Instrumentally measurable earthquake precursors are derived by considering earthquakes as a phase transition in cellular automaton. The existence of the phase transition in CA-184 is implied by considering the space-time diagram of the CA-184 as the worldsheet of the Polyakov action in string theory. The CA-184 is the rule-184 cellular automaton (CA), which is a special case of Burgers cellular automaton (BCA) rigorously derived through transforming the one-dimensional Burgers equation. Then, $p$-CA-184, the CA-184 with probabilistic fluctuation and $p$-BCA, the BCA with probabilistic fluctuation, are associat-ed with the earthquake. The Fourier transforms of $p$-CA-184 and $p$-BCA dynamics near the phase transition reproduce the Fourier transforms of the ground vibration data before and after the earthquake, respectively. Consequently, we consider an earthquake as the phase transition of CA-184. Two precursors of the phase transition of the CA-184, therefore the earthquake precursors, are derived with $p$-CA-184 by introducing the Gumbel distribution defined in the framework of extreme value theory. To evaluate the pre-cursors, the ground vibration data measured at three locations over a period of approxi-mately 10 years has been investigated. One of the derived precursors is observed before every studied earthquake with seismic intensity greater than 4, and the other precursor is observed selectively before the large earthquake of magnitude 9. Furthermore, the two pre-cursors calculated for different frequencies and time scales are observed at similar timing before the magnitude 9 earthquake. The phase transition model of earthquakes provides the practical and reliable earthquake prediction method.

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.

This paper paves the way for a direct comparison of the process of megathrust earthquakes with cellular automaton (CA) and for modeling the catastrophic singularity of seismic events as a phase transition phenomenon. It is shown that the entropy production rate (EPR), which is a property of thermodynamically non-equilibrium systems, occasionally decreases sharply in the seismic process of the Great East Japan Earthquake (GEJE) of magnitude 9. The timing of the EPR decrease is found to be clearly different from that of earthquakes of magnitude less than 9, but close to the timing of the earthquake of magnitude 9. The decrease indicates a qualitative change from a time-dependent non-equilibrium system towards a static equilibrium system, which can be a phase transition. In the GEJE process, EPR is calculated from the binarized velocity deviation of ground vibrations found to be equivalent to velocity. The equivalence attributes to that the transformation between them does not change the α-tremor which is the curvature of the Fourier amplitude spectrum of the velocity, and that an arbitrary ground vibration can be defined by α-tremor. The α-tremor is a noise. However, it is associated with microearthquakes whose epicenter is close to the GEJE epicenter, and is an important component of the GEJE process. The binarization equivalence allows the ground vibration to be viewed as CA which consists of binary numbers.

The entropy production rate (EPR), which is a property of thermodynamically non-equilibrium systems, occasionally decreases sharply in the seismic process of the Great East Japan Earthquake (GEJE) of magnitude 9. The decrease indicates a state change towards an equilibrium system where no time-dependent change occurs. The timing of the EPR decrease is found to be clearly different from that of earthquakes of magnitude less than 9, but close to the timing of the earthquake of magnitude 9. In the GEJE process, EPR is calculated from the binarized velocity deviation of ground vibrations found to be equivalent to velocity. The equivalence attributes to that the transformation between them does not change the α-tremor which is the curvature of the Fourier amplitude spectrum of the velocity, and that an arbitrary ground vibration can be defined by α-tremor. The α-tremor is a noise. However, it is associated with microearthquakes whose epicenter is close to the GEJE epicenter, and is an important component of the GEJE process. By binarizing the velocity deviation with “0” and “1”, the vibrational state at a time interval can be defined as the number of clusters of “1” at the time interval. Once the thermodynamic state is defined, the master equation that explains the time evolution of the state can be written down and the EPR is mathematically formulated. EPR is evaluated for ground vibration data acquired every 0.05 seconds from 2006 to 2018 at a seismic station 188 km from the GEJE epicenter.

\sout\sout Sharp decrease of entropy production rate (EPR) is observed in the process of the Great East Japan Earthquake (GEJE) of magnitude 9. The EPR, a thermodynamic property of a fluctuating system, is calculated from the binarized velocity deviation of the background vibration. The background signal of the GEJE process includes a micron / second scale velocity signal that exhibits the dominant frequency of 1 Hz to 10 Hz in the Fourier amplitude spectrum. Paying attention to the negative curvature of the spectrum in the frequency range, we define alpha-tremor as the degree of negative curvature of the spectrum in the frequency range from 2.97 Hz to 9.80 Hz. The positive and non-positive alpha-tremor represent an arbitral weak velocity signal. The alpha-tremor has been shown to be invariant in binarizing the velocity fluctuation signal. Therefore, the binarized velocity and the raw velocity signal are equivalent as long as the background vibration is considered as the alpha-tremor fluctuation. The binarized velocity signal is divided into sets with 10 data, and the vibration state is defined for each set considering the degree of dispersion of the 10 signals. Then the transition rate from one state to the other is calculated, followed by the EPR calculation. The EPR is evaluated for ground vibration data acquired every 0.05 seconds from 2008 to 2014 at the seismic station 188 km away from the epicenter of GEJE which occurred in 2011.