Earth's Inner Core --- Discoveries and Conjectures

Paul G. Richards

February 2000, but see a comment at the end, added September 2007


The inner core has long been recognized as a part of the process by which fluid core convection is maintained, and as an influence upon the magnetic field. Evidence from several seismological studies in recent years has mounted to indicate that the inner core has anisotropic velocities with large-scale (degree one) variation in strength of the differences from isotropy, and fine-scale (~ few km) inhomogeneities of structure. Indications have also been found, of systematic changes in the travel time of seismic waves passing through the inner core --- which have been interpreted as evidence that the inner core is rotating in an easterly direction, relative to the mantle, at a rate fast enough to be perceived on human time scales. Song and Richards' (1996) original estimate of the rate has been characterized as too slow, too fast or physically impossible, but additional evidence has accumulated in support of what may be an emerging consensus that the inner core has a super-rotation of a few tenths of a degree per year.

Figure 1. The mantle and part of the crust have been cut away here to show the relative sizes of the Earth's fluid and solid cores. As the Earth's deepest interior loses primordial heat (principally by slow convection through the mantle), iron at the base of the fluid core solidifies and the inner core slowly grows (~ 1 cm/100 yr). Release of latent heat at the base of the fluid core drives convection which maintains the magnetic field, applying a couple to the inner core (Glatzmaier and Roberts, 1995, 1996). The inner core is at temperatures greater than the surface of the Sun.


The Earth's inner core, composed principally of solid iron, has radius about 1220 km and mass about 10**20 metric tons (~ 30% greater than the mass of the Moon). As shown in Figure 1, it lies at the centre of the much larger fluid core (which has almost 55% of the Earth's radius). Since the fluid core has very low viscosity and is thought to convect with particle velocities on the order of 1 cm/s, it might appear that the inner core itself could move with respect to the solid mantle --- for example, by having a different rotation rate. In 1995, Glatzmaier and Roberts reported the first numerical solution for 3-D convective dynamo motions within the fluid core that successfully reproduced the Earth's typical observed magnetic field strength, its dominantly dipolar pattern, and its propensity to reverse polarity. In their model the solid inner core was free to rotate and they wrote that its rotation rate "is almost always eastward, i.e. prograde relative to the initial non-convecting state. It can be as large as a few times 10**(-9) rad/s and changes on a time-scale of about 500 years."

This model rate, about 5 degrees/yr, seemed fast enough to Xiaodong Song and me to warrant a search for seismological indications. At first it seemed that systematic study of seismic reflections from the inner core/outer core boundary might show evidence of rotation, provided this boundary had topographic features which could affect the amplitude and possibly the timing of reflections. But in February 1996 we realized that a better way would be to use seismic waves that are transmitted through the inner core, rather than reflected from it.

In this paper, I first review the seismological evidence behind our original claim (Song and Richards, 1996) that Earth's inner core rotates eastward at about 1 degree/yr faster than the mantle's daily rotation. Second I describe reactions to this proposal, which came from many quarters and included papers arguing that our evidence was inadequate, as well as papers advocating (a) super-rotation with a rate faster than 1 degree/yr, or (b) a rate lower than 1 degree/yr, or (c) a rate indistinguishable from zero. And third I review additional evidence that has accumulated in the last three years in support of our original claim of an eastward super-rotation, but at a rate amounting to a few tenths of a degree per year, which is still fast enough to be perceptible on human time scales.

Recent research indicates significant inhomogeneity in the inner core (Song and Helmberger, 1998; Vidale and Earle, 2000), and the possibility that it supports the propagation of shear waves which can be observed at the Earth's surface, after the necessary conversion to compressional waves on passage through the fluid core (Okal and Cansi, 1998; Deuss et al., 1999).

Evidence for the original claim of super-rotation

Beginning in 1983, a series of papers noted that compressional elastic waves traverse the inner core about 3 or 4% faster in directions parallel to the north-south axis, than in directions parallel to the equatorial plane (Poupinet et al., 1983; Morelli et al. 1986; Creager, 1992; Song and Helmberger, 1993). Also, free oscillations of the Earth with significant energy in the inner core display anomalous mode splitting (Masters and Gilbert, 1981; Woodhouse et al., 1986; Tromp, 1993). Both these phenomena indicated the inner core is anisotropic, having a fast axis of cylindrical symmetry aligned approximately with the Earth's rotation axis. This type of anisotropy is appropriate for crystalline iron with hexagonal close-packed structure, which has long been proposed as the likely form of iron at inner-core temperatures and pressures (e.g., Takahashi and Bassett, 1964).

Figure 2. The plane shown here contains three ray paths by which seismic waves, travelling through the core, propagate from a source region in the South Sandwich Islands to an observing region in Alaska. Two of these rays, labelled BC and AB, pass through the fluid core. DF, with part of its path coloured violet, passes also through the solid core. The blue arrow, out of the plane of the rays, gives the fast direction of anisotropy. In general, the plane of the rays contains neither the fast axis nor the north-south axis. If the inner core rotates eastward about the north-south axis, carrying the fast axis along with it, the angle the fast axis makes with the (violet-coloured) ray path in the inner core will be reduced, reducing the travel time along the DF ray path. This travel time becomes stationary when fast axis and ray are in the same plane. An alternative explanation of travel-time change, is that the inner core is inhomogeneous and material of different seismic velocity moves into the (violet-coloured) path. Both mechanisms, anistropy and inhomogeneity, may be present.

An important revision to this anisotropic model, indicated by numerous travel-time observations as the inner core began to be studied outside an isotropic framework, was to take its axis of anisotropic symmetry in a direction slightly different (about 10 degrees) from north-south (e.g., Shearer and Toy, 1991; Su and Dziewonski, 1995). If such an anisotropic inner core rotates about the north-south axis at a rate different from the mantle, then travel times will change systematically for repeated earthquakes sending signals along a path between source and observing-station positions fixed in the upper regions of the Earth, if part of the propagation path lies in the inner core. This situation is shown in Figure 2, with a source and observing station separated by about 150 degrees --- a favourable configuration for observing the three indicated seismic waves passing through the Earth's deep interior. Song and I reasoned that evidence of inner core rotation might come from changes, for a series of earthquakes over a period of years, in the relative times between different core phases (DF compared with BC, and/or DF compared with AB).

The principal advantage of making relative rather than absolute travel-time measurements, is a reduced sensitivity to errors in source location. The method needs a combination of source region and observing-station region that are linked by seismic rays through the inner core with an orientation expected to have sensitivity to the hypothesized rotation. Thus, paths close to the equatorial plane would be unsuitable, and source-station pairs at high latitude (but in opposite hemispheres) could be favorable. Given the practical need for ready access to the seismogram archive of a station that had operated reliably for many years, at a suitable distance from a source region with seismicity levels high enough to produce frequent signals of adequate magnitude, the best dataset in our original study was provided by South Sandwich Island earthquakes recorded at station COL, in College, Alaska.

Figure 3. Seismograms recorded at station COL in Alaska, for South Sandwich Island earthquakes occurring over 28 years. These signals are aligned on the time of the BC arrival, and a slight time shift is applied to the first 7 s of record including the DF arrival, in order to correct the relative position of BC and DF to that expected at a common source-station distance of 151 degrees. (The time shift to a standard distance is necessary because these earthquakes actually occurred at slightly different locations.) The time difference between DF and BC arrivals is seen to increase over these decades by about 0.3 s. Figure, courtesy of X. Song.

Within a few days of starting the search for suitable data, we found seismograms indicating that the path DF, shown in Figure 2 and partly lying in the inner core, has become slightly faster over the last few decades. Figure 3 shows the basic phenomenon. Also, a DF path from earthquakes in the Kermadec region of the SW Pacific, to a station in Norway, appeared to become slightly slower. Given our then best estimate of the parameters of inner core anisotropy, Figure 4 shows the sensitivity of velocity through our best-fitting model of inner core anisotropy, to changes in the angle x between ray and fast direction. We concluded that the apparent change in DF travel time by 0.3 s over a 28-year period, for the path between South Sandwich Islands and Alaska, is evidence of eastward inner core rotation at about 1.1 degrees/yr (Song and Richards, 1996).

Figure 4. For the inner core anisotropy model developed by Song and Richards (1996), the red curve shows the % velocity perturbation (from an isotropic model) as a function of the angle xi between ray path and fast direction. The grey curve shows sensitivity to changes in this perturbation as xi varies --- as would be caused by inner core rotation. xi is the angle between the fast direction (blue arrow) and the violet-coloured ray in the inner core.

Some reactions

Our 1996 conclusion received popular attention, with numerous reporters eager to convey descriptions of a Moon-sized object inside the Earth, making a complete revolution on a time scale of hundreds of years (headlines).

The claim that inner core rotation could be detected seismically received attention also from fellow scientists, because the inner core is important in dynamo theory and for understanding properties of the magnetic field (both present and paleo), for heat flow studies (especially temperature and energy in the Earth's deepest interior), for understanding core history and composition, and possibly for its interaction with the Earth's interior gravity field.

This last issue was analysed by Buffett (1996), who had earlier pointed out that subducted lithosphere, in slab structures with anomalously high densities, penetrating to depths on the order of 1000 km into the mantle, would generate aspherical gravity anomalies inside the Earth. Such perturbations can be expected to raise long wavelength low-amplitude bumps on the inner core/outer core boundary, because the inner core is near melting throughout its interior. (Though "solid" on short time scales, inner core material will slowly flow to achieve equilibrium in the aspherical gravity field to which it is subjected.) The resulting bumps, predicted to have height up to about 100 m, would then provide a mechanism by which the inner core could become gravitationally locked to the aspherical field dominated by the mantle, and a couple with moment about 10**20 or 10**21 N-m would be required to break the lock. These values are ten or a hundred times greater than that available from estimates of the magnetic coupling derived from dynamo action in the fluid core, which tends to make the inner core rotate (Glatzmaier and Roberts, 1996). However, Buffett showed the argument could be turned around, and used to give a useful limit on the inner core's viscosity. He found that as long as this viscosity is less than 3 x 10**16 Pa s, which is not unreasonable, the configuration of the bump surface can be locked into the rotation rate of the mantle, while material throughout the volume of the inner core can flow in a fashion that maintains the bumps yet on average rotates differentially at a 1 degree/yr prograde rate driven by magnetic coupling to the fluid core. To the extent the differential rotation rate is slower than that proposed by Song and Richards (1996), Buffett's viscosity bound is proportionally higher.

So what is the current best estimate of the rate? Before answering this question, it must first be recognized as imposing a potentially unacceptable framework in which the inner core is thought of as rotating essentially as a rigid body, when instead a low-viscosity inner core will deform as well as undergoing rotation on average.

Su et al. (1996), using an anisotropy model similar to that of Figures 2 and 4 with fast axis tilted over from north-south, analysed many thousands of reported absolute arrival times of the DF phase, and proposed a rotation rate about three times faster than that of Song and Richards (1996). Though their method had the great merit of a very large database, with hundreds of thousands of observations, it is much more susceptible to errors in source location and origin time than are methods based on measurement of relative time between different phases as shown in Figure 2, so that their estimate of the rotation rate has large uncertainties. Dziewonski and Su (1998) subsequently concluded their data and method of analysis "implies a zero, or non-detectable, rotation rate." (See their abstract.)

Recent studies

Underlying this view, was a series of studies within the last three years that have demonstrated the inadequacy of modelling inner-core seismic velocities by cylindrically-symmetric anisotropy with constant fast-axis direction --- whether or not this axis is tipped over from north-south, and whether or not some depth-dependent variability in anisotropy strength is also included. An early such study was that of Tanaka and Hamaguchi (1997), who made the remarkable observation, shown here in Figure 5, that there is great variability of travel times for paths approximately north-south through the inner core. Paths beneath Africa, South America and the Caribbean, and the eastern Pacific, have values of the relative time between BC and DF with residuals (i.e., relative times after correcting for the predictions of an isotropic model) amounting typically to about 4 s. Just such observations had led in the 1980's and early 1990's to the understanding of an inner core with anisotropic properties, then thought to be approximately cylindrically symmetric and homogeneous. But Figure 5 also shows Tanaka's and Hamaguchi's observation that the BC - DF residuals are only about 1 s, or less, for north-south paths beneath eastern Asia, Australia, and the western Pacific. It thus appeared as if the inner core were inhomogeneous, with approximately a degree one pattern in which a western hemisphere is significantly anisotropic, and an eastern one is only weakly anisotropic. Subsequent studies, some using free oscillations and the theory of mode splitting, have now documented complex patterns of inner core seismic velocities, and anisotropy (e.g. Durek and Romanowicz, 1999). Creager (1999), using more than 2000 relative travel-time measurements of and BC - DF and the ray-theoretical framework, concludes that the "inner core is strongly anisotropic (2-4% on average) throughout most of the western hemisphere from near the surface to its center and into the lowermost several hundred kilometers of the eastern hemisphere. In contrast, the outer half of the eastern hemisphere from 40 degrees E to 160 degrees E ... exhibits very weak anisotropy ... The symmetry direction is the fast direction and lies on or near the spin axis ... The inner core appears to be organized in a very simple way with 60--90% of its volume containing well-aligned crystals ... "

Figure 5. From Tanaka and Hamaguchi (1997). Copyright 1997 by the American Geophysical Union.

The fact that some north-south paths through the inner core will show only weak anisotropy, means that for these paths there will be little travel time change between BC and DF arrivals over periods of several years, even if the inner core is rotating on the order of 1 degree/yr. Souriau (1998a) looked for this BC - DF travel time change at the station DRV in eastern Antarctica for the years from 1966 to 1988 using signals from large underground nuclear explosions in Novaya Zemlya --- a path that Tanaka's and Hamaguchi's (1997) results (indicated here in Figure 5) show would be quite insensitive to any rotation of the inner core. She did not find a significant travel time change but concluded that an eastward rotation at 1 degree/yr cannot be rejected. Souriau et al. (1997) and Souriau (1998b) went on to ask: "Is the rotation real?" Presentations at scientific meetings by several authors raised questions as to whether the presence of spatial inhomogeneities in seismic velocities, either at the base of the mantle or associated with subduction zones underneath source and/or station, combined with systematic mislocations associated with changes in the global network of stations used to produce bulletins of seismicity, might lead to travel-time artefacts which could be misinterpreted as evidence for temporal change in travel times.

One of the most interesting studies that avoided the assumption of homogeneous anisotropy, in the interpretation of travel time changes for BC-DF residuals, is that of Creager (1997). His paper was the first to seek an explanation in terms of lateral heterogeneity in the inner core. Creager used a network of 37 stations in Alaska in addition to station COL, to obtain core phases arriving from earthquakes in the South Sandwich islands. He was able separately to estimate the spatial distribution of BC-DF residuals as well as the temporal distribution. He confirmed the temporal changes reported by Song and Richards (1996) (namely that the DF phase had speeded up by about 0.3 s over a 28-year period), but interpreted them as due to easterly rotation of an inner core in which the DF phase was subject to the effect of a lateral velocity gradient. Creager proposed that the tendency of the DF phase from South Sandwich Islands to Alaska to speed up in recent decades (see Figure 3), is due to an increase from east to west in the seismic velocities of the part of the inner core that lies below the northern part of South America, as shown in Figure 6. This is a map view of the mid-points of the DF rays between the South Sandwich Islands and stations in Alaska. These rays are faster than average; and compressional-wave velocities are increasingly fast, from about 2.1% to 2.6%, along the line from B to A. An eastward rotation of the inner core, with this gradient, brings faster material into the propagation path of the DF ray. In this interpretation of the observed travel-time change, there is a trade-off between the inner core rotation rate and the lateral gradient of velocities in the inner core. Creager independently estimated this lateral gradient using observations of three earthquakes in 1991 in the South Sandwich Islands observed at a spatially extended network of stations in Alaska, and reached the conclusion that a non-zero rotation rate of about 0.2 to 0.3 degrees/yr is needed to explain the temporal changes in BC-DF residuals at station COL.

Figure 6. Adapted from Creager (1997).

Another approach to investigating inner core rotation was initiated by Sharruck and Woodhouse (1998), who studied the splitting structure of normal modes which have enough of their energy within the inner core to be somewhat influenced by the inner core's lateral variations in structure. If the inner core is rotating, normal mode data of adequate quality can use these lateral variations in structure as a marker. From data for a 20-year period, these authors concluded there is some indication of inner core rotation but that the preferred direction is retrograde (i.e. to the west). However they showed that the 90% confidence interval for the estimated rotation rate included prograde (eastward) values up to about 1 degree/yr.

Laske and Masters (1999) presented a normal mode analysis, also for a 20-year period, to determine splitting functions for core-sensitive modes. After correcting for the effect of aspherical structure in the mantle, they determined the best estimate of relative rotation of the lateral heterogeneities in the inner core for years going back from 1998 to 1977. Their approach, as summarized by Dahlen (1999), confidently rules out a differential rotation as high as 1 degree/yr, but is "marginally consistent" with the 0.2 - 0.3 degrees/yr eastward rate found by Creager's (1997) body-wave study.

Recent developments

In the past three years, several new seismological studies of core-phase relative travel times have been carried out, that find systematic travel time changes generally indicating eastward inner core rotation at a few tenths of a degree per year.

Thus, Ovtchinnikov et al. (1998) measured time variation in BC - DC residuals recorded at the station Novolazarevskaya (NVL) in Antarctica for the years 1966 to 1990 using the signals from nuclear explosions at the northern test site on Novaya Zemlya (location indicated in Figure 5). Location estimates for these seismic sources are much more accurate than for typical earthquakes -- and the sources lie within a geographic region only about 30 km in diameter. The DF path from Novaya Zemlya to NVL lies beneath Africa, and, as might be expected from Figure 5, it is significantly fast compared to standard Earth models. These authors found that the residuals decreased by about 0.4 s over this 24-year time period, which is opposite to the behaviour indicated in Figure 3, but would be expected for a cylindrically-symmetric inner core whose fast symmetry axis is moving away from the inner core part of the DF path during these years, as predicted by the Song and Richards (1996) model of fast axis location. Li and Richards (1998) reported a rather small decrease of about 0.1 s in the AB - DF residuals for the path from Novaya Zemlya to the station at Scott Base, Antarctica (SBA) --- a path which would not be expected to show a strong response to inner core rotation because it lies in the eastern hemisphere of low anisotropy (Figure 5). This study also pointed out that the best fit to Souriau's (1998a) data indicates a slight time decrease in BC - DF residuals, so the results for three Antarctic stations are consistent in providing some support for inner core rotation.

The most extensive recent work on measuring BC - DF residuals is that of Song and Li (1999) and Song (1999). The first of these studies reported an increase of about 0.6 s over a 37-year period for paths through the inner core from earthquakes in Alaska to the seismographic station at the South Pole (operated since 1956). The second study greatly expanded the database and analysis, beyond that of Song and Richards (1996), for paths through the inner core from earthquakes in the South Sandwich Islands recorded in Alaska. Thus, Song (1999) was able to extend the original (Figure 3) 28-year time period of observations at the COL station to a 45-year period, and found that the trend shown in Figure 3 extended back to earlier years. He found a similar trend over decades of data at three other Alaska stations. He also combined these data (for long time periods at four stations) with study of BC - DF residuals for over 100 stations of the Alaska Seismographic Network during the 1990's, in order to evaluate the effects of a lateral gradient in the inner core, and of mantle heterogeneities. Remarkably, as shown in Figure 7, he found evidence of inner core rotation just from data in the 1990's.

Figure 7. These maps of circles and crosses are similar to Figure 6, showing the mid-points of DF rays between South Sandwich Islands earthquakes and stations in Alaska. The pattern of circles and crosses indicates a lateral velocity change within the inner core. This change is shown as a sequence of changes in colour, which provide a marker of the inner core's position, assuming that all the change in DF travel time is due to motion of this lateral gradient, bringing material of faster velocity into the DF ray paths as the inner core rotates eastward. By comparing the position of the colour pattern in these three time periods, we see that there is motion from west to east, indicating an eastward super-rotation from less than ten years of data. Figure from Song (1999).

Interpreting all these data (more than 600 paths from the same general source region in the southernmost S. Atlantic to Alaska) in terms of a rigid body inner core rotation, in which travel time change in BC - DF is interpreted as due to rotation of an inner core with lateral velocity gradient, Song (1999) concluded that the rotation rate must lie in the range 0.3 - 1.1 degrees/yr faster than the mantle. If part of the observed travel time change is due to the additional effect of a change in the angle between the DF ray and the fast direction of averaged anisotropy, then these estimates of the rotation rate must be somewhat reduced.

A different approach to studying inner core properties and its possible rotation has been taken by John Vidale and his colleagues. They have used short-period seismic waves, called "coda", back-scattered from the inner core. In a first study, Vidale and Earle (2000) document 200 s of seismic waves scattered from the inner core following the expected arrival time of the reflection (called PKiKP) from the inner-core boundary, for 12 earthquakes and 4 underground nuclear explosions. Their observations, using the Large Aperture Seismographic Array (LASA) which operated in Montana, USA, in the 1960's and 1970's, indicate a few % stiffness variations in the inner core with a scale length of about 3 km. (LASA, with hundreds of borehole seismometers in hard rock, was a better facility than any operating today for study of scattered waves from the inner core. Like a directional microphone, it allowed measurements to be made of signals scattered from different parts of the finite inner core.) Vidale et al. (1999) compared the LASA data for PKiKP coda of two Novaya Zemlya nuclear explosions which occurred in 1971 and 1974 at almost the same location. They found that over this three-year time period the western hemisphere of the inner core appears to have moved toward LASA, and the eastern hemisphere has moved away --- which is what would be expected for an easterly inner core rotation; the rate appears to be about 0.15 degrees/yr. The method potentially enables changes in inner core rotation rate to be measured over times scales of a few years, provided appropriate pairs of co-located seismic sources can be found.

In conclusion

A paper with the title "Argon, a New Constituent of the Atmosphere" was co-authored by Rayleigh and presented at a meeting of the Royal Society on January 31, 1895. The findings were criticized on grounds that so heavy an element could not possibly be a gas. Rayleigh replied: "The result is no doubt very awkward ... and all we can do is apologize for ourselves and the gas." I am tempted to make a similar apology for the change in travel times that my colleagues and I have reported for certain seismic waves that have travelled through the inner core.

The original claim of evidence for inner core rotation was predicated upon a homogeneous cylindrically-symmetric model of inner core anisotropy with fast axis tipped over from north-south. Subsequent work has shown the need for inhomogeneity in anisotropy. It is interesting that the indications of travel time change in DF signals between South Sandwich Islands and Alaska, Alaska and the South Pole, Novaya Zemlya and different parts of Antarctica, are all for paths that are faster than average.

Because of the complicated effects of inner core lateral velocity gradients, upon travel times as the inner core rotates, it might seem that several years of work will be needed to elucidate inner core inhomogeneities in order to interpret travel time changes in terms of more precise rotation rates. The picture is also complicated by allowing for the possibility of low viscosity and hence deformation that is not well-summarized by rigid body rotation of the inner core. However, the new methods of Vidale and his colleagues may speed us toward an overall interpretation because these methods appear to be more sensitive to movement (rotation) of large volumes of inner core material.

While it may be frustrating not to know all the answers now, let us acknowledge that there are some handicaps. The inner core is far less accessible to us than the surface of any planet in the solar system. It resides at the centre of a much larger planetary tank of fluid iron almost 7000 km across (Figure 1), itself generating the magnetic field and curtained from us behind almost 3000 km of solid mantle rock.

In the last few years, claims of discovery have been made that the inner core is rotating with respect to the mantle, that it is layered, that it supports observable shear waves, that it stabilizes the Earth's magnetic field, and that it has significant inhomogeneities indicating the incorporation of material additional to the solid iron of which it is principally composed. I chose the title of this lecture to recognize the fact that not all of these recent claims are yet accepted, but that they are at least stimulating conjectures. The inner core is an interesting place.


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Paul G. Richards is Mellon Professor of the Natural Sciences, in the Lamont-Doherty Earth Observatory and Department of Earth and Environmental Sciences, Columbia University, Palisades, NY 10964, USA. He thanks Xiaodong Song for his ideas, hard work, and careful analyses --- and for his good company on an exciting and sometimes stormy voyage. This research has been supported principally by the U.S. National Science Foundation.

A shorter version of this paper is published in the February 2000 issue of Astronomy & Geophysics, The Journal of the Royal Astronomical Society. It is Lamont-Doherty Earth Observatory contribution number 6032.

Note added in September 2007. For several years after the July 1996 publication of the Song and Richards Nature paper, questions were repeatedly raised on the validity of its conclusions, and of those in the Jeffreys lecture presented above. If we were making an extraordinary claim, then did we not need extraordinary evidence? It was proposed several times, that we had been misled by inadequate knowledge of the relative locations of the events we were using in the South Sandwich Islands; and that our claims of a travel-time change were false, being instead an artefact, resulting perhaps from our use of incorrect event locations. Indeed, our claims of a travel time change amounting to only 0.1 s per decade, was not far from the noise level.
It was difficult to counter the skeptics (who were doing what skeptics are supposed to do), although Xiaodong Song tried hard to counter them by writing several papers that refuted specific criticisms of the analysis in Song & Richards (1996). Then, beginning in 2003, we found ourselves able to present stronger evidence that did not depend upon making a correction, to the observed seismograms, for any differences in the source locations we were using. The key was to work with doublets, an idea that I had tried to develop beginning in the early 1980s, and which, at last, worked out for us when we began to find the right events. Our new approach appeared first in the paper "Using earthquake doublets to study inner core rotation and seismicity catalog precision" (Anyi Li and Paul G. Richards, G-Cubed, 9 September 2003, 1072, doi:10.1029/2002GC000379).
And then in 2005 we published a SCIENCE paper that seems to contain the desired level of extraordinary evidence to persuade our earlier critics (who, to repeat, were doing exactly what critics are supposed to do) that indeed there is travel-time change amounting to about 0.1 second per decade, in the PKP(DF)-phase for paths from the South Sandwich Islands to Alaska. See the paper
Jian Zhang, Xiaodong Song, Yingchun Li, Paul G. Richards, Xinlei Sun, and Felix Waldhauser, Inner core differential motion confirmed by earthquake waveform doublets, Science, 309, 1357--1360, 26 August 2005. PDFs: main paper (456K); also supplementary online material (5.9M). [This latter file contains many examples of doublets in which the time shift of PKP(DF) with respect to PKP(BC) and PKP(AB) is clearly shown.]

When using high-quality doublets there is very little need for analysis, since the claim of some type of travel-time change is essentially self-evident, directly from the comparison of doublet waveforms. They look the same, except that in some cases there is a time shift for the part corresponding to a phase that has traversed the inner core.

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