Advances in Conception about Earthquakes - Earthquake Engineering for Structural Design - page 128

analyzing the double pendulum behavior is the great sensitivity to the initial
conditions. Two identical double pendulums, but with very small differences (in
order of 0.00001) in the initial conditions, have completely different oscillations
(Wheatland, 2007).
4.4.2 Applications of Chaos Theory in Seismology
The relation between Chaos Theory and Seismology is given by the Burridge-
Knopoff model (Saito and Matsukawa, 2007). In case of the interplate earthquake
type, where an ocean lower plate goes downward beneath an upper land plate (Fig.
4.17 shows the case of tectonic plates of Japan), the fault is composed by some
segments. Burridge and Knopoff introduced a model which exhibited some
characteristics similar to the dynamics of an earthquake fault. They were interested
in the role which friction plays with regard to the earthquake mechanism. The basic
configuration of this model would consist of some blocks (modeling the fault
segments) connected to the upper plate by linear springs. The blocks are also
connected to each other by linear springs. The frictional forces act between the
blocks and the lower plate. The upper plate is driven with constant velocity. When
the friction cannot hold the blocks, they will move forward to a certain distance to
release the energy in the springs. Due to the coupling between the blocks, the
number of blocks involved in a single slip event has a very broad distribution. If
only one of the blocks slips, the event is small. If a great number of the blocks are
involved in slipping, the event is large.
During the slipping, a vibration of blocks around the initial position occurs. For
a symmetric model, as in the original Burridge-Knopoff one, the system presents a
Figure 4.17 Burridge-Knopoff model: The interplate fault model (modified after
Saito and Matsukawa, 2007)