The relation between the FOURIER series method and the sinx/x method for gravity interpretations has been investigated and it is shown that the two methods are representing the same thing in the limiting case.

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This is an extension of the sin x/x method which was introduced by Y. TOMODA and K. AKI for two dimensional gravity interpretations. Numerical tables facilitating three dimensional gravity interpretations are presented.
Gravity values given at two dimensional grid points on the earth's surface are to be multiplied by corresponding tabular values and the products added up. The sum when divided by 2πG will represent the surface mass density at the assumed depth and immediately beneath the central grid point.

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Geodetic and seismological characteristics due to a fault movement have been studied on the basis of a simple model. It is intended to examine whether or not such a model is acceptable as a possible representation of earthquake origins. The model is proposed from the standpoint similar to that of REID's hypothesis and the sudden occurrence of a fracture fault in the upper part of the earth's crust is taken as the immediate cause of earthquake shocks as well as of crustal deformations.
First, we deal with statical deformation of the earth's crust caused by stress change (shear) on the fault plane, which is assumed to be developed from the surface vertically down to a certain depth. It has been found that by this model, the general decrease of horizontal displacement of triangulation points with distance from the fault is explained reasonably well. From the comparison of the theory with the observed geodetic data, probable conditions at the actual earthquake fault can be surmised. In the case of the Gomura fault (Tango earthquake), for instance, the depth (H) is estimated at 15km, while the stress change on the fault plane (Y_x)0 and the total amount of strain energy (Efault), at 3×10⁷c.g.s. and 4×10²²ergs, respectively (length of the fault being assumed to be 30km).
Discussion is also made about the characteristics of seismic waves which are generated by the supposed fault movement. The analysis based on a two-dimensional model has shown that the push-pull distribution of the initial P-wave is of the quadrant type, one of the nodal lines coinciding with the fault. The maximum of the spectral intensity (P-wave) falls on the component, whose wave-length (referred to S-wave) is approximately 1.2 times as large as the fault's length.
These results also agree satisfactorily well with the observed seismological data. The deduced conditions at the fault are also acceptable judging from the mechanical strength of the crust which is already known. The model adopted here affording satisfactory explanations of various aspects of the Tango earthquake, we might say that the physical conditions at the seismic origin do not differ much from those of the model. Possibility of applying the similar model to other cases is also discussed.

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A temporary observation of near-by microearthquakes was made with Ultra Sensitive Seismometers at Matsushiro. The purpose of this experiment was to see the relation between the frequency of near-by microearthquakes and the annual number of near-by shocks felt at Matsushiro.
The results and conclusions are as follows. An average of one microearthquake occurs every hour. The average annual number of earthquakes felt at Matsushiro is about 1.2. As M of the microearthquakes are from less than -l to 0, and M of near-by felt earthquakes are about 4-5, we have an equation,
log N=3.6-0.77M,
where N is the annual number of earthquakes whose M are between M-0.5 and M+0.5. This equation holds good in the relation between N and M of earthquakes with M from -1 to 5 occurring in the vicinity of Matsushiro (area≈60×60kmkm2).
As the equation is valid in such a wide range of M, it will be possible to determine the seismicity of a certain region within a rather short period of time through observing microearthquakes.
The E of the minimal recorded earthquake was about 109ergs in this experiment. Its M was approximately -2.

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The notion of earthquake province has been introduced. It is a domain within which various portions show sympathetic seismic activities. It may be interpreted to be representing a stationary site over which one seismic field continues to exist, although its intensity may vary according to time. By means of correlation studies of earthquake numbers in various compartments, six such earthquake provinces have been established in Japan.

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