In this paper, we treat quasi-static deformations of a viscoelastic half-space due to a rectangular fault. Analytical expressions of displacement and strain fields are derived by applying the correspondence principle of linear viscoelasticity. The rheology of the medium is assumed to be elastic dilatational and Maxwell or Voigt deviatoric, and the time function of the displacement dislocation is taken to be of a step type. The quasi-static deformation consists of an instantaneous response at the time of faulting and a transient deformation after the event. In the case of either the Maxwell or Voigt solids, the time dependence of the transient part is characterized by two time constants. Expressions of the quasi-static stresses are obtained from those of the strains on the basis of the Laplace transform. Features of the quasi-static deformations in a viscoelastic half-space are investigated in a vertical plane which bisects a rectangular fault. First, we examine the deformation fields in the Maxwell solid. In the case of a strike-slip fault, the transient viscoelastic movement progresses so as to decrease the instantaneous elastic response. Such a tendency is not remarkable in the case of a dip-slip fault, and the viscoelastic displacement field shows a more complicated pattern than the elastic deformation. The total stress field in the Maxwell solid tends to zero as time increases. Next, we examine the quasi-static deformations in the Voigt solid, and compare the results with those for the Maxwell solid. The pattern of quasi-static deformation due to the strike-slip fault does not strongly depend on the rheological properties of the medium. In the case of the dip-slip fault, on the other hand, both instantaneous and transient parts of the deformation field show different patterns from those in the Maxwell solid. The total stress field in the Voigt solid converges to the elastic stress field with increase of time.

View full abstract

The pulse width of the initial P wave was measured for about 300 aftershocks of the western Nagano, Japan earthquake of September 14, 1984. Based on the data set, the statistical relationship between the fault length L (km) and earthquake magnitude determined by the Japan Meteorological Agency M_J, log L= 0.58M_J - a was established for the magnitude range of M_J = 3-5. The constant a takes the value of 2.48-2.64 depending on the fault type assumed. It appears that this formula may give a good estimate of the fault length even for larger earthquakes of M_J up to 8. The L-M_J relation is converted to M_O = b × 10²²L^2.3 where M_O is the seismic moment (dyn · cm), and b is a constant taking the value of 4.9-11.4 corresponding to a. This relation predicts that the stress drop associated with fault rupture increases with the seismic moment of an earthquake.

View full abstract

Single station group velocities over the period range 15-100 s are computed for nine fundamental mode Rayleigh wave propagation paths that cross tectonic provinces of the Fiji region. These computations are based on recordings of the earthquakes around the Fiji Islands by the WWSSN (World Wide Standard Seismic Network) stations AFI (Afiamalu), HNR (Honiara), and WEL (Wellington). The inversion of the derived dispersion curves for shear velocity-depth structure shows that uppermost mantle velocity beneath South Fiji basin, Lau basin, and North Fiji basin is slightly lower than that derived for the Pacific ocean region of similar age by Yu and MITCHELL (1979). The uppermost mantle lid is almost absent beneath these marginal basins, and the shear velocity is between 4.0-4.3 km/s in the depth range from Moho down to 220 km.

View full abstract

Response of the upper mantle structure near the East Pacific Rise to Rayleigh and Love waves for periods less than 200 s is investigated through the group velocity partial derivatives with respect to changes of shear and compressional wave velocities and density. A noteworthy characteristic of the partial derivatives with respect to shear wave velocity is that the maximum amplitude of the group velocity partial derivatives of Rayleigh waves of the first two modes is about twice that of the phase velocity partial derivatives. Using the group velocity partial derivatives of Rayleigh and Love waves, the structures of the asthenosphere are determined and discussed with special respect to accuracy and resolution. The detailed structures exhibit significant discrepancies between the profiles of vertically and horizontally polarized shear wave velocities at depths of 60-90 km in the asthenosphere, with a minimum vertically polarized shear wave velocity of 4.0 km/s at those depths. The profile of horizontally polarized shear wave velocity does not possess a clear boundary between the lithosphere and the low velocity zone.

View full abstract

Based on Akaike's Bayesian Information Criterion (ABIC), a new method is proposed for detecting changes in the magnitude-frequency relation. Earthquakes are classified into a few magnitude classes and the ratio between the numbers of shocks in these classes is estimated by using ABIC. The time variation of the magnitude-frequency relation is investigated by this method for the source areas of three events with magnitude 6.0 and above in central Japan; the Southern Ibaraki Earthquake of 1983, the Eastern Yamanashi Earthquake of 1983 and the Western Nagano Earthquake of 1983. In.the southern Ibaraki and the Eastern Yamanashi regions, the frequency of larger shocks in comparison with smaller shocks increased about 1 year preceding the main shocks. In the Western Nagano region, the number of large shocks may have increased 2 years before the main shock. The time variations of the former cases are statistically significant.

View full abstract