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In this study, we obtain a set of 2-D global phase velocity and attenuation maps for Rayleigh waves between 5 and 25 mHz. Correcting the effect of focusing–defocusing is crucial in order to obtain reliable attenuation structure. Great circle linearized ray theory, which has been used to date, can give useful predictions of this effect if careful attention is paid to how the phase velocity model is smoothed. In contrast, predictions based on the 2-D finite-frequency kernels are quite robust in this frequency range and suggest that they are better suited as a basis for inversion. We use a large data set of Rayleigh wave phase and amplitude measurements to invert for the phase velocity, attenuation, source and receiver terms simultaneously. Our models provide 60–70 per cent variance reduction to the raw data though the source terms are the biggest contribution to the fit of the data. The attenuation maps show structures that correlate well with surface tectonics and the age progression trend of the attenuation is clearly seen in the ocean basins. We have also identified problematic stations and earthquake sources as a by-product of our data selection process. [ABSTRACT FROM AUTHOR]

The inverse problem for Earth structure from normal mode data is strongly non-linear and can be inherently non-unique. Traditionally, the inversion is linearized by taking partial derivatives of the complex spectra with respect to the model parameters (i.e. structure coefficients), and solved in an iterative fashion. This method requires that the earthquake source model is known. However, the release of energy in large earthquakes used for the analysis of Earth's normal modes is not simple. A point source approximation is often inadequate, and a more complete account of energy release at the source is required. In addition, many earthquakes are required for the solution to be insensitive to the initial constraints and regularization. In contrast to an iterative approach, the autoregressive linear inversion technique conveniently avoids the need for earthquake source parameters, but it also requires a number of events to achieve full convergence when a single event does not excite all singlets well. To build on previous improvements, we develop a technique to estimate structure coefficients (and consequently, the splitting functions) using a derivative-free parameter search, known as neighbourhood algorithm (NA).We implement an efficient forward method derived using the autoregresssion of receiver strips, and this allows us to search over a multiplicity of structure coefficients in a relatively short time. After demonstrating feasibility of the use of NA in synthetic cases, we apply it to observations of the inner core sensitive mode 13S2. The splitting function of this mode is dominated by spherical harmonic degree 2 axisymmetric structure and is consistent with the results obtained from the autoregressive linear inversion. The sensitivity analysis of multiple events confirms the importance of the Bolivia, 1994 earthquake. When this event is used in the analysis, as little as two events are sufficient to constrain the splitting functions of 13S2 mode. Apart from not requiring the knowledge of earthquake source, the newly developed technique provides an approximate uncertainty measure of the structure coefficients and allows us to control the type of structure solved for, for example to establish if elastic structure is sufficient. [ABSTRACT FROM AUTHOR]

Various factors need to be considered when inverting for surface wave azimuthal anisotropic structure. This paper focuses on the 2ϕ terms for Rayleigh wave azimuthal anisotropy and shows that the uncertainties of earthquake locations also have significant impacts on the resulting anisotropic structure. We use the global Rayleigh wave phase velocity data set collected in a previous study to demonstrate this effect. The differences between azimuthal anisotropic patterns with and without source relocations are greatest near plate boundaries. Large differences around the South American plate are also identified. Although most of the earthquakes are shifted by less than 15 km from the CMT locations, earthquakes near the Andes can be systematically shifted by more than 30 km. Our final epicentres for earthquakes on ridge-transform fault systems better match the plate boundaries. [ABSTRACT FROM AUTHOR]

A new method is developed to measure Rayleigh- and Love-wave phase velocities globally using a cluster analysis technique. This method clusters similar waveforms recorded at different stations from a single event and allows users to make measurements on hundreds of waveforms, which are filtered at a series of frequency ranges, at the same time. It also requires minimal amount of user interaction and allows easy assessment of the data quality. This method produces a large amount of phase delay measurements in a manageable time frame. Because there is a strong trade-off between the isotropic part of the Rayleigh-wave phase velocity and azimuthal anisotropy, we include the effect of azimuthal anisotropy in our inversions in order to obtain reliable isotropic phase velocity. We use b-splines to combine these isotropic phase velocity maps with our previous group velocity maps to produce an internally consistent global surface wave dispersion model. [ABSTRACT FROM PUBLISHER]

Recent seismological observations suggest the existence of a ≈150-km-thick density-stratified layer with a P-wave velocity gradient that differs slightly from PREM. Such a structure can only be caused by a compositional gradient, effects of a slurry or temperature being too small and probably the wrong sign. We propose a stably stratified, variable concentration layer on the liquidus. Heat is transported by conduction down the liquidus while the light and heavy components migrate through the layer by a process akin to zone refining, similar to the one originally proposed by Braginsky. The layer remains static in a frame of reference moving upwards with the expanding inner core boundary. We determine the gradient using estimates of , the concentration in the main body of the outer core, and , the concentration of the liquid at the inner core boundary. We determine the depression of the melting point and concentrations using ideal solution theory and seismologically determined density jumps at the inner core boundary. We suppose that determines , the jump from normal mode eigenfrequencies that have long resolution lengths straddling the entire layer, and that determines , the jump determined from body waves, which have fine resolution. A simple calculation then yields the seismic, temperature, and concentration profiles within the layer. Comparison with the distance to the C-cusp of PKP and normal mode eigenfrequencies constrain the model. We explore a wide range of possible input parameters; many fail to predict sensible seismic properties and heat fluxes. A model with , and layer thickness 200 km is consistent with the seismic observations and can power the geodynamo with a reasonable inner core heat flux of ≈2 TW and nominal inner core age of ≈1 Ga. It is quite remarkable and encouraging that a model based on direct seismic observations and simple chemistry can predict heat fluxes that are comparable with those derived from recent core thermal history calculations. The model also provides plausible explanations of the observed seismic layer and accounts for the discrepancy between estimates of the inner core density jumps derived from body waves and normal modes. [ABSTRACT FROM AUTHOR]

We model the inner core by an alloy of iron and 8 per cent sulphur or silicon and the outer core by the same mix with an additional 8 per cent oxygen. This composition matches the densities of seismic model, Preliminary Reference Earth Model (PREM). When the liquid core freezes S and Si remain with the Fe to form the solid and excess O is ejected into the liquid. Properties of Fe, diffusion constants for S, Si, O and chemical potentials are calculated by first-principles methods under the assumption that S, O, and Si react with the Fe and themselves, however, not with each other. This gives the parameters required to calculate the power supply to the geodynamo as the Earth's core cools. Compositional convection, driven by light O released at the inner-core boundary on freezing, accounts for half the entropy balance and 15 per cent of the heat balance. This means the same magnetic field can be generated with approximately half the heat throughput needed if the geodynamo were driven by heat alone. Chemical effects are significant: heat absorbed by disassociation of Fe and O almost nullify the effect of latent heat of freezing in driving the dynamo. Cooling rates below 69 K Gyr−1 are too low to maintain thermal convection everywhere; when the cooling rate lies between 35 and 69 K Gyr−1 convection at the top of the core is maintained compositionally against a stabilizing temperature gradient; below 35 K Gyr−1 the dynamo fails completely. All cooling rates freeze the inner core in less than 1.2 Gyr, in agreement with other recent calculations. The presence of radioactive heating will extend the life of the inner core, however, it requires a high heat flux across the core–mantle boundary. Heating is dominated by radioactivity when the inner core age is 3.5 Gyr. We, also, give calculations for larger concentrations of O in the outer core suggested by a recent estimation of the density jump at the inner-core boundary, which is larger than that of PREM. Compositional convection is enhanced for the higher density jumps and overall heat flux is reduced for the same dynamo dissipation, however, not by enough to alter the qualitative conclusions based on PREM. Our preferred model has the core convecting near the limit of thermal stability, an inner-core age of 3.5 Gyr and a core heat flux of 9 TW or 20 per cent of the Earth's surface heat flux, 80 per cent of which originates from radioactive heating. [ABSTRACT FROM AUTHOR]

The power required to drive the geodynamo places significant constraints on the heat passing across the core–mantle boundary and the Earth's thermal history. Calculations to date have been limited by inaccuracies in the properties of liquid iron mixtures at core pressures and temperatures. Here we re-examine the problem of core energetics in the light of new first-principles calculations for the properties of liquid iron. There is disagreement on the fate of gravitational energy released by contraction on cooling. We show that only a small fraction of this energy, that associated with heating resulting from changes in pressure, is available to drive convection and the dynamo. This leaves two very simple equations in the cooling rate and radioactive heating, one yielding the heat flux out of the core and the other the entropy gain of electrical and thermal dissipation, the two main dissipative processes. This paper is restricted to thermal convection in a pure iron core; compositional convection in a liquid iron mixture is considered in a companion paper. We show that heat sources alone are unlikely to be adequate to power the geodynamo because they require a rapid secular cooling rate, which implies a very young inner core, or a combination of cooling and substantial radioactive heating, which requires a very large heat flux across the core–mantle boundary. A simple calculation with no inner core shows even higher heat fluxes are required in the absence of latent heat before the inner core formed. [ABSTRACT FROM AUTHOR]

Examines the matrix autoregressive analysis of free-oscillation coupling and splitting in earthquakes. Use of mode splitting analysis in determining the occurrence of earthquake; Splitting matrices of the coupled mode; Motion of the spherical-earth singlets.

Describes the autoregressive estimation of the splitting matrix of free-oscillation multiplets from earthquakes. Measurement of singlet frequencies and the level of splitting; Sensitivity of axisymmetric structure on multiplet; Use of displacement scalars to perform two-step linear inversion.

Reports on the use of free-oscillation splitting functions in the measurement of differential rotation of the Earth's inner core. Why free oscillation is more accurate than formerly used seismic body-wave studies; Role of earthquakes in the measurement process; Conclusion that the inner core is probably gravitationally locked to the Earth's mantle.

This paper establishes connections between Braithwaite's theory of reintegrative shaming, relational justice, and the ethic of care of feminist philosophy. The paper uses Heidensohn's Portia and Persephone to represent the justice and care ethics, and presents empirical material on victim-offender mediation, family group conferencing, and a Japanese approach to social control to argue that procedures allowing for the expression of caring as a response to offending are both theoretically well founded and practically feasible. The paper examines criticism of the Portia model court, with a significant element of critique being Portia's tendency to neglect or abuse victims. The article suggests the importance of condemning offenses to convey the acts as unacceptable, but Portia extends the condemnation to the actor, and the person is labeled unacceptable. By rendering the victim invisible, Portia acts as if no relationship between offender and victim exist. Examples illustrate how the approach and possible outcome of Perspehone differ. It is suggested that relational justice is a distinctly feminine approach to crime and conflict. Reintegrative shaming as it related to Japan's low crime rates is discussed.

Presents the algorithms for the stable computation of generalized and ordinary spherical harmonics. Speed of algorithms; Use of algorithms for computation of harmonics; Implementation of algorithsm in Fortran and C programs.

Precise measurements of the impulse response of the ocean sound channel were made during the 1983 reciprocal acoustic transmission experiment at the 300-km range with source and receiver near the sound channel axis. The transmitted pulse was centered at 400 Hz and had approximately 10-ms resolution. Using measured XBT data and the technique of inverse theory, a range-dependent sound-speed field had previously been computed such that the measurements were consistent with the prediction of range-dependent ray theory (Howe et al., 1986). Predictions made for the range-averaged sound-speed profile using normal mode theory, the WKBJ approximation, and ray theory were found to be in excellent agreement (though a small discrepancy with the measurements remained, since range dependence was neglected). By allowing for range dependence through the use of adiabatic normal mode theory, this discrepancy was largely removed. We conclude that ray theory or WKBJ theory is an adequate prediction technique at 400 Hz in this geometry. [Work supported by NSF and ONR.] [ABSTRACT FROM AUTHOR]

Discusses the results of a paper which present tomographic images of the earth that will help geochemists to understanding mantle flow of the Earth's crust. The factors which make this contribution notable; The display of narrow compressional velocity anomalies in the lower mantle; Other significant aspects; The paper by van der Hilst and others in the April 10, 1997 issue of `Nature.'