An elastic wave equation in a heterogeneous medium is solved by means of the WKB method. If it refers to the connection formula around a turning point, a solution that formally expresses a progressive wave, A(x)cos{ωt-k(x)x}, does not always satisfy the principle of energy conservation. The wave propagation with physical significance should be discussed using the structure of the heterogeneous medium intervening between two homogeneous half spaces.

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The faulting process of a moderate-size shallow earthquake on inland Japan, the central Gifu earthquake of September 9, 1969(M=6.6), has been investigated by synthesizing all available seismic and geodetic data.
The focal mechanism solution based on data from Japanese and WWSSN stations and the spatial distribution of aftershocks indicate that the earthquake was caused by left-lateral strike-slip motion along a vertical fault plane with dimensions of 20 by 10km striking in the N30°W direction. The strong-motion records from five JMA stations within a distance of 80km are compared with the synthetic seismograms computed from dynamic dislocation models. The comparison yields estimates for the seismic moment, average fault displacements, rise time, and rupture velocity. The pattern of vertical tectonic movements from pre- and post-earthquake leveling data along two nearby routes is generally consistent with that derived from the corresponding static models, but there is some possibility that displacements over the northwestern part of the fault might be considerably larger than the average. The strain steps that have been recorded during the earthquake on 23 strain meters at ten crustal movement observatories are not always consistent with theoretically expected values.
In relation to the faulting process, pre-earthquake data from leveling and tiltmeter observations are also examined from the viewpoint of earthquake prediction, and tectonic implications of the earthquake are discussed.

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As a special case of a relaxation source, a theoretical study is made of the seismic wave radiation from the sudden formation of a spherical fluid region in an infinite elastic medium subjected to pre-existing shear stress. The results are discussed in comparison with those for a spherical void cavity model in the same initial stress field. Almost or exactly identical results be-tween the present liquefaction model and the cavity model are found for (1) the spectral density of zero frequency limit at a large distance, Which coincides also with the displacement amplitude expected for an equivalent double-couple point source, (2) the ratio of P wave to S wave corner fre-quency, which is approximately equal to the velocity ratio of P waves to S waves, and (3) the total wave energy. Differences between the two models appear in (1) the predominant period of the displacement spectrum, (2) waveform of P waves in particular, and (3) the energy ratio of S waves to P waves (6.8 for the liquefaction model and 4.7 for the cavity model).

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Surface deformations due to the fault spreading over several layers in a multi-layered medium are investigated. Machine program is developed by which contour map of vertical components and vector map of horizontal components around the focal area can be drawn, designating focal para-meters as the inputs.
Some numerical examples of surface deformations are presented for the purpose of comparison with those obtained for a homogeneous semi-infinite model.
For a vertical dip-slip fault, for example, it is known that the vertical displacement at the surface is upheaval on one side of the strike of the fault and subsidence on the other side. For a multi-layered model, however, subsidence area appears even in the upheaval area mentioned above. We call this reverse area. Thus the displacement field shows different pattern from that for a semi-infinite model.

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In order to clarify basic characteristics of seismic waves in the near-field as well as in the far-field, exact solutions for free surface displacements generated from a shear fault with an arbitrary orientation in a semi-infinite medium are obtained in a cylindrical coordinate system. First, taking the free surface effects into account, expressions for Laplace transforms of displacements with respect to time are derived, and secondly exact transient solutions are obtained by using the Cagniard's method which gives the inverse Laplace transforms in a very ingenious manner when the source time function is of the ramp type.
In sections 2, 3 and 4, mathematical expressions are derived, and the results and interpretations of numerical computations for a point source are presented in section 5. Basic characteristics of each phase are summarized as follows:
P pulse has basically a rectangular form. The initial pulse amplitudes in a semi-infinite medium are, even in rather near-field, close to those in an infinite medium with correction of surface effects due to plane wave incidence.
SP pulse, which radiates from the source as S phase, is incident onto the free surface with a critical angle and then is propagated along the surface with the speed of P-wave velocity, has a relatively large amplitude in the near-field and cannot be neglected when the wave form on the free surface is discussed. This pulse is observed when the epicentral distance is greater than the critical distance.
S pulse forms are quite different at epicentral distances less than and greater than the critical distance. S pulse beyond the critical distance has logarithmic infinities at the arrival time of S phase, tS, and t_S+t₀, t₀ being the rise time of the source function. Therefore a plane-wave correction can-not be applied successfully as in the case of an onset of the P pulse.
The Rayleigh pulse is well developed when the epicentral distance is about five to ten times as large as the focal depth and its form is not very much affected by the rise time of the source function.
For surface focus, S pulse has no logarithmic infinity but the Rayleigh pulse has infinities at the arrival time t_R and tR+t₀.
It is shown that the solutions for a moving source can be obtained by numerical integrations of the solutions for the point source. This case will be dealt with in a subsequent paper.

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Detailed laboratory experiments have been performed on the stick-slip characteristics of friction of granite, particularly in relation to such environmental conditions as the stiffness of loading system, the velocity of ram advance in a testing machine and the normal load across sliding surfaces. It is found that the stick-slip amplitude Δμ=ΔF/N(ΔF: force drop and N: normal load) decreases at high stiffness, at high velocity and at high nomal load, and that there are the interre1ated effects of the stiffness, the velocity and the normal load on stick-slip. The somewhat conflicting observations so far on the effect of stiffness on stick-slip amplitude are explained system-atically considering the interrelated effects. Stiffness influences not only the slip amplitude, but the time of slipping, which corresponds to the rise time of the source time function of an earthquake. Frictional behavior is also investigated for various rock types in relation to roughness and bulk hardness of sliding surfaces. Stick-slip diminishes on rough fault surfaces. Hard rocks tend to increase stick-slip amplitude.
The in situ stiffness k for the unilaterally propagating fault of an earthquake was estimated in a previous paper as k=μ(υ/β)²W=ρυ²W, where μ is rigidity, υ is the propagating velocity of dislocation, β is shear wave velocity, W is fault width, and ρ is density. The in situ stiffness obtained from the above formula for a large shallow focus earthquake is 6 or 7 orders of magnitude more than the stiffness of a typical testing machine in a laboratory. It has been pointed out that the stress drop associated with earthquakes is remarkably small compared with that accompaning fracture or stick-slip in laboratory experiments. This difference may be partly due to the different stiffnesses of the two systems.

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Molodenskii's solution of the geodetic boundary-value problem is approximately derived by computing G₁, a kind of terrain correction to the gravity anomaly. In the present paper, the G₁ distributions over some models of topographic relief are evaluated. It is concluded that, although G₁ sometimes amounts to a great quantity in mountainous regions, the Molodenskii correction is practically not necessary in computations of gravimetric geoidal height, but on the other hand, it should be taken into account in computations of the deflection of the vertical.

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"Residual gravity anomalies", RGA, in the north Pacific are calculated from the explosion seismic results and examined as a function of the sea-floor age deduced from the geomagnetic anomalies. The RGA, which implies the mass anomaly in the upper mantle, increases systematically as the age increases; this suggests gradual cooling of the upper mantle away from the midocean ridges.
The RGA in the Hawaii region, which is smaller than predicted by the standard RGA vs. age curve by about 100 mgal, implies hot material beneath this region. On the other hand, the RGA in the Parece Vela Basin is larger than predicted by the standard curve by about 100 mgal. This deviation can be expected if the upper mantle material beneath the marginal seas is of higher density than that beneath the normal ocean.
The thickness of the "plate" inferred from the RGA is approximately proportional to the square root of the age.

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