Page 256 - Contributed Paper Session (CPS) - Volume 4

CPS2219 Hasih P. et al.
3. Result and Discussion
Linked Stress Release Model
Large earthquakes are usually followed by other large earthquakes that
are far enough away from the first event and large events can inhibit
subsequent events. Inter-regional interactions can affect the time and
magnitude of an earthquake event that is explained by the stress transfer.
Suppose for region, the stress function of equation (1) is written as
() = (0) + − () (2)

Suppose that the accumulated stress release during an earthquake event in
region over a period of time (0. ) is written as (). The displaced stress

from region to region has a fixed proportion of positive or negative values
symbolized by with = 1,2,3, … , and = 1,2,3, … , . Accumulated stress

for several regions after stress transfer from region with = 1,2,3, … , is
() = () + () + ⋯ + ()

2 2

1 1
= ∑ () (3)

Based on equations (2) and (3), the pressure function for some subregions is
written as
= (0) + − ∑ () (4)

Equation (4) is a linked stress release model.
Conditional Intensity Function
The hazard function () states the probability of an earthquake
occurring in a time interval (, + ) approaching (()) + () for
which is quite small. It is assumed that the hazard function () is an
exponential function written as
() = exp ( + ) (5)
with and ≥ 0. The α parameter describes the initial pressure value and
the β parameter describes the combined strength and heterogeneity of the
earth's crust in the area. The probability of an earthquake occurring can be
determined using the conditional intensity function of the linked stress
release model. The conditional intensity function () with the history

condition = {( , ); = 1,2, … , } is a hazard function of () pressure,

which is written as
(| ) = ( ()) (6)

Substituting equations (4) and (5) into equation (6) is obtained
(| ) = exp ( + (0) + ( − ∑ ())). (7)

245 | I S I W S C 2 0 1 9