Antipodal Distances Research Articles

Analyses of anomalous amplitudes of antipodal PKIIKP waves

Approaching the distance of 180°, seismic focusing greatly amplifies the normally weak PKIIKP phase (underside reflection from the inner core boundary). Anomalously strong amplitudes of the PKIIKP phase reported previously at near antipodal distances (at seismic station TAM in North Africa) have been interpreted to infer anomalous structure(s) of the inner core boundary (including a sharp drop of compressional wave speed in the bottommost outer core or a near-zero shear wave speed in the topmost inner core). However, our observations of 12 earthquakes located antipodal to TAM (including the previously cited four events) suggest, for several reasons, that the anomalous PKIIKP energy might be a seismic phase misidentification. The anomalous phase appeared at distances less than 179.6° but not at larger distances (~179.8°). The phase appears consistently from antipode to distances less than 160° and has horizontal slowness similar to the PKIKP phase (going straight through the inner core). Its travel times vary greatly and show a systematic difference between two groups of events at different distances. A simple point scatter provides a good match to the travel times and the systematic variation of the anomalous phase at most stations, suggesting that it could originate from scattering off strong heterogeneities in the mantle wedge above the subducting Tonga slab. The phase misidentification suggests that the previously proposed inner core boundary structure(s) based on the anomalous phase need to be re-evaluated.

Seismic anisotropy in the Earth's innermost inner core: Testing structural models against mineral physics predictions

AbstractUsing an updated data set of ballistic PKIKP travel time data at antipodal distances, we test different models of anisotropy in the Earth's innermost inner core (IMIC) and obtain significantly better fits for a fast axis aligned with Earth's rotation axis, rather than a quasi‐equatorial direction, as proposed recently. Reviewing recent results on the single crystal structure and elasticity of iron at core conditions, we find that an hcp structure with the fast c axis parallel to Earth's rotation is more likely but a body‐centered cubic structure with the [111] axis aligned in that direction results in very similar predictions for seismic anisotropy. These models are therefore not distinguishable based on current seismological data. In addition, to match the seismological observations, the inferred strength of anisotropy in the IMIC (6–7%) implies almost perfect alignment of iron crystals, an intriguing, albeit unlikely situation, especially in the presence of heterogeneity, which calls for further studies.

Detection of inner core solidification from observations of antipodal PKIIKP

AbstractPKIIKP waves, reflected from the underside of the inner core boundary, are very sensitive to the S velocity in the uppermost 80 km of the inner core at antipodal distances, undergoing a phase change and a factor of 4 amplification as the distance approaches 180°. Modeled PKIIKP waveforms are consistent with a near‐zero shear modulus in the uppermost inner core in a 20–40 km thick patch beneath the eastern equatorial hemisphere. This bright spot of PKIIKP reflection correlates with a thin zone of low P velocity inferred from the complexity of PKIKP waveforms sampling this patch. Estimates of grain sizes from seismic attenuation, the absence of backscattered PKiKP coda in this region, and a prediction for enhanced heat flow through this patch suggest that it is a region of solidification rather than melting.

Antipodal focusing of seismic waves observed with the USArray.

We present an analysis of the Mw = 5.3 earthquake that occurred in the Southeast Indian Ridge on 2010 February 11 using USArray data. The epicentre of this event is antipodal to the USArray, providing us with an opportunity to observe in details the antipodal focusing of seismic waves in space and time. We compare the observed signals with synthetic seismograms computed for a spherically symmetric earth model (PREM). A beamforming analysis is performed over the different seismic phases detected at antipodal distances. Direct spatial snapshots of the signals and the beamforming results show that the focusing is well predicted for the first P-wave phases such as PKP or PP. However, converted phases (SKSP, PPS) show a deviation of the energy focusing to the south, likely caused by the Earth's heterogeneity. Focusing of multiple S-wave phases strongly deteriorates and is barely observable.

The history detectives: Establishing the parameters of the 1960 Perth-Bermuda antipodal acoustic propagation experiment

In 1960 three 300-lb explosive shots were detonated off Perth, Australia at 3 am, 22 March (local) by HMAS Diamantina to determine if those sound signals could propagate the antipodal distance to the Bermuda SOFAR station. These data offer a rare measure of the ocean temperature a half century ago, averaged across large stretches of the Southern, South Atlantic, and North Atlantic Oceans. The accuracy of these data are determined by the accuracy of the essential parameters of the experiment, e.g., the time and position of the shots. The narrative of HMAS Diamantina the night of 21 March 1960 was reconstructed from the ship's log, the captain's Report of Monthly Proceedings, and other information. The experiment was conducted with care to obtain a precise measurement, subject to the resources available to the ship at the time. The largest uncertainty is in the position of the shots, determined by triangulation from shore landmarks in the evening, celestial navigation at dawn, and dead reckoning in between. In addition, the depth was measured at the time of the shots. The 1960 position was measured to an equivalent travel-time accuracy of about 3 s, biased toward closing the range to Bermuda.

Seismic Characterization of the Chelyabinsk Meteor's Terminal Explosion

Online Material: Figures of waveform fit, apparent source time functions, and video of impact of shock wave at factory. Impacts with our planet cause seismic shaking by a variety of mechanisms. Catastrophic ground motion, even at antipodal distances, can be generated by the extremely infrequent, hypersonic collisions with large asteroids or comets (Meschede et al. , 2011). Fortunately, the atmosphere effectively shields the smaller (and far more common) meteoroids, greatly reducing their initial kinetic energy at high altitude, causing them to slow down, break up, and even vaporize, producing a meteor (Ceplecha and Revelle, 2005). In most instances, the ground shaking is triggered by the atmospheric shock wave of a meteor, not by the impact of the surviving meteorites (Edwards et al. , 2008). A particularly strong shock wave can be generated by explosive fragmentation of the meteoroid in one or several final airbursts (Ceplecha and Revelle, 2005; Edwards et al. , 2008). Such disruptions are triggered when the pressure (ram pressure) caused by atmospheric drag exceeds the internal strength of a meteoroid. They are accompanied by a sudden increase in the meteor luminosity (a flare), because they imply a sharp increase in the surface area being subject to ablation. On 15 February 2013 at 03:20 UTC, an exceptionally large meteor in the region of Chelyabinsk, Russia, produced a powerful shock wave, which caused unprecedented damage to people and property. According to official news reports, glass windows were shattered in over 7300 buildings (some of these even experienced slight structural damage), and falling debris hurt more than 1600 people. The meteorite fragments that survived the atmospheric entry hit the ground at subsonic terminal velocity (Schiermeier, 2013), and did not cause any seismic shaking detectable at regional distances. However, the meteor produced the strongest atmospheric infrasound signal ever recorded (Stone, 2013) and …

On D. G. Higman's note on regular 3-graphs

We introduce the notion of a t -graph and prove that regular 3-graphs are equivalent to cyclic antipodal 3-fold covers of a complete graph. This generalizes the equivalence of regular two-graphs and Taylor graphs. As a consequence, an equivalence between cyclic antipodal distance regular graphs of diameter 3 and certain rank 6 commutative association schemes is proved. New examples of regular 3-graphs are presented.

Inner core freezing and melting: Constraints from seismic body waves

Hypotheses for the mechanisms of growth of Earth’s inner core can be tested from observations of lateral variations of elastic and anelastic properties near the inner core boundary. Differential travel times of PKIKP–PKiKP and the apparent travel time of P waves diffracted around the inner core are consistent with the existence of a stably stratified, globally uniform, region of reduced velocity gradient at the bottom of the outer core. This layer may be a zone of iron enrichment relative to the bulk of the outer core, representing a zone either of crystallization or melting of the inner core. Weak backscattered PKiKP in the equatorial eastern hemisphere can be made consistent with either a hypothesis of freezing or melting. In a melting hypothesis, the eastern hemisphere is texturally older and smoother, with larger crystals or smaller elastic contrasts across grain boundaries providing weaker backscatter to the coda of PKiKP. Additional observations consistent with higher homologous temperature and melting in this region are the existence of a thin low velocity layer in the uppermost inner core inferred from multipathing of PKIKP + PKiKP waves and a bright spot in the amplitude of PKIIKP waves observed at antipodal distances. Alternatively, a freezing hypothesis in the eastern hemisphere is an inner core that is growing radially outward with crystals stretched in the vertical direction. This hypothesis can simultaneously explain weak backscattered PKiKP coda and high attenuation of transmitted PKIKP from the loss of backscattered energy at angles perpendicular to vertically oriented crystals. Strong backscattering observed in the coda of PKiKP sampling the equatorial western hemisphere of the inner core agrees best with a heterogeneity having an isotropic distribution of scale lengths in the uppermost inner core.

A new construction of antipodal distance regular covers of complete graphs through the use of Godsil-Hensel matrices

New constructions of regular distance regular antipodal covers (in the sense of Godsil-Hensel) of complete graphs K n are presented. The main source of these constructions are skew generalized Hadamard matrices. It is described how to produce such a matrix of order n 2 over a group T from an arbitrary given generalized Hadamard matrix of order n over the same group T . Further, a new regular cover of K 45 on 135 vertices is produced with the aid of a decoration of the alternating group A 6 .

Using Algebraic Properties of Minimal Idempotents for Exhaustive Computer Generation of Association Schemes

During the past few years we have obtained several new computer classification results on association schemes and in particular distance regular and strongly regular graphs. Central to our success is the use of two algebraic constraints based on properties of the minimal idempotents $E_{i}$ of these association schemes : the fact that they are positive semidefinite and that they have known rank. Incorporating these constraints into an actual isomorph-free exhaustive generation algorithm turns out to be somewhat complicated in practice. The main problem to be solved is that of numerical inaccuracy: we do not want to discard a potential solution because a value which is close to zero is misinterpreted as being negative (in the first case) or nonzero (in the second). In this paper we give details on how this can be accomplished and also list some new classification results that have been recently obtained using this technique: the uniqueness of the strongly regular $(126,50,13,24)$ graph and some new examples of antipodal distance regular graphs. We give an explicit description of a new antipodal distance regular $3$-cover of $K_{14}$, with vertices that can be represented as ordered triples of collinear points of the Fano plane.

B‐Substituted (Arene)ruthenacarborane–Sulfonium, –Thioether and–Mercaptan Complexes: Mild Single and Double Dealkylation and Structural Implications in the Antipodal Distance

AbstractReactions of [RuCl2(η6‐arene)]2 (arene = benzene, p‐cymene) with nido‐[7‐R‐10‐L‐7,8‐C2B9H9]– in THF at room temperature for 3 d give the (arene)ruthenacarborane complexes closo‐[3‐Ru(η6‐arene)‐1‐R‐8‐L‐1,2‐C2B9H9]+ {arene = benzene, R = H [L = Me2S (1a), THT (1b), EtPhS (1c)], R = Me [L = Me2S (2a)]; arene = p‐cymene, R = H [L = Me2S (3a)]} and mercaptan closo‐[3‐Ru(η6‐arene)‐1‐R‐8‐HS‐1,2‐C2B9H9] [arene = benzene, R = H (4), Me (5); arene = p‐cymene, R = H (6)] in yields of 20–40 % and 22–29 %, respectively. The asymmetric ligand nido‐[9‐Me2S‐7,8‐C2B9H10]– leads to the thioether complex closo‐[3‐Ru(η6‐benzene)‐7‐MeS‐1,2‐C2B9H10] (8) in 34 % yield under the same reaction conditions. The crystal structure of 1a is described and compared with those of 4 and 8. The fully assigned 11B NMR spectroscopic data for a whole series of ruthenacarboranes having B‐substituted sulfonium, thioether and mercaptan groups are presented. These data show a relation between antipodal cluster atom distances (antipodal distance) and antipodal effect (AE) in the crystal structures of these complexes and for other families of heteroboranes such as closo‐[EB11H11] and closo‐[EB9H9]. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

Distinct seismic anisotropy at the centre of the Earth

Although arrival times of PKP DF (or PKIKP) phases from epicentral distances between 120° and 173° are consistent with an anisotropy model obtained from a joint inversion of normal-mode and body-wave data, PKP DF measurements from nearly antipodal distances (between 173° and 180°) exhibit deviations from this model. We demonstrate that this behaviour is coherent, and that the characteristics associated with these data are still those of transverse isotropy. We also perform a systematic search for the location of the symmetry axis. Results suggest that the axis may be significantly tilted away from the geographic pole; however, higher-quality data are required to draw a firm conclusion. Inversion of the data with the symmetry axis at the geographic pole yields a model of anisotropy that is considerably different from that of the inner-core between 300 and 1220 km radius. These observations imply that there is a seismically distinct region at the centre of the Earth with radius of about 300 km.

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

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

Global lightning acquisition system installed

A global network of seven time‐synchronized, high‐precision magnetometers around the world is ready to triangulate individual lightning flashes on planet Earth to monitor the temporal and spatial evolution of global lightning activity.This global network of magnetometers is able to detect the electromagnetic radiation of distant lightning flashes and makes possible remote sensing of the temporal evolution and spatial migration of global lightning activity [Füllekrug and Constable, 2000]. These results have led to international interest in a new measurement campaign with a large network of high‐precision magnetometers. The magnetic field changes are measured with ∼10‐14 Tesla accuracy (which corresponds to ∼10‐7% of the main geomagnetic field). The Global Positioning Satellites (GPS) provide time alignment of 0.00002 seconds between two measurement stations at antipodal distances (20×103, km), and the digital equipment makes possible continuous, high‐frequency recordings with 2000 samples per second.

Reception of ELF signals at antipodal distances

Measurements of 82‐Hz radio signals from a Russian ELF transmitter located on the Kola Peninsula are described. The measurements were made at several locations around the world, including Dunedin, New Zealand, and Arrival Heights, Antarctica, which are close to the antipodal point for the transmitter. This is the first time man‐made ELF signals have been observed over such long distances, and their clear reception makes possible a comparison of the theoretically predicted and measured amplitudes near the antipode. The agreement is excellent.

Anisotropy in central part of inner core

The anisotropy in the central part of the inner core has been difficult to study because of the paucity of PKP data at antipodal distances, especially for those paths running nearly north‐south (polar paths). In this paper, we systematically search through the International Seismological Center (ISC) picks of PKIKP travel times for polar paths at near‐antipodal distances reported recently by Su and Dziewonski [1995]. Corresponding seismograms were obtained from the Worldwide Standardized Seismographs Network (WWSSN) film chip library at Lamont‐Doherty Earth Observatory. By using seismograms, we can impose quality control on the data, measure differential times (AB‐DF in this case) by cross correlation and use long‐period waveforms if available. Nonpolar paths at near‐antipodal distances are assembled as well, to address biases from lateral variation in the lowermost mantle on AB‐DF times. Our results show large AB‐DF residuals of 2 to 8 s for the polar paths at near‐antipodal distances. Moreover, the absolute DF travel times for the polar paths exhibit fast anomalies of the same magnitude relative to nonpolar paths, while AB times show no obvious difference between polar and nonpolar paths. These observations are consistent with an axisymmetric anisotropy of ∼3% around the spin axis throughout the bulk of the inner core, with the possibility of even stronger anisotropy near Earth's center. This degree of anisotropy is still greater than what the most recent models based on normal modes would indicate.

Global acoustics

Spiesberger etal. [J. Acoust. Soc. Am. (to be published)] has demonstrated the feasibility of phase-coherent processing of 250-Hz coded acoustic signals transmitted from Hawaii to the West Coast over ranges of 3000 to 4000 km. The Heard Island Test [W. Munk etal., J. Acoust. Soc. Am. (to be published)] extended the range for 57-Hz transmission to antipodal distances. Such low-frequency long-range acoustics transmissions are well suited for monitoring ocean climate variability. The acoustic travel time between two fixed points are a measure of the average temperature of the intervening ocean. Basin scale averages suppress the intense mesocale eddies (order 100 km) that would otherwise dominate over the climatic variations. Propagation problems that are peculiar to global-scale transmissions will be discussed. Acoustic thermometry of ocean climate (ATOC) is scheduled for the North, Central, and South Pacific starting 1994 as a beginning of a global network. [Work supported by ONR, ARPA, NOA, NSF, and DOE.]

Distance regular covers of the complete graph

Distance regular graphs fall into three families: primitive, antipodal, and bipartite. Each antipodal distance regular graph is a covering graph of a smaller (usually primitive) distance regular graph; the antipodal distance graphs of diameter three are covers of the complete graph, and are the first non-trivial case. Many of the known examples are connected with geometric objects, such as projective planes and generalised quadrangles. We set up a classification scheme, and give new existence conditions and new constructions. A relationship with the theory of equi-isoclinic subspaces of R m , as studied by Lemmens and Seidel, is investigated.

Seismic waves at the epicenter's antipode

The antipodal region (178° ≤ Δ ≤ 180°) of a seismic wave source is investigated in detail and shown to provide a new set of remarkable data to use in the exploration of the earth's interior. Body and surface waves converge individually at antipodal distances after having sampled laterally the totality of the planet. The waves are focused and strongly amplified up to 1 order of magnitude with respect to the normal phase recorded 2° or more away. The delicate interference patterns thus formed yield information on departures from lateral homogeneity and sphericity of the core and mantle, the structure of the inner core, global dissipation characteristics of the upper mantle, and provide strong constraints on earth models. Seismograms have been synthesized that closely reproduce the phases Pdiff, PKIKP, PKIIKP, PKP(BC), PKP, and PP observed at World‐Wide Standard Seismographic Network long‐period instruments located within 5° from the antipode of the New Zealand Inangahua earthquake of May 23, 1968. Preliminary results indicate that the lower mantle and upper core are laterally homogeneous as seen by 15‐s waves, but the core‐mantle boundary region is probably laterally inhomogeneous. The inner core‐outer core boundary appears to be a sharp transition with a P wave velocity jump of the order of 0.8 km/s. The resolution of the long‐period data is poor, but the potential richness of the method when better data sets are available strongly motivated the investigation. Suggested future lines of research using antipodal observations include monitoring of inner core phases, study of focal processes of large earthquakes, and the exploration of planetary interiors.

On the focusing of seismic body waves at the epicentre's antipode

Summary. This note reports on the remarkable focusing of seismic body waves at or near the antipode (Δ= 180°) of an earthquake's epicentre. The particular seismic velocity structure and sphericity of the Earth cause body-wave phases such as P(diff), PKP, PP, PPP, PcPPKP, SKSSKS, SS, etc. to converge individually at antipodal distances after being diffracted, reflected or refracted at discontinuities. This focusing strongly amplifies each signal up to almost one order of magnitude with respect to the normal phase recorded two or more degrees away. Since the signal/noise ratio is enhanced in the same proportion, seismograms at antipodal distances provide clear and strong arrivals of otherwise weak phases. Antipodal monitoring of seismic waves is suggested as a powerful means of exploring the Earth's interior. The study of these ‘seismic images’ generated at focal points of seismic rays will yield information on the departures from lateral homogeneity and sphericity of the core, as well as stronger constraints on earth models. To interpret the observations correctly, the data must be compared with theoretically generated seismograms. Since the appropriate ray theory equations (see, e.g. Scholte; Gilbert & Helmberger; Richards) are singular at Δ=180°, a corrective measure is taken which provides a formal expression for the wave amplitude that remains finite at the antipode, and reproduces the usual expressions at other distances.