Page 257 - Contributed Paper Session (CPS) - Volume 4

CPS2219 Hasih P. et al.

Suppose that + (0)) = = , and = , thus equation (7) is

,

written as
(| ) = exp( + ( − ∑ ())) (8)

The parameter of the conditional intensity function in equation (8) is
estimated using the maximum likelihood method with its likelihood function
2
= [∏ =1 (| )]exp (− ∫ (| )), (9)

2
and the Log-likelihood function
2
log = ∑ =1 log (| ) − ∫ (| ), (10)

2
with time internal ( , ).
2
1
This section provides the application of conditional intensity function from
the linked stress release model on earthquake data on Java and Bali-Nusa
Tenggara. The earthquake data is secondary data sourced from the United
States Geological Survey. Earthquake data includes , , component area

; , with states that the time of the -earthquake and states the

magnitude of the -earthquake. The period of the earthquake data occurred
from January 2010 to December 2017 with a magnitude of ≥5 mb and a depth
of <70 km. Plot of time and magnitude of earthquake in Java and Bali-Nusa
Tenggara is shown in Figure 1.
(a) (b)
Figure 1: Plot magnitude and time for earthquake data in Java (a) and Bali-Nusa Tenggara (b)
Based on Figure 1 (a), there were three earthquakes in Java with the largest
magnitude, namely in the south of Java Island on 3 April 2011 with a
magnitude of 6.5 mb, in the southeast of Adipala on 25 January 2014 with a
magnitude of 6.1 mb, and in the northwest of Bunisari at 6 April 2016 with a
magnitude of 6.1 mb. Based on Figure 1 (b), there were three earthquakes in

Bali-Nusa Tenggara with the largest magnitude, namely in the Sumbawa on 8
May 2010 with a magnitude of 6.0 mb, in the south of Bali Island on 13
October 2011 with a magnitude of 6.1 mb, and in the west of Komerda on 12
February 2016 with magnitude 6.3 mb.

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