Sains Malaysiana 52(2)(2023): 655-667

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

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesia

Diserahkan: 7 Ogos 2022/Diterima: 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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^*Pengarang untuk surat-menyurat; email: choiruddin@its.ac.id