When the first estimates of the gravitational constant and the Earth's mean density become possible (5.48 g cm −3 by Cavendish [ 1798 ] and 5.46–5.52 g cm −3 by Poynting [ 1891 ]), and they exceeded those of the rocks found at the Earth's surface, it became sensible to speculate about a denser deep Earth's interior. The discovery of the IC became possible in the first half of the twentieth century due to advances in theoretical seismology, then a relatively new discipline, and technological advances in analog instrumentation recording ground motion from earthquakes which enhanced observational seismology. In the framework of Halley's philosophy, the Lehmann's discovery [ Lehmann , 1936 ] of the Earth's IC, as she termed it, could be thought of as a proof of the concept that the inner globe, separated from the outer shells of the planet by the liquid, outer core (OC), existed in the Earth's interior. Lehmann noticed arrivals of compressional waves termed P ' at the angular distances from earthquakes where it had not been possible to predict their presence with just a liquid core and the mantle surrounding it. She modeled the Earth's interior by placing a smaller solid core inside the liquid core. In her model, earthquake compressional waves propagating through the Earth's interior travel faster through the IC than through the OC, so that apart from transmission, a reflection occurs when the waves reach the IC. Due to insufficient data, Lehmann assumed the compressional velocity of the IC and OC to be 8.6 and 8.0 km/s, the values lower than the modern day values [e.g., Dziewonski and Anderson , 1981 ; Kennett et al. , 1995 ] and as a result obtained an IC with a radius of about 1405 km. The theoretical predictions matched the available observations at the time, but with more data gradually becoming available, the radius of the IC was adjusted to ∼1221 km. The IC became a modern term and was used in the new edition of traveltime curves published in 1939 [ Jeffreys , 1939 ]. Bullen [ 1946 ] suggested that the IC was solid, but it was not until 1971 that an evidence for the solidity of the IC came from a seismological study of Earth's free oscillations [ Dziewonski and Gilbert , 1971 ].

This “Hollow Earth” model was driven by erroneous estimates of the Earth‐Moon density ratio [ Newton , 1687 ], but the idea persisted in literature for centuries. In the context of the time in which it was published, it was a paradigm shift that introduced some revolutionary concepts such as the existence of “a planet within a planet,” the origin of time‐varying magnetic field in the Earth's center, and the “differential rotation” of planetary shells, all the phenomena for which more complete explanations are still being sought at the present time.

The Earth's core within the realm of natural philosophy was first mentioned probably by Halley [ 1686 ], as a “nucleus” or “inner globe,” detached from the Earth's external shell. According to Halley's model, the inner globe was described as a solid sphere with two moveable magnetic poles in the Earth's center, rotating differentially with respect to the rest of the planet. Its existence was invoked to explain observations of apparent four magnetic poles, which were later understood as the spatial variation of a magnetic field containing a superposition of both dipole and nondipole components. In one of the model's variations, the Moon‐sized inner globe is separated from the outer, 800 km thick shell, by the liquid interior, sharing the same axis of diurnal rotation and the center of gravity.

The sections that follow describe a transition from simple models of the IC to more complex models driven by the need to fit seismological observations. More specifically, in section 3 , classic papers that led to major discoveries and developments of modern conceptual frameworks were discussed. Section 4 describes how we gradually moved toward more complex models of the IC, particularly how the idea of the existence of the harmonic degree 1 structure developed. This hemispherical dichotomy will be discussed in section 5 from a viewpoint of the seismological observables and a discussion on how most geodynamical models that were put forward interpret it. The second part of the same section describes a modern view of the IC, which is characterized by a laterally varying isotropic and anisotropic velocities, complex inner core boundary (ICB), complex attenuation, and finally, complex rotational dynamics. In section 6 , several ideas are proposed to advance seismological studies of the IC and make a faster progress in this field. This consists of three parts, offering different strategies for progress.

This review also discusses the most significant obstacles in seismological studies. In the section following the introduction and a short note on the history of the IC, a perspective is offered on why seismologists struggle to make a faster progress toward the understanding of structure and dynamics of the IC. This is accompanied by a review of current IC‐sensitive data sets of body waves and their sampling of the IC, which should be helpful in understanding some seismological results and their limitations.

There have been recent review articles on the Earth's core from a seismological perspective [e.g., Souriau , 2007 ; Tkalc̆ić and Kennett , 2008 ; Deuss , 2014 ]. Those reviews provide a comprehensive account of published contemporary work and a lot of information on various seismological studies that helped shaping our views on the IC. Yet they are still imperfect in that, inevitably, some research will be omitted. This review is an attempt to present the current state of seismological studies and their connection to the most recent geodynamical models of the IC. This cannot be done without a description of how different paradigms on the IC developed and how they shifted from one to another. Therefore, the descriptions of early discoveries and simple IC models in this review are instrumental as a prerequisite to understand current paradigms. It is noted that the connection between seismology of the IC and other disciplines is present at many other levels, but it is beyond the scope here to review relevant topics other than from a seismological point of view. For example, experimental and theoretical accessibility of mineral phase diagrams at IC conditions or behavior of magnetic field secular variations are some of these topics. The reader is referred to the recent reviews from a geodynamical and mineral physics perspective [e.g., Deguen , 2012 ; Hirose et al. , 2013 ].

The focus of seismological studies of the IC these days remains on exploring seismic parameters that are not yet fully resolved through the application of imaging techniques, but whose improved resolution will lead to a capacity to decode structure and dynamics of the IC. The topics and targets of interest in conjunction with the Earth's IC slightly evolved in the last several years from those mentioned in Tkalc̆ić and Kennett [ 2008 ]. The most studied research topics in the seismological community these days are (i) the hemispherical distribution of various seismological parameters, including isotropic velocity, attenuation, and anisotropic velocity; (ii) texture of the IC; (iii) general patterns of anisotropy of seismic wave speeds in the IC; (iv) attenuation and attenuation anisotropy in the IC, (v) the inner core boundary (ICB) topography; (vi) IC rotational dynamics and (vii) the nature of the lowermost OC just above the ICB. These topics are direct subjects of seismological studies, but there is a range of physical characteristics of the IC that can be derived via the above mentioned seismological parameters, among other things, the mineralogical state of iron in the IC, solidity, viscosity, and various rheological features (melt, interdendritic fluid, liquid inclusions, grains and their boundaries, porosity, shear modulus, dendrites, the extent and characteristics of a mushy zone compatible with the observations of isotropic and anisotropic velocity and attenuation, etc.). The studied features range in scale from hundreds of meters (minimum size of seismologically discernible individual grains) to the scale length of a thousand kilometers (e.g., ICB topography or IC hemispheric dichotomy). Apart from spatial variations, temporal variation of seismic properties is relevant in investigating rotational dynamics of the IC with respect to the mantle. The analysis of traveltimes and amplitudes as well as the entire wavefield sensitive to the IC can lead to the explanation of the observed phenomena, and this enables interpretation of fine details of IC texture. This, in turn, leads to the understanding of IC dynamic growth and its role in the geodynamo.

Seismological observations have been the pivotal points for major advances in our understanding of the deepest Earth shells. The nature of seismological observations is that they often lead, less often follow geodynamical predictions. Indeed, in most recent years, several geodynamical models of the IC dynamics emerged as a result of seismological observations from the last two decades, and most of them have fixated on a peculiar property of the IC known as a hemispherical dichotomy (harmonic degree 1 variation in physical properties such as isotropic velocity and attenuation and anisotropic velocity and attenuation).

Since the early 1980s of the twentieth century, with the growing number of modern seismographs installed on the Earth's surface, also grew our understanding of the inner core (IC). However, a challenge that exists in many studies of the IC is that various interpretations are possible because the seismic data sensitive to the IC are insufficient. These interpretations can be maintained as long as they are not contradicted with the new data.

Having covered various limitations that can affect PKP traveltime analysis, we can focus on some of the existing data sets that were painstakingly collected over the years. In particular, it is relevant to examine the present‐day volumetric coverage of the top 350 km of the IC by PKIKP wave raypaths associated with seismograms on which both PKIKP and PKPbc arrivals were observed, thus allowing the PKPbc ‐ PKIKP technique to be utilized. Figure 5 illustrates the volumetric coverage of three such data sets consisting of the data from the last two and a half decades, much of which is recurrent in all three data sets by the virtue of similar source‐receiver paths. In the Tkalc̆ić et al. [ 2002 ] data set (Figure 5 a), the differential traveltimes are measured using cross correlation. The data set is complemented with the highest‐quality waveform correlation measurements from McSweeney et al. [ 1997 ], Tanaka and Hamaguchi [ 1997 ], and Souriau and Romanowicz [ 1997 ] (Figure 5 d) for those waveform data that were not widely available. In general, the circumpacific belt is covered well, but there are vast poorly sampled volumes under the oceans. The Garcia et al. [ 2006 ] data set for deep events (Figure 5 b) is compiled by the use of an innovative nonlinear inversion algorithm that will be described in more detail in the last section. A limited number of new paths is introduced, but most data for deep events are subset of the data set shown in Figure 5 a. Independently, the data set by Irving and Deuss [ 2011 ] (Figure 5 c) is compiled also using the cross correlation and contains more recent data; however, the raypath coverage remains a subset of previous coverage. The Souriau and Romanowicz [ 1997 ] data set (Figure 5 d) was used to study a relationship between IC attenuation and velocity anisotropy. Only very good (quality a) and good (quality b) data are shown, while poor (quality c) and very poor (quality d) data are omitted. The Garcia et al. [ 2006 ] data set for shallow events (Figure 5 b) clearly shows a dramatic improvement over previous data sets, especially under Europe, Australia, and the Pacific Ocean. This is due to inclusion of a number of shallow events in Africa, North America, and mid‐ocean ridges (red stars). Despite this promising improvement, the shallow earthquake data are of a lower quality and show a much larger scatter than the deep earthquake data [ Garcia et al. , 2006 ]. Finally, Figure 5 f illustrates a combined IC coverage with exception of shallow events shown in Figure 5 e. This combined coverage demonstrates a potential for future imaging studies of IC using tomographic techniques, although we should keep in mind that the surface projections of raypaths might create a wrong impression that the volumetric coverage of the IC and cross pathing is dense (the readers are reminded here that the volumetric sampling is poor, as illustrated in Figure 3 .

Using differential (as opposed to absolute) traveltimes of seismic phases sensitive to the core reduces biases stemming from mislocation in space and time, as well as unwanted effects imposed by source and receiver structure. This can be achieved owing to the proximity of the paths of the two rays in the crust and the upper mantle [e.g., Cormier and Choy , 1986 ; Sylvander and Souriau , 1996 ], although it has been argued that the effects of mantle heterogeneity influencing independently each raypath remain significant along their paths [ Tkalc̆ić , 2010 ]. Since the source and receiver effects have a similar influence on both rays, the residual traveltime anomaly can be ascribed to deep Earth structure. This is particularly true for PKPbc and PKIKP raypaths, which are similar through the mantle, unlike the PKPab ‐ PKIKP pair in which PKPab raypath through the lowermost mantle is entirely different from that of PKIKP raypath. Therefore, it could be said that the PKPbc ‐ PKIKP is a favored tool to investigate IC structure. While it comes with a great advantage over other differential traveltime pairs due to the vicinity of raypaths in the mantle, the PKPbc ‐ PKIKP pair can only sample the top several hundred kilometers of the IC due to the fact that PKPbc phase does not exist beyond about 155.5°. This is illustrated in Figure 4 . More precisely, for Δ = 155.5° and the source at the Earth's surface, PKIKP bottoms at the radius of 865.0 km, which is 352.5 km below the ICB in ak135 model [ Kennett et al. , 1995 ]. From this, it follows that PKPbc ‐ PKIKP differential traveltime technique can only yield inferences on the top 352.5 km of the IC. The investigated depth in the IC could be extended with a differential traveltime technique only if PKPbc diffracted or PKPab are considered in conjunction with PKIKP waves. However, the uncertainties imposed by the ICB topography effects on the PKPbc diffracted phase and mantle heterogeneity on the PKPab phase are likely greater than the benefits of using the differential traveltime technique itself. Reaching greater depths of the IC by measuring absolute PKIKP traveltimes does appears to be, arguably, a better practice than using available differential traveltimes for the same purpose.

It should be mentioned here that large collections of traveltime data sensitive to the Earth's core exist and are available to researchers. For example, one such collection is the phase arrival data of the Bulletin of the International Seismological Centre. These data have played a significant and important role in many studies and discoveries. However, let us keep in mind that these data are contributed by seismological agencies around the world, meaning that apart from collecting arrival times of standard seismic phases such as P and S , the core‐sensitive phase arrivals are collected by various technicians employed by these agencies. While picking arrival times of P and S waves can become a routine practice, picking arrival times of PKP waves is not trivial due to the triplication of PKP waves and the fact that these phases are recorded at the seismogram significantly attenuated and masked by both microseismic and event‐generated noise. Most importantly, differential traveltimes cannot be simply treated by subtracting one phase arrival time from another. This is particularly true for PKP phases, because PKIKP is an attenuated version of PKPbc , and PKPab is a Hilbert‐transform version of PKPbc due to the fact that it is not a minimum time phase. For this reason, any study that uses the core‐sensitive phases traveltimes collected by picking absolute times of arrivals should be aware of its limitations as it will contain inherent errors that could otherwise be avoided. For example, for PKPab ‐ PKIKP , if absolute arrival times are simply subtracted one from another, this error could be on the order of 1–2 s. To illustrate to a nonseismologist how significant an error of 1–2 s is, it is enough to say that this amounts to a typical total traveltime correction accumulated by PKP waves along the entire path through the Earth's mantle due to its heterogeneity. Apart from that, seismograph frequency responses across the world are not homogeneous. The frequency dependence (dispersion) of the B caustic is visible at low frequencies, while scattered CMB precursors to PKIKP waves are visible at higher frequencies. Both of these frequency‐dependent, nonray theoretical arrivals interfere with PKIKP and PKiKP picks. Together with multipaths in triplication distances Δ = 145°−152° they have made bulletin picks virtually useless between 125 and 152°. Traveltime data in this epicentral distance range were therefore excluded from the bulletin data that led to standard Earth models like preliminary reference Earth model (PREM) [ Dziewonski and Anderson , 1981 ]. Therefore, in the times when we try to understand the IC fine structure, the limitations of the bulletin data are, unfortunately, large enough to preclude precise studies of the IC or the lowermost mantle. In the remaining discussion here, only data sets collected by careful examination of waveforms by several researchers are considered.

Illustration ofraypaths traversing the IC of the Earth in 3‐D from the existing data sets ofdifferential traveltimes by waveform correlation []. The IC is shown by the yellow‐orange globe in the center. (a) Quasi‐polarraypaths, defined by an angle≤ 35°. Colors of raypaths correspond to different values of traveltime residuals, blue marking fast, white marking neutral, and red marking slow paths through the IC. Orange and yellow colors represent quasi western and quasi eastern hemispheres of the IC, defined by]. (b) Quasi‐equatorialraypaths, defined by an angle≥ 35°. All color definitions are the same as in Figure 3 a. (c) The same as Figure 3 a but viewed from the north pole. (d) View through the Earth centered on the Atlantic Ocean with a transparent upper and midmantle, and thewave velocity tomographic image of the lowermost mantle from], red corresponding to slow and blue corresponding to fast regions relative to the reference model []. The transparent parts in the tomographic model are not sampled, therefore no information exists about thewave velocity, but the IC can be seen through. Allpaths (quasi‐polar and quasi‐equatorial) are shown, and their color definitions are the same as in Figure 3 a. Green balls are stations and red balls are earthquakes that are used to form thedifferential traveltime data set by waveform correlation.

It should then not come as a surprise that there are currently much less quasi‐polar paths than quasi‐equatorial paths. The definition of a transition between polar and equatorial sampling is somewhat arbitrary, but if we consider ξ ≤ 35° to represent quasi‐polar paths, then Figures 3 a and 3 b clearly illustrate this. In addition, Figure 3 c shows how sparse the quasi‐polar sampling is in both hemispheres of the IC. In particular, South Sandwich Islands earthquakes produce anomalously advanced PKIKP traveltimes in the quasi western hemisphere of the IC (the bundle of dark blue raypaths), and this might be taken as evidence of hemispherical nature of IC anisotropy in its top part. Yet the vast volumes of the IC remain poorly sampled or not sampled at all, which is visible in Figure 3 d, which shows virtually no sampling of the lowermost mantle and the core under the Atlantic Ocean. The same figure also demonstrates the sparsity of seismic stations contributing continuous waveform data on the African and South American continents, and equally inopportune situation in Antarctica. Now that we illustrated the natural limitations in IC sampling, let us take a closer look at the existing data sets collected over the years by waveforms correlation.

(a) Map of the angle ξ between the PKIKP waves in the IC and the rotation axis of the Earth for any given source‐receiver pair at the Earth's surface such that the epicentral distance is Δ ≥ 145°. Source and receiver latitude is plotted on horizontal and vertical axes. Colors correspond to different values of ξ . White areas are source‐receiver pairs for which PKIKP either do not exist or do not penetrate deep enough in the IC to be useful to study its internal structure (Δ < 145°). (b) Map of the angle ξ between the antipodal PKIKP waves Δ ≥ 170° in the IC and the rotation axis of the Earth for any given source‐receiver pair at the Earth's surface in this epicentral distance range. Source and receiver latitude is plotted on horizontal and vertical axes. Colors correspond to different values of ξ . White areas indicate source‐receiver pairs at epicentral distances Δ < 170°.

To illustrate how critical this limitation is for the studies of anisotropy, the angle between PKIKP waves and the rotation axis of the Earth ξ is computed for all hypothetical source‐receiver pairs on the Earth's surface. Figure 2 a illustrates that for a hypothetical earthquake located at the equator, a range of angles ξ that can be achieved by PKIKP waves traversing the IC to the recording stations at any given location on the Earth's surface, is 70–90°. In order to achieve IC sampling by the angles smaller than 30°, either the source or the receiver have to be located at the latitudes 60° or at higher latitudes toward the poles. Figure 2 b shows that to achieve the same kind of sampling in the centermost part of the IC ( PKP waves are almost antipodal), both the source and the receiver must lie at latitudes of 60° or even closer to the geographic poles.

(a) A diagram of PKP waves sampling the Earth's core at the epicentral distance Δ = 153°. Note that PKIKP is known as PKPdf , and PKiKP is known as PKPcd in some seismological studies. (b) A diagram of “exotic” inner core‐sensitive seismic phases for the epicentral distance Δ = 70°. The raypath of a PKiKP phase at 70° is shown for reference. The source is assumed at the Earth's surface and is shown with a star. Major discontinuities within the Earth are marked by ICB (inner core boundary) and CMB (core‐mantle boundary). The station is shown with a triangle.

A complete sampling of the IC by compressional waves in all directions is critical for studying IC elastic anisotropy. The direction of sampling of PKIKP waves (also referred in many studies as PKPdf waves (Figure 1 a)) through the IC is typically expressed by an angle that PKIKP waves form with the rotation axis of the Earth, namely, the angle between the tangent to the bottoming point of the PKIKP raypath in the IC and the rotation axis of the Earth, ξ , that can be defined in the range 0° ≤ ξ ≤ 90°. However, due to uneven global distribution of earthquakes and stations, there is a lack of raypaths that traverse the IC in north‐south direction. Note that instead of absolute traveltimes of individual seismic phases, the differential traveltimes (i.e., difference in traveltimes of the seismic phases in the following pairs: PKPbc ‐ PKIKP , PKPab ‐ PKIKP , PKIKP ‐ PKiKP , PKiKP ‐ PcP , etc.) are used to cancel out near‐source and near‐receiver effects as both types of waves are equally affected on their passage through the crust and the upper mantle. The differential traveltime residuals normally refer to the difference between the observed and predicted differential traveltimes.

In the last two and a half decades, we witnessed a remarkable expansion of seismic broadband stations. Despite such a drastic increase in the number of global seismic stations, many unsettled questions in the seismology of the Earth's IC stem from the fact that the spatial sampling of the IC by body waves is still far from perfect. There are two reasons for this incomplete sampling. First, the majority of significant earthquakes occur in the subduction zones that are principally confined to moderate latitudes. There are occasional seismic events in more extreme latitudes, such as those in the South Sandwich Islands subduction zone, which acts as a reliable factory producing a high rate of large earthquakes (and repeating earthquakes; see section 5 ). There are also occasional large events at extreme latitudes including those in the South Pacific, the Svalbard Sea, and Siberia. In the past, there were nuclear explosions at higher latitudes (such as those in Novaya Zemlya). These sources have momentous importance for seismology not only because they enable better understanding of seismic sources but also because they add to the spatial sampling of the IC, which is particularly poor in the north‐south direction.

The scientific community interested in this problem did not wait for too long to see yet another development in detecting a differential rotation of the IC. The new method, presented by Creager [ 1997 ] abandoned the need for a uniform cylindrical anisotropy framework as a measurement necessity tool. Instead, it used an observation of a heterogeneous volume with volumetric gradients in isotropic velocity in the IC, whose presence was documented from studies of traveltimes of the SSI earthquakes observed in Alaska. According to this method, a quasi‐fixed source‐receiver path will sample a volume of the IC with a known isotropic velocity as a function of time as there are many earthquakes in the SSI region and the recording in Alaska is continuous. If the IC spins with a different rate than the mantle, this would cause PKIKP waves of more recent earthquakes to traverse the IC faster as the PKIKP path traverses through increasingly faster material. This was in accord with the observations. The obtained differential rotation was about 0.3°/yr faster than the mantle and although lower than previous estimates, it confirmed the super rotation of the IC. This result was received with skepticism because of significant uncertainties in conjunction with the earthquake location parameters and a likely contamination of traveltimes by short‐scale inhomogeneities in the crust and mantle [ Souriau , 1998 ]. A joint inversion for the IC rotation and mantle heterogeneity confirmed a very robust lateral velocity gradient in the IC and found the superrotation to be between 0.3 and 1.1°/yr [ Song , 2000 ]. However, in a study of normal modes sensitive to the IC, Laske and Masters [ 2003 ] showed the differential rotation rate to be insignificant, only 0.11 ± 0.13°/yr. In their analysis, the normal mode splitting functions sensitive to the IC structure are used to detect the rotation of a rigid body. They design a method of detection by forcing all normal modes to give the same rotation rate, and for a given mode, all events in a given time window have to give the same rotation rate, the plausible assumption to make if the IC rotates as a rigid body. The obtained rotation rate of the IC was shown to be relatively insensitive to the tomographic model chosen to correct for the mantle structure, and this was a positive development. However, in a most optimistic scenario, the obtained differential rotation rate was too small to be reconciled with the results from body wave studies. This was interpreted as another setback in a divided community part of which was convinced that the seismological methods were sophisticated enough to measure this captivating phenomenon taking place in the Earth's center, and part of which who saw it as “the last nail in the coffin” to the seismological attempts to observe it. However, the application of another idea to study the IC rotation was waiting for daylight. This development will be discussed in the next section.

The differential rotation of the IC with respect to the mantle is one of the phenomena that is perhaps easier to comprehend in the context of other similar phenomena occurring in nature and the universe. Recently, Hinode Solar Mission discovered that the Sun's magnetic field is much more complex than anticipated. Sun's plasma rotates faster at its equator than at the poles, a result of convection in the Sun and movement of mass due to steep temperature gradients. This causes magnetic field lines of the Sun to get twisted and tangled, which in turn is responsible for Sun's magnetic field reversals. Solar supertornadoes plow through the Sun's atmospheric layers, in a form of hot gas and twisted magnetic lines powered by the nuclear reactions in the solar core [ Wedemeyer‐Bohm et al. , 2012 ]. We do not have to stretch our intuition too far to imagine that the Earth's magnetic field must be spectacularly complex, too. However, the complexity of Sun's magnetic field revealed in surface plasma motions is hidden in the case of Earth's convecting OC. This is because smaller‐scale spatial complexity of the magnetic field cannot be observed at the surface as it decays at higher powers of distance from the core. The modeling of this small‐scale turbulence is also inaccessible and remains a challenge to geodynamo modelers. The observations of the magnetic field at the Earth's surface, usually presented in terms of spherical harmonic expansion, are just a glimpse into the real complexity of the Earth's magnetic field. Therefore, it is not surprising that the differential rotation of the Earth's IC with respect to the mantle emerges in geodynamo simulations [ Gubbins , 1981 ]. Its strength and direction in those simulations are, unsurprisingly, sensitive to the imposed viscous boundary conditions at the ICB [e.g., Glatzmaier and Roberts , 1996 ; Kuang and Bloxham , 1997 ] and the balance between the gravitational and electromagnetic torques [ Aurnou and Olson , 2000 ]. Although temporal changes in the IC were suggested from the waveforms of PKIKP waves observed in the late 1980s at the Warramunga Station in Australia (A. Souriau, personal communication, 2012), these observations were received with skepticism in the seismological community. Several years later, Song and Richards [ 1996 ] reported systematic variations in traveltimes of PKIKP waves from earthquakes in South Sandwich Islands (SSI) region observed in Alaska and interpreted them as a signal from the IC spinning faster than the mantle, which was in line with geodynamical predictions. The main assumption at that time that opened a way to this interpretation was that the fast axis of cylindrical anisotropy is tilted with respect to the Earth's rotation axis. In these early studies, a quasi‐fixed source‐receiver raypath can be thought of as a reference frame and the fast axis of cylindrical anisotropy then moves in time relative to it. When this assumption is made in the analysis of the traveltimes of PKIKP waves collected over years at a selected station for a fixed source region, an angle between PKIKP raypath in the IC and the fast axis of anisotropy must decrease in time to cause earlier arrivals of PKIKP waves (observed), while the part of the waveform traversing the OC remains unaffected. The estimates of differential rotation rate varied, but all workers agreed in the sign and assumed a steady rotation, the resulting rates varying between 1.1 and 3.0°/yr in the eastward direction (superrotation) [ Su et al. , 1996 ]. Souriau et al. [ 1997 ], however, disputed the validity of this method showing that the fast axis of anisotropy cannot be uniquely determined; therefore, the assumption about a fixed fast anisotropy axis could not be made any longer, making it impossible to measure the rotation rates.

The motivation for attenuation studies of the IC first came as a result of discrepancy between the observed attenuation at high‐frequency body waves and low‐frequency normal modes, and from the need to estimate viscosity in the core [e.g., Gans , 1972 ; Stevenson , 1981 ; Jeanloz and Wenk , 1988 ]. Namely, Q μ − 1 (shear attenuation) estimates from body wave observations [e.g., Doornbos , 1974 ] were relatively larger than those from spheroidal normal modes [ Buland and Gilbert , 1978 ]. It is worth noting that Doornbos [ 1974 ] recognized the importance of considering frequency‐dependent attenuation. He also argued that it increases as a function of depth by about 10 times from the ICB to the Earth's center. The radial modes 0 S 0 , 0 S 1 , 0 S 2 , etc. (a subset of spheroidal modes with no surface nodes and all motion in radial direction) have a convenient feature that the observed loss of energy can be attributed exclusively to the bulk modulus‐related losses as the vibrations are purely compressional. These modes have most energy in the deep Earth, and measuring their bulk attenuation enables modeling the distribution of bulk attenuation in the lower mantle and the core (a highly nonunique problem). On the other hand, estimates from the observations of PKJKP (compressional waves converted to shear waves at the ICB—they propagate through the IC as shear waves but are converted back to the compressional ways on the way out of the IC) can put complementary constraints on the shear attenuation Q μ − 1 , while caution should be exercised regarding the frequency content of the PKJKP phase and the depth dependence of attenuation. The early models of attenuation in the IC focused on viscoelastic attenuation, with two competing mechanisms: a shear mechanism from fluid flow possible due to the existence of partial melt inclusions and a bulk mechanism representing a phase change induced during the passage of compressional waves, which would also require a presence of partial melt.

Spherically symmetric 1‐D reference Earth models [e.g., Jeffreys , 1926 ; Dziewonski and Anderson , 1981 ; Kennett et al. , 1995 ] do not consider the general (isotropic) heterogeneity and treat the Earth's IC as a laterally homogeneous sphere. However, as more PKIKP data accumulated by the early 1980s, it became clear that a homogeneous sphere representing the IC cannot explain traveltime observations [ Poupinet et al. , 1983 ]. Intrigued by this problem, Morelli et al. [ 1986 ] inverted the traveltimes of PKIKP waves reported in the International Seismological Centre bulletin to investigate isotropic heterogeneity patterns in the IC. When they corrected for mantle structure and CMB topography and assumed that all analyzed PKIKP traveltimes are caused by the general heterogeneity in the IC, they found a pronounced zonal pattern of heterogeneity for the waves sampling the innermost part of the IC. This was significantly different from PKIKP data that sample shallower parts of the IC. The conclusion of their work was that it would be physically implausible to explain 2–3 s of anomalous traveltimes with an isotropic heterogeneity near the Earth's center (also, not agreeing with the splitting of the normal modes [ Ritzwoller et al. , 1988 ]), and instead, argued that a cylindrical anisotropy with a fast axis parallel to the rotation axis of the Earth is a more likely hypothesis, not excluding the existence of the isotropic heterogeneity in the IC. Obviously, a large trade‐off existed between the isotropic and anisotropic velocity structures in the IC to explain traveltimes of PKIKP waves, but the appeal was a simplicity of cylindrical anisotropy, and from today's perspective, this still appears as a relatively uncomplicated IC model. A cylindrical anisotropy with a fast axis parallel to the spin axis of the Earth was then also supported from the consideration of normal mode splitting [ Woodhouse et al. , 1986 ]. Thus, the original consideration of varying isotropic velocity in the IC actually led to the establishment of one of the most prominent conceptual frameworks in the studies of the IC in the last several decades. This pioneering seismological work was then followed by many, including mineral physicists and geodynamo modelers, and a number of explanations for anisotropy in the IC were discussed and mechanisms put forward.

By the late 1970s and early 1980s, the boundary of the IC with the OC was thought to be smooth and sharp as suggested earlier [ Jeffreys , 1939 ; Engdahl et al. , 1974 ], and the argument was that there is an extremely small variation in temperature in the OC [e.g., Stevenson , 1987 ]. There is a straightforward connection between the age of the IC and its radius, i.e., how quickly the ICB moves outward as the IC solidifies. Early estimates of the IC radius [e.g., Engdahl et al. , 1974 ], did not reveal any peculiarities in the shape of the IC, although it was suggested by Poupinet et al. [ 1983 ] that the IC might have a prolate shape to explain differences in traveltimes of PKIKP waves traversing the IC (these traveltime anomalies were later hypothesized to be due to IC elastic anisotropy). There was a strong trade‐off between the estimates of the velocities in the OC and its radius with the radius of the IC, but the estimates of the IC radius gradually settled to values between 1220 and 1230 km, with a strong dependency on the velocity in the OC just above the ICB. The density discontinuity at this boundary provides invaluable constraints on the dynamics of solidification and it is crucial for calculations of thermal evolution of the Earth's core, i.e., estimating the rate of cooling and the effect on the operation of geodynamo [e.g., Buffett et al. , 1996 ; Nimmo et al. , 2004 ]. Early seismological estimates of the density contrast at the ICB from the amplitude ratio of PKiKP and PcP waves (compressional waves reflecting from the Earth's OC [ Bolt and Qamar , 1970 ; Souriau and Souriau , 1989 ] were generally sparse in global coverage of the ICB and predicted a higher density contrast by factors of 2 or more than that predicted from normal modes 550–600 kg/m 3 [ Dziewonski and Anderson , 1981 ]. The body wave method takes advantage of direct measurements of amplitude ratios of PKiKP and PcP waves, and makes a number of assumptions about boundary conditions and Earth structure, including a frequency independent attenuation. Shearer and Masters [ 1990 ] considered both body waves and normal modes, but found too few probable appearances of PcP and PKiKP waves on the same seismogram. The conclusion from body waves was that the density contrast at the ICB must be less than 1000 kg/m 3 , while normal modes required even lower values (550 kg/m 3 ). At about the same time, Loper [ 1983 ] argued that the region of mixed solid and liquid in which the phase change is actively occurring is much smaller than the typical wavelength of body waves (at the frequency of 1 Hz, this is on the order of about 10 km in that region), making it indistinguishable from a first‐order discontinuity in density and elastic moduli.

As mentioned in the note about the history of the IC discovery, evidence for the solidity of the IC came from a seismological study of Earth's free oscillations by Dziewonski and Gilbert [ 1971 ]. They modeled eigenfrequencies of spheroidal modes with predominant compressional and shear energy in the IC and observed a theoretically predicted behavior with an increase in rigidity or the introduction of a liquid IC into the theory. Namely, an increase in rigidity requires a decrease in bulk modulus, and this in turn enhances compressional energy while it diminishes shear energy of the modes sensitive to the IC. An introduction of a liquid IC to fit the modes with predominant compressional energy yields physically implausible, denser OC than the IC. Hence, they strongly favored a solid IC to fit the observations.

4 Toward Complexity

In the previous section we have seen that the physical phenomena proposed to characterize the IC from seismological observations were simple at first. They may have been simple as they were capable to satisfy the observations, which, arguably, were also simple in their paucity. In many cases it becomes clear that simple models have to be abandoned when new data stop supporting them. This should be a straightforward paradigm shift in cases where an initial, simple model, fits the data but is not required by the data. In other cases the old ideas resonate longer because the new data are not abundant enough and there might even be competing alternative models that fit the data but they cannot be rejected. We will see here how different ideas on IC structure and dynamics evolved further and become increasingly complex.

4.1 More Complex State and the Boundary of IC PKJKP waves have been elusive, yet they have not ceased to fascinate observational seismologists. Several studies reported new observations of these waves, but the seismological community still remains divided on the issue whether or not these observations are robust. From the time of the study of Julian et al. [1972], a study of Okal and Cansi [1998] opened a series of several studies on this subject. Although Deuss et al. [2000] argued that the previous observations of PKJKP waves were actually observations of simultaneous arrivals of pPKJKP and SKJKP waves, Cao et al. [2005] showed a new observation of PKJKP by the Graffenberg array. One of the conclusions from this study was that the S wave velocity profile in the IC is 1.5% faster than in PREM model [Dziewonski and Anderson, 1981], resulting in about 9 s more advanced PKJKP arrivals than predicted. The density contrast at the ICB is larger than it would be for a phase transition alone. Kennett [1998] argues that the constraints imposed on the polynomials for the different depth intervals in spherically symmetric density models are based on mathematical convenience rather than an attempt to allow for different physical processes. During the time the data was sparse, it was suggested that the observations of PKiKP at 10–70° most likely represents extreme conditions (probably enhanced through focusing on mantle heterogeneities), so that the density contrast estimates would actually present an upper bound [Shearer and Masters, 1990]. It is feasible that strong reflections of PKiKP waves could be observed from the ICB if the liquid fraction is small near the boundary or if the thickness of the mushy zone at the top of the IC is several hundred meters [Loper, 1983], which is less than the wavelength of the observed PKIKP waves sensitive to IC structure. According to the same study, the solid fraction rapidly grows with depth and increases 1 order of magnitude in only several hundred kilometers. However, a mushy zone extending tens of kilometers below the ICB has also been invoked, if it is interpreted in terms of melt‐fraction content [Cao and Romanowicz, 2004a]. Masters and Gubbins [2003] recalculated the density jump from normal mode data and showed that the previous estimate based on normal modes was too low and that it could be raised to about 820 kg/m3. Cao and Romanowicz [2004b] investigated body waves and found a density contrast of 850 kg/m3 from five observations. Thus, the results from two independent data sets converged to the same value resulting in a reconciliation of an old discrepancy, although other studies that used body waves still produced a range of different results. This could be a result of the fact that the sampling of the ICB in each study was different. Koper and Dombrovskaya [2005] argued for a lateral variation in ICB properties based on a regional coherence in the PKiKP/P ratio that varies by up to 2 orders of magnitude. Krasnoshchekov et al. [2005] used observations at arrays and measured absolute PKiKP amplitudes from waveforms that recorded different nuclear explosions at known locations around major test sites. To form beams they normalized the strength of each source to a fixed explosive yield. They found that the observed amplitudes at 50–100° could not be explained by spherically symmetric Earth models of the ICB region and suggested that the variability of the inferred ICB density contrast 450–1660 kg/m3 may signify a mosaic of lateral variation in the physical properties across the ICB. Their interpretations included the possibility of strong gradients in shear modulus on either the top or the bottom side of the ICB. Possibly consistent with observed lateral variations in P wave velocity gradient in the lowermost OC [Yu et al., 2005] is a region of laterally varying viscosity associated with a frequency dependent shear modulus in the lowermost OC [Cormier, 2009]. Lateral variations in this region above the ICB may be coupled to lateral variation in the solidification process of the IC [Cormier, 2007] and lateral variations of flow in the OC [Aubert et al., 2008]. Motivated by a multitude of results for a density contrast at the ICB, Tkalčić et al. [2009] proposed a new approach to integrate effects of microseismic and signal‐generated noise with the amplitude measurements and account for the uncertainty. They applied a new method to high‐quality arrivals of PcP and PKiKP waves from a nuclear explosion observed at epicentral distances 10–20°. The resulting uncertainties are high‐precluding precise estimates of the ICB density contrast, but provide a robust estimate of an upper bound from body waves of about 1100 kg/m3. They observed a small density contrast of 200–300 kg/m3 at some locations of the ICB, which suggests the existence of zones of suppressed density contrast at the ICB, a density contrast stronger than 5000 kg/m3 at the CMB, or a combination of both. In addition, in an independent study, it was shown that the amplitudes of PKiKP and PcP could be negatively correlated as a result of a small‐scale heterogeneity in the crust and upper mantle [Tkalc̆ić et al., 2010]. These later studies illustrated that the ray theory has limitations, and while it can place upper bounds on the estimates, it might not be the most appropriate tool for precise measurements of the ICB density ratio.

4.2 More Complex Isotropic and Anisotropic P Wave Velocity Distribution in IC The development of concept of a hemispherical dichotomy (degree 1) of properties of the IC dates back to the 1990s. It is interesting to follow, chronologically, how the pieces of puzzle came together with the access to better quality data. Back in the early 1990s, Shearer and Toy [1991] based on the traveltime data from the International Seismological Centre (ISC) catalogue argued that PKPbc‐PKIKP traveltime residual patterns can be explained either by heterogeneity or anisotropy in the IC with about 1% variation, which they described as the aspherical symmetry. This was revisited in a paper of Creager [1992] who analyzed short‐period seismograms on a global scale. Due to the fact that the residuals in his study were geographically widely distributed and interspersed with normal residuals, he discarded a possibility that an aspherical structure is due to large‐scale isotropic heterogeneity and instead, he argued for the existence of axisymmetric anisotropy in the upper part of the IC with a fast axis quasi‐parallel to Earth's spin axis. Tanaka and Hamaguchi [1997], however, did not find evidence from broadband waveforms for anomalous residuals in the eastern latitudes. This meant that a simple model of IC anisotropy quasi‐parallel with Earth's spin axis was not valid. Their measurements revealed a clear harmonic degree 1 variation in isotropic compressional velocity, with the quasi eastern hemisphere (qEH) of the IC (43°E to 177°E) approximately 1 s faster than the remaining, quasi western hemisphere (qWH). Since they had only a small number of the north‐south raypaths of PKIKP and PKPbc waves and because their qWH data set composed only of the South Sandwich Islands earthquakes recorded in northern latitudes, the authors concluded that if the observed traveltime anomalies are indeed due to the existence of IC anisotropy, that anisotropy cannot be simple. They had a solid evidence to reject hypotheses that the complexity in the PKPbc‐PKIKP differential traveltime residuals stemmed from the near core‐mantle boundary structure and/or from a tilt in the symmetry axis of IC anisotropy. Because they did not have data to deny a hypothesis that a cylindrical anisotropy existed only in the qWH but not in the qEH, they accepted it. They then proposed that the hemispherical structure in isotropic compressional velocities probably reflects ancient core dynamics soon after its formation. It is important to note that the PKIKP waves whose traveltimes are measured differentially with respect to PKPbc traveltimes, only sample the top 400 km of the IC—the uppermost inner core (UIC). Thus, the evidence for the hemispherical dichotomy from the PKPbc‐PKIKP differential traveltime data only applied to the UIC. It is difficult to extend our probes deeper, because the signal in PKPab‐PKIKP differential traveltimes cannot be easily decoupled from lowermost mantle structure, where raypaths of PKIKP and PKPab waves are now significantly different one from another. The hemispherical dichotomy was confirmed in the studies using the same kind of traveltime data, although augmented by more measurements on a global scale [e.g., Creager, 1999; Garcia and Souriau, 2000; Tkalc̆ić et al., 2002]. Moreover, the top of the IC can be studied with a different set of traveltimes that consists of differential PKiKP and PKIKP traveltimes [e.g., Niu and Wen, 2001; Yu et al., 2005]. This data set has an advantage in that the raypaths of PKiKP and PKIKP are almost the same outside the I; therefore, the signature seen in traveltime residuals should be that of the IC. On the other hand, the downside of this utilizing this data set is that it can only sample down to about 85 km beneath the ICB. Nonetheless, the hemisphericity in isotropic velocities is confirmed by this independent data set.

4.3 More Complex Seismic Attenuation in IC In most studies on the IC, the attenuation of energy contained in the wavefield is expressed in form of its inverse, the so‐called quality factor (Q), and there are two main contributors to the loss of energy: the heat and internal friction during the passage of elastic waves (viscoelastic attenuation) evident on a microscopic scale, and the reflection, refraction, and conversion of energy during the passage (scattering attenuation) evident on a macroscopic scale. For a more detailed description, see Cormier [2011]. At the same time PKIKP and PKPbc data were collected and analyzed, a global data set of PKiKP and PKIKP waveforms was also analyzed by waveform modeling to investigate the attenuation characteristics of the IC [Wen and Niu, 2002]. Apart from confirming a hemispherical differences in isotropic compressional velocity, the study revealed a hemispherical difference in attenuation. Namely, according to [Wen and Niu, 2002], the quality factor was larger in the qWH (600) and smaller in the qEH (250), and according to the authors, a possible mechanism that explains this observation involves different geometric inclusions of melt and crystal alignment in the two hemispheres of the UIC. This model would explain the observed hemispherical differences and it was supported by a study that showed not only how seismic velocity can depend on the viscosity but also on the fraction and the geometry of the melt inclusions [Singh et al., 2000]. The conditions to support the above mentioned mechanism would be achieved by invoking a different vigorousness of convection in the UIC on each quasi hemisphere, which would be thermally driven by a heat flow variation at the bottom of the OC. It would likely require that the viscosity is small enough for the convection to develop within the solid IC. Also, this model with a limited radial extent of convection (confined to the UIC only) would work well to preserve crystal alignment at greater depths of the IC, needed to explain, at that time, a widely accepted idea of a cylindrical IC anisotropy. At the same time, the convection confined within the UIC but with hemispherical differences would explain a well documented observation of a hemispherically varying thickness of the isotropic layer. The conclusions of this work thus sparked a new conceptual framework in which there is a spatial correlation between the compressional wave velocity and the quality factor Q in the IC. A new image emerging was an IC with a fast and more attenuating qEH and a slow and less attenuating qWH. In the above study, the depth extent of the hemispherical variation in attenuation was not quantified due to a limited depth range of sampling (the ICB—85 km below the ICB). Although, it is implicit that high attenuation in the qEH might extend deeper below the ICB than in the qWH if the same physical mechanism (i.e., IC convection) is responsible for a positive correlation between isotropic compressional velocity and the quality factor Q (i.e., high velocity versus high attenuation in the qEH and low velocity versus low attenuation in the qWH). At the same time, Cormier and Li [2002] studied the radial variation of Q in the IC using the forward scattering analysis of pulse dispersion. The scattering Q broadens the PKIKP pulse by transferring scattered high frequency into the later coda. Li and Cormier [2002] studied the same assuming a viscoelastic attenuation. Not focusing on lateral variations in Q, the papers reported a depth‐dependent attenuation in the IC, arguing for a significant contribution from scattering versus viscoelastic attenuation (at least 25%). This was an important piece of evidence that the distribution of grains and their varying size might be an omnipresent phenomenon in the IC. A study of Cao and Romanowicz [2004a] went a step further in estimating the attenuation quality factor on a global scale in the UIC placing seismological observations within the context of rheological properties of IC, such as porosity (melt fraction) and connectivity of liquid inclusions. Their analysis of PKiKP and PKIKP amplitude ratios in the time domain suggested the existence of a transition zone in the depth profile of Q in the qWH. According to their results, Q in the qWH first decreases in going from the ICB from almost infinite values typical for the OC to ∼210 at about 85 km depth beneath the ICB. It then increases with depth toward the center of the IC. If a mushy zone is present in the UIC [Fearn et al., 1981], a better connectivity of liquid inclusions (a higher porosity) results in a lower compressional velocity and a lower attenuation. On the contrary, they did not observe such a transition in the qEH, but they inferred that it must be located in the top 32 km (the upper limit of sampling of PKiKP and PKIKP waves in their study) of the IC. They argued that this inference is supported by the study of Stroujkova and Cormier [2004] that found a low‐velocity layer in the UIC in the qEH. The liquid inclusions are well isolated and the porosity is lower in the qEH, causing higher compressional wave velocity and higher attenuation. The observed hemispherical pattern and the positive correlation between the compressional wave velocity and attenuation were interpreted invoking the mechanism proposed by Sumita and Olson [1999], which predicts a varying heat flow in the OC near the ICB. If a higher porosity is a result of faster freezing (faster crystallization of the IC), the results of Cao and Romanowicz [2004a] suggest that the qWH is colder and the qEH is warmer. Another result from this work was that the signature of hemisphericity does not extend deeper than about 85 km beneath the ICB, which the authors interpreted as a direct constraint on the thickness of the mushy zone. However, Deguen et al. [2007] pointed out that due to uncertainties in conjunction with iron conditions at high temperature/pressure, it is difficult to estimate the thickness of the mushy zone layer, but that it probably does not extend down to the center of the IC as it would collapse under its own weight. They estimated that the size of the interdendritic spacing does not exceed a few meters. As mentioned in the previous section, previous work revealed a difference for shear attenuation observed from body waves and normal modes, the latter displaying lower values than the former (i.e., the quality factor Q μ − 1 was contained to be 280 from body wave studies [e.g., Cormier, 1981], whereas in normal more studies it was constrained to be 1500–3800) [e.g., Masters and Gilbert, 1981; Fukao and Suda, 1989]. Today, it is generally well accepted that any difference in the estimates of attenuation in the IC between body wave and normal mode studies must come from frequency dependence of bulk attenuation [Andrews et al., 2006].