This paper links ground vibration velocity fluctuation (GVF) recorded near an epicenter of the Great East Japan Earthquake of magnitude 9 (GEJE) with a cellular automaton (CA), and provides a data mining methodology using the CA to extract GEJE-related information from the GVF. Although the GVF can be discussed in the framework of the master equation which represents the thermodynamics of a stochastically fluctuating non-equilibrium system, the relation between the thermodynamic parameters and seismology-related phenomena is not clear. On the other hand, this relation can be relatively easily derived in CA. So, the thermodynamic equivalence between GVF and CA makes it possible to extract the seismology-related information from GVF by deriving the thermodynamic parameter associated with seismology-related information in CA. In the demonstrated example of data mining, the stress relaxation signal immediately after GEJE is discovered from the recorded GVF data by deriving the thermodynamic parameters representing the stress relaxation of CA and evaluating these thermodynamic parameters with respect to the recorded GVF data. Furthermore, the elastic rigidity and viscosity of the underground structures are estimated from the stress relaxation signal. The non-traditional features of this study are that the GVF of interest is a weak fluctuation signal with no specific waveform and that CA is not used to model ground motions.