Based on some examples of the vertical crustal movenent accompanied with earthquakes, the detailed phases of a cycle of seismic crustal movement are formulated as follows,
α: steady state movement
β₁: state of dilatancy
β₂: unstable movement following β₁ phase
γ₁: pre-seismic slip
γ₂: co-seismic slip
γ₃: post-seismic slip
δ: transient state movement.
The crust is deformed lineary with time under tectonic stress field (α phase). After the accumulation of strain, the multiplication of cracks starts (β₁ phase). The unstable and pulsative movement follows to the β₁ phase (β₂ phase). The β₁ and β₂ phases might correspond to the stress concentration around the future slip plane. Just before the earthquake, the pre-seismic slow slip may be caused on the fault plane (γ₁ phase). At the time of earthquake, rapid slip on the fault plane emits the elastic waves(γ₂ phase). Following the earthquake movement of β and γ phases, the transient phase may be caused under tectonic stress (δ phase).
Analysing the selected eight examples of precursoy crustal movement, duration period of β₁ and β₂ phases, that is, the period from the start of anomalous crustal movement to the occurence of earthquake, are estimated. There exists a relation between the estimated duration period t and the magnitude of earthquakes M:
logt(year)=0.52M-2.80.
On the other hand, the equated radius r of anomalous crustal movement is expressed as
logr(km)=0.51M-2.27(Dambara, 1966).
Then, the duration period of anomalous crustal movement and the radius of anomalous area seems to be in linear relation, r=3.4km/year·t.
This fact can be interpreted as follows. As anomalous crustal movement appears, the dilatancy starts from nucleus points or lines in the area and grows out with the constant velocity of several kilometers per year. The existence of this kind of propagation can be assumed from the equation of diffusion in the theory of porous medium. Finally the dilatancy will fill up some volume, which may correspond to the earthquake volume. The author discussed in other paper the horizontal propagation of precursory movement in case of the Niigata earthquake of 1964, and found that the velocity of expansion is 2-3km/year in its beginning and 10km/year in the last. This observed velocity shows a good coincidence with the derived value mentioned above.