The generalized nonvolcanic tremor has been proposed for characterizing the seismic process of megathrust earthquakes. A tremor signal with a vibrational velocity of microns per second exhibit the dominant frequency of 1 Hz to 10 Hz in the Fourier amplitude spectrum. Paying attention to the negative curvature of the spectrum, we generalize the tremor and define alpha-tremor as the degree of the negative curvature of the spectrum in the frequency range of 2.97 Hz to 9.80 Hz. Significant tremors and background vibrations are respectively represented by large positive alpha-tremors and non-positive alpha-tremors. Alpha-tremor is evaluated for ground vibration data acquired every 0.05 seconds for approximately 10 years at three seismic stations. At the station 188 km away from the epicenter of the Great East Japan Earthquake (GEJE) of magnitude 9, symmetries regarding the seismic process of the GEJE have been found. Among the observed 9 prominent peaks of the positive alpha-tremor, the first and last peak appears 3 years before and after GEJE, respectively. The frequency distributions of the alpha-tremor during 3 years before and after GEJE match by 99.95%. The statistical distribution that properly approximates the frequency distribution of the positive alpha-tremor is found to be the Gumbel distribution, rather than the Gaussian distribution. The time evolution of the frequency distribution of the alpha-tremor at the seismic station 1170 km away from the GEJE epicenter suggests that GEJE may have affected the ground motion there, and initiated the seismic process of the M7.3 earthquake that occurred near the station.