The geographical coincidence of the ICB and CMB anomalies may suggest strong thermal coupling of the mantle and the core. Dynamic models include a bumpy ICB rotating with the IC itself or a transient slurry boundary containing a mixture of molten materials and solidified patches of iron crystals, which is rapidly modified by the turbulence at the base of the convecting outer core. If the former is the main cause of the observed temporal change of the topography, the IC rotation is required to be an oscillation, whose half period has an upper limit of a few hundred years.

THE INNER CORE OF ACUPUNCTURE

THE INNER CORE OF ACUPUNCTURE

Using PKiKP coda to determine inner core structure: 2. Determination of QC

Despite the similar and rather uniform composition of two components of the core, the solid inner part presents a much larger attenuation compared to the liquid outer part. More over, several authors have reported evidence of scattered seismic energy coming from the inner core (IC). This implies that the IC has lateral variations in structure or composition with a scale length from one to tens of kilometers. These seismic scatterers could be caused by changes in crystal grain size, variations in the orientation of anisotropy, or the presence of partial melt and/or impurities. This work pursues the characterization of inner core scattering (ICS) using a global data set of high‐frequency PKiKP waveforms recorded at short‐period, small‐aperture seismic arrays. We apply a methodology used in the study of heterogeneities in the crust and upper mantle that consists of curve fitting of the observed scattered energy with a standard model, along with a stripping technique to isolate the PKiKP coda from the rest (e.g., P, PcP, and PP codas). From the observed PKiKP codas we found an average QC ∼ 500 for the inner core, reflecting a scattering attenuation at least comparable to the intrinsic attenuation. We found a geographical dependence in the observations of PKiKP coda, with most of them coming from the Pacific Ocean and Asia, and relatively few observations coming from the Atlantic Ocean. The simplest explanation is that the ICS has a quasi‐hemispherical variation, similar to other properties such as P wave velocity jump at the inner core boundary, attenuation in the upper IC, strength of anisotropy and/or thickness of an overlaying isotropic layer. This phenomenon is probably related to the solidification texturing of iron crystals, showing hemispherical differences in the growth of the inner core.

Using PKiKP coda to determine inner core structure: 1. Synthesis of coda envelopes using single‐scattering theories

Previous seismic studies have reported evidence of scattered seismic energy coming from the inner core (IC). This implies that the IC has lateral variations in structure or composition with a scale length of tens of kilometers. In the present study, we focus on synthesizing the coda following precritical PKiKP and try to determine the location of the heterogeneities that produce this coda, using previously reported observations as a guide. Using a single‐scattering approximation and ray theory, we generate synthetic PKiKP coda envelopes from six distinctive places inside the Earth: within the lower mantle on the source and receiver side, along the core‐mantle boundary on the source and receiver side, along the inner core boundary, and within the inner core. We use two approaches to generate synthetic coda from topography on a boundary surface and one that is appropriate for volumetric scattering. In our computations we calculate the arrival time, ray parameter, and amplitude of the seismic waves and take into account errors in the back azimuth, as well as source and receiver effects. We find that previously reported “spindle”‐shaped or growing coda can only be produced from volumetric heterogeneities located in the shallowest 350 km of the IC; however, strong trade‐offs between the different parameters describing the volumetric heterogeneities (i.e., characteristic wavelengths, RMS velocity or impedance contrast, and total volume) preclude the determination of a unique model. Additionally, we find that reasonable models of topography at the core‐mantle boundary can produce large variations of the PKiKP amplitude due to focusing and defocusing effects. Therefore complexity at the inner core boundary is not necessarily required to account for dramatic amplitude variations in the direct PKiKP amplitudes.

Magnetization dynamics in wire-shaped amorphous magnetic materials as probed by Barkhausen noise measurement

Magnetic Barkhausen noise and hysteresis loops have been measured in the presence of various tensile stresses from three wire-shaped amorphous magnetic materials having different domain structures. Long duration large Barkhausen pulse indicates the presence of an inner core (IC) domain in positive magnetostrictive glass-coated Co83.2Mn7.6Si5.8B3.3 and Co58.59Fe4.41Ni10Si11B16 microwires where magnetization takes place by ∼180° rotation of domain magnetization. This long duration Barkhausen pulse is missing in the case of low negative magnetostrictive Co68.1Fe4.4Si12.5B15 wire indicating a negligible volume of IC domain in it. Short duration pulses observed in all three samples suggest the presence of a multi-domain outer shell where small angle rotation and domain wall displacement are responsible for the magnetization process. The shapes of the hysteresis loops support the Barkhausen noise studies.

Attenuation in the uppermost inner core from PKP recordings at African seismological stations

The attenuation factor QP at the top of the inner core is evaluated by using the amplitude spectral ratio of PKPdf and PKPbc phases observed at African stations (BGCA mostly), from strong deep earthquakes in the Pacific Ocean area. The maximum depth of penetration of the PKPdf phase into the inner core (IC) is roughly 377 km, and the sampled region of IC is centered beneath the Southern Indian Ocean. The derived mean value of QP is 249 ± 31 (95% confidence level) in the frequency range 0.2–2 Hz, where no frequency dependence of attenuation has been reliably observed. By using Student’s t-test, we show that the value is statistically significantly different (with a probability greater than 95%) from other mean values of Q derived by using the same method, for both the western (180 °W to 40 °E) and eastern (40 °E to 180 °E) hemispheres of the IC. The decrease of Q with the radius of the turning point (denoted by rTP), according to QP = 840 − 0.62 rTP, has a moderate statistical support (the R-squared value is 38%). A slightly increase of Q as a function of the angle of the PKPdf path within the inner core with respect to the Earth’s spin axis is observed, in agreement with various investigations performed in the time domain. However, the value of the anisotropy, if any, is suggested to be around 3%.

Uppermost inner core attenuation from PKP data observed at some South American seismological stations

SUMMARY QP factor at the top of the inner core (IC) is derived using the amplitude spectral ratio (PKPbc versus PKPdf) method applied to the waveforms of suitable, strong (magnitude >6.0) intermediate depth and deep (h > 150 km) earthquakes recorded at some selected South American stations. In most cases, the sampled volume of the IC is centred beneath the Pacific Ocean, but some QP values correspond to volumes under South Africa and under Northern Atlantic. The obtained value of QP is 323 ± 16 (at 95 per cent confidence level), close to a normal (Gaussian) distribution. The maximum depth of penetration of the PKPdf phase into the IC is roughly 333 km, suggesting a possible increase of QP with depth, although the large scatter in data prevents a definite conclusion. As regards the geographical patterns no variation was observed.

On the lack of seismic discontinuities within the inner core

Recent work has suggested that seismic discontinuities might exist within the inner core (IC). Such boundaries could be caused by changes in the strength and orientation of anisotropy, by variations in the fraction of partial melt or by a solid—solid phase transition involving iron. In this work, we search for evidence of IC discontinuities with reflection seismology techniques that use precritical PKiKP waveforms as empirical source pulses. Because any phase reflected from an IC discontinuity will have a small amplitude, we develop a technique combining source and receiver stacks in the search. We perform resolution tests where we compare the data with synthetic waveform stacks created using generalized ray theory and appropriate attenuation operators. Our results show that the IC lacks a significant (impedance jump >3 per cent), sharp (thickness <3–4 km), global discontinuity to depths of 800 km below the boundary with the outer core.

The Louisiana Purchase, Expansion, and the Limits of Community: The Example of Arkansas

GIVEN THAT THE GREAT INNER CORE of the North American continent, called for a recent moment of its long history the Louisiana Purchase, has been for the past two centuries one of the most exploited spots on the face of the earth-chopped, sprayed, drained, filled, stripped, and ripped to the full limit of the human capacity to do these things-one hesitates to disturb it yet again. But this will be a relatively benign disturbance, limited in space and time to the small part of it that became the Arkansas Territory, harmless to the area and yet useful, one hopes, to our understanding of an important aspect of the American republican experiment. The plan here is to try to learn something about a very grand subject-the theory and practice of republicanism-through a case study of a rather modest area. To begin with the grand: part of the general restructuring necessary to the emergence of modern Western societies was both a reconception and a redefinition of the concept of community. Kinship linkings, the necessarily quite local standard that had served for centuries to define community, had to be supplemented by a standard that would allow for the creation of much larger communities. Community now pushed far beyond family connections. This created problems everywhere, but some of the most interesting ones appeared in the British colonial system. There, through a naturalization procedure authorized by Parliament in the late colonial period, persons routinely excluded from other colonial systems could find their way into that of Great Britain (a subject of the King of France, by contrast, would find a home in the dominions of the King of Spain only under exceptional circumstances).1 As a consequence, English North America by the time of the independence movement had become a place of striking heterogeneity. Among other things, this would mean that the most common way of defining a national community, which was, fundamentally, to rely upon the webbing of a long historical homogeneity, would not work. Complicating things even was the heavy reliance upon republican theory. In a traditional European setting, the relationship between members of a national community was not too pressing a matter, for all were tied together through a common relationship to their sovereign. But as the resistance movement in English North America came to rely and heavily upon republican concepts, to the point of rejecting outright the very notion of the monarch as the link between all members of the national community, it became and necessary to define the relationship of those members in a new way: not to a monarch but to each other. This, it should be noted, was not just a matter of interest to political philosophers (although in that remarkably philosophic age that would not have made it a preoccupation as peripheral as it would in our own). Concern with the communal relationship is present in the great document of separation, the Declaration of Independence, though it is, for most readers, lost under the attack upon the king. In the Declaration's penultimate paragraph-a place of prime significance in eighteenth-century writing-Thomas Jefferson turned from the British king to the British people, declaring their apathy toward the plight of their transatlantic brethren to be a collective forfeit of the bond of community.2 But to recognize the need for a new concept of community was not to define it. To that problem, a complicated solution emerged. Clearly, only the individual colonies could come anywhere near to being the imagined of modern nationalism.3 As such, they would obviously remain, renamed as states. But other forces-the existence of a common enemy, the prospect of postwar dismemberment, the need for a unified economic system-at once exposed the need for a larger community and strengthened the basis for one. The result was the Constitutional Convention and the more perfect Union of 1787, within which, and under a redefined federalism, state and national communities would presumably enjoy a harmonious, synchronized existence. …

Table of Contents

Abstract Hesselbein + Company FRANCES HESSELBEIN THE SEARCH FOR COMMON GROUND Redefining what we do against a new appreciation of why we do what we do. SAM T. MANOOGIAN MAINTAINING YOUR FOCUS How to find time to deal with the critical issues that can make or break you. MARSHALL GOLDSMITH TRY FEEDFORWARD INSTEAD OF FEEDBACK Focus on the promise of the future rather than the mistakes of the past. CHARLES W. ROBINSON BACK TO REALITY Leaders need to rethink attitudes and change approaches. Executive Forum LARRY BOSSIDY THE DISCIPLINE OF GETTING THINGS DONE Leaders who do not pay attention to how their companies get things done are running companies that don't do things well. DANIEL GOLEMAN LEADING RESONANT TEAMS How leaders can release energy in their teams so that everyone can focus on getting the job done. JAMES CHAMPY BUILDING TRUST BETWEEN LEADERS AND CAPITAL MARKETS Increasing demands for financial transparency are creating new challenges for leaders. GERVASE R. BUSHE THE INNER CORE OF LEADERSHIP Leaders need to balance deep human needs. RAY SMILOR LEADERSHIP LESSONS FROM EMPLOYEE‐OWNED COMPANIES How to create organizational citizens. From the Front Lines GLOBAL TEAMS PEOPLE COUNT MORE THAN STRUCTURE Getting the informal relationships right is tougher than aligning the structure—and more important. COMPETITIVE ADVANTAGE SIX KEYS TO INTELLIGENT PARTNERING A smart partner is worth as much as or more than a smart system. NEW PARADIGMS INNOVATIVE FORMS OF ORGANIZATION Companies that seek to lead in innovation need to look beyond the R&amp;D lab. THE RESILIENT LEADER FALL DOWN SIX TIMES, GET UP SEVEN How to thrive in perilous and unpredictable times.

Variations in length of day and inner core differential rotation from gravitational coupling

Gravitational coupling between the inner core (IC) and mantle exchanges angular momentum between them and causes variations in the length of day (LOD) and the IC differential rotation. We simulate the coupled rotation of a triaxial ellipsoidal Earth — IC, outer core (OC) and mantle — using gravitational and pressure coupling torques and integrate the angular momentum equations in the time domain. The IC differential rotation is found directly from the resulting time series, whereas LOD oscillations are determined from a spectral analysis of the mantle rotation. The LOD oscillation period depends on the choice of triaxiality model for the IC, and varies between 4 and 18 years. We show that a previous formulation of this problem, in which the IC rotates about a fixed axis, is a special case of the present approach which adopts a general rotation allowing both axial rotation and wobble-nutation motions. The differences in the IC gravitational torque between the two formulations are that there is only one torque term in the simple rotation while there are two terms (called p-related and q-related torques) in the general rotation. It is found that the q-related torque corresponds to that in the case of simple rotation, and the p-related torque can be larger than the q-related torque. We also find that a differential rotation of the IC with respect to the mantle, caused by the gravitational torque, is controlled by the IC obliquity. Although it is unlikely that the gravitational torque alone creates a super rotation similar to that reported from some of the recent seismic observations, the gravitational torque effect should probably not be neglected. A few degrees in the IC obliquity produces an IC differential rotation larger than that suggested by seismology, implying that the figure axis of the IC probably deviates from that of the mantle by less than 1°. If that is correct, it may suggest that the IC anisotropy axis is not aligned with the IC figure axis (a difficult and unresolved issue), since it is observed from conventional seismology that the former deviates from the earth's rotation axis by 5–10°. One of the advantages of our time domain approach is that the problems of LOD, IC differential rotation, and wobble-nutation can be investigated consistently. Triaxiality of the earth (in particular, the IC) is necessary to produce axial gravitational torques between the IC and mantle, and hence LOD variations and IC differential rotation, but triaxiality does not change the periods of wobble-nutation modes obtained in previous studies for small obliquities ≪1°.

The coupled rotation of the inner core

SUMMARY The rotation of the inner core (IC) is influenced by the rest of the Earth through a number of coupling mechanisms. Among four possible coupling mechanisms, gravitational, pressure, viscous and electromagnetic, the first two torques are dominant. Numerous existing IC gravitational torque estimates have been shown to agree very well with one another (Xu & Szeto 1996). It is shown in this paper that diVerent estimates of the IC pressure torque are also in good agreement.

The Earth's inner core and the geodynamo: Determining their roles in the Earth's history

Inge Lehmann, the Danish seismologist who died recently at the age of 105, deduced nearly 60 years ago that the Earth has a solid inner core (IC). Interest in the IC has continued since then with particular focus on the role it may play in the generation and maintenance of the Earth's magnetic field. A fundamental question concerning the Earth's magnetic field is what drives the geodynamo. The two main contenders are thermal convection and compositional convection. Braginsky [1963] suggested that freezing of material at the inner core boundary (ICB) would separate a heavy fraction (mainly Fe) leaving behind a lighter liquid fraction in the outer core (OC) that would be buoyant leading to compositionally driven convection. Since then it has generally come to be accepted that gravitational convection dominates over thermal convection in the OC.

The effects of the solid inner core and nonhydrostatic structure on the Earth's forced nutations and Earth tides

Recent highly accurate nutation results from very long baseline interferometry (VLBI) disagree with the 1980 International Astronomical Union (IAU) nutation model by about 2 milliarcseconds (mas). Most of the discrepancy is at the retrograde annual frequency, and it has been interpreted as being due to a nonhydrostatic core‐mantle boundary (CMB) ellipticity [Gwinn et al., 1986]. The ellipticity affects the eigenfrequency of the free core nutation (FCN) normal mode, predominantly a relative rotation about an equatorial axis between the fluid outer core (OC) and the solid mantle. This interpretation in terms of a nonhydrostatic CMB shape is consistent with inferences from diurnal tidal gravity measurements [Levine et al., 1986; Neuberg et al., 1987]. The theory that this interpretation is based on assumes that the inner core (IC)is a fluid. Furthermore, the Earth is presumed to be everywhere hydrostatically prestressed, and so it is inconsistent to use results from this theory to infer information about nonhydrostatic structure. In this paper, we extend the theoretical results to include the effects of a solid IC, and of nonhydrostatic structure. The presence of the IC is responsible for a new, nearly diurnal, prograde normal mode (for a hydrostatically prestressed Earth, the frequency is (1 – 1/471) cycles per day) that involves a relative rotation between the IC and OC about an equatorial axis. We call this newly modeled normal mode the free inner core nutation (FICN). The FICN causes a perturbation in the prograde semiannual nutation amplitude of close to 0.2 mas, but the contribution to the retrograde annual nutation is only 0.003 mas, not enough to explain the VLBI discrepancy. Its effects on the diurnal Earth tide are negligible. Nonhydrostatic structure affects the eigenfrequency of this mode and causes the nutation and Earth tide amplitudes to depend on IC‐OC boundary, CMB, and outer surface topography at all spatial scales. The dependence, though, falls off as the (l ‐ 1)th power of the ratio of the IC radius divided by the OC radius, for the simplified case of a homogeneous, rigid IC and mantle, and homogeneous, incompressible OC (l, here, is the angular order in the spherical harmonic expansion of the boundary shape). For small l, nonhydrostatic effects on the FICN are of the same order as hydrostatic effects for this specialized case. Neither the IC nor the nonhydrostatic terms significantly affect the conclusions about the values of the CMB ellipticity.

Dynamics of a fluid core with inward growing boundaries

In both physical and mathematical models of the Earth's core it has been difficult, so far, to discuss all the terms in the magneto-hydrodynamic energy equation under one unifying theory and to relate all the physical mechanisms involved in a specific model. The reason for this is mainly the uncertainty about the energy sources, or, when they could be accounted for, with uncertainty about their location. In the following article we deduce and examine a model of the Earth's core which can be regarded as a sequel to theories of the formation of a fluid core in the course of the Earth's thermal evolution.General cooling and pressure-freezing cause the formation of solid phases at the boundaries of the fluid core, leading to a solid inner core (IC) and a lower mantle shell (Bullen's D″ layer) from slow overgrowth at the mantle–core (MC) boundary. For simplicity, the core fluid is assumed to consist of two major phases, one conducive to solid metallic core formation, and the other to crystallization of a lower mantle phase from "solution" in a metal "solvent." The presence of a third, minor constituent, by selective partitioning between phases, acts as a solid phase growth regulator.On the basis of this model the energy available for fluid core motion and thereby for maintenance of the magnetic field, is related directly to the time rate of change of the growth of the solid phases at the IC and MC boundaries. Most of the available energy is gravitational and is associated with density and concentration currents which offset density inhomogeneities caused by selective acceptance and rejection of the fluid core constituents by the two solid phases.A very conservative estimate of the net gain per second in gravitational potential energy resulting from the mass redistribution via density currents and solid phase formation is 2.6 × 1013 W which may become available in different forms. The fraction which is converted into kinetic energy associated with differential circulatory motion around the rotation axis amounts to 3.4 × 1011 W, based on radial interchange with respect to the Earth's centre. The heat liberated as a result of IC solidification is 2.7 × 1011 W, assuming that the metallic phase is mainly iron. Since our ideas of other constituents of the core fluid are less definite we can draw only very general conclusions about the MC boundary. If silicates and oxides are likely candidates, it is possible that in the crystallization of the mantle phase from the core fluid, heat is being absorbed, thus creating a heat sink at the MC boundary. An estimate of the net strain energy associated with compression of IC material by about 1.4% and expansion of MC material by, on the average, 0.4% gives 1.5 × 1011 W.Magnetic polarity reversals might be explained as due to epochs during which the solid phase growth rate which dominates the fluid motion shifts from the IC to the MC boundary and vice versa. Intensity changes might be due to significant variations in the ratio of the radial and horizontal velocity components of the fluid motion.