We present an updated empirical relationship between moment magnitude (Mw), epicentral intensity (I0, EMS), and macroseismic focal depth (hm, km) for earthquakes in Croatia and its surroundings. The analysis is based on the updated, revised and uniformly processed Croatian Macroseismic Database and the corresponding Croatian Macroseismic Catalogue, which together provide a homogeneous macroseismic dataset spanning the period 1520–2022. From these, 139 triplets (Mw, ℎm, I0) were selected corresponding to events with independently determined moment magnitudes and reliably derived macroseismic parameters. A three-axes weighted orthogonal regression was performed to obtain a symmetric relationship linking the three variables. The resulting triaxial regression plane is expressed as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$-0.390 \,{M}_{w}+0.960 \log\left({h}_{m}+1\right)+0.285\,{I}_{0}=1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>0.390</mn> <mspace width="0.166667em" /> <msub> <mi>M</mi> <mi>w</mi> </msub> <mo>+</mo> <mn>0.960</mn> <mo>log</mo> <mfenced close=")" open="("> <msub> <mi>h</mi> <mi>m</mi> </msub> <mo>+</mo> <mn>1</mn> </mfenced> <mo>+</mo> <mn>0.285</mn> <mspace width="0.166667em" /> <msub> <mi>I</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> from which closed-form expressions allow consistent estimation of any one parameter given the other two. The new relations exhibit stable predictive performance under out-of-sample conditions, and provide improved consistency across the full range of observed magnitudes, intensities, and focal depths. They also agree well with the most commonly used Croatian macroseismic relation that relates magnitude to epicentral intensity and focal depth. These results enable coherent reassessment of magnitudes for historical earthquakes and rapid post-event estimation of maximum intensity. Adoption of the new relationships would also support the homogenization of macroseismic magnitudes in the Croatian Earthquake Catalogue and provide a solid foundation for future intensity-based seismic hazard assessments in the region.

Revision of the magnitude–epicentral intensity–focal depth relation for earthquakes in Croatia and the surrounding areas

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发表日期：

2026年4月10日

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Marijan Herak,
Davorka Herak

摘要

We present an updated empirical relationship between moment magnitude (M_w), epicentral intensity (I₀, EMS), and macroseismic focal depth (h_m, km) for earthquakes in Croatia and its surroundings. The analysis is based on the updated, revised and uniformly processed Croatian Macroseismic Database and the corresponding Croatian Macroseismic Catalogue, which together provide a homogeneous macroseismic dataset spanning the period 1520–2022. From these, 139 triplets (M_w, ℎ_m, I₀) were selected corresponding to events with independently determined moment magnitudes and reliably derived macroseismic parameters. A three-axes weighted orthogonal regression was performed to obtain a symmetric relationship linking the three variables. The resulting triaxial regression plane is expressed as $-0.390 \,{M}_{w}+0.960 \log\left({h}_{m}+1\right)+0.285\,{I}_{0}=1$ $- 0.390 M_{w} + 0.960 log (h_{m} + 1) + 0.285 I_{0} = 1$ from which closed-form expressions allow consistent estimation of any one parameter given the other two. The new relations exhibit stable predictive performance under out-of-sample conditions, and provide improved consistency across the full range of observed magnitudes, intensities, and focal depths. They also agree well with the most commonly used Croatian macroseismic relation that relates magnitude to epicentral intensity and focal depth. These results enable coherent reassessment of magnitudes for historical earthquakes and rapid post-event estimation of maximum intensity. Adoption of the new relationships would also support the homogenization of macroseismic magnitudes in the Croatian Earthquake Catalogue and provide a solid foundation for future intensity-based seismic hazard assessments in the region.