Solusi Numerik Teorema Probabilitas Total Gempa Bumi dengan Aproksimasi Distribusi Normal
Abstract
Abstract. This study discusses the application of the normal cumulative distribution approximation method to solve Probabilistic Seismic Hazard Analysis (PSHA). The primary focus of this research is to develop a sequential integral hazard computation approach using normal distribution approximation while considering the epicentral distance of earthquakes relative to the study location. The analysis is conducted using earthquake data from Morioka, Japan, spanning the years 2015 to 2023. This study compares sequential calculation methods with two approximation methods, namely the Tocher and Lin methods, to evaluate the effectiveness of each approach. The results indicate that the Lin approximation method provides values closer to the exact solution compared to the other methods. The peak ground acceleration (PGA) obtained is 0.2g, with an occurrence frequency of 0.0001663 times per year. The hazard curve reveals that the addition of earthquake data does not significantly impact the results beyond a certain threshold.
Abstrak. Penelitian ini membahas penerapan metode aproksimasi distribusi kumulatif normal untuk menyelesaikan Probabilistic Seismic Hazard Analysis (PSHA). Fokus utama penelitian adalah mengembangkan pendekatan komputasi integral hazard sekuensial secara aproksimasi distribusi normal dengan mempertimbangkan jarak episentrum gempa terhadap lokasi penelitian. Analisis dilakukan dengan menggunakan data gempa bumi kota Morioka, Jepang, tahun 2015 sampai 2023. Penelitian ini membandingkan metode perhitungan sekuensial dengan dua metode aproksimasi, yaitu metode Tocher dan Lin, untuk menentukan efektivitas masing-masing pendekatan. Hasil penelitian menunjukkan bahwa metode aproksimasi Lin memberikan hasil yang lebih mendekati nilai eksakta dibandingkan metode lainnya. Nilai puncak percepatan tanah (PGA) yang dihasilkan adalah 0.2g dengan frekuensi kejadian sebesar 0.0001663 kali per tahun. Kurva hazard menunjukkan bahwa penambahan data gempa tidak memberikan dampak signifikan setelah titik tertentu.
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