In this paper, we present a method for handling uncertainties in the determination of the source parameters of earthquakes from spectral data. We propose a robust framework for estimating earthquake source parameters and relative uncertainties, which are propagated down to the estimation of basic seismic parameters of interest such as the seismic moment, the moment magnitude, the source size and the static stress drop. In practice, we put together a Bayesian approach for model parameter estimation and a weighted statistical mixing of multiple solutions obtained from a network of instruments, providing a useful framework for extracting meaningful data from intrinsically uncertain data sets. The Bayesian approach used to estimate the source spectra parameters is a simple but powerful mechanism for non-linear model fitting, providing also the opportunity to naturally propagate uncertainties and to assess the quality and uniqueness of the solution. Another important added value of such an approach is the possibility of integrating information from the expertise of seismologists. Such data can be encoded in a prior state of information that is then updated with the information provided by seismological data. The performance of the proposed approach is demonstrated analysing data from the 1909 April 23 earthquake occurred near Benavente (Portugal).

In this paper we achieve three goals: (1) We demonstrate that crack tips governed by friction laws, including slip weakening, rate- and state-dependent laws, and thermal pressurization of pore fluids, propagating at supershear speed have slip velocity functions with reduced high-frequency content compared to crack tips traveling at subshear speeds. This is demonstrated using a fully dynamic, spontaneous, three-dimensional earthquake model, in which we calculate fault slip velocity at nine points (locations) distributed along a quarter circle on the fault where the rupture is traveling at supershear speed in the inplane direction and subshear speed in the antiplane direction. This holds for a fault governed by the linear slip-weakening constitutive equation, by slip weakening with thermal pressurization of pore fluid, and by rate- and state-dependent laws with thermal pressurization. The same is also true even assuming a highly heterogeneous initial shear stress field on the fault. (2) Using isochrone theory, we derive a general expression for the spectral characteristics and geometric spreading of two pulses arising from supershear rupture, the well-known Mach wave, and a second lesser known pulse caused by rupture acceleration. (3) We demonstrate that the Mach cone amplification of high frequencies overwhelms the de-amplification of high-frequency content in the slip velocity functions in supershear ruptures. Consequently, when earthquake ruptures travel at supershear speed, a net enhancement of high-frequency radiation is expected, and the alleged ‘‘low’’ peak accelerations observed for the 2002 Denali and other large earthquakes are probably not caused by diminished high-frequency content in the slip velocity function, as has been speculated.

The quantitative estimate of earthquake damage due to ground shaking is of pivotal importance in geosciences, and its knowledge should hopefully lead to the formulation of improved strategies for seismic hazard assessment. Numericalmodels of the processes occurring during seismogenic faulting represent a powerful tool to explore realistic scenarios that are often far from being fully reproduced in laboratory experiments because of intrinsic, technical limitations. In this paper we discuss the prominent role of the fault governing model, which describes the behavior of the fault traction during a dynamic slip failure and accounts for the different, and potentially competing, chemical and physical dissipative mechanisms. We show in a comprehensive sketch the large number of constitutive models adopted in dynamic modeling of seismic events, and we emphasize their prominent features, limitations, and specific advantages. In a quantitative comparison, we show through numerical simulations that spontaneous dynamic ruptures obeying the idealized, linear slip‐weakening (SW) equation and a more elaborated rate‐ and state‐dependent friction law produce very similar results (in terms of rupture times, peaks slip velocity, developed slip, and stress drops), provided that the frictional parameters are adequately comparable and, more importantly, that the fracture energy density is the same. Our numerical experiments also illustrate that the different models predict fault slip velocity time histories characterized by a similar frequency content; a feeble predominance of high frequencies in the SW case emerges in the frequency ranges [0.3, 1] and [11, 50] Hz. These simulations clearly indicate that, even forgiving the frequency band limitation, it would be very difficult (virtually impossible) to discriminate between two different, but energetically identical, constitutive models, on the basis of the seismograms recorded after a natural earthquake.

Though mode II shear fractures (primarily strike-slip earthquakes) can not only exceed the shear wave speed of the medium, but can even reach the compressional wave speed, steady-state calculations showed that speeds between the Rayleigh and shear wave speeds were not possible, thus defining a forbidden zone. For more than 30 years it was believed that this result in which the rupture jumps over the forbidden zone, also holds for 3-D ruptures, in which mode II and mode III (mainly dip-slip faulting) are mixed. Using unprecedentedly fine spatial and temporal grids, we show that even in the simple configuration of homogeneous fault properties and linear slip-weakening friction law, a realistic 3-D rupture which starts from rest and accelerates to some higher velocity, actually does pass smoothly through this forbidden zone, but very fast. The energy flux from the rupture tip is always positive, even within the so-called forbidden zone, contrary to the 2-D case. Finally, our results show that the width of the cohesive zone initially decreases, then increases as the rupture exceeds the shear wave speed and finally again decreases as the rupture accelerates to a speed of  90% of the compressional wave speed.

Laboratory friction slip experiments on rocks provide firm evidence that the static friction coefficient mu has values  0.7. This would imply large amounts of heat produced by seismically active faults, but no heat flow anomaly is observed, and mineralogic evidence of frictional heating is virtually absent. This stands for lower mu values ~ 0.2, as also required by the observed orientation of faults with respect to the maximum compressive stress. We show that accounting for the thermal and mechanical energy balance of the system removes this inconsistence, implying a multi-stage strain release process. The first stage consists of a small and slow aseismic slip at high friction on pre-existent stress concentrators within the fault volume but angled with the main fault as Riedel cracks. This introduces a second stage dominated by frictional temperature increase inducing local pressurization of pore fluids around the slip patches, which is in turn followed by a third stage in which thermal diffusion extends the frictionally heated zones making them coalesce into a connected pressurized region oriented as the fault plane. Then, the system enters a state of equivalent low static friction in which it can undergo the fast elastic radiation slip prescribed by dislocation earthquake models.

The focus of this study is the relocation of these two events with the use of modern hypocentral location methods and the analysis of the historical seismicity of the area. A complete seismic source parameterization is out of the scope of this preliminary study. In the following, we describe the regional geological setting and the gas reservoir characterization, introduce the context of historical seismicity, provide a description of the mainshock relocation, discuss the uncertainties of the hypocentral parameters, and estimate the variation of the stress field due to extraction activities. We consider this revision necessary to be able to discuss the possibility that these two events were not induced by human activity, as well as to improve the quality of the dataset for decision makers involved in risk evaluation.

The style of faulting and distributions of nodal planes are essential input for probabilistic seismic hazard assessment. As part of a recent elaboration of a new seismic hazard model for Italy, we defined criteria to parameterize the styles of faulting of expected earthquake ruptures and to evaluate their representativeness in an area-based seismicity model. Using available seismic moment tensors for relevant seismic events (Mw   4:5), first arrival focal mechanisms for less recent earthquakes, and also geological data on past activated faults, we collected a database for the last ~100 years by gathering a thousand data points for the Italian peninsula and regions around it. In this dataset, we adopted a procedure that consists, in each seismic zone, of separating the available seismic moment tensors into the three main tectonic styles, making a summation within each group, identifying possible nodal plane(s), taking into account the different percentages of styles of faulting, and including where necessary total or partial (even in terms of tectonic style) random source contributions. Referring to the area source model used, for several seismic zones we obtained robust results; e.g., along the central and southern Apennines we expect future earthquakes to be mostly extensional, although in the outer part of the chain reverse and strike-slip events are possible. In the northern part of the Apennines we expect different styles of faulting for different hypocentral depths. In zones characterized by a low seismic moment release, the possible style of faulting of future earthquakes is less clear and it has been represented using different combinations of random sources. The robustness of our results is confirmed when compared with recent relevant earthquakes occurring in Italy.

We derive a unifying formulation, reliable at all scales, linking Anderson’s faulting theory with the earthquake size-distribution, whose exponent is known as the b-value. Anderson’s theory, introduced in 1905, related fault orientation to stress conditions. Independently, laboratory measurements on acoustic emissions have established that the applied differential stress controls their b-value. Our global survey revealed that observed spatial variations of bare controlled by different stress regimes, generally being lower in compressional (subduction trenches and continental collisional systems) and higher in extensional regimes (oceanic ridges). This confirmed previous observations that the b-value depends on the rake angle of focal mechanisms. Using a new plunge/dip-angles-based b-value analysis, we also identified further systematic influences of faulting geometry: steep normal faults (also typical of the oldest subduction zones) experience the highest proportion of smaller events, while low-angle thrust faults (typical of youngest subduction zones) undergo proportionally larger, more hazardous, events, differently from what would be expected by only allowing for rake-angle dependency. To date, however, no physical model has ever been proposed to explain how earthquakes size-distribution, differential stress and faulting styles relate to each other. Here, we propose and analytically derive a unifying formulation for describing how fault orientation and differential stresses determine b-value. Our formulation confirms that b-values decay linearly with increasing differential stress, but it also predicts a different dip-dependent modulation according to the tectonic environment, opening up new ways of assessing a region’s seismic hazard.

At Mt. Etna (Italy), volcano-tectonic earthquakes produce impressive surface faulting despite their moderate magnitude (M < 5.5), with historically well-documented ruptures featuring end-to-end lengths up to 6–7 km. The 26 December 2018, Mw 5.0 earthquake represents the strongest event of the last 70 years, with ground ruptures extending for 7.5 km along the Fiandaca fault, a partially hidden structure in the volcano's eastern flank. Field data collected by the EMERGEO Working Group (INGV) are here integrated with high-resolution photogrammetric surveys and geological-morphological observations to enable a detailed structural analysis and to reconstruct the morphotectonic process of fault growth. The deformation zone develops in a transtensional regime and shows a complex pattern, consisting of brittle structures arranged in en-échelon scale-invariant overlapping systems. Offsets and kinematics vary along the strike due to a major bend in the fault trace. We reconstructed a prevailing right-lateral displacement in the northern section of the fault and a dextral oblique slip in the southern one (max 35 cm); the dip-slip component increases southward (max 50 cm) and overall resembles the along-strike pattern of the long-term morphological throw. The kinematic analysis indicates a quasi-rigid behavior of the two fault blocks and suggests a geological model of rupture propagation that explains both the location of the seismic asperity in the northern section of the Fiandaca fault and the unclamping in the southern one. These findings are used to propose a conceptual model of the fault, representing insights for local fault-based seismic hazard assessment

On 29 December 2020, a shallow earthquake of magnitude Mw 6.4 struck northern Croatia, near the town of Petrinja, more than 24 hr after a strong foreshock (ML 5). We formed a reconnaissance team of European geologists and engineers, from Croatia, Slovenia, France, Italy and Greece, rapidly deployed in the field to map the evidence of coseismic environmental effects. In the epicentral area, we recognized surface deformation, such as tectonic breaks along the earthquake source at the surface, liquefaction features (scattered in the fluvial plains of Kupa, Glina and Sava rivers), and slope failures, both caused by strong motion. Thanks to this concerted, collective and meticulous work, we were able to document and map a clear and unambiguous coseismic surface rupture associated with the main shock. The surface rupture appears discontinuous, consisting of multi-kilometre en ´echelon right stepping sections, along a NW–SE striking fault that we call the Petrinja-Pokupsko Fault. The observed deformation features, in terms of kinematics and trace alignments, are consistent with slip on a right lateral fault, in agreement with the focal solution of the main shock. We found mole tracks, displacement on faults affecting natural features (e.g. drainage channels), scarplets and more frequently breaks of anthropogenic markers (roads, fences). The surface rupture is observed over a length of ∼13 km from end-to-end, with a maximum displacement of 38 cm, and an average displacement of ∼10 cm. Moreover, the liquefaction extends over an area of nearly 600 km2 around the epicentre. Typology of liquefaction features include sand blows, lateral spreading phenomenon along the road and river embankments, as well as sand ejecta of different grain size and matrix. Development of large and long fissures along the fluvial landforms, current or ancient, with massive ejections of sediments is pervasive. These features are sometimes accompanied by small horizontal displacements. Finally, the environmental effects of the earthquake appear to be reasonably consistent with the usual scaling relationships, in particular the surface faulting. This rupture of the ground occurred on or near traces of a fault that shows clear evidence of Quaternary activity. Further and detailed studies will be carried out to characterize this source and related faults in terms of future large earthquakes potential, for their integration into seismic hazard models.

On 26 April 1917, an earthquake Mw 6.0 (known as the Monterchi earthquake) struck the upper Tiber basin, central Italy. This Quaternary basin is situated on the hanging wall of a segmented low-angle normal fault (LANF) named the Alto Tiberina fault (ATF), whose capability to act with stick-slip behavior is debated. We reanalyzed instrumental historical data and performed a relocation of the hypocenter along with a reassessment of the scalar moment and magnitudes (Mw and Ms); we calculate the fault radius and stress drop and propose a focal solution based on first-arrival polarities. The methodologies that we applied strongly take into account the intrinsic uncertainties present in the historical data to obtain solutions that provide well-defined error estimates. The hypocentral solution is consistent with the known macroseismic scenario and is plausible in terms of rootmean square (rms) and error ellipse. The calculated focal depth at ≈8 km, even considering the depth uncertainty of  4 km, locates the earthquake source inside the ATF footwall. TheMw distribution (median Mw 5.8) suggests an overestimate of the macroseismic Mw probably due to seismic amplification caused by site effects. A preferred focal solution (strike 60/dip 84/ rake −162) defines an antiapenninic-oriented fault, with predominantly right-lateral slip. Our results strongly suggest that the 1917 Monterchi earthquake did not nucleate on one of the splays of the low-angle ATF but rather was generated by a deeper seismic source, which could be referred to as a structural transfer zone responsible for the Quaternary LANF segmentation.

We integrate paleoseismic data sets along the Mt. Vettore‐Mt. Bove normal fault system rupturing at the surface in the 30 October 2016 Norcia earthquake. Through the analysis of new trenches from this work and a review of the preexisting data, we correlate events among trench sites along antithetic and synthetic fault splays. We recognize seven M 6.5, 2016 Norcia‐type (or larger) surface‐faulting events in the last ~22 kyr, including 2016. Before 2016, one event occurred in the past two millennia (260–575 CE) and possibly corresponds to the event damaging Rome in 443 or 484/508 CE. Three previous events occurred between 10590 and 415 BCE, whereas the two oldest ones date between 19820 and 16540 BCE. The average recurrence time is 3,360–3,640 years for the last ~22 kyr and 1,220–1,970 years for the last ~4 kyr. We infer a minimum dip‐slip rate of 0.26–0.38 mm/year on the master fault in the central portion of the Mt. Vettore–Mt. Bove normal fault system and a dip‐slip rate of at least 0.10 mm/year on the southernmost portion. We infer a Middle–Late Pleistocene inception of the long‐term scarp of the investigated splays. The along‐strike variation of slip rates well reproduces the trend of the 2016 surface slip; thus, the time window exposed in the trenches is representative for the present fault activity. Based on trenching data, different earthquake rupture scenarios should be also considered for local hazard assessment.

Deformation across structural complexities such as along-strike fault bends may be accommodated by distributed faulting, with multiple fault splays working to transfer the deformation between two principal fault segments. In these contexts, an unsolved question is whether fault activity is equally distributed through time, with multiple fault splays recording the same earthquakes, or it is instead localized in time and space across the distributed faults, with earthquakes being clustered on specific fault splays. To answer this question, we studied the distributed deformation across a structural complexity of the Mt. Marine fault (Central Apennines, Italy), where multiple fault splays accommodate the deformation throughout the change in strike of the fault. Our multidisciplinary (remote sensing analysis, geomorphological-geological mapping, geophysical and paleoseismological surveys) study identified five principal synthetic and antithetic fault splays arranged over an across-strike distance of 500 m, all of which showing evidence of multiple surface-rupturing events during the Late Pleistocene-Holocene. The fault splays exhibit different and variable activity rates, suggesting that fault activity is localized on specific fault splays through space and time. Nonetheless, our results suggest that multiple fault splays can rupture simultaneously during large earthquakes. Our findings have strong implications on fault-based seismic hazard assessments, as they imply that data collected on one splay may not be representative of the behaviour of the entire fault. This can potentially bias seismic hazard calculations.

The Campi Flegrei caldera has been experiencing volcanic unrest since 2005, rising concern in the population and in local and national authorities. On May 20, 2024, the largest local earthquake ever instrumentally recorded up to that time produced substantial damage, forcing the evacuation of tens of buildings west of the epicenter. At Campi Flegrei, M > 4 earthquakes are rare and their analysis is crucial to understand the unrest dynamics and the relation between rupture and ground shaking pattern, which is essential to mitigate the damage of future earthquakes. We analyse seismic waveforms at local to regional distances to reconstruct the source geometry and kinematics. We estimate millimetric to submillimetric coseismic surface subsidence– below the sensitivity of any standard geodetic technique– which, compared to the general uplift, highlights the crucial role of deep pressurized fluids in earthquakes’ generation. Our results also indicate that rupture directivity and local amplification determined the damage distribution.