Stochastic perturbation theory is used to study the propagation of plane seismic waves in a medium in which random fluctuations in local density and elastic shear modulus are considered. Random horizontal stratification is modeled by the use of anisotropic correlation functions for these variables. The results indicate that the P-wave (S-wave) group velocity is increased (decreased) when kl>1; the oppossite occurs when kl<1. The changes for the phase velocities are in the opposite sense. Attenuation coefficients are given for the P, SH and SV components. The results agree with a calculation (BOURRET, 1980) using the parabolic approximation (valid only for kl>1).

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A statistical study of the earthquake catalogue compiled by the Japan Meteorological Agency during 1961-1979 suggests empirical rules on earthquake prediction in Japan. In each earthquake sequence, the magnitude of the largest event which has already occurred by time t is defined as M₁. Similarly, those of the largest fore- and aftershocks with respect to M₁ are defined as F₁ and A₁, respectively. The proposed rules are: (1) When seismic activity occurs with M₁-F₁≤0.4 within about a week, it may be a foreshock sequence followed by a larger event. The probability is 25-30% for M₁-F₁≤0.2, and 20% for 0.3≤M₁-F₁≤0.4. (2) A similar rule is also applicable for M₁-A₁≤0.2. The probability is 20%. (3) If 0.5≤M₁-F₁ and 0.3≤M₁-A₁, the probability is, roughly speaking, 5-10% or less. In these cases, M₁ is expected with high probability to be a main shock. (4) The magnitude of the expected event is larger than M₁ by about 0.5 on the average. (5) About 40-45% and 80% of the expected events occur within a day and a week, respectively, after criterion (1) or (2) is satisfied. Time intervals of F₁-M₁ and M₁-A₁ may also help to estimate the time of the expected event. (6) If no larger events actually occur within a day or a week after criterion (1) or (2) is satisfied, the probability that a larger event is still expected drops to 3/5 or 1/5 of the initial value, respectively.

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This paper presents a method for the computation of quasi-static surface displacements caused by the sudden appearance of a dislocation in a stratified elastic half-space with an intervenient, Maxwellian viscoelastic layer. Integral representations of the displacements are derived from those in the associated elastic case by applying the correspondence principle of linear viscoelasticity. Evaluation of the integral is carried out by using a method of approximating a part of the integrand by an analytical function.
The surface motion consists of an instantaneous elastic rebound at the time of faulting and a transient viscoelastic movement after the event. Time dependent properties of the viscoelastic movement are formally prescribed by a certain number of time constants, those are functions of a wave number determined by the rheological structure of the medium.
General features of the viscoelastic movement are investigated from various aspects. First, changes in the displacement profiles with dip-angle are examined for the point dislocation sources located in the elastic surface layer of a three-layered model at different depths. Second, variations of the displacement profiles with time are examined for various structure models with different thicknesses of the viscoelastic layer. Finally, the vertical and horizontal displacement fields due to a finite-dimensional fault are calculated for a three-layered model, and compared with those for different types of structure models, such as a viscoelastic half-space model and a two-layered model which consists of an elastic layer overlying a viscoelastic half-space.

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It is proposed that a preseismic fault slip process provides one of the possible mechanisms that explain observations of relatively long-term, anomalous surface deformations preceding large crustal earthquakes.
The process in a two-dimensional dip-slip fault zone is numerically analyzed by using the finite element method with a new element model. The process is modeled in terms of (1) constitutive laws for the fault zone and surrounding material and (2) a nonuniform distribution of the shear stress relative to yield strength along the fault zone. The constitutive law for the fault zone is assumed to be expressed by a mechanical model of elastic-elastoplasticity, which is composed of two kinds of springs and a slider. The law draws support from the data obtained by the recent stick-slip experiments with pre-faulted rock samples.
Preseismic slip in a certain portion of the fault zone, which is caused by remotely applied displacements acting parallel to the fault, is represented by a crack-like solution. The portion of the fault zone undergoing slip elongates in response to the remotely applied, successively increasing displacements, controlled by pre-existing nonuniformity of the shear stress relative to yield strength along the fault zone. Therefore, various types of the change of reseismic, anomalous surface deformation with time can be explained by assuming suitable variations of shear stress and/or yield strength along an earthquake fault.

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The present system to observe the bottom pressure by use of a quartz pressure sensor was laid at a depth of 2, 200m on the sea bed 100km off the south coast of the Tokai district, Japan, in August, 1978. The on-line real-time bottom pressure signal is transmitted to the shore through a submarine cable. The system is designed so as to have high reliability, which assures us of fruitful observation for more than ten years. Characteristic instrumental noises are occasionally recognized on the records. It is inferred that the noises are caused by the short period bottom temperature changes. The utility of the data, however, is not significantly impaired by them. A linear trend of the record due to the aging of quartz is +9.6cmH₂O/year in 1979. This may make it impossible to discriminate the secular vertical crustal movement, but the record has an advantage over the coastal tide records for the detection of the large precursory vertical movement just prior to a great earthquake, because the meteorological and oceanographic disturbances on the ocean bottom are far less than those on the coastal sea surface. It is shown that the pressure sensor also acts as a long-period accelerometer of the frequency band 0 to 1/6Hz and a resolution of 0.01 Gal.

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