Macroseismic intensity attenuation models calibrated in Mw for Italy

This study aims at developing new macroseismic intensity attenuation models valid for Italy by exploiting the most updated macroseismic dataset and earthquakes catalogue, as well as the information obtained from a critical analysis of the most recent models in the literature. Several different attenuation models have been calibrated as a function of the moment magnitude (Mw) and epicentral distance from 16,260 intensity data points, that are related to 119 earthquakes occurred after 1900. According to trends and residuals analysis, the preferred calibrated intensity attenuation function is a Log-Linear model for epicentral distance (Repi in km) and a linear model for Mw as:
I(MCS) = 1.81 − 2.61LogR − 0.0039R + 1.42Mw
with pseudo hypocentral distance R = √R2 + (9.87)2 ; the estimated standard deviation is
epi
σ=0.75. Also noteworthy is another model for macroseismic intensity attenuation that proved to be as good as the best model and shows higher sensitivity to physical parameters, such as focal depth and magnitude, especially in the epicentral area. Performance of all calibrated models was also checked on an independent set of 15 post-1900 Italian earth- quakes. One of the results of the present work is the opportunity to define earthquake sce- narios (e.g. probabilistic seismic hazard maps) in terms of Macroseismic Intensity and its related standard deviation, avoiding the uncertainties due to the conversion of various ground shaking parameters into intensity values.

Albarello D, Bosi V, Bramerini F, Lucantoni A, Naso G, Peruzza L, Rebez A, Sabetta F, Slejko D (2000) Carte di pericolosità sismica del territorio nazionale. Quaderni di Geofisica, 12, Roma, p 7, CD-Rom, 4 allegati (in Italian)
Albarello D, D’Amico V (2004) Attenuation relationship of macroseismic intensity in Italy for probabilistic seismic hazard assessment. Boll Geof Teor Appl 454(4):271–284
Allen TI, Wald DJ, Worden BC (2012) Intensity attenuation for active crustal regions. J Seismol 16:409– 433. https://doi.org/10.1007/s10950-012-9278-7
Ambraseys NN (1985) Intensity-Attenuation and magnitude-intensity relationships for Northwest European earthquakes. Earth Eng Struct Dyn 13:733–778. https://doi.org/10.1002/eqe.4290130604
Archivio Macrosismico GNDT (1995) Studi preliminari di terremoti attraverso i repertori sismologici. Archivio macrosismico del GNDT, Milano, (in Italian)
Atkinson GM, Worden BC, Wald D (2014) Intensity prediction equations for North America. Bull Seismol Soc Am 104(6):3084–3093. https://doi.org/10.1785/0120140178
Azzaro R, Barbano MS, D’Amico S, Tuvè T (2006) The attenuation of seismic intensity in the Etna region and comparison with other Italian volcanic districts. Ann Geophys 49:1003–1020. https://doi.org/10. 4401/ag-3113
Bakun WH, Wentworth CM (1997) Estimating earthquake location and magnitude from seismic intensity data. Bull Seismol Soc Am 87:1502–1521. https://doi.org/10.1785/BSSA0870061502
Bakun WH, Wentworth CM (1999) Erratum to Estimating earthquake location and magnitude from seismic intensity data. Bull Seism Soc Am 89:557
Bakun WH (2005) Magnitude and location of historical earthquakes in Japan and implications for the 1855 Ansei Edo earthquake. J Geophys Res B: Solid Earth 110:B02304. https://doi.org/10.1029/2004J B003329
Bakun WH (2006) Estimating locations and magnitudes of earthquakes in southern California from modi- fied Mercalli intensities. Bull Seismol Soc Am 96:1278–1295. https://doi.org/10.1785/0120050205
Bakun WH, Scotti O (2006) Regional intensity attenuation models for France and the estimation of magni- tude and location of historical earthquakes. Geophys J Int 164(3):596–610. https://doi.org/10.1111/j. 1365-246X.2005.02808.x
Bakun WH, Gomez Capera AA, Stucchi M (2011) Epistemic Uncertainty in the Location and Magnitude of Earthquakes in Italy from Macroseismic data. Bull Seismol Soc Am 101(6):2712–2725. https://doi. org/10.1785/0120110118
Baumont D, Manchuel K, Traversa P, Durouchoux C, Nayman E, Ameri G (2018) Intensity predictive atten- uation models calibrated in Mw for metropolitan France. Bull Earthq Eng 16:2285–2310. https://doi. org/10.1007/s10518-018-0344-6
Beauval C, Yepes H, Bakun WH, Egred J, Alvarado A, Singaucho JC (2010) Locations and magnitudes of historical earthquakes in the Sierra of Ecuador (1587–1996). Geophys J Int 181:1613–1633. https:// doi.org/10.1111/j.1365-246X.2010.04569.x
Berardi R, Petrungaro C, Zonetti L, Magri L, Mucciarelli M (1993) Mappe di sismicità per l’area italiana. ISMES/ENEL, p 51
Blake A (1937) On the estimation of focal depth from macroseismic data. Bull Seismol Soc Amer 31(3):225–231. https://doi.org/10.1029/TR018i001p00120
Boschi E, Guidoboni E, Ferrari G, Valensise G, Gasperini P (1997) Catalogo dei Forti Terremoti in Italia dal 461 a.C. al 1990- ING-SGA, Bologna, p 644
Boschi E, Guidoboni E, Ferrari F, Mariotti D, Valensise G, Gasperini P (2000) Catalogue of Strong Italian Earthquakes from 461 B.C to 1997. Ann Geophys 43:609–868
CEN (2004) EN 1998-1, 2004 (English): Eurocode 8: design of structures for earthquake resistance. Part I: general rules, seismic actions and rules for buildings [Authority:The European Union Per Regulation 305/2011]. (Directive 98/34 EC, Directive 2004/18/EC)
Chandra U, McWhorter J, Nowroozi A (1979) Attenuation of intensities in Iran. Bull Seismol Soc Am 69(1):237–250. https://doi.org/10.1785/BSSA0690010237
Chavez M, Castro R (1988) Attenuation of Modified Mercalli intensity with distance in Mexico. Bull Seis- mol Soc Amer 78(6):1875–1884. https://doi.org/10.1785/BSSA0780061875
CPS, Centro di Pericolosità Sismica, Seismic Hazard Center http://www.ingv.it/it/risorse-e-servizi/centri/ centro-pericolosita-sismica-cps. Accessed 6 April 2023
Ciccotti M, Negri N, Sassi L, Gonzato G, Mulargia F (2000) Elastic and fracture parameters of Etna, Stromboli and Vulcano lava rocks. J Volcanol Geoth Re 98:209–217. https://doi.org/10.1016/S0377- 0273(99)00154-7
Cornell CA (1968) Engineering seismic risk analysis. Bull Seismol Soc Amer 58(5):1583–1606. https://doi. org/10.1785/BSSA0580051583
CPTI Working Group (2004) Catalogo Parametrico dei Terremoti Italiani, versione 2004 (CPTI04). Istituto Nazionale Di Geofisica e Vulcanologia. https://doi.org/10.6092/INGV.IT-CPTI04
Cua G, Wald DJ, Allen TI, Garcia D, Worden CB, Gerstenberger M, Lin K, Marano K (2010) Best practices for using macroseismic intensity and ground motion intensity conversion equations for hazard and loss models in GEM1. GEM Technical Report 2010-4, GEM Foundation, Pavia, Italy
D’Amico V, Gomez Capera AA, Meletti C (2009) Project S2: Development of a dynamical model for seis- mic hazard assessment at national scale. Consolidated models for attenuation of macroseismic inten- sity. DPC Project S2, Deliverable D3.2, p 10
Dowrick DJ, Rhoades DA (1992) Attenuation of Modified Mercalli Intensity in New Zealand. Earthq Eng Struct Dyn 21:181–196. https://doi.org/10.5459/bnzsee.32.2.55-89
ENEL (Ente Nazionale Energia Elettrica) (1975) Catalogo dei terremoti italiani dall’anno 1000 al 1975. Compilato da Geotecnico Spa, Roma, computer printout [riservato] (in Italian)
Gasperini P, Bernardini F, Valensise G, Boschi E (1999) Defining seismogenic sources from historical earthquake felt reports. Bull Seism Soc Am 89:94–110. https://doi.org/10.1785/BSSA0890010094
Gasperini P (2001) The attenuation of seismic intensity in Italy: A bilinear shape indicates dominance of deep phases at epicentral distances longer than 45 km. Bull Seismol Soc Amer 91:826–841. https:// doi.org/10.1785/0120000066
Gasperini P, Vannucci G, Tripone D, Boschi E (2010) The location and sizing of historical earthquakes using the attenuation of macroseismic intensity with distance. Bull Seismol Soc Am 100:2035–2066. https://doi.org/10.1785/0120090330
Gasperini P, Lolli B, Vannucci G (2013) Empirical calibration of local magnitude data sets versus moment magnitude in Italy. Bull Seism Soc Am 103:2227–2246. https://doi.org/10.1785/0120120356
Gizzi FT (2012) Il "Terremoto Bianco" del 21 Agosto 1962. Aspetti macrosismici, geologici, risposta istituzionale. Zaccara editore, p 736, (in Italian)
Gomez-Capera AA, Salcedo Hurtado E (2002) Leyes de atenuación de la intensidad macrosísmica en Colombia. Earth Sci Res J 6:53–61 (in Spanish)
Gomez-Capera AA (2006) Seismic hazard map for the Italian territory using macroseismic data. Earth Sci Res J 10(2):67–90
Gomez-Capera AA, D’Amico V, Meletti C (2008a) Calibrating the Bakun Wentworth’s Method for the mac- roseismic estimation of earthquake parameters in Italy. In Programme and Abstracts of 31st General Assembly (ESC), Hersonissos, p 66, 7–12 September, Crete Island, Greece
Gomez-Capera AA, Rovida A, Meletti C, Stucchi M (2008b) Application of the Bakun Wentworth’s method for the macroseismic estimation of parameters of Italian earthquakes. In Programme and Abstracts of 31st General Assembly (ESC), p 65, 7–12 September, Hersonissos, Crete Island, Greece
Gomez-Capera AA, Meletti C, Musson R, Stucchi M (2009) The European Earthquake Catalogue (1000– 1600), demo version. Part 1-The NA4 Calibration Initiative, Deliverable D5. NERIES, Distributed Archive of Historical Earthquake Data (NA4), EC Project number 026130, internal report, p 100 https://emidius.mi.ingv.it/neries_NA4/docs/NA4_D5.pdf. Accessed 6 April 2023
Gomez-Capera AA, D’Amico V, Meletti C, Rovida A, Albarello D (2010) Seismic hazard in terms of mac- roseismic data intensity in Italy: a critical analysis from the comparison of different computational procedures. Bull Seism Soc Am 100(4):1614–1631. https://doi.org/10.1785/0120090212
Gomez-Capera AA, Garcia Pelaez J, Chuy Rodríguez TJ, Salcedo-Hurtado E, Stucchi M (2013) Calibración y validación del algoritmo de Bakun and Wentworth para calcular localización y magnitud de terre- motos históricos a partir de datos macrosísmicos en Cuba Oriental. Boletín De Geología 35(2):113– 127 (in Spanish)
Gomez-Capera AA, Stucchi M, Arcila M, Bufaliza M, Choy J, Minaya E, Leyton L, Pirchiner M, Rendón H, Sarabia A, Tavera H, Yepes H (2020) Catálogo de terremotos de América del Sur homogéneo en Mw para el periodo pre-1964. GEOS 40(1):1–40 (in Spanish)
Gomez-Capera AA, Salcedo-Hurtado E, Santulin M, Rios LF, Blandon JC (2022) Estimating Magnitude and Location from macroseismic data of the 1925 Colombian earthquake. Bull Geophys Oceanogr 63(3):377–402. https://doi.org/10.4430/bgo00386
Grandori G, Drei A, Perotti F, Tagliani A (1991) Macroseismic intensity versus epicentral distance: the case of Central Italy. Tectonophysics 193:165–171. https://doi.org/10.1016/0040-1951(91)90196-Y Greenhalgh S, Denham D, McDougall R, Rynn JM (1989) Intensity relations for Australian earthquakes.
Tectonophysics 166:255–267. https://doi.org/10.1016/0040-1951(89)90218-7
Grünthal G ed (1998) European Macroseismic Scale 1998. Cahiers du Centre Européen de Géodynamique
et de Séismologie 15, Luxembourg, 99 pp
Gruppo di lavoro CPTI (1999) Catalogo Parametrico dei Terremoti Italiani. ING, GNDT, SGA, SSN, Bolo-
gna, p 92. https://doi.org/10.6092/ingv.it-cpti99 (in Italian)
Gruppo di lavoro CPTI (2004) Catalogo Parametrico dei Terremoti Italiani (CPTI04). Istituto Nazionale
di Geofisica e Vulcanologia (INGV), Bologna. https://doi.org/10.6092/INGV.IT-CPTI04 (in Italian) Guidoboni E, Ferrari G, Mariotti D, Comastri A, Tarabusi G, Valensise G (2007) CFTI4Med, Catalogue of Strong Earthquakes in Italy (461 BC-1997) and Mediterranean Area (760 BC-1500), INGV-SGA.
Available from http://storing.ingv.it/cfti4med/
Gupta IN, Nuttli OW (1976) Spatial attenuation of intensities for Central US earthquakes. Bull Seismol Soc
Amer 66:743–751. https://doi.org/10.1785/BSSA0660030743
Gutenberg B, Richter CF (1942) Earthquake magnitude, intensity, energy and acceleration. Bull Seismol
Soc Amer 32:163–191. https://doi.org/10.1785/BSSA0320030163
Hinzen KG, Oemisch M (2001) Location and magnitude from seismic intensity data of recent and historic
earthquakes in the Northern Rhine Area, Central Europe. Bull Seismol Soc Am 91:40–56. https://doi.
org/10.1785/0120000036
Howell BF, Schultz TR (1975) Attenuation of Modified Mercalli intensity with distance from the epicenter. Bull Seismol Soc Amer 65(3):651–665. https://doi.org/10.1785/BSSA0650030651
ING (1981) Catalogo dei terremoti italiani del 1450 aC al 1980. Rapporto interno, Roma (in Italian)
Kaila KL, Sarkar D (1982) Earthquake Intensity Attenuation pattern in the United States. Geophys J R Astr Soc
70:31–39
Kövesligethy R (1906) Mathematikai és Természettudomanyi Értesitö 24:349–368 (in Hungarian)
Le Goff B, Borges JF, Bezzeghoud M (2014) Intensity-distance attenuation laws for the Portugal mainland
using intensity data points. Geophys J Int 199:1278–1285. https://doi.org/10.1093/gji/ggu317
Locati M, Camassi R e Stucchi M (a cura di) (2011) DBMI11, la versione 2011 del Database Macrosismico Italiano. Istituto Nazionale di Geofisica e Vulcanologia, Milano, Bologna, http://emidius.mi.ingv.it/
DBMI11, https://doi.org/10.6092/INGV.IT-DBMI11, (in Italian)
Locati M, Camassi R, Rovida A, Ercolani E, Bernardini F, Castelli V, Caracciolo CH, Tertulliani A, Rossi A,
Azzaro R, D’Amico S, Antonucci A (2022) Database Macrosismico Italiano (DBMI15), versione 4.0.
Istituto Nazionale di Geofisica e Vulcanologia (INGV). https://doi.org/10.13127/DBMI/DBMI15.4 Lopez Casado C, Molina Palacios S, Delgado J, Pelaez JA (2000) Attenuation of intensity with epicentral dis- tance in the Iberian Peninsula. Bull Seismol Soc Amer 90(1):34–47. https://doi.org/10.1785/0119980116 Mak S, Clements RA, Schorlemmer D (2015) Validating intensity prediction equations for italy by observa-
tions. Bull Seismol Soc Am 105(6):2942–2954. https://doi.org/10.1785/0120150070
Mappa di Pericolosità Sismica (MPS) Working Group (2004). Redazione della mappa di pericolosità sismica prevista dall’Ordinanza PCM del 20 marzo 2003 n.3274 All. 1, Rapporto conclusivo per il Dipar- tamento della Protezione Civile, Istituto Nazionale di Geofisica e Vul- canologia, Milano–Roma, 178 pp.,
available at http://zonesismiche.mi.ingv.it/ (in Italian; last accessed August 2023)
Margottini C, D. Molin (1983) Risultati preliminari delle ricerche di sismica storica condotte nell’Appennino
tosco-emiliano. ENEA, PAS-ISP BR (83):2, Roma, p 130 (in Italian)
Margottini C, Ambraseys NN, Screpanti A (1993) La magnitudo dei terremoti italiani del XX secolo. ENEA,
rapporto interno, Roma, p 57 (in Italian)
Medvedev S, Sponheuer W, Karník V (1964) Neue seismische Skala Intensity scale of earthquakes. In: 7 Tagung der Europäischen Seismologischen Kommission vom 24.9. bis 30.9.1962, in Jena, Veröff. Institut für Bodendynamik und Erdbebenforschung in Jena, Deutsche Akademie der Wissenschaften zu Berlin, 77:69–76 (in German)
Meletti C, Galadini F, Valensise G, Stucchi M, Basili R, Barba S, Vannucci G, Boschi E (2008) A seismic source model for the seismic hazard assessment of the Italian territory. Tectonophysics 450:85–108. https://doi.org/10.1016/j.tecto.2008.01.003
Meletti C, Marzocchi W, D’Amico V, Lanzano G, Luzi L, Martinelli F, Pace B, Rovida A, Taroni M, Visini F, and the MPS19 Working Group (2021) The new Italian seismic hazard model (MPS19). Ann Geophys 64(1): SE112 https://doi.org/10.4401/ag-8579
Mezcua J, Rueda J, Garcia Blanco RM (2004) Revaluation of historic earthquakes in Spain. Seismol Res Lett 75:75–81. https://doi.org/10.1785/gssrl.75.1.75
Mezcua J, Rueda J, Garcia Blanco RM (2020) Characteristics of a new regional seismic-intensity prediction equation for Spain. Nat Hazards 101:817–832. https://doi.org/10.1007/s11069-020-03897-x
Milne WG, Davenport AG (1969) Earthquake risk in Canada. Bull Seismol Soc Amer 59:729–754. https://doi. org/10.1785/BSSA0590020729
Molin D, Galadini F, Galli P, Mucci L, Rossi A (1999) Terremoto del Fucino del 13 gennaio 1915. Studio macrosismico. In: S. Castenetto e F. Galadini (eds.), 13 gennaio 1915. Il terremoto nella Marsica, Roma, 321–340; 631–661 (in Italian)
Monachesi G., Stucchi M (1997) DOM4.1, un database di osservazioni macrosismiche di terremoti di area italiana al di sopra della soglia del danno, GNDT, Milano, p 1052. https://emidius.mi.ingv.it/DOM/ (in Italian)
Mori F, Mendicelli A, Moscatelli M, Romagnoli G, Peronace E, Naso G (2020) A new Vs30 map for Italy based on the seismic microzonation dataset. Eng Geol. https://doi.org/10.1016/j.enggeo.2020.105745
Musson RMW, Cecic I (2002) Macroseismology. In: Lee W, Kanamori H, Jennings P, Kisslinger C (eds) (2002). International handbook of earthquake and engineering seismology, Part A, Academic Press, pp 807–822
Papazachos C, Papaioannou Ch (1997) The macroseismic field of the Balkan area. J Seismolog 1:181–201.
https://doi.org/10.1023/A:1009709112995
Pasolini C, Gasperini P, Albarello D, Lolli B, D’Amico V (2008a) The attenuation of seismic intensity in Italy part I: theoretical and empirical backgrounds. Bull Seism Soc Am 98(2):682–691. https://doi.org/10. 1785/0120070020
Pasolini C, Albarello D, Gasperini P, D’Amico V, Lolli B (2008b) The attenuation of seismicity in Italy, Part II: Modelling and validation. Bull Seismol Soc Am 98:692–708. https://doi.org/10.1785/0120070021
Peruzza L (1996) Attenuating Intensities. Ann Geophys 39(5):1079–1093. https://doi.org/10.4401/ag-4037 Peruzza L (2000) Macroseismic attenuation relationships of Italian earthquakes for seismic hazard assessment
purposes. Boll Geof Teor Appl 41:31–48
Pino NA, Giardini D, Boschi E (2000) The December 28, 1908, Messina Straits, Southern Italy, earthquake:
waveform modelling of regional seismograms. J Geoph Res 105(B11):25473–25492
Postpischl D (ed) (1985) Catalogo dei terremoti italiani dal 1000 al 1980. Quaderni La Ricerca Scientifica 114,
2B, PFG-CNR, Bologna, p 239
Provost L, Scotti O (2020) QUake-MD: open-source code to quantify uncertainties in magnitude-depth esti-
mates of earthquakes from macroseismic intensities. Seismol Res Lett 91:2520–2530. https://doi.org/10.
1785/0220200064
Quadros L, Assumpçao M, Trindade de Souza AP (2019) Seismic intensity attenuation for intraplate earth- quakes in Brazil with re-evaluation of historical seismicity. Seismol Res Lett 90:2217–2226. https://doi. org/10.1785/0220190120
Rovida A, Camassi R, Gasperini P, Stucchi M (eds) (2011) CPTI11, the 2011 version of the Parametric Cata- logue of Italian Earthquakes. Milano, Bologna. https://doi.org/10.6092/INGV.IT-CPTI11
Rovida A, Locati M, Camassi R, Lolli B, Gasperini P (2016) CPTI15, the 2015 version of the Parametric Cat- alogue of Italian Earthquakes. Istituto Nazionale Di Geofisica e Vulcanologia. https://doi.org/10.6092/ INGV.IT-CPTI15
Rovida A, Locati M, Camassi R, Lolli B, Gasperini P (2019) Catalogo Parametrico dei Terremoti Italiani (CPTI15), version 2.0, Istituto Nazionale di Geofisica e Vulcanologia. https://doi.org/10.13127/CPTI/ CPTI15.2
Rovida A, Locati M, Romano C, Lolli B, Gasperini P (2020) The Italian earthquake catalogue CPTI15. Bull Earthq Eng 18:2953–2984. https://doi.org/10.1007/s10518-020-00818-y
Rovida A, Locati M, Camassi R, Lolli B, Gasperini P, Antonucci (2021) Catalogo Parametrico dei Terremoti Italiani (CPTI15), versione 3.0. Istituto Nazionale di Geofisica e Vulcanologia (INGV). https://doi.org/ 10.13127/CPTI/CPTI15.3
Rovida A, Antonucci A (2021) EPICA - European PreInstrumental Earthquake CAtalogue, version 1.1. Istituto Nazionale di Geofisica e Vulcanologia (INGV). https://doi.org/10.13127/epica.1.1
Rovida A, Locati M, Camassi R, Lolli B, Gasperini P, Antonucci A (2022a). Catalogo Parametrico dei Terre- moti Italiani (CPTI15), versione 4.0, Istituto Nazionale di Geofisica e Vulcanologia (INGV). https://doi. org/10.13127/CPTI/CPTI15.4
Rovida A, Antonucci A, Locati M (2022b) The European Preinstrumental Earthquake Catalogue EPICA, the 1000–1899 catalogue for the European Seismic Hazard Model 2020. Earth System Science Data. Coper- nicus GmbH. https://doi.org/10.5194/essd-14-5213-2022
Sieberg A (1930) Scala MCS (Mercalli-Cancani-Sieberg). Geologie Der Erdbeben, Handbuch Der Geophysik 2(4):552–555
Slejko D, Peruzza L, Rebez A (1998) Seismic hazard maps of Italy. Ann Geophys 41(2):183–213. https://doi. org/10.4401/ag-4327
Stucchi M, Camassi R, Rovida A, Locati M, Ercolani E, Meletti C, Migliavacca P, Bernardini F, Azzaro R (2007). DBMI04, il database delle osservazioni macrosismiche dei terremoti italiani utilizzate per la compilazione del catalogo parametrico CPTI04. Quaderni di Geofisica, 49, INGV, Roma, p 38. https:// doi.org/10.6092/INGV.IT-DBMI04 (in Italian)
Stucchi M, Rovida A, Gomez Capera AA, Alexandre P, Camelbeeck T, Demircioglu MB, Gasperini P, Kousk- ouna V, Musson RMW, Radulian M, Sesetyan K, Vilanova S, Baumont D, Bungum H, Fäh D, Lenhardt W, Makropoulos K, Martinez Solares JM, Scotti O, Živčić M, Albini P, Batllo J, Papaioannou C, Tat- evossian R, Locati M, Meletti C, Viganò D, Giardini D (2013) The SHARE European earthquake cata- logue (SHEEC) 1000–1899. J Seismol 17:523–544. https://doi.org/10.1007/s10950-012-9335-2
Synergy Software (2021) KaleidaGraph 4.5.4 [Software]. Synergy Software, Frederick
Willmott CJ, Ackleson SG, Davis RE, Feddema JJ, Klink KM, Legates DR, O’Donnell J, Rowe CM (1985) Statistics for the evaluation and comparison of models. J Geophys Res 90(C5):8995–9005. https://doi.
org/10.1029/JC090iC05p08995
Wolfram Research, Inc (2022) Mathematica 12.0 [Software]. Wolfram Research, Inc, Champaign
Wood HO, Neumann F (1931) Modified Mercalli intensity scale of 1931. Bull Seismol Soc Am 21:277–283.
https://doi.org/10.1785/BSSA0210040277