Stress analysis shows slight increase in seismic hazard near Zagreb

We find that the Petrinja earthquake raised the chances of another large, damaging shock nearer to Zagreb by a factor of three, but the probability is still low, at about a 1% chance over the next year.

By Ross S. Stein, Ph.D., Temblor, Inc., and Shinji Toda, Ph.D., IRIDeS, Tohoku University

Citation: Stein, R. S., Toda, S., 2021, Stress analysis shows slight increase in seismic hazard near Zagreb, Temblor,

Editor’s note: Article updated Jan. 8, 2021
Croation translation of key information from full scientific analysis included below

On Dec. 29, 2020, a magnitude-6.4 quake struck Central Croatia, near Petrinja. Aftershocks are ongoing, and so far, have occurred along a trend that extends for 20 kilometers to the northwest of the likely fault rupture.

Which fault ruptured, and are any faults primed for future rupture?


map of area around Petrinja, Croatia, with aftershocks plotted as green circles
A screenshot from the animated sequence presented here. The area of this map is shown in the map below, which covers a larger area that includes Zagreb.


Aftershocks located in the Seismological Survey of Croatia seismic network appear concentrated along a 30-kilometer-long trend, and are more tightly concentrated than those in the European Mediterranean Seismic Centre (EMSC) catalog shown in the map below. So, the Seismological Survey of Croatia map is probably more reliable. Somewhere within this band of aftershocks lies the 15-25-kilometer-long extent of the fault that ruptured in the magnitude-6.4 mainshock.

Map of Central Croatia with aftershocks plotted in shades of red (based on date).
Although the EMSC locations shown here are about 5-10 kilometers more scattered than that of the Seismological Survey of Croatia, which covers only the boxed area, apparent remote aftershocks of the magnitude-6.4 mainshock are seen closer to Zagreb. These are also closer to the site of the March 2020 events.


When we consider recent quakes over a larger area — using the EMSC real time catalog — a half-dozen more shocks appear after the magnitude-6.4 mainshock. These quakes occurred near the Jastrebarkso and Podsljeme Faults closer to Zagreb, and closer to the site of the magnitude-5.2 shock on 22 Mar 2020. Are these remote aftershocks of the magnitude-6.4 event? It’s unlikely that they have been mislocated by 30-40 kilometer, but this is possible. Further, there have been 5-6 shocks in the past four days, and none in the preceding 30 days (evident from the quake colors). So, if these were aftershocks of the much smaller Mar. 22, 2020 shocks, why were there none in the month before the magnitude-6.4? It seems more likely that these are aftershocks of the 29 Dec. 29 quake.

Within this region, the 2012 Database of Seismogenic Faults, part of the European Database of Seismogenic Faults (EDSF), identifies three northwest-striking ‘sources’ with components of right-lateral and thrust slip, and six sources that strike to the east-northeast, with components of left-lateral and thrust slip. In other words, neither pure strike-slip nor pure thrust slip is expected on faults in this area. (“Right-lateral” simply means that whatever side of the fault you are on, the other side moves to the right, in response to shear. “Thrust” faults stack up one side of the fault over the other in response to compression.)

Map of Central Croatia with sources plotted as orange rectangles.
The Database of Seismogenic Faults maps the complex structure of an active fault comprising its subsurface extension and geometry their uncertainties. The applied approach tends to include the different possible surface traces and the fault geomorphic imprint which is important in cases where there is no evidence of previous surface faulting or fault surface exposure.


So, how did the database fare in comparison to the March 2020 Zagreb and December 2020 Petrinja earthquakes? Ironically, the March events were pure thrust, and the December event was pure right-lateral. The March events can perhaps be associated with the Bistra Fault, identified as left-lateral oblique in the database, although Markušic et al. (2020) propose a Medvednica Mountains Thrust Fault in the same location. On the basis of the magnitude-6.4 aftershocks, the December event lies close to the Petrinja Fault, and so the database performed well.

“The Petrinja fault is actually a composite seismogenic source, meaning that it may comprise different fault surfaces, especially in terms of its surface and subsurface area,” said Vanja Kastelic, a researcher at the Istituto Nazionale di Geofisica e Vulcanologia (INGV), who mapped these features for the database. “It is difficult to map or predict possible ruptures of secondary splays and accompanying structures, so in this sense the composite source possibly includes also those that just ruptured,” she said.

Photo of person standing next to camel.
Vanja Kastelic, Ph.D., is a researcher at the Istituto Nazionale di Geofisica e Vulcanologia (INGV) in L’Aquila, Italy. She has carried out extensive field mapping of the active faults of the Balkans. This 2005 photo was taken during fieldwork in Mongolia Credit: William D. Cunningham.


A ‘hiccup’ in the life of a fault

Kastelic says that an individual earthquake is not the whole story of a fault, which is a long-lived structure that slips in countless quakes. She said: “The Petrinja Fault in the database ranges from right-lateral to oblique slip to match the geomorphologic imprint and the regional stress direction. Given that an earthquake is a ‘hiccup’ in the life of its fault, its symptoms are of course important, but understanding the fault long-term behavior and its deformation state, together with its accompanying rock volume, is just as important. Given all these, my best ‘bet’ is that the Petrinja fault is the culprit of the magnitude-6.4 quake.”

Was there surface fault rupture in the M 6.4 earthquake?

Kastelic said: “There are reports of surface deformation, definitely liquefaction and ruptures, but for now, I cannot express my opinion of those being the primary coseismic faulting or effects of shaking due to differential compaction, gravity etc. A thorough field investigation will be able to give more precise answers.”

Changes in seismic hazard

We use Coulomb stress transfer and rate-and-state friction theory to assess how the magnitude-6.4 quake changed seismic hazard in the region. Essentially, the earth is treated as a slab of stiff slab of rubber. The fault slip distorts the rubber and we calculate the resulting strains and stresses on surrounding ‘receiver’ faults. Faults are brought closer to failure when they are sheared in their expected slip direction, when they are unclamped, or when both occur (Stein, 1999).

Map with blue and red shapes, identifying areas of decreased and increased stress respectively. Black circles show aftershock locations. Dark green lines show fault locations. Light green line shows Patrinja Fault
Stress calculation using Coulomb 3.4 (Toda et al, 2011). Guided by the Seismological Survey of Croatia aftershocks and the U.S. Geological Survey (USGS) mainshock ‘moment tensor’ (which gives the geometry, sense of slip, and energy release), we assume a 24-kilometer-long by 10-kilometer-wide fault dipping 76° to the southwest, with 0.6 meters of right-lateral and 0.01 meter of reverse slip, with its upper edge buried 2.6 kilometers below the surface. The diversity of aftershock focal mechanisms means our source model is likely over-simplified.


In this first calculation, we looked to see if the aftershock locations are consistent with a simple stress transfer model, by assuming that they struck on faults parallel to the mainshock. We see a good correspondence that suggests that the fault or faults extend to the northwest, as does the seismogenic source in the European database. Stresses 10 kilometers northwest of the rupture reach about 1 bar, making this the most likely candidate for another large earthquake.

Map with blue and red shapes, identifying areas of decreased and increased stress respectively. Black circles show aftershock locations. Green lines show fault locations.
Stress calculation at a depth of 7.5 kilometers using Coulomb 3.4 (Toda et al, 2011).


Next, we consider a region populated by oblique left-lateral thrust faults that strike east-northeast (strike/dip/rake = 60°/60°/35°), with a fault friction of 0.4. Lower values of friction, corresponding to more slippery flat-lying faults, may be appropriate, as inferred by Kastelic and Carafa (2012). We find that the eastern portion of the Jastrebarsko Fault is brought about 0.15 bars closer to failure by the magnitude-6.4 rupture, but the Podsljeme Fault is brought 0.05 bars farther from failure. These are small but significant stress changes.

Map of Central Croatia with colored boxes along a line. Aftershocks are plotted as orange circles.
Stress calculation on receiver fault patches using Coulomb 3.4 (Toda et al, 2011). We assume a slip direction (‘rake’) of 80° for the Medvednica Mountains Thrust based on Markušic et al. (2020), and 35° for the Podsljeme Fault based on Kastelic and Basilli (2012).


Next, we zero in on the receiver faults thought by Kastelic and Markušić to best represent the faults near Zagreb. Again, we see that the eastern Jastrebarsko Fault is brought closer to failure, but failure is inhibited on the Podsljeme Fault and the Medvednica Mountains Thrust.

Chance of another large shock is low — but three times higher than normal

When we combine the Coulomb stress transfer results with the theory of rate-and-state friction, which describes how seismicity responds to small, sudden changes in stress (Toda and Stein, 2020), we find that the chance of another shock of magnitude-5.0 or greater over the next year is about 15%, the chance of a magnitiude-6.0 or greater shock is about 1.5%, and the chance of another magnitude-6.4 event is about 0.6%. These probabilities are, fortunately, low. However, they are about three times higher than the long-term averages, and so while the hazard is small, it has increased.

Our results suggest that the chances of a large shock on the Petrinja Fault, Jastrebarsko Fault or other fault near Zagreb in the next year are low — on the order of 1 in 100. Of these, the most likely candidate is the section of the Petrinja immediately northwest of the Dec. 29 rupture. If one of those faults were to rupture, the consequences could be grave, and so we believe it important to assess this possibility and present it to the public and our colleagues.

Could the magnitude-6.4 quake be followed in short order by another large, damaging quake on an orthogonal or adjacent fault? It happened in Ridgecrest, California in 2019 when a magnitude-6.4 quake was followed 34 hours later by a magnitude-7.1 shock on an orthogonal fault that was brought closer to failure by the first shock (Toda and Stein, 2020). It happened in Kumamoto, Japan, in 2016 when a magnitude-6.0 shock was followed 28 hours later by a magnitude-7.0 quake on an adjacent fault section that was also brought closer to failure (Kato et al., 2016; Stein and Sevilgen, 2016). These are only recent examples; there are many others in which a second shock occurred days to years after the first shock.

A key outcome of our calculations is that the earthquake rate is forecast to be about three times higher over the next year than in a typical 12-month period. So, the benefits of seismic retrofit and earthquake insurance are now three times greater than they were before Dec. 29.

Ažuriranje 8. siječnja 2020:

Važne informacije iz cjelovite znanstvene analize

Pri kombiniranju rezultata Coulombove prijenosa naprezanja i teorijom trenja ovisnim o brzini i stanju, što opisuje kako seizmičnost odgovara na male, iznenadne promjene u naprezanju (Toda i Stein, 2020), nalazimo kako je mogućnost za još jedan potres magnitude 5.0 ili veće kroz sljedeću godinu oko 15 posto, a mogućnost da se dogodi potres magnitude 6.0 ili jači oko 1.5 posto, dok je mogućnost još jednog potresa magnitude 6.4 oko 0.6 posto. Ove vjerojatnosti su, srećom, niske. No, one su, ipak, oko tri puta veće nego dugoročni prosjeci, pa iako je rizik malen, ipak je porastao.

Naši rezultati upućuju kako je mogućnost jakog potresa na petrinjskom rasjedu, rasjedu Jastrebarsko ili drugim rasjedima pored Zagreba u sljedećoj godini malena, u omjeru od 1:100, jedan posto. Od spomenutih rasjeda, najizgledniji je kandidat dio petrinjskog rasjeda odmah sjeverozapadno od epicentra potresa koji se dogodio 29. prosinca. Ako se neki od ovih rasjeda pukne, posljedice bi bile ozbiljne, pa vjerujemo da je važno procijeniti ovu vjerojatnost i predstaviti je javnosti i našim kolegama.

Da li bi ubrzo nakon potresa magnitude 6.4 uslijedio jači, rušilački potres na ortogonalnom ili susjednom rasjedu? Takvo što dogodilo se u Ridgecrestu, država Kalifornija, 2019. godine kada je 34 sata nakon potresa magnitude 6.4 uslijedio potres magnitude 7.1 na ortogonalnom rasjedu kojega je prvi potres pogurnuo bliže slomu (Toda i Stein, 2020). Slično se dogodilo i u Kumamotu, Japan, 2016. godine kada je 28 sati nakon potresa magnitude 6.0 uslijedio potres magnitude 7.0 na dijelu susjednog rasjeda kojega je prvi potres također pogurnuo bliže puknuću (Kato et al., 2016; Stein i Sevilgen, 2016). Ovo su samo nedavni primjeri, postoje i mnogi drugi primjeri kod kojih se drugi potres dogodio u razmaku dana ili čak godina nakon prvog.

Ključni je rezultat naših izračuna to da je dobivena vjerojatnost potresa u sljedećih godinu dana tri puta veća nego u uobičajenom 12-mjesečnom periodu. Tako, koristi su povećavanja seizmičke otpornosti građevina te osiguranja od potresa sada oko tri puta veće nego što su bile prije 29. prosinca.

Update, Jan. 8, 2021: Prof. Hrvoje Tkalčić has graciously brought to our attention that what we call the ‘Petrinja Fault’, the name given in the European Database of Seismogenic Faults, is designated the ‘Pokupsko Fault’ by Croatian researchers and by the Geological Survey of Croatia. We apologize for the confusion our terminology may have caused.

Update Jan. 6, 2021: In response to reader requests, we furnish this table, which gives the probabilities for magnitude-5.0 and greater and magnitude-6.0 and greater earthquakes within 50 and 100 kilometers from Zagreb. The probability gains of about 4-5 are larger than what we report in the article because these calculations cover a smaller area that is more strongly influenced by the Dec. 29 magnitude-6.4 earthquake.



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