Abstract
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.