Several new digital techniques have been developed to improve the quality of information which may be extracted from surface wave recordings. The main topics covered by this progress report are
(1) Moving window analysis and the multiple filter technique which are automatic digital processes of considerable utility in the measurement of multi-mode dispersion.
(2) Combined multi-component analytic techniques for the identification and separation of wave types.
(3) Time-variable filtration in the frequency domain, based upon the fast Fourier transform. This permits the separation of a mode of interest from a multi-mode recording, with insignificant disturbance of the desired phase information.
(4) Cross-correlation for inter-station phase and group velocity measurements.

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A procedure has been presented for the numerical computation of synthetic seismo-grams of the reflected wave (including head waves and continuously refracted waves) arising from the incidence of a spherical wave on an inhomogeneous transition zone with arbitrary depth-dependent variation of the elastic moduli and density. The reflection phenomenon will be discussed in the frequency domain where the method of stationary phase gives a rapid estimate of the important features of the reflected wave field as a function of frequency, phase velocity and distance. Using this estimate synthetic seismograms are obtained by numerical integration with respect to wave number and by applying a fast Fourier transform technique. Synthetic seismogram sections for three typical examples of crust-mantle transition zones are discussed in detail. The procedure described in this paper provides a new means of placing more severe bounds on possible crustal and upper mantle models.

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It is often possible to carry out lengthy and tedious but otherwise routine algebra involved in geophysical calculations on a computer. The technique yields confidence in the accuracy of the analysis and allows an approach to complex algebra which permits more attention to be paid to the broad principles of the problem and less to the details.
FORMAC is a recent approach to the problem of manipulation of algebraic expressions. It is a preprocessor for PL1-like input to the IBM/360. An earlier version was a preprocessor for FORTRAN-like input to the IBM/7094. The language provides a group of commands which will manipulate symbolic expressions algebraically, differentiate these expressions and execute input and output for these expressions onto printers or direct access storage.
Applications are made of FORMAC to several complex algebraic expressions which arise in geophysics.

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A new type of filter which separates areal dilatation and rotation from horizontal seismograms was designed. Using long-period seismograms recorded by LASA as input, its effectiveness was demonstrated.

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It has been pointed out by many seismologists that the space, time and magnitude distributions of earthquakes should be combined with each other and be discussed from the unified and systematic viewpoint. Because of lack of good data, however, only a few studies on seismicity have dealt with these distributions this way.
This author wants to study these distributions of earthquakes from the above-mentioned standpoint. This is the first step to this purpose. Aftershocks of great earthquakes give a considerable amount of good data.
The followings are the main results of the present study:
(1) In the initial stage of aftershock activity where most of the largest aftershocks occur successively on a line including the epicenter of a main shock, the distribution of shocks has the strong tendency of clustering in space and time.
(2) In the later stage of aftershock activity, the distribution of shocks has the tendency of randomness in space and time. In addition, some related problems such as randomness and non-randomness of events in space and time is briefly mentioned.

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A series of chemical explosions in Hudson Bay in 1965 has been studied using array techniques on the recordings at the Yellowknife seismic array. An upper mantle velocity model valid for the Churchill Province of the Canadian Shield has been derived, using the Wiechert-Herglotz method for the upper layers. A strong velocity gradient is required for the first 150km under the Mohorovicic discontinuity, underlain by a weak P-wave low velocity layer. Comparison with array results from the 1966 Early Rise shots in Lake Superior strongly suggests significant Pvelocity differences in the upper mantle under the different provinces of the Canadian Precambrian Shield.

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Employing the pulse travel time technique, many measurements on crustal rocks comprising 25 rock types were attempted and experimental data on longitudinal and shear velocities were collected. Velocity measurements as a function of directional propagation leading to the evaluation of the degree of anisotropy; and the results on the density and attenuation in these rocks were also obtained and the ranges noticed in such values are included and discussed. Results on five rock types that were subjected to a uniform pressure of about 2 kilobars are also presented. Studies under uniform pressure, covered the aspects of velocity and amplitude changes; the effect of loading and unloading; and changes due to cyclical loading. A steady increase in wave velocity and amplitude was observed in these pressure studies. A considerable flattening of the pressure-velocity curves was noticeable even under these low pressures showing the effect of compaction and the elimination of porosity.

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Finite difference methods have been applied to solve seismic pulse propagation problems mainly in cases when analytic solutions have not been found or are lengthy. The following problems are discussed: The motion of an elastic quarter space due to an explosive line-source, showing diffraction of surface and body waves at the corner; the response of a layered halfspace to an impulsive point-source-showing excellent agreement with previous analytic results, and giving additional information about refraction arrivals and interface waves.
The same method has been applied to pulse propagation in a sphere. As an example, the motion of a fluid sphere is given showing effects of heterogeneity and of deviations from sphericity.

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The atmosphere-hydrosphere-lithosphere-biosphere at the planetary surface forms a complicated network system where the energy and materials are exchanged with the outer space and the planetary interior. This system is simulated following a concept of chemical plant design. Evolution or secular variation in the planetary state is studied based upon the assumption of dynamic equilibrium.
The following unit process simulaters are developed: EQCOMV, MAGMA, EQCOMS, EQDSTB, CARBON, and SEDSIM. Combining the above processes a synoptic characteristics of the system is discussed. The authors present the hypothesis that the planetary evolution is progressed by the optimum process control under the condition: entropy production rate=minimum.

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Digital methods have been applied to extend the period range of the group velo-city measurement of surface waves. The group velocities up to periods of about 120 seconds were obtained from a seismograph system comparable to the 15-90 Press-Ewing seismograph. For both the Rayleigh and Love waves, the group velocities are significantly lower on the continental side than on the oceanic side of the island arc. This difference can be interpreted in terms of a shear velocity contrast of 0.3 to 0.4km/sec over a depth range 30 to 60km.

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This paper reports a study based on the data obtained from the routine observation of micro-earthquake activity in the vicinity of Kyoto, Central Honshu, Japan. Analysis of recordings of six seismographic observation stations obtained from Oct. 1964 to Aug. 1967 provided 386 hypocentral determinations and 2607 magnitude determinations for events with magnitudes greater than or equal to 1.0. Hypocentral determinations were carried out by using P arrivals that are based on an approximated three-layer model derived from the crustal structure in this district.
Micro-earthquakes in the vicinity of Kyoto concentratedly occur in a belt-like zone lying from the west coast of Lake Biwa to Osaka Bay. All focal depths determined lie in the crust. This seismically active zone corresponds to the mountains characterized by upheaval from geologic viewpoint. Micro-earthquake active zones besides the belt-like zone correspond to the zone of upheaval.
There exist many Quaternary active faults along the east end of the belt-like seismically active zone. Destructive earthquakes in history occurred in the fault zones. It may be considered that micro-earthquake energy is concentratedly released in the one side of the fault zones where destructive earthquakes frequently occurred, as is seen in the case of aftershock energy release.
Focal machanism study by use of first motions of P waves leads to a conclusion that the radiation pattern of the micro-earthquakes treated here is of quadrant type with the principal axis of pressure lying in the E-W direction. The direction of the maximum pressure of micro-earthquakes agrees fairly well with that of the larger earthquakes occurring in this district. The agreement of the direction of one of the nodal lines with the direction of the largest fault is suggestive to consider the relation between the stress producing earthquakes and the tectonic force acting in this zone.
Magnitude determinations were used for obtaining magnitude-frequency relation
log N=3.71-0.98M.
The recurrence times of earthquakes with various magnitudes which were estimated from the above magnitude-frequency relation agree fairly well with the observed recurrence times.
Auto-correlogram and power spectrum estimations based on hourly count seem to suggest that micro-earthquakes occur at random concerning time distribution. Any dominant frequency suggesting to correlate earthquake occurrence with natural phenomena, say, the earth tide was not found from the daily and hourly counts.

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The motion of a heterogeneous fluid sphere due to an impulsive point source is calculated by several finite difference schemes and is interpreted in terms of reflected and diffracted pulses. The deviations due to heterogeneity from the results for the homogeneous sphere are calculated explicitly. Calculations show the change in amplitude of pulses and dispersion due to continuous variation of compressional velocity c, as compared with discontinuities in c.

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