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Petrinja Earthquake, Mw = 6.4 on 29/12/2020 Quantectum Technical Report

© by Quantectum, 2021

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EDITORIAL NOTE The Quantectum terminology and explanation of the Omega-Theory may be found at: https://quantectum.com/ Quantectum Technical Report © by Quantectum, 2021 Churerstrasse 80 8808 Pfäffikon SZ The right of publication in print, electronic, and any other form and in any language is reserved by Quantectum. Short extracts from Quantectum publications may be reproduced without authorization, provided that the complete source is clearly indicated. Editorial correspondence and requests to publish, reproduce, or translate this publication in part or in whole should be addressed to Quantectum.

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Petrinja earthquake (Croatia); preliminary technical report (c) by Quantectum 2021 Time: 29/12/2020 at 11:19:54 UTC Location: 45.42, 16.26 Magnitude: 6.4 Depth: 10 km Introduction The region where the Petrinja 2020 earthquake happened is part of the External Dinarides. Here, the deformation is mostly accommodated by the active NW-SE trending thrust faults (Korbar et al., 2020). Historically, many moderate earthquakes happened in the vicinity of the studied earthquake, such as Zagreb 1880 (Prelogović and Cvijanović, 1981), Ljubljana 1895 (Tiberi et al., 2018), Petrinja 1909 (Mohorovičić, 1910), Friuli 1976 (Carulli and Slejko, 2005), Bovec 1998 and 2004 (Bajc et al., 2001, Bressan et al., 2009) and finally, Zagreb 2020 (Markušić et al., 2020) earthquakes.

Figure 1: Map showing epicentres (marked as stars) of large historical earthquakes in the region of the Northern Balkan and the Southern Alps. Focal mechanisms of some latest earthquakes are illustrated as beachballs. Small black dots are aftershocks (according to EMSC) of the Petrinja earthquake, 2020.

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Figure 2: Location of the Petrinja 2020 earthquake sequence. Circles represent earthquakes (EMSC) where the size means the magnitude. Red lines are active faults as reported in the European database of active faults (Basilic et al., 2013). On Tuesday, 29/12/2020, at 11:19:54 UTC, a strong Mw6.4 earthquake hit the region of Petrinja, Croatia causing widespread damage and several casualties in the cities of Petrinja and Sisak. It reached a maximum macroseismic intensity of IX on the Modified Mercalli Intensity (MMI) scale and was felt at least up to 300 km from its epicentre (Figure 4). The mainshock happened along the NW-SE trending strike-slip fault at an estimated depth of 10 km as reported by EMSC (www.emsc-csem.org). The mainshock was preceded by two M5+ foreshocks a day before, which produced only a few smaller magnitude aftershocks. The following report describes the results of the preliminary analysis of this event by Quantectum.

Figure 3: Petrinja sequence temporal evolution. Earthquake data is obtained from EMSC (www.emsc-csem.org). Foreshock sequence is denoted by blue background while mainshock and its aftershock sequence are denoted with red background.

http://www.emsc-csem.org/http://www.emsc-csem.org/

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Figure 4: Rapid estimation of the felt shaking and damage levels produced by the Mw6.4 Petrinja earthquake. A conversion relation between the Peak Ground Accelerations (obtained from the Ground Motion Prediction Equation of Campbell and Bozorgnia, 2014) and the macroseismic intensities (Caprio et al., 2015) is used. The red star indicates the epicentral location of the earthquake. Petrinja earthquake; stress-strain analysis We performed the stress/strain analysis of the focal mechanisms of M4+ earthquakes within the CMT catalog after the year 1976 and within a 300 km radius around the epicentre of the Petrinja 2020 earthquake. For the analysis, we used the T-TECTO software (Žalohar and Vrabec, 2007, 2008) and the Right Dihedra Method (RDM) by Angelier and Mechler (1977). The results describe the long-term average stress/strain field in the Northern Balkan. The NW-SE trending nodal plane associated with the Petrinja earthquake is assumed to be the real fault plane. It is illustrated with a red line on the stereograms in Figures 5 and 6.

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Figure 5: (A) Results of the stress/strain inversion according to the methodology by Žalohar and Vrabec (2007). The stress/strain axes are illustrated as black squares on the stereogram. Numerical results are on the right side. Yellow circles are principal stresses according to the Right Dihedra Method (Angelier and Mechler, 1977). Numerical results are on the left. (B) The orientation of the macrorotation axis according to the methodology by Žalohar and Vrabec (2008). (C) Focal mechanism of the Petrinja earthquake according to the CMT catalog (https://www.globalcmt.org/). See text for details. Stress inversion results (Figure 5A) indicate the N-S compressional stress regime with predominantly reverse faulting. The ratio between the principal stresses is S1 : S2 : S3 = 0.54 : -0.23 : -0.31. The parameter D = (S1-S2)/(S1-S3) = 0.1. Angle of friction used in the analysis was set to 30 degrees. The orientations of the principal stress/strain axes (illustrated as back squares) are as follows; e1: 184/13, e2: 88/23, e3: 300/63. The minimum principal stress/strain axis is sub-vertical and indicates relative vertical thickening of the crust for 48 % of the maximally possible deformation that the strain tensor can produce. The intermediate stress/strain axis indicates 77 % of the maximally possible extension in the W-E direction. Right Dihedra Method (RDM, Figure 5A, coloured fields) indicates the N-S compressional stress regime with the following orientation of principal stresses/strains; maximum principal axis: 177/7, minimum principal axis: 48/80, intermediate principal axis: 268/8. The magnitudes of homogeneity along the maximum and minimum principal axes are 98 % and 96 %, respectively. This indicates very stable stress/strain regimes. Figure 5B illustrates the orientation of the regional macrorotation axis, which indicates moderate CCW rotations accommodated by the active tectonic faulting in the region. This is surprising since we would expect that the active faulting along the predominantly strike-slip Dinaric faults accommodates CW macrorotation. Figure 5C illustrates the focal mechanism of the Petrinja earthquake (according to the CMT catalog (https://www.globalcmt.org/), which indicates the strike-slip faulting, possibly along the NW-SE trending dextral fault (Dinaric direction). This focal mechanism is compatible with the N-S compression.

https://www.globalcmt.org/https://www.globalcmt.org/

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Figure 6: (A) Visualization of the Gauss Function (VGF, Žalohar and Vrabec, 2007). Black squares are principal stresses according to the inverse method (Žalohar and Vrabec, 2007). Yellow circles are principal stresses according to the VGF method. Numerical results are right of the stereogram. (B) Mohr circles diagram illustrating the state of stress on the Petrinja earthquake fault plane (red circle) and other fault planes used in the calculation (black circles). See text for details. Visualization of the Gauss Function (VGF, Figure 6A) also indicates the N-S compressional stress regime with the following orientation of principal stresses/strains; maximum principal axis: 183/11, minimum principal axis: 317/74, intermediate principal axis: 91/11. This method also allows for the estimation of the angle of friction to approximately 30 degrees, which was also used in the stress/strain inversion analysis. The Mohr diagram for this angle of friction and for the stress tensor calculated based on the stress/strain inversion is illustrated in Figure 6B. Here, the parameters are the following: mu – coefficient of friction, tau – shear stress, sigmaN – normal stress, FS – factor of stability, Dsigma – driving stress = tau – mu*SigmaN. The state of stress on the NW-SE directed nodal plane associated with the Petrinja earthquake is illustrated with a red circle. The factor of stability (FS) is lower than 1, which indicates slight instability of this fault plane in the N-S compressional stress regime. However, the sub-vertical strike-slip faults do not have a very favourable orientation with respect to the long-term average stresses. In addition, the inversion results suggest even larger instability of the conjugate NE-SW trending nodal plane associated with the Petrinja earthquake, with the factor of instability equal to 0.79. This is in agreement with the model proposed by Croatian seismologists (https://www.hgi-cgs.hr/priopcenje-za-medije-izvjesce-hrvatskog-geoloskog-instituta-o-potresima/), who also proposed reactivation of the NE-SW trending sinistral fault.

https://www.hgi-cgs.hr/priopcenje-za-medije-izvjesce-hrvatskog-geoloskog-instituta-o-potresima/https://www.hgi-cgs.hr/priopcenje-za-medije-izvjesce-hrvatskog-geoloskog-instituta-o-potresima/

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Current regional tectonic deformation (Figure 7) Quantectum stress forecasting system (Žalohar et al, 2020a, b) indicates that the region of Alps and Dinarides is currently characterized by predominantly reverse faulting and thickening of the Earth’s crust (Figure 7). This state of the relative vertical deformation favours inverse faulting in the region.

Figure 7: Chart of the relative vertical deformation of the Euro-Mediterranean region for the time period 01/02/2020 – 01/02/2021. The blue colour illustrates the thinning of the crust and predominant normal faulting. The yellow colour illustrates predominant strike-slip faulting, while the red colour illustrates the thickening of the crust and predominant reverse faulting. Small circles illustrate the M6+ events during the time-window.

Figure 8: Chart of the normalized shear stress of the Euro-Mediterranean region for the time period 01/02/2020 – 01/02/2021. The blue colour illustrates weak normalized shear stress (values around 0.5), the red colour illustrates moderate normalized shear stress (values around 0.75). Small circles illustrate the M6+ events during the time-window. Short lines illustrate the maximum horizontal compression.

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Regional tectonic shear stress and maximum horizontal compression (Figure 8) The region of Northern Croatia and Southern Slovenia is currently characterized by relatively weak normalized shear stress (Žalohar et al, 2020a, b) equal to 0.62 (Figure 8), which defines the maximum possible magnitude Mmax in the region to approximately 6.4. The maximum horizontal compression is in the NNW-SSE direction. Higher normalized shear stress fields can be found near Gibraltar, Romania, in the Ionian and Aegean Seas. Regional tectonic driving stress (Figures 9 and 10) The region of Northern Croatia and Southern Slovenia is currently characterized by relatively high driving stress (Žalohar et al., 2020a, b) equal to 0.73 (Figure 9), which defines the maximum possible magnitude Mmax in the region to approximately 6.9.

Figure 9: Chart of the driving stress of the Euro-Mediterranean region for the time period 01/02/2020 – 01/02/2021. The blue colour illustrates weak normalized shear stress (values around 0.5), the red colour illustrates moderate to high normalized shear stress (values around 0.75). Small circles illustrate the M6+ events during the time-window. Short lines illustrate the maximum horizontal compression.

Figure 10: Time-dependence of the tectonic driving stress (S) within the 200 km radius around the Petrinja mainshock.

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The graph in Figure 10 illustrates the time-development of the tectonic driving stress within a 200 km radius around the Petrinja mainshock. Since 2019, the driving stress indicates a constant average increase. Time-synchronizations (Figure 11) We analyzed the ISC seismic catalog with the lower magnitude cut-off Mc = 2.5 within the radius of 40 km around the Petrinja mainshock. Ensemble analysis of the T-synchronizations along the NW-SE Dinaric fault near Petrinja has been performed according to the methodology by Žalohar (2018) and shows that this fault is under a stable fourth-order T-synchronization. Such synchronizations are usually related to strong earthquakes. This means that the fault is highly unstable and is likely to interact with the global shear-traction field with a probability of at least 75 % (local interaction potential, Pl). The T-synchronization will last till September 2021. During that time, stronger tectonic waves will likely trigger additional moderate to strong aftershocks along this fault. The probability for earthquake triggering will oscillate and will depend on the value of the shear-traction field produced by the tectonic waves and their global seismic activity.

Figure 11: Results of the ensemble analysis of T-synchronizations along the NW-SE trending active fault south from Petrinja, Croatia. The red line illustrates the synchronization function, which is the mean number of time-synchronized geometric and periodic Omega-sequences. Thin grey lines illustrate the minimum and the maximum number of the synchronization function, and the thick green lines are the standard deviation. The fourth-order T-synchronization started after September 2020 and will last till September 2021. During that interval, the region will be highly unstable. Red vertical columns are earthquakes in the ISC catalog. The Petrinja mainshock is illustrated with the red-yellow column. Results of the Ensemble Earthquake Forecasting System (Figure 12) The Ensemble Earthquake Forecasting System shows that at the time of the Petrinja earthquake the region of Northern Balkan was under the influence of several tectonic waves having the largest

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wavelength up to 21.000 km and with velocities up to 80 km/day. These waves only caused relatively weak shear traction around 0.23. Based on the shear traction field, the maximum possible magnitude Mmax was around 5.3. The probability for earthquake triggering with magnitudes above 4.5 was 30 % (global interaction potential, Pg), for the magnitudes above 5.5, the probability was 10 %, and for the magnitudes above 6, the probability was 5 %. These are relatively low probabilities. The following graph (Figure 12) illustrates the time-dependence of the global interaction potential Pg for various magnitudes, which describes the maximum possible probability for earthquake triggering in unstable tectonic zones.

Figure 12: Probability-synchrogram illustrating the time-dependence of the global interaction potential (Pg) in the epicentral region of the Petrinja earthquake. Lines with different colours are probabilities for different magnitudes according to the legend above. Blue columns are earthquakes within the radius of 500 km, red columns are earthquakes within the radius of 100 km. The Petrinja mainshock is illustrated as a black column. Results of the Direct Earthquake Warning System (DEWS): In spite of relatively low values of the global interaction potential, the Quantectum Direct Earthquake Warning System (DEWS) detected the presence of highly active tectonic waves that passed through the region of Central Italy and Northern Balkan in the days before the Petrinja mainshock. These waves triggered several moderate to strong earthquakes worldwide: M5.0 on 2020-12-22; Mindanao, Philippines, M5.1 on 2020-12-24; Molucca Sea M5.3 on 2020-12-24; Solomon Islands M5.1 on 2020-12-25; Mindanao, Philippines M5.1 on 2020-12-25; Sumba Region, Indonesia M5.5 on 2020-12-27; Eastern Turkey M6.7 on 2020-12-27; Off Coast of Los Lagos, Chile M5.1 on 2020-12-28; Kepulauan Talaud, Indonesia M5.2 on 2020-12-28; Owen Fracture Zone Region M5.5 on 2020-12-28; Molucca Sea Figure 13 illustrates the global shear traction field produced by tectonic waves, which are visible as coloured shadows. The active tectonic waves that passed through the region of Northern Balkan at the

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time of the Petrinja earthquake are illustrated with coloured solid lines. The above earthquakes on these waves are marked with concentric circles.

Figure 13: Global synchronization field ( = approximation of the shear traction field) in the time period 24/12/2020 – 31/12/2020. The blue colour illustrates a weak synchronization field (shear traction field), while the red-black colour indicates a high synchronization field (shear-traction field). The largest earthquake on the waves that passed through the region of Northern Balkan was M6.7 earthquake near Los Lagos, Chile on 27/12/2020. This earthquake happened along the wave passing through the region of Central Italy and Northern Balkan with the wavelength of approximately 10.500 km and velocity of approximately 5 km/day. Along this wave (also in the region of Central Italy and Northern Balkan), the probability for earthquake triggering (global interaction potential, Pg) with magnitudes above 4.5 increased to 98 %, the probability for magnitudes above 5.5 was 30 % ( = Pg), while the probability for magnitudes above 6 was 17 % ( = Pg). This means that after the Chile event, the weak to moderate events along the wave through Chile and Northern Balkan were expected and highly probable. The probability for strong M6+ events was also relatively high. Medium-term forecasts for January and February 2021 (Figures 14 and 15) Quantectum Earthquake Forecasting System (QEFS) indicates that in January, the region of Northern Balkan will be under the influence of few tectonic waves with relatively low wavelengths that will cause relatively weak oscillations of the shear-traction field and relatively low earthquake triggering probabilities (global interaction potential). The first significant maximum will be around 23/01/2021 due to the passage of tectonic waves with maximum wavelength up to 23.500 km and maximum velocity up to 125 km/day. These waves will pass through the entire length of the Balkan Peninsula from Greece toward the Alps.

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In February, the number of tectonic waves affecting the region of Balkan and the entire Euro-Mediterranean will gradually increase. The waves will also have larger wavelengths. This will significantly increase the earthquake triggering probabilities in the Euro-Mediterranean region along the traces of the tectonic waves. The animation, which shows the time-development of the shear-traction field based on the tectonic waves with the wavelengths above 16.000 km (MES sum N[1] model), can be accessed on the following link: https://gis.quantectum.com/forecasts/2a0cd367a9465f0b86dbf1c1ce6057a9/178dca40efc244f188d29a12326f6ba1.mp4 Figure 14 illustrates the time-development of the global interaction probability (Pg) in the epicentral region of the Petrinja earthquake for two models (MES sum N[1] for wavelengths above 16.000 km and MES max N[1] for wavelengths above 10.000 km). The global interaction potential describes the maximum possible earthquake triggering probability by tectonic waves.

A

B

Figure 14: Time-development of the global interaction probability (Pg) in the epicentral region of the Petrinja earthquake for two models (A - MES sum N[1] for wavelengths above 16.000 km and B - MES max N[1] for wavelengths above 10.000 km).

https://gis.quantectum.com/forecasts/2a0cd367a9465f0b86dbf1c1ce6057a9/178dca40efc244f188d29a12326f6ba1.mp4https://gis.quantectum.com/forecasts/2a0cd367a9465f0b86dbf1c1ce6057a9/178dca40efc244f188d29a12326f6ba1.mp4

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Figure 15: Two snapshots of the medium-range forecasts for the Euro-Mediterranean; A – in the time period 20/01/2021 – 27/01/2021 (above) and 22/02/2021 – 01/03/2021 (below). The blue colour illustrates a weak synchronization field (shear traction field), while the red-black colour indicates a high synchronization field (shear-traction field).

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Long-term forecast (Figure 16) The long-term forecast for the next 10 years (till 2030) is based on the T-synchronization analysis. Quantectum ensemble models suggest several T-synchronization maxima, which indicate increased instability of the Petrinja fault. T-synchronizations define periods of increased local interaction potential (Pl), which describes the instability of the fault. The following periods can be extracted from Figure 16: The period between September 2021 and July 2024: will be characterized by unstable T-synchronizations and the local interaction potential below 0.5. The period between July 2024 and April 2026: will be characterized by global and stable fourth-order T-synchronization, and the local interaction potential above 0.75. The maximum of this T-synchronization will be in April 2025. The period between June 2026 and March 2028: will be characterized by local and stable fourth-order T-synchronization, and the local interaction potential around 0.75 ± 0.1. The maximum of this T-synchronization will be in August 2027. These T-synchronizations will increase the probability of earthquake triggering by tectonic waves. The presence or absence of tectonic waves is currently only possible to calculate for 2 months ahead. Therefore, constant monitoring of the Petrinja fault and other faults in the region will be necessary. Future events will be possible especially around 2025 (plus/minus one year), 2027 (plus/minus one year), and toward 2030. Exact dates and probabilities will be defined by the passage of the tectonic waves and will be forecasted by the Quantectum Ensemble Forecasting System a few months ahead.

Figure 16: Multi-ensemble of four different T-synchronization ensemble models. Coloured solid lines illustrate the ensemble mean for each ensemble: green – Mc = 2.4, second-order T-synchronizations; black – Mc = 2.6, second-order T-synchronizations; orange – Mc = 2.4, fourth-order T-synchronizations; red – Mc = 2.6, fourth-order T-synchronizations. The dark-red columns illustrate earthquakes near Petrinja.

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Summary The Petrinja M6.4 earthquake on 29/12/2020 was an unusual event, accompanied by relatively low shear-stress and shear-traction fields. Therefore, no medium-term forecasts for this event were possible based on the analysis of shear-traction fields produced by tectonic waves. The increased probability for a possible strong earthquake near Petrinja was only evident based on the long-term forecasts of T-synchronizations, which defined the fourth-order T-synchronization between September 2020 and September 2021. Finally, the M6.4 earthquake near Petrinja on 29/12/2020 was a consequence of a passage of highly active tectonic waves through the region of Northern Balkan, which significantly increased the earthquake triggering probability two days before the event. Future forecasts for the Petrinja region suggest continuous high instability of the region till September 2021 characterized by the fourth-order T-synchronization. The subsequent significant fourth-order T-synchronizations and high local interaction potentials will be around 2025 (plus/minus one year), 2027 (plus/minus one year), and toward 2030. Exact dates and probabilities of the possible future earthquakes will be defined by the passage of the tectonic waves, and can only be forecasted by the Quantectum Ensemble Forecasting System few months ahead. Results of the Quantectum analysis show that continuous real-time monitoring of the T-synchronizations along the Petrinja fault is needed. Similar monitoring should also be performed along other faults, for example, along Silovec, Kalnik, Jastrebarsko, Bistra, Podsljeme, Kutina, and Bosiljevo faults. Together with the analysis of the forecasted shear-traction fields, this allows for calculating the actual probabilities of future events along these faults. References

1. Angelier, J., Mechler, P., 1977. La reconstitution dynamique et géométrique de la tectonique de failles à partir demesures locales (plans de faille, stries, sensde jeu, rejects): quelques précisions. Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences D285, 637 - 640.

2. Bajc, J., Aoudia, A., Sarao, A., & Suhadolc, P. (2001). The 1998 Bovec‐Krn Mountain (Slovenia) Earthquake Sequence. Geophysical Research Letters, 28(9), 1839-1842. Chicago

3. Basilic, R., Kastelic, V., Demircioglu, M. B., Garcia Moreno, D., Nemser, E. S., Petricca, P., ... & Caputo, R. (2013). The European Database of Seismogenic Faults (EDSF) compiled in the framework of the Project SHARE.

4. Bressan, G., Gentile, G. F., Perniola, B., & Urban, S. (2009). The 1998 and 2004 Bovec-Krn (Slovenia) seismic sequences: aftershock pattern, focal mechanisms and static stress changes. Geophysical Journal International, 179(1), 231-253.

5. Campbell, K. W., Bozorgnia, Y., 2014. NGA-West2 Ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthquake Spectra 30(3), 1087-1115.

6. Caprio, M., Tarigan, B., Worden, C. B., Wiemer, S., Wald, D. J., 2015. Ground Motion to Intensity Conversion Equations (GMICEs): a global relationship and evaluation of regional dependency. Bulletin of the Seismological Society of America 105(3), 1476-1490.

7. Carulli, G. B., &Slejko, D. (2005). The 1976 Friuli (NE Italy) earthquake. Giornale di Geologia Applicata, 1, 147-156.

8. Korbar, T., Markušić, S., Hasan, O., Fuček, L., Brunović, D., Belić, N., ... & Kastelic, V. (2020). Active Tectonics in the Kvarner Region (External Dinarides, Croatia)—An Alternative Approach Based on Focused Geological Mapping, 3D Seismological, and Shallow Seismic Imaging Data. Frontiers in Earth Science, 8, 504.

9. Markušić, S., Stanko, D., Korbar, T., Belić, N., Penava, D., &Kordić, B. (2020). The Zagreb (Croatia) M5. 5 Earthquake on 22 March 2020. Geosciences, 10(7), 252. Chicago.

10. Mohorovičić, A. (1910). Potres od 8. X. 1909. (Das Bebenvom 8. X. 1909.). Godišnje izvješće Zagrebačkog meteorološkog opservatorija za godinu 1909, 9 (4/1), 1–56, (and English translation in 1992, Earthquake of 8 October 1909 Geofizika, 9, 3–55). Geofizika, 9, 3-55.

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11. Prelogović, E., & Cvijanović, D. (1981). Potres u Medvednici 1880. godine. 12. Tiberi, L., Costa, G., Rupnik, P. J., Cecić, I., & Suhadolc, P. (2018). The 1895 Ljubljana earthquake: can the

intensity data points discriminate which one of the nearby faults was the causative one?. Journal of seismology, 22(4), 927-941.

13. Žalohar, J., Vrabec, M., 2007. Paleostress analysis of heterogeneous fault-slip data: the Gauss method. Journal of structural Geology, 29, 1798–1810.

14. Žalohar, J., Vrabec, M., 2008. Combined kinematic and paleostress analysis of fault-slip data: The Multiple slip method. Journal of Structural Geology 30, 1603-1613.

15. Žalohar, J., 2018. The Omega-Theory; A News Physics of Earthquakes. Elsevier, 558 pp.