Weak velocity anomaly in the Earth’s outer core from seismic data

Experimental data on the differential travel time t _BC–t _DF of seismic waves PKP_DF and PKP_BC in the Earth’s core under Africa and Australia are analyzed. The differential travel-time residuals beneath Africa in a narrow range of angles from 21° to 25° between the direction of the seismic ray in the core and the Earth’s rotation axis exhibit a scoop-shaped peculiarity not accounted for by cylindrical anisotropy in the inner core. A model with a 0.2–0.8% P-wave velocity anomaly with a radius of 1375 km in the cylindrical region in the outer core is proposed, which closely fits the experimental data. We suggest that the velocity anomaly is generated by the dynamical processes occurring in the outer core, namely, the growth of the inner core and the convection in the outer core, both leading to the formation of a low-density anomaly in the outer core.     

Estimation of PKP times from ISC data

The International Seismological Centre (ISC) treats reports of the earliest observed core phase arrivals from earthquakes as PKIKP observations and provides residuals based on Jeffreys-Bullen PKIKP times. An analysis of some 30 000 such data from ISC bulletins for the year 1967 has shown that the data include, in addition to PKIKP, many observations of PKP₁ and precursors to PKP. By the use of simple truncation and trimming techniques, travel-time curves (expressed as differences from JB), with standard errors, have been obtained for PKIKP in the ranges 110 to 139° and 152 to 173°, and for PKP₁ in the range 144 to 154°. The PKIKP curve in these ranges agrees quite closely with the curve obtained by Cleary and Hales, and with one derived from model 1066B of Gilbert and Dziewonski, except that the Cleary-Hales curve is up to 0.7 s earlier at distances below 120°, and the 1066B curve is up to 1 s later beyond 152°. The PKP₁ curve is in good agreement with that derived from 1066B.A plot of the number of observations in each 1° distance interval has been used to estimate the positions of the cusps B, C and D on the PKP curve as 144, 152.5 and 115°, again in reasonable agreement with 1066B.     

Evidence of multiplicity in the P-travel time curve beyond 30 degrees

Slowness measurements on first and later arrivals from earthquakes in the Philippine and Taiwan regions recorded at the Warramunga array in Australia indicate abrupt decreases in slowness of the first arrival as well as triplications in the travel time curve at epicentral distances of about 38 and 43°. These results imply the presence of regions of rapid or discontinuous velocity increase at depths of about 900 and 1050 km, respectively. Between these regions of sharp velocity increases the dT/dΔ measurements indicate that the velocity gradients are lower than those determined by previous investigators. The observed extensions of the 650- and 770-km branches out to 50° can be explained in terms of the triplications if small negative velocity gradients of the order of 0.1 km/s per 100 km exist between 650–770 and 770–900 km depths. An alternative explanation of these observed extensions may be provided in terms of underside reflections from the bottom of the velocity discontinuities. Either of the two explanations require sharp velocity gradients at the depth of the velocity discontinuities. These observations are at variance with earth models where the P-wave velocity increases continuously with depth below a depth of 650 km.     

The thermal boundary-layer interpretation of D″ and its role as a plume source

The “anomalous” layer in the lowermost mantle, identified as D″ in the notation of K.E. Bullen, appears in the PREM Earth model as a 150 km-thick zone in which the gradient of incompressibility with pressure, $\text{d}\text{K}\text{d}\text{P}$, is almost 1.6, instead of 3.2 as in the overlying mantle. Since PREM shows no accompanying change in density or density gradient, we identify D″ as a thermal boundary layer and not as a chemically distinct zone. The anomaly in $\text{d}\text{K}\text{d}\text{P}$ is related to the temperature gradient by the temperature dependence of K_s, for which we present a thermodynamic identity in terms of accessible quantities. This gives the numerical result (?K_s/?T)_P=?1.6×10⁷ Pa K^?1 for D″ material. The corresponding temperature increment over the D″ range is 840 K. Such a layer cannot be a static feature, but must be maintained by a downward motion of the lower mantle toward the core-mantle boundary with a strong horizontal flow near the base of D″. Assuming a core heat flux of 1.6 × 10¹² W, the downward speed is 0.07 mm y^?1 and the temperature profile in D″, scaled to match PREM data, is approximately exponential with a scale height of 73 km. The inferred thermal conductivity is 1.2 W m^?1 K^?1. Using these values we develop a new analytical model of D″ which is dynamically and thermally consistent. In this model, the lower-mantle material is heated and softened as it moves down into D″ where the strong temperature dependence of viscosity concentrates the horizontal flow in a layer ～ 12 km thick and similarly ensures its removal via narrow plumes.     

Evidence for a sharp increase in P-wave velocity at about 770 km depth

Slowness data from earthquakes in the Mindanao and Philippine regions recorded at the Warramunga array indicate a small, but abrupt, decrease in dT/dΔ at a distance of 29.5°. There is evidence also of a triplication in the P travel-time curve at about this distance. These data strongly suggest the presence of a rapid or discontinuous velocity increase of about 2% in P-wave velocity at a depth of about 770 km. Such a velocity increase is consistent with the occurrence of more than one phase change between 600 and 900 km, as predicted by the pyrolite model of Ringwood.Previous observations of increasing dT/dΔ with distance may have resulted from the predominance of the 650-km branch as it approaches its cusp. If so, then it is not necessary to invoke a decrease in velocity with depth near 800 km to explain the increase in mdT/dΔ observed between 32–34°.     

Applications of liquid state physics to the Earth's core

By use of the modern theory of liquids and some guidance from the hard-sphere model of liquid structure, the following new results have been derived for application to the Earth's outer core. (1) dK/$\text{d}\text{P ? 5 ? 5. 6P}$/K, where K is the incompressibility and P the pressure. This is valid for a high-pressure liquid near its melting point, provided that the pressure is derived primarily from a strongly repulsive pair potential φ. This result is consistent with seismic data, except possibly in the lowermost region of the outer core, and demonstrates the approximate universality of dK/dP proposed by Birch (1939) and Bullen (1949). (2) dlnT_M/dlnρ = (γC_V ? 1)/($\text{C}{}_{\mathrm{<mtext>V</mtext>}}\text{?}\text{3}\text{2}\text{),}\text{where}\text{T}{}_{\mathrm{<mtext>M</mtext>}}$ is the melting point, ρ the density, γ the atomic thermodynamic Grüneisen parameter and C_V the atomic contribution to the specific heat in units of Boltzmann's constant per atom. This reduces to Lindemann's law for C_V = 3 and provides further support for the approximate validity of this law. (3) It follows that the “core paradox” of Higgins and Kennedy can only occur if $\text{γ <}\text{2}\text{3}$. However, it is shown that $\text{γ <}\text{2}\text{3}\text{? ∫}{}^{\mathrm{\infty }}{}_0\text{(?g/?T)}{}_{\mathrm{\rho }}\text{r(}\text{d}\text{/}\text{d}\text{r)(r}{}^2\text{φ)}\text{d}\text{r > 0}$, which cannot be achieved for any strongly repulsive pair potential φ and the corresponding pair distribution function g. It is concluded that $\text{γ >}\text{2}\text{3}$ and that the core paradox is almost certainly impossible for any conceivable core composition. Approximate calculations suggest that γ ～ 1.3–1.5 in the core. Further work on the thermodynamics of the liquid core must await development of a physically realistic pair potential, since existing pair potentials may be unsatisfactory.     

Melting temperature distribution and fractionation in the lower mantle

The melting curve of perovskite MgSiO₃ and the liquidus and solidus curves of the lower mantle were estimated from thermodynamic data and the results of experiments on phase changes and melting in silicates.The initial slope of the melting curve of perovskite MgSiO₃ was obtained as $\text{d}\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{/}\text{d}\text{P?77}\text{K}\text{GPa}{}^{\mathrm{?1}}$ at 23 GPa. The melting curve of perovskite was expressed by the Kraut-Kennedy equation as $\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{(}\text{K}\text{)=917(}\text{1+29.6ΔV}\text{V}{}_0\text{)}$, where T_m?2900 K and P?23 GPa; and by the Simon equation, $\text{P(}\text{GPa}\text{)?23=21.2[}\text{(T}{}_{\mathrm{<mtext>m</mtext>}}\text{(}\text{K}\text{)}\text{2900)}{}^{1.75}\text{?1}\text{]}$.The liquidus curve of the lower mantle was estimated as $\text{T}{}_{\mathrm{<mtext>liq</mtext>}}\text{? 0.9 T}{}_{\mathrm{<mtext>m</mtext>}}$ (perovskite) and this gives the liquidus temperature T_liq=7000 ±500 K at the mantle-core boundary. The solidus curve of the lower mantle was also estimated by extrapolating the solidus curve of dry peridotite using the slope of the solidus curve of magnesiowüstite at high pressures. The solidus temperature is ～ 5000 K at the base of the lower mantle. If the temperature distribution of the mantle was 1.5 times higher than that given by the present geotherm in the early stage of the Earth's history, partial melting would have proceeded into the deep interior of the lower mantle.Estimation of the density of melts in the MgOFeOSiO₂ system for lower mantle conditions indicates that the initial melt formed by partial fusion of the lower mantle would be denser than the residual solid because of high concentration of iron into the melt. Thus, the melt generated in the lower mantle would tend to move downward toward the mantle-core boundary. This downward transportation of the melt in the lower mantle might have affected the chemistry of the lower mantle, such as in the D″ layer, and the distribution of the radioactive elements between mantle and core.     

The caustic and other properties of SKP

The caustic of SKP is found at an epicentral distance Δ_C = 129.5° for surface foci and at Δ_C = 128.9° for foci at 400 km depth, by means of amplitude-distance graphs based upon short-period time-domain measurements. These results are essentially confirmed by long-period time-domain measurements of SKP as well as by frequency-domain studies, even though the spectra are less accurate for such determinations. The average period of SKP is $\text{T}\text{= 1.45 ± 0.45}\text{sec}$ from short-period records, significantly different from the corresponding PKP-period of 1.00 ± 0.31 sec. Likewise, the long-period averages of SKP = 10.8 ± 4.5 sec and of PKP = 7.7 ± 3.0 sec are significantly different from each other. A travel-time table of SKP1 is deduced, covering the epicentral distance range of 130–143° and the focal depth range of 100–700 km. All results are based on measurements on seismograms of the Swedish network of stations, deriving almost exclusively from earthquakes in the southwest Pacific area.     

Melting of the silica isotypes SiO 2, BeF 2 and GeO 2 at elevated pressures

The melting curves of the structural analogues SiO ₂, BeF ₂ and GeO ₂ have been studied at pressures ?40 kbar in a piston-cylinder apparatus. The initial slopes dT_m/dP of the β-quartz-liquid boundaries for SiO ₂ and BeF ₂ are ～35° while the slope of the rutile-liquid boundary for GeO ₂ is approximately 32°C/kbar. These large values of dT/dP reflect the unusually low entropies of fusion for these compounds in which strong structural similarities exist between the crystalline phases and the melt. Implications for the extended phase diagram of silica are discussed and it is concluded that either: (1) a maximum exists on the coesite melting curve, or (2) estimates of the melting temperature of stishovite need to be revised upwards.     

Q and its effect on the observation of upper mantle travel-time branches

There is broad agreement among various seismological studies that the upper mantle has two regions where high positive velocity gradients or transition zones exist. The presence of these zones implies that two major triplications should exist in the travel-time curve for distances less than 30°. Approximately 200 earthquakes from the New Guinea, New Britain, and Solomon Island regions recorded at the Warramunga Array were analyzed using adaptive processing methods in an attempt to identify the positions of the later arrival branches. From measurements made along the first 20 sec of the arrivals, a retrogade travel-time branch associated with the “650-km” discontinuity was clearly identified as extending from 21° to 26°, and some evidence was found near 16° for the lower portion of the triplication associated with the “400-km” discontinuity. A careful search revealed however that the upper portions of the replicated travel-time branches were missing. There were no observed values ofdt/dΔ in the 12–13 sec/deg range for Δ greater than 20°. In this study it was found that if anelastic effects (Q) were not taken into consideration or ifQ were kept constant, the models derived from observed travel-time data all predicted large amplitude arrivals where non existed. The difficulty with the first triplication was resolved by the introduction of a lowQ region at depths of 85–315 km. This region may be associated with “the low-velocity region” but it is not necessary to decrease the P velocity to explain the observations.The difficulty with the second triplication was resolved by the introduction of a layer at a depth of 575–657 km which has no velocity gradient and a value ofQ significantly less than that for the material just below the “650-km” discontinuity. This layer may well represent the return path for an upper mantle convection cell.     

Solidus and liquidus temperatures and mineralogies for anhydrous garnet-lherzolite to 15 GPa

A review of experimental data for systems, pertaining to anhydrous fertile garnet-lherzolite shows strong convergence in the liquidus and solidus temperatures for the range 6.5–15 GPa. These can converge either to a common temperature or to temperatures which differ by only ～ 100°C. The major-element composition of magmas generated by even minor degrees of partial melting may be similar to the primordial bulk silicate Earth composition in an upper-mantle stratigraphic column extending over 160 km in depth.The convergence of the solidus and liquidus temperatures is a consequence of the highly variable $\text{d}\text{T}\text{d}\text{P}$ of the fusion curves for minerals which crystallize in peridotite systems. In particular, $\text{d}\text{T}\text{d}\text{P}$ for the forsterite fusion curve is much less than that for diopside and garnet. Whether or not the solidus and liquidus intersect, the liquidus mineralogy for undepleted garnet-lherzolite compositions changes from olivine at low pressures to pyroxene, garnet, or a complex pyroxene-garnet solid solution at pressures in excess of 10–15 GPa. Geochemical data for the earliest Archean komatiites are consistent with an upper-mantle phase diagram having garnet as a liquidus phase for garnet-lherzolite compositions at high pressures. All estimates of the anhydrous solidus and liquidus for the range 10–15 GPa are consistent with silicate liquid compressibility data, which indicate that olivine may be neutrally buoyant in ultramafic magmas at these pressures.     

Evidences for a low-velocity core-mantle transition zone

Using the spectral ratios $\text{P}\text{PcP}\text{,}\text{ScS}{}_{\mathrm{n+1}}\text{ScS}{}_{\mathrm{n}}\text{,}\text{sScS}{}_{\mathrm{n+1}}\text{sScS}{}_{\mathrm{n}}\text{and}\text{SKS}\text{ScS}$, models for the core-mantle boundary are found. The models have close similarity with each other, implying an irregular surface with lateral variation in the core-mantle properties. The models are characterized by two to four low-velocity, high-density layers imbedded between the mantle and the core half space. The velocities of the imbedded layers decrease towards the core boundary with a lower bound of 9.3 km/sec for the compressional wave and 3.5 km/sec for the shear wave. The models fitted to the empirical data support the hypothesis of a finite rigid outer core with a higher bound for the shear velocity of 1.4 km/sec. Based on this finite rigidity in the outer core and a layered core-mantle transition zone, the value of Q for the whole mantle is 2,000. For the outer core Q ranges from 100–1,000 , which may indicate that it is chemically zoned.     

Anelastic degradation of acoustic pulses in rock

Measurements on acoustic pulses propagating in massive rock lead to a simple empirical relationship between the pulse rise time, τ and the time of propagation of a pulse, t:

$\text{τ=τ}{}_0\text{+C}\text{∫}\text{)}\text{T}\text{Q}{}^{\mathrm{?1}}\text{d}\text{t}$

where τ₀ is the initial rise time (at t = 0), Q is the anelastic parameter which may be expressed in terms of the fractional loss of energy per cycle of a sinusoidal wave, Q = 2π(ΔE/E)^?1, and is assumed to be essentially independent of frequency, and C is a constant whose value we estimate experimentally to be 0.53 ± 0.04. Of the linear theories of seismic pulse attenuation, model 2 of Azimi et al. (1968) is favoured. Pulse shapes computed from equations of Futterman (1962) also give C = 0.5, but the pulse arrives earlier than in a non-attenuating medium with the same elasticity and density. Pulse shapes calculated using Strick's (1967, 1970, 1971) theory give values of C incompatible with our results. The observations suggest that a method of estimating the Q-structure of the earth from seismic pulse rise times may have a particular advantage over the spectral ratio method.     

Magnetic properties of ulvöspinel

Magnetisation measurements on ulvöspinel have shown that there is a transition from the weakly ferromagnetic state to an essentially antiferromagnetic one at T ～ 60–100 K when moderate measuring fields (24 kOe) are used. Cooling from above 100 K in the presence of a magnetic field of several kilooersteds produces a reversed remanence for $\text{T ? 40}\text{K}$ and the resulting thermomagnetic curve is Néel N-type. Magnetisation in 80 kOe produces a spontaneous moment extrapolated to 0 K of 0.015 μ_B, although this may not be completely saturated. An explanation for the magnetic transition is suggested in terms of an increased anisotropy possibly associated with a crystal transition.     

How strong is the magnetic field in the Earth's liquid core?

A crucial step in the investigation of the energetics of motions in the Earth's core and the generation of the geomagnetic field by the hydromagnetic dynamo process is the estimation of the average strength $\text{B}$ of the magnetic field B = B_p + B_T in the core. Owing to the probability that the toroidal field B_T in the core, which has no radial component, is a good deal stronger than the poloidal field B_p, direct downward extrapolation of the surface field to the core-mantle interface gives no more than an extreme lower limit to $\text{B}$. This paper outlines the indirect methods by which $\text{B}$ can be estimated, arguing that $\text{B}$ is probably about 10^?2 T (100 Γ) but might be as low as 10^?3 T (10 Γ) or as high as 5 × 10^?2 T (500 Γ).     

Is the lower mantle homogeneous?

Comparison of some array dt/dΔ studies with the global travel times of Dziewonski and Anderson (1983) leads to the conclusion that a discontinuity in the P travel times between 80° and 85° is consistent with both sets of data. This discontinuity in dt/dΔ corresponds to an increase in velocity of about 0.1 km/sec between depths of 2400 and 2600 km. Models of the P velocity distribution which match the Dziewonski and Anderson travel times reasonable well have the shadow zone for short-period “diffracted” P beginning at about 110° arc distance.     

Are anharmonicity corrections needed for temperature-profile calculations of interiors of terrestrial planets?

It is shown that there is linearity between the thermal pressure P_TH and T between the Debye temperature θ and some high temperature $\text{T}{}^1$. $\text{T}{}^1$ has been measured at 1 atm and is reported for several minerals including, for example, MgO (1300 K) and forsterite (1200 K). The change in thermal pressure from room temperature for five solids, so far measured, indicate striking linearity with T at high temperatures.It is further shown that the value of $\text{T}{}^1$ increases greatly as the pressure increases. It is therefore concluded that P_TH is probably linear with T for mantle minerals under mantle conditions. The proportionality constant is derived from the measurements of thermal expansivity and bulk modulus at high temperature and zero pressure.The argument is then reversed. Assuming that the thermal pressure is in fact linear with T for the various shells in a planet, the resulting density and temperature profile of the planet is derived. The resulting density profile of the Earth compares favorably with corresponding values of recent seismic profiles.     

Rupture process of the Miyagi-Oki,Japan, earthquake of June 12, 1978

The faulting mechanism and multiple rupture process of the M = 7.4 Miyagi-Oki earthquake are studied using surface and body wave data from local and worldwide stations. The main results are as follows. (1) P-wave first motion data and radiation patterns of long-period surface waves indicate a predominantly thrust mechanism with strike N10° E, dip 20°W, and slip angle 76°. The seismic moment is 3.1 × 10²⁷ dyne-cm. (2) Farfield SH waveforms and local seismograms suggest that the rupture occurred in two stages, being concordant with the two zones of aftershock activity revealed by the microearthquake network of Tohoku University. The upper and lower zones, located along the westward-dipping plate interface, are separated by a gap at a depth of 35 km and have dimensions of 37 × 34 and 24 × 34 km², respectively. Rupture initiated at the southern end of the upper aftershock zone and propagated at N20°W subparallel to the trench axis. About 11 s later, the second shock, which was located 30 km landward (westward) of the first, initiated at the upper corner of the lower aftershock zone and propagated down-dip N80°W. Using Haskell modelling for this rupture process, synthetic seismograms were computed for teleseismic SH waves and nearfield body waves. Other parameters determined are: seismic moment $\text{M}{}_0\text{= 1.7 × 10}{}^{27}\text{dyne-cm, slip dislocation}\text{u}\text{= 1.9}\text{m}\text{, Δσ = 95}\text{bar, rupture velocity}\text{ν = 3.2}\text{km s}{}^{\mathrm{?1}}\text{,}\text{rise time}\text{τ = 2}\text{s}$, for the first event; $\text{M}{}_0\text{= 1.4 × 10}{}^{27}\text{dyne-cm}\text{,}\text{u}\text{= 2.4}\text{m}\text{, Δσ = 145}\text{bar}$, for the second event; and time separation between the two shocks ΔT = 11 s. The above two-segment model does not explain well the sharp onsets of the body waves at near-source stations. An initial break of a small subsegment on the upper zone, which propagated down-dip, was hypothesized to explain the observed near-source seismograms. (3) The multiple rupture of the event and the absence of aftershocks between the two fault zones suggests that the frictional and/or sliding characteristics along the plate interface are not uniform. The rupture of the first event was arrested, presumably by a region of high fracture strength between the two zones. The fracture energy of the barrier was estimated to be 10¹⁰ erg cm^?2. (4) The possible occurrence of a large earthquake has been noted for the region adjacent to and seaward of the area that ruptured during the 1978 event. The 1978 event does not appear to reduce the likelihood of occurrence of this expected earthquake.     

Magnetic properties of synthetic titanomagnetites

Magnetic properties and crystal structure parameters of synthetic solid solutions Fe₃O₄Fe₃TiO₄, Fe₂O₄MgFe₂O₄ and Fe₃O₄Mg₂TiO₄ have been studied. Basic regularities in the behaviour of saturation magnetisation (I_s), Curie temperature (T_C) and cubic lattice parameter a during the substitution of Ti and Mg ions for Fe ions have been found. As the concentration of Ti ions increases, I_s reduces from 70 Gs·cm³ g^?1 to 0, T_C changes from 580 to 130°C and a from 8.391 to 8.520 Å. Growth of the Mg concentration leads to changes in I_s to 19.8 Gs·cm³, g^?1, T_C, to 440°C and a, to 8.360 Å. The full Fe ions substitution gives $\text{“a”=8.440}\text{A}\text{?}$.Chemical compositions of the samples, in which the valency variation of Fe ions at oxidation leads to an increase in susceptibility and T_C, have been determined.