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Sains Malaysiana 52(2)(2023):
http://doi.org/10.17576/jsm-2023-5202-25
On the
Earthquake Distribution Modeling in Sumatra by Cauchy Cluster Process:
Comparing Log-Linear and Log-Additive Intensity Models
(Mengenai Pemodelan Taburan Gempa Bumi di Sumatera oleh
Proses Kelompok Cauchy: Membandingkan Model Keamatan Log-Linear dan Log-Tambahan)
TABITA YUNI SUSANTO, ACHMAD
CHOIRUDDIN* & JERRY DWI TRIJOYO PURNOMO
Received: 7 August 2022/Accepted: 16 November 2022
Abstract
Inhomogeneous
cluster point processes have been considered for modeling the distribution of
earthquake epicenters with the spatial trend and clustering patterns. In particular, the spatial trend is
assessed by the intensity model involving geological variables. However, for
intensity with a log-linear form, it may be too restrictive and not appropriate
for earthquake distribution. In this study, we consider the Cauchy cluster process with the log-additive
intensity model to analyze the distribution of major earthquake occurrences in
Sumatra, Indonesia. The estimation procedure follows the standard two-step
estimation technique, where the first step adapts the method for the
Generalized Additive Models (GAMs) using penalized iteratively reweighted least
squares (PIRLS) algorithm, and the second step employs the second-order
composite likelihood. For the earthquake analysis in Sumatra, the log-additive
intensity shows more flexibility to determine the contribution of each
geological factor, especially to capture the effect of the nearest distance to
the fault which is far from log-linear. In addition, compared to the log-linear
model, the Cauchy cluster process with a log-additive intensity model performs
better with a smaller Akaike Information Criterion’s (AIC) value and a sharper
envelope K-function. The estimated number of mainshocks is around 114 with
aftershocks spread by 14 km around the mainshocks. We detect three hotspots for
the major earthquake in Sumatra: the northern part (Aceh and North Sumatra),
the western part (Mentawai, Nias, and Simeulue), and Bengkulu.
Keywords: Disaster risk
reduction; earthquake modeling; generalized additive models; spatial point
process; subduction
Abstrak
Proses titik kelompok tidak homogen telah dipertimbangkan untuk memodelkan taburan pusat gempa bumi dengan arah aliran ruang dan corak kelompok. Khususnya, trend ruang dinilai oleh model keamatan yang melibatkan pemboleh ubah geologi. Walau bagaimanapun, untuk keamatan dengan bentuk log-linear, ia mungkin terlalu terkawal dan tidak sesuai untuk taburan gempa bumi. Dalam kajian ini,
kami mempertimbangkan proses kelompok Cauchy dengan model keamatan log-tambahan untuk menganalisis taburan kejadian gempa bumi besar di Sumatera,
Indonesia. Prosedur anggaran mengikut teknik anggaran dua langkah piawai dengan langkah pertama menyesuaikan kaedah untuk Model Tambahan Am (GAM) menggunakan algoritma kuasa dua terkecil ditimbang semula secara berulang (PIRLS) berhukum dan langkah kedua menggunakan kemungkinan komposit tertib kedua. Bagi analisis gempa bumi di Sumatera, keamatan log-tambahan menunjukkan lebih kefleksibelan untuk menentukan sumbangan setiap faktor geologi, terutamanya untuk menangkap kesan jarak terdekat dengan sesar yang jauh daripada log-linear. Di samping itu, berbanding model log-linear, proses kelompok Cauchy dengan model keamatan log-tambahan berprestasi lebih baik dengan nilai Kriteria Maklumat
Akaike (AIC) yang lebih kecil dan fungsi K sampul yang lebih tajam. Anggaran bilangan gegaran utama adalah sekitar 114 dengan gegaran susulan tersebar sejauh 14 km di sekitar gegaran utama. Kami mengesan tiga titik panas untuk gempa bumi besar di Sumatera: bahagian utara (Aceh dan Sumatera Utara), bahagian barat (Mentawai, Nias dan Simeulue) dan Bengkulu.
Kata kunci:
Model tambahan am; pemodelan gempa bumi; pengurangan risiko bencana; proses titik ruang; subduksi
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*Corresponding
author; email: choiruddin@its.ac.id
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