Estimating the risks of big earthquakes based solely on the empirical relationship between intensities and rates of occurrences after incorporating temporal clustering correction

Abstract The Headquarters for Earthquake Research Promotion (HERP) in Japan publishes earthquake hazard maps. However, these maps failed to emphasize the risk on the northern Noto Peninsula, where a disastrous earthquake struck on January 1, 2024. Such earthquake models have inherent uncertainties regarding prediction of both epicenter (or hypocenter) location and how the shocks might propagate. As an alternative, we propose a method that does not rely on such seismological knowledge. The objectives of this study were as follows: 1) to establish a method for estimating the relationship between rates of occurrences and intensities (RIRO), incorporating temporal clustering corrections; 2) to compare our estimated rates of occurrences of Japan Meteorological Agency (JMA) seismic intensity 6 plus or greater ground shakings (ERO6+) and the observed intensity of the 2024 Noto Peninsula earthquake; and 3) to create a nationwide contour map of ERO6+. For each station and intensity of JMA seismic data, we calculated the temporal clustering correction factors by extrapolating the gradually decreasing part of the survival functions of inter-earthquake intervals to interval zero. We then multiplied these factors by the counts of each intensity. Using the corrected RIRO, we evaluated ERO6+ by taking the values at intensity 6.5. Our major findings revealed the following. 1) The RIRO exhibited good linearity in semilog plots for intensity $$\ge 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . Our temporal clustering correction substantially reduced the discrepancies in the RIRO among different analysis periods; after correction, the RIRO was reduced to approximately one line, which suggests the existence of some intrinsic RIRO unaffected by the occurrence of big earthquakes. 2) Our ERO6+ on the Noto Peninsula has strong correlation with the observed intensities of the 2024 Noto Peninsula earthquake. 3) Our contour map shows that all eight intensity 7 hit stations have $$\log _{10}\mathrm {ERO6+}&gt;-2.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo>log</mml:mo> <mml:mn>10</mml:mn> </mml:msub> <mml:mrow> <mml:mi>ERO</mml:mi> <mml:mn>6</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mo>-</mml:mo> <mml:mn>2.5</mml:mn> </mml:mrow> </mml:math> and that five of them have $$\log _{10}\mathrm {ERO6+}&gt;-2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo>log</mml:mo> <mml:mn>10</mml:mn> </mml:msub> <mml:mrow> <mml:mi>ERO</mml:mi> <mml:mn>6</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mo>-</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . Statistical analysis confirmed that intensity 6 or greater ground shakings occurred at high ERO6 sites; however, the results suggest that our ERO6+ might be overestimated. We consider that our method could complement existing earthquake hazard maps because it successfully captured the risk on the Noto Peninsula lacking in the HERP map.