Benford yasası ve uç değer yaklaşımı ile depremlerde anomali tespiti

Abstract

Türkiye, depremlere yol açan önemli tektonik hareketlerin düzenli olarak meydana geldiği aktif fay hatları üzerinde yer almaktadır. Kuzey Anadolu Fay hattında yer alan Batı Anadolu, daha yüksek bir deprem riskine sahiptir. Bu çalışma, Türkiye'de 1970-2021 yıllarını kapsayan deprem büyüklüklerindeki anomalileri tespit etmeye odaklanmaktadır. Analizde deprem büyüklüğü verilerinin uygunluğunu incelemek ve potansiyel anomalileri belirlemek için Benford Yasası ve Blok Maksima çerçevesinde Genelleştirilmiş Uç Değer dağılımını kullanmaktadır. Bu çalışma, söz konusu yöntemleri özellikle Ege Bölgesi’ne uygulayan ilk çalışmalardan biri olmakla beraber tektonik açıdan aktif bu bölgede deprem riski üzerine yeni bakış açıları sunmaktadır. Büyüklüğü 3.0 ve üzerinde olan 15845 sismik olaydan oluşan veri seti her iki istatistiksel yöntem kullanılarak değerlendirilmiştir. Benford Yasası, verilerin doğal örüntülere uygun olduğunu göstermiş ve istatistiksel testler büyüklük verilerindeki ilk rakamların beklenen dağılımını doğrulamıştır. Blok Maksima yaklaşımıyla uygulanan Genelleştirilmiş Uç Değer dağılımı, ekstrem olayların beklenen büyüklüğünün daha uzun geri dönüş süreleriyle arttığını, geri dönüş seviyelerinin 2 yıl için 4,77 Mw, 20 yıl için 5,81 Mw ve 100 yıl için 6,36 Mw olarak tahmin edildiğini ortaya koymuştur. Bu sonuçlar, sismik riskleri değerlendirmek ve deprem verilerindeki potansiyel anomalileri belirlemek için bu istatistiksel yöntemlerin kullanılmasının önemini vurgulamaktadır.

Keywords

• Benford yasası
• blok maksima
• deprem tehlikesi
• genelleştirilmiş uç değer yaklaşımı

Anomaly detection of earthquakes with Benford’s law and extreme value approach

Abstract

Türkiye is located on active fault lines where significant tectonic movements occur regularly leading to earthquakes. Western Anatolia, being in the North Anatolian Fault Zone, has a higher earthquake risk. This study focuses on detecting anomalies in earthquake magnitudes in Türkiye, spanning the years 1970 to 2021. The analysis utilizes Benford's Law and the Generalized Extreme Value distribution within the Block Maxima framework to examine the conformity of earthquake magnitude data and identify potential anomalies. This study is one of the first to apply these methods specifically to the Aegean Region, providing new insights into the seismic risk in this tectonically active region. The dataset, comprising 15845 seismic events with magnitudes of 3.0 and above, was evaluated using both statistical methods. Benford's Law indicated that the data conforms to natural patterns, with statistical tests confirming the expected distribution of first digits in the magnitude data. The Generalized Extreme Value distribution, applied through the Block Maxima approach, revealed that the expected magnitude of extreme events increases with longer return periods, with return levels estimated at 4.77 Mw for 2 years, 5.81 Mw for 20 years, and 6.36 Mw for 100 years. These findings highlight the importance of using these statistical methods to assess seismic risks and identify potential anomalies in earthquake data.

Keywords

• Benford's Law
• block maxima
• earthquake hazard
• generalized extreme value approach.

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