Fine Recording in Time Direction for Seismological Observation

Transcription

1 Fine Recording in Time Direction for Seismological Observation by S. Suyehiro Meteorological Research Institute, Tokyo (Received June 4, 1959) Abstract In the routine seismological observation, the running speed of the recording paper or film is 1 mm/sec at the highest owing to operational restrictions ; consequently, the time accuracy can hardly attain higher than 0.1 sec by the recorder of the conventional type. An accuracy of 0.01 sec is required in the continuous tripartite observation of natural earthquakes. To meet the requirement, an improved optical recording system has been developed ; the main features are a horizontal slit in front of the galvanometer mirror and a cylinder lens in front of the recording film, which make the time resolving power of the system as high as the film grains allow. By this system, a time accuracy of 0.01 sec has been made possible even with the ordinary running speed, 1 mm/sec. In designing the optical system, the effect of the diffraction has been prudently taken into account. 1. Introduction A continuous recording is necessary in order to record an earthquake from its very start if the pick-up and the galvanometer are connected directly through a passive network (no generator, no electronic tube, or no rectifier being involved) and no delay starter is available. The frictionless optical recording has been employed extensively in such continuous observations. In optical recording with photographic paper or film for continuous observation, the running speed is usually 1 mm/sec at the highest, for the cost and labour for the running do not allow a higher speed. With this running speed, a time accuracy of 0.1 sec, which is required in ordinary seismological observation, can possibly be kept if sufficient care is taken of the driving mechanism and the time marking system of the recording instrument. When a higher accuracy is required in seismic prospecting work or in explosion seismological observation, the running speed is made much higher and the time mark is placed more frequently. Namely, the time per unit length on the record is made shorter so that a higher time resolving power can be given. On the other hand, the observation time is usually limited to less than an hour. The spot o f the optical image which is focused on the photographic recording paper or film by the optical system of conventional type is microns or more

2 1959Fine Recording in Time Direction for Seismological Observation 45 in its geometrical width, and the edge of such width is dulled by the diffraction and the aberration of lens and mirror. Therefore, the time resolving power has a limit depending on the running speed of the recording paper or film ; the time accuracy also has a limit no matter how accurately and uniformly the recording paper or film runs. Seeing that the resolving power of the motion-picture film (positive film) is as high as 150 (one hundred and fifty black lines can be separately photographed in a distance of 1 mm on the film ; that is, two points about 4 microns apart can be resolved), a time accuracy or a time resolving power of 0.01 sec cannot be impossible even with a running speed of 1 mm/sec if the width of the image in the time direction is made sufficiently small and the edge of the image, sufficiently sharp. The high time resolving power by a comparatively low running speed, described in the above, has been demanded for the continuous tripartite observation of earthquakes, and an improved optical system has been developed. 2. Optical system The optical system employed is shown in Fig. 1. The image of the filament of the electric lamp which is orientated horizontally is focused by the lens L1 on the rotational mirror of the galvanometer M, and the image of the vertical slit Si, the clearance of which is 40 microns, is focused by the lens L2 on the film ; there is no difference from the conventional method up to this point. In the present system, however, the second slit S2, the clearance of which is 180 microns, is newly inserted horizontally about 5 mm in front of the mirror, and its image is focused by the cylinder lens L3 on the film. The combined image given on the film is rectangular if the diffraction is ignored. The right and left edges, which give a width of the recording trace in the direction of " amplitude ", are given by the image of Si, which moves in accordance with the rotational oscillation of the galvanometer mirror. This system Si, consisting only of the slit Si, the lens L2, the mirror M, and the film, is equivalent to the system 1

3 in Fig. 2 ; that is, a line light source of 40 microns in length is placed at the infinity from a lens of 30 cm in focal length, a slit aperture of 0.5 cm in clearance, which is equal to the width of the galvanometer mirror, is placed in front of the lens, and the image of the light source is focused on a film 30 cm away from the lens. The effect of the diffraction by the parallel aperture is seen on the image ; the sharpness of the image depends largely on this effect. First, let us consider a point light source on the optical axis. The light intensity distribution Yp in the direction perpendicular to the parallel aperture of clearance D, which is given by the Fraunhofer diffraction of parallel aperture, is given by where ç is the angular distance, x is the distance from the image center on the image plane, A is the wave length, and f is the focal length of the lens. The line source can be considered as a continuous disposition of point source ; however, it should be taken into account whether the line source is coherent or not. Actually, the source is given by the slit S1 in Fig. 1, the light comes from the line filament through the lens L1, and the slit S1 is not on the image plane of the filament ; therefore the line source in question is coherent to some extent. In this paper, however, the line source is considered to be incoherent, for no essential difference can be found for the present purpose especially in the direction of " amplitude ", which is independent of the time resolving power. Then the light intensity distribution 171 on the image of a line source is given by an integral of the intensity distribution due to a point source moving within a distance of the line in question. Thus, The interval " 1 to +1" is given by the geometrical width of the image in rt-scale. In the system Si or the system 1, D is 0.5 cm, f is 30 cm, A of the maximum

4 intensity is 4 x 10-5 cm*, and the geometrical width of the image is from x= 20 to x=20 (in microns) The calculation of the integral was done with different is by P. H. VAN CITTERT**, and the graphical presentation is given in Fig. 3. The effect of the diffraction is seen even in the center of the image, and the sharp edge cannot be expected. Some improvement could be possible by making f shorter and D larger. The former shortens the length of the optical lever and reduces the magnification, and the latter makes the galvanometer mirror larger and reduces its sensitivity ; therefore the present condition is probably optimal. The upper and lower edges, which give the resolving power in the direction of " time ", are given by the image of the slit 52. This system S2 consists only of the slit S2, the cylinder lens 1-3, and the film and is equivalent to the system 2 as shown * Considering the intensity distribution in the optical source with respect to wave length, the absorption by lenses, and the sensitivity of the film, the resultant maximum intensity lies near 4,000 A. ** P.H. VAN CITTERT : Zum Einfluss der Spaltbreite auf die Intensitatsverteilung in Spektral-,linien. Zeitschrift fiir Physik, 65, , 1930.

5 in Fig. 4 ; the geometrical width in the direction of " time " is 6 microns, and the effect of the diffraction can be considered similarly to that in the system S1. The slit S2, which is the light source of this system, is almost on the image plane of the filament by the lens L1, and the light source can be considered to be incoherent. The integration (4) can, therefore, be applied strictly. Here, D is 0.3 cm, f is 1 cm, and the width of the image is from x= 3 to x=3 (in microns) ; consequently, 1 in the integral (4) is (8) 1= 2.3 7r. The integral (5) is then its graphical presentation being given in Fig. 5. The resolving power reaches almost that of the film itself and corresponds to 0.01 sec or even shorter when the running speed is 1 mmisec, for the width from 0.2 to 0.2 in the relative intensity is only less than 7 microns corresponding to sec. The effect of the diffraction is much limited, and the sharpness of the edge is satisfactory. An advantage of the present optical system is that none of the constituents of the system S1, which gives the width in the direction of " amplitude ", is involved in the system S2, and that, therefore, the time resolving power can be made higher only by the system S2 ; a curvature of the galvanometer mirror which is very difficult to eliminate or the rotation of the mirror cannot reduce the time resolving power. The clearance of the slit S2 and the focal length of the cylinder lens can be made smaller as far as the mechanical and optical conditions allow in order to make the width in the " time " direction smaller and sharper. 3. Mechanical features and results The present improvement in the optical system has been tentatively made with the film recorder HES-R, which has shown good performance in the ordinary seismological observation. The film recorder employs originally a pin-hole light source ; the improvement has been more or less restricted by the original design. For instance, the width of the cylinder lens, D in the system S2, could be larger, or the clearance of the slit S2 could be smaller if a new recorder were designed originally according to the present principle, and even a better result would be possible. As for the light source, no change has been made, and a sufficient light intensity is obtained on the film through the improved optical system. Adjustments of the

6 optical system are not difficult. Fig. 6 shows the film recorder HES-R in which the present improvement has been made, and Fig. 7 shows galvanometers with and without the horizontal slit S2. Fig. 8 is a microscopic photograph of the vibration of 20 cps recorded by the improved recorder with a running speed of 1 mm/sec ; forty lines are easily placed in 1 mm. Naturally, the resultant resolving power is Fig. 9*. Example of observation by the recorder. Time marks of every second, minute, and hour are placed. Running speed is 0.66 mm/sec. TS=1/3 sec, Tg =1 sec. The sharpness in the photographs has been reduced by enlarging and printing. The examination of the seismogram obtained by this recorder should be made directly on the original record by means of optical comparator or microscope.

7 affected also by other elements such as the aberration of the cylinder lens, the mechanical accuracy, the processing procedures of the film, etc., and the present result is somewhat lower than the theoretical value ; nevertheless the observational purpose is satisfied with the present recorder. Fig. 9 shows an actual example' of the observation which is now being made with the recorder in the Matsushiro Seismological Observatory. Acknowledgements The author is indebted to Dr. G. KUWAHARA of Tokyo University, who has given the benefit of his experience, and to Dr. T. ASADA of Tokyo University, who has stimulated the author in the present work. All figures have been drafted by Miss S. SASAMOTO, to whom the author is obliged.