Appearance times of earthquake precursory phenomena are analyzed to calculate the synthesized probability of earthquake occurrence when multiple disciplines of precursors are observed. Various disciplines of precursors are classified into three groups: long, middle and short terms. We assume they are independent mutually. By analyzing the precursor time (T_p) data for each term using Weibull distribution function, it is found that distributions of T_p data for long, middle, and short terms have the properties of increasing, decreasing, and nearly constant hazard rates, respectively. Using Weibull parameters estimated for each term, we calculate the conditional probability of earthquake occurrence on the basis of the appearance times of precursors; where "conditional" means calculating probability on the condition that no earthquake has happened yet by the current time. Reliability parameter r is introduced for each term to take account of such a possibility that a part of the "precursors" are spurious ones. Introducing of the parameter r (<1) has an effect to make the conditional probability for every term decrease monotonously long after the appearance of each precursor. The synthesized probability is obtained by the formula of Utsu (1977, 1983). A probability change is calculated for the case of the Izu-Oshima-Kinkai earthquake of 1978 by applying this method to the observed precursor data.

View full abstract

We compare the theoretical excitation of surface waves and tsunamis by sources represented by single forces and double-couples. We first show that an average single force, whose orientation and exact depth are unknown, should excite any seismic wave proportionally to wavelength, relative to a similarly average double-couple, having the same source time function. Because of the condition of zero impulse on the whole planet, the spectrum of a single force source has an additional ω² factor at low frequencies. As a result, a general deficiency in long period energy is expected. However, we show on a number of examples that it can be observed only at the extreme low-frequency end of the spectrum of mantle waves, and probably would escape routine seismological observation.
We explore the possibility of identifying single force sources on the basis of single-station inversions of Love and Rayleigh waves, through the systematic inversion of synthetic spectra. Inversion of double-couple spectra for single forces (and vice versa) have variance reductions on the order of 70%, which may be too performant to allow discrimination under operational conditions, including noise and inaccurate epicentral distances. An important case is that of the pure dip-slip double-couple geometry on a purely vertical fault, which can be recognized from a single horizontal force, provided both Rayleigh and Love waves are used over a sufficiently broad range of frequencies. Previous controversy, notably in the case of the 1975 Kalapana, Hawaii earthquake, may reflect the use of band-pass filtered Love waves.
In the case of tsunami excitation, and because of the ω² term brought about by the condition of zero-impulse, single forces are significantly deficient tsunami generators, by as much as 1.5 orders of magnitudes, relative to a double-couple exciting comparable mantle waves. The enhanced tsunamis occasionally excited by events successfully modeled as single forces are due to the mechanical interaction of the source, whatever its nature, with softer layers in the vicinity of the surface.

View full abstract

The recent recognition of cyclically laminated tidal rhythmites provides a new approach to tracing the dynamic history of the Earth-Moon system. Late Proterozoic (-5650 Ma) elastic rhythmites in South Australia represent an unsurpassed palaeotidal record of -560 years' duration that provides numerous palaeorotational parameters. At -5650 Ma there were 13.1+-0.1 lunar months/year, 400+-7 solar days/year, and 30.5+-0.5 solar days/lunar month. The lunar apsides and lunar nodal cycles were then 9.7+-0.1 years and 19.5+-0.5 years, respectively. The indicated mean Earth-Moon distance of 58.28+-0.30 Earth radii at -5650 Ma gives a mean rate of lunar retreat of 1.95+-0.29 cm/year since that time, about half the present rate of lunar retreat of 3.7+-0.2 cm/year obtained by lunar laser ranging. The rhythmite data imply a substantial obliquity of the ecliptic at -5650 Ma, and indicate virtually no overall change in the Earth's moment of inertia, which militates against significant Earth expansion since -5650 Ma. Early Proterozoic (-52, 500 Ma) cyclic banded iron-formation in Western Australia, that may record submarine fumarolic activity triggered by earth tides, suggests -514.5+-0.5 lunar months/year and a mean Earth-Moon distance of -554.6 Earth radii at -52, 500 Ma. The combined rhythmite data suggest a mean rate of lunar retreat of -51.27 cm/year during the Proterozoic (-52, 500-650 Ma); the indicated increasing mean rate of lunar retreat since -52, 500 Ma is consistent with increasing oceanic tidal dissipation as the Earth's rotation slows. A close approach of the Moon during earlier time is uncertain. Continued study of tidal rhythmites promises to further illuminate the evolving dynamics of the Earth-Moon system.

View full abstract

Long-wavelength seismic velocity studies for the mantle indicate that mantle structure is dominated by very large-scale heterogeneity, shown predominantly by harmonic degrees l=1 and 2 for the whole mantle; near the surface l=5 and 6 produce a secondary peak. Dominance of these anomalies suggests the existence of similarly large-scale convection currents. The qualitative differences between the upper and the lower mantle are evident in the distribution of heterogeneity and in the shift of l=2 velocity variation components. Along with other geophysical observables such as attenuation parameters (Q) and viscosity, different styles of dynamics are implied for the upper and lower mantle. In particular, the shift of the l=2 velocity variation pattern is a fairly robust and common feature among recent three-dimensional Earth models and seems to favor the predominantly layered convection model. There is, however, evidence that the boundary layer between the upper and lower mantle, if it exists, is not as strong as those boundary layers at the top and the bottom of the mantle.

View full abstract

In an earlier paper the variation of melt fraction with temperature near the solidus of a rock with the composition of a garnet peridotite was parameterized as a continuous function of temperature. A number of people have suggested that eutectic melting is a better description of the behaviour near the solidus. Therefore a 'eutectic' parameterization is used here, and requires a finite melt fraction to be produced at the solidus before the temperature can increase further. The resulting changes in melt volumes and compositions are small, and are of similar magnitude to the likely errors in the earlier calculations.

View full abstract