It is shown that a simple system without a cavity exhibits optical bistability with no hysteresis but with symmetry-breaking or pitchfork bifurcation. The optical system is composed of a cell containing atoms with spin in the ground state, a A,/8 plate and a mirror, and an incident light beam linearly polarized and nearly resonant with the atomic absorption line. The system has a positivefeedback loop for the rotation of polarization through competitive optical pumping by a+ circularly polarized components. %hen the intensity of the incident light exceeds a critical value, symmetry breaking occurs and its polarization is subject to rotation in the clockwise or anticlockwise sense. Correspondingly, atomic spin polarization is produced spontaneously in a direction parallel or antiparallel to the incident beam. This new type of optical bistability is found to be explained well in context with the cusp catastrophe, as well as the ordinary one with hysteresis. It is also found that, in the presence of a transverse magnetic field, self-sustained spin precession occurs, which results in the steady-state modulation of the light polarization at about the Larmor frequency. Experimental evidence of the symmetry breaking and pitchfork bifurcation is obtained by using sodium vapor.

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ABSTRACT1 Department of Geophysics, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan * Corresponding author address: Prof. Taishi Okamoto, Department of Geophysics, Graduate School of Science, Kyoto University, Sakyo, Kyoto, Japan; E-mail: dollar@kugi.kyoto-u.ac.jp doi: 10.3319/ TAO.2007.18.4.681(T) Yamada and Yomogida (1997) applied the discrete wavelet transform (DWT) to group velocity measurements for the first time. Although their study is one of the pioneering works in application of DWT to seismological analysis, their method gives an inaccurate value as a group velocity in some cases and requires modification. In this report, we point out the problem and propose a modified DWT method for overcoming the problem. In our method, DWT is carried out not for an analysed signal itself but for its complex envelope (Farnbach 1975). A computation algorithm for DWT coefficients for our method is given and shown to be almost the same as that by Yamada and Ohkitani (1991). The influence of the difference between the conventional method and our method on identification of group arrival times of a wave is also shown by a numerical experiment. If analysts want to identify group arrival times using DWT, our method must be adopted instead of the conventional method.

ABSTRACT1 Department of Geophysics, Graduate School of Science, Kyoto University, Kyoto, Japan 2 Matsushiro Seismological Observatory, Japan Meteorological Agency, Nagano, Japan 3 Seismological and Volcanological Department, Japan Meteorological Agency, Tokyo, Japan * Corresponding author address: Prof. Taishi Okamoto, Department of Geophysics, Graduate School of Science, Kyoto University, Kyoto, Japan; E-mail: dollar@kugi.kyoto-u.ac.jp doi: 10.3319/ TAO.2007.18.3.547(T) We proposed a simple method to evaluate local effects on a strain seismogram, and applied the method to investigation of the effects at Matsushiro Seismological Observatory, Japan Meteorological Agency, central Japan, for a Love wave in a period range of 170 -400 sec. First, we took a ratio of EW to NS component strain for a Love wave on a timefrequency plane. Although NS and EW component strain for a Love wave travelling in any direction have the same amplitude theoretically, the ratio of observed EW to NS component strain was 0.7. Next, we compared the strain seismogram with a velocity seismogram recorded with STS-1 broadband seismometer. A ratio of a partial derivative of a displacement field with respect to time to that with respect to wave propagation direction equals a phase velocity of the wave theoretically. Utilizing the fact, we estimated the phase velocity of a Love wave using the observed velocity and strain seismogram, after NS component strain had been multiplied by 0.7. The result was 24% smaller than the theoretical phase velocity. Finally, we compared the velocity seismogram with other velocity seismograms recorded by STS-1 seismometers at F-net observation stations near Matsushiro and by STS-2 seismometer at Matsushiro, and found that the every deviation from Matsushiro was less than 10%. From these results, we conclude that the EW and NS component strain seismograms have been amplified by factors of 1.32 and 1.88 for a Love wave, respectively. This fact, which may Terr. Atmos. Ocean. Sci., Vol. 18, No. 3, August 2007 548 be because of local geology and/or topography effects, must be taken into account when the strain seismogram is used for seismological applications such as the CMT inversion and research on earth's free oscillations.