A key step in our seismic hazard assessment is modeling epistemic uncertainty through a comprehensive logic-tree approach (Kulkarni et al. 1984; Budnitz et al. 1997; Bommer and Scherbaum 2008). The ESHM13 is based on three branching levels: (1) the earthquake source models, (2) the maximum magnitude, and (3) the ground motion models (Fig. 5); tectonic regionalisation is not a branching level but it is used to define the GMPEs set to be used. The earthquake source models (AS, FSBG, SEIFA) represent established approaches to model earthquake occurrences based on seismological, geological, tectonic and geodetic information, with a varying degree of importance represented in the source typologies (Fig. 6). As we discuss in better detail in Sect. 3.3, we assume full seismic coupling over the entire study region, i.e. that all tectonic and geodetic moment goes into seismic moment. We are aware that this is a simplification and may not be true everywhere (e.g. Ergintav et al. 2014); the coupling coefficient is indeed a crucial parameter, yet it remains rather controversial and very hard to assess homogenously at the scale of the entire continent.
The three earthquake source models are characterised by alternative options to calculate and spatially distribute future seismic activity (Fig. 5). They were used to model crustal seismicity with depth ≤40 km. The seismicity of subduction zones and of the Vrancea region was modelled separately.
Area source model
For several years the evaluation of seismic hazard has largely relied on area source models (Grünthal et al. 1998; Sleijko et al. 1998; Grünthal and GSHAP Working Group Region 3 1999; Musson 1999; Sleijko et al. 1999; Grünthal and Wahlström 2000; Musson 2000; Jimenez et al. 2001; Demircioglu et al. 2004; Meletti et al. 2008; Wiemer et al. 2009b; Papaioannou and Papazachos 2010), both in Europe and worldwide (e.g. Giardini 1999). Area source zones are designed with the assumption that seismicity may occur anywhere within each zone. The delineation considers seismicity, tectonics, geology and geodesy upon expert evaluation, generally without assigning uncertainties to the zone boundaries and only infrequently documenting the importance of the data used for the zonation (Burkhard and Grünthal 2009; Musson et al. 2009; Schmid and Slejko 2009; Wiemer et al. 2009a; Vilanova et al. 2014). Our zonation approach, based on the ESHM13 AS-model previously described, was applied to crustal seismicity down to a depth of 40 km.
The ESHM13 AS-model is based on the latest national area source models and on the former Euro-Mediterranean model (Jimenez et al. 2001) that have been merged and harmonised at national borders (Arvidsson and Grünthal 2010). Besides a number of political issues, challenges in the construction phase included the variability of seismotectonic environments, the differences in the nature of documentation, data availability and philosophies of the former models, and the need to harmonise the AS-model with the other datasets being compiled simultaneously within SHARE. In a final harmonisation step, small area sources that turned out to be devoid of seismicity were removed for consistency with the final datasets compiled within the project. The final area model consists of 432 area sources depicted as black lines in Fig. 7b.
The considerable differences in the tectonic environments across Europe are reflected in the final delineation of the area sources. In the Mediterranean area, and especially in the Balkans, Greece, Turkey, and Italy, mapped active faults played a major role in defining the area sources. The knowledge on active faults of southern Spain, which was improved during the SHARE project, allowed for a redefinition of existing source models. In contrast, very few active structures are known in the continental shield of northern Europe. In these areas, seismicity was the main basis for the designing the area source model. Only a few major tectonic structures, such as the Rhine Graben in Central Europe, are represented in the zonation with a higher level of detail than large structures like the Baltic Shield. The AS-model was matched with the tectonic regionalisation (Fig. 7a, b) in order to define, for each area source, the prevailing style-of-faulting, the upper and lower bounds of the characteristic seismogenic depth, and the distribution of hypocentral depth.
As the declustered catalogue contains about 8000 events, a large number of the area sources contain only a few data; for instance, 196 zones contain 10 events or less. Those that did not contain any seismicity were assigned an activity rate by regional experts, or a water-level annual activity for M
≥ 4.5 of 5 × 10−8 events per km2.
We estimated activity rate parameters using a Bayesian penalized maximum likelihood (PML) approach (Johnston et al. 1994; Coppersmith et al. 2012) that updates the prior b-value only if it is supported by local data. The prior b-values are estimated in the specific b-value superzones with the method by Weichert (1980). The PML-estimates for the a–b-value pairs and their associated uncertainty recover well the distribution of seismicity, also for sources with little data. The estimates are, however, guided by the more abundant small magnitude data. Two observations were made based on the PML-results as shown in the examples in Fig. 8—an apparent underestimation of rates in the moderate to large magnitude events in the range 5.5 ≤ M
≤ 7.0, and a relatively large variation in b-values.
Like any maximum likelihood estimator, the PML-estimator is largely driven by the more abundant small magnitude seismicity. Thus, underestimating the rate of moderate to large events may result from how the catalogue completeness is assessed, from the variability of magnitude determinations for different time periods (e.g. historical vs. instrumental) and, more generally, from spatio-temporal variations of the observed seismicity. As such, this problem may be rooted both into the data and into the selected methods of data analysis. In many regions the rates of small magnitude events are mainly governed by recent instrumental data, whereas the larger magnitude events are mainly historical earthquakes. Due to their origin from intensity assessments, the magnitudes of historical earthquakes can only assume a limited number of discrete values; as such they are binned differently from instrumental earthquakes, which may cause artificial perturbations in the seismicity rates.
We carefully analyzed each individual fit to the data and replaced the PML-results by subjective judgment in case b-values deviated more than ∆b = 0.4 from the global estimate of the SHEEC catalogue (b = 0.9: Hiemer et al. 2014). The b-values obtained using the PML-approach for area sources characterised by very few data were constrained in the range 0.8–1.2, with the only exception of volcanic and swarm-type seismicity area sources, for which the b-value was allowed to increase up to 1.5 based on observed data.
The a–b-value pairs, with the a-value defined at M
= 0, were then used to calculate a weighted mean frequency–magnitude distribution (FMD) considering the weights of the maximum magnitude distribution (Fig. 8, solid black line). We calculated the incremental FMDs truncated at the different maximum magnitudes and then stacked them with the weights of the M
. Uncertainties are plotted for the 2.5 %/15 %/85 %/97.5 % percentiles of the distribution (Fig. 8, red and green dashed lines).
We illustrate our results for two area sources, one in southwestern Switzerland (CHAS089) and one in the Central Apennines (ITAS308), containing 8 and 52 events above completeness, respectively (Fig. 8). For CHAS089, the difference between the two estimates is substantial (a = 2.4, b = 0.9; a
= 2.71, b
= 1.03; Fig. 8a). In contrast, for ITAS308 the difference between the estimates taken from the current Italian Seismic Hazard Model (a = 4.2, b = 1; Stucchi et al. 2011) and the PML (a
= 3.92, b
= 0.98) is negligible. Figure 8 also illustrates the difference in the uncertainties when estimating rates for magnitudes in the small and in the large magnitude ranges: for CHAS089 these uncertainties are much larger in the upper magnitude range than for ITAS308 due to the limited amount of data.
The AS-model activity rates are fully defined by the a–b-values and by the distribution of M
. The time-independent annual rate forecast for M
≥ 4.5 varies across the continent and highlights the higher activity rates along the active fault systems of Southern Europe, Turkey and Iceland in comparison to the lower activity rates observed in stable continental regions (Fig. 9a). The rates are computed from the productivity parameter (a-value), that varies strongly across the continent, and from the b-value, that by construction varies only in a limited range (Fig. 9b, c).
Kernel-smoothed stochastic rate model considering seismicity and fault moment release (SEIFA-model)
In contrast to the other source models, this refined smoothed seismicity model uses estimates of the total productivity and frequency–magnitude distribution by fitting the entire declustered SHEEC catalogue using the catalogue completeness levels of the superzones simultaneously first. In a second step, earthquakes rates are spatially distributed according to a weighted combination of two spatial probability density functions (Hiemer et al. 2014). These are estimated from past seismicity and from accumulated moment release along faults, inferred from their slip rates and geometry. The relative weights of these two spatial density functions depend on the earthquake magnitude and are determined by pseudo-prospective forecasting experiments. The model, initially developed for California (Hiemer et al. 2013), is applied at the European scale: we generated a crustal model using earthquakes shallower than 40 km depth and active faults of the European Database of Seismogenic Faults (EDSF; Basili et al. 2013). We separately modelled seismicity in subduction zones in combination with the models of the Calabrian, Hellenic and Cyprus arcs with their complex 3D geometry. We treat active faults and subduction zones in the same way, as they are all characterised by their size, geometry and slip rate converted to moment release per unit area (discretized to 5 km2 patches). The following sections provide a general description of the model; full details are given in Hiemer et al. (2014).
The SEIFA-model assumes that (1) the frequency–magnitude distribution of past earthquakes is the best estimate of productivity and size distribution, (2) future earthquakes will occur in the vicinity of past events, (3) larger earthquakes occur more likely on mapped faults, and more likely along fast-slipping than along slow-slipping faults. These assumptions are parameterised to estimate the annual earthquake rate as a function of space and magnitude. The total productivity and the Gutenberg–Richter relations are estimated from the entire catalogue considering the space–time completeness histories as defined for the superzones (Hiemer et al. 2014). The cumulative annual earthquake rate forecast log10
≥ 4.5) for crustal seismicity depicts a relatively smooth image with higher rates in currently active regions and along active fault systems (Fig. 10) as compared to the stable continental areas. This earthquake rate forecast shows more smaller scale variability in regions of frequent seismicity, a feature that can also be observed in the hazard map calculated only from this model (Fig. 16b).
We estimate the activity rate parameters (a-, b-value) for the entire catalogue including the space–time completeness variations (Hiemer et al. 2014). The combined maximum likelihood estimate for crustal seismicity is a = 5.87 ± 0.04, b = 0.9 ± 0.01, equaling a total annual number of events N
≥ 4.5) = 65.6. For the subduction zones, these values are a = 5.21 ± 0.36/0.39 and b = 0.95 ± 0.07/0.08, yielding N
≥ 4.5) = 8.6 per year.
The model allows for a maximum magnitude of M
= 8.6 for crustal events throughout Europe and Turkey. As the annual rates of larger magnitude earthquakes are locally very small, however, the actual maximum magnitude that entered the hazard calculations varies as we disregard magnitude bins for which the inferred annual rates are smaller than 10−6 (Fig. 5c). According to our sensitivity tests, the contribution of these very low rate events to PGA hazard up to return periods of 5000 years is negligible, thus they were removed.
Fault sources and background (FSBG) model
In the FSBG-model, activity rates of the mapped fault sources are determined from the available deformation data as inferred from geodetic and geological methods (Basili et al. 2008, 2009; Haller and Basili 2011; Basili et al. 2013). The activity rates in this model are primarily dependent on the slip rate and the maximum magnitude of the fault sources. As crustal seismogenic faults are not known over the entire area covered by SHARE, and more specifically lack in regions of low tectonic deformation far from plate boundaries, the sources comprising the AS-model are used and adjusted in size and productivity at the edges of the background sources.
Background sources were delineated with consideration for the distribution of fault sources. A background source polygon includes an entire fault system and does not cut across any fault source. A background zone is assumed to include a complete set of fault sources, i.e. one or several sources are embedded in one background source. Within one background zone we assume that all fault sources capable of generating M
≥ 6.5 earthquakes are known and dominate the seismic moment release. Events with magnitudes M
≥ 6.5 are modelled on the 3D geometry of the fault sources; their exact location varies depending on the modelled hypocentral location (Pagani et al. 2014), magnitude, and determined area, however, never extends beyond the mapped structures. Earthquakes in the magnitude range 4.5 ≤ M
≤ 6.4 can occur throughout the background source and are homogeneously distributed.
The earthquake potential of each fault source is evaluated by converting the long-term tectonic moment rate into an earthquake activity rate. The tectonic moment rate is obtained from Ṁ
0 = µAḊc, where µ is rigidity, A is the area of the fault source, Ḋ is the slip rate and c is the seismic coupling, which indicates how much of the tectonic moment goes into the seismic moment. The earthquake rates are calculated assuming that all the accumulated tectonic moment is released seismically, thus the seismic coupling was set to c = 1 everywhere. We also adopted the maximum slip rate assigned to fault sources, thereby providing an upper bound of the cumulative tectonic moment.
After considering several methods for obtaining earthquake activity rates from slip rates (e.g. Anderson and Luco 1983; Youngs and Coppersmith 1985; Frankel et al. 2002; Stirling et al. 2002; Field et al. 2009; Stirling et al. 2012) we opted for the original contribution proposed by Anderson and Luco (1983), which generates activity rates that conform to a double-truncated Gutenberg–Richter distribution (Anderson and Luco 1983; Youngs and Coppersmith 1985; Bungum 2007).
The scale-invariant, power-law decay of the distribution is controlled by the b-value. Within a background zone the b-value is assumed to be the same everywhere, though it varies between background zones. Similarly to the AS-model, it is computed with the PML-method (Johnston et al. 1994; Coppersmith et al. 2012). The right-hand tail of the distribution, instead, is controlled by the maximum magnitude of the fault source. The total productivity within one background zone is the sum of the contribution of all fault sources. As a whole, the distribution complies with the moment conservation principle by summing up to the calculated seismic moment rate.
The model is illustrated for a background zone covering the Northern Apennines, Italy, that contains eight fault sources, all contributing to the overall productivity with their maximum slip rate (Fig. 11, source ITBG068, dashed grey lines). The b-value is estimated using the penalised maximum likelihood approach and equals b
= 1.3. The summed activity using the maximum slip rates (Fig. 11, red line) defines well an upper bound of the cumulative frequency–magnitude distribution of the observed seismicity. Summing the productivity from the minimum slip rates matches the observed seismicity (Fig. 11, dashed green line) and overlies the PML-estimate. The tail of the distribution resembles a staircase function emerging through the summation of the activity rates calculated for each fault source that all have individual maximum magnitudes (Fig. 11, red line). We consistently used the maximum slip rates to estimate activity rates on fault sources which, as illustrated, often defined an upper bound of activity compared to the data observed in the catalogue.
The FSBG-model covers mostly southern Europe and Turkey and some structures in Northern Europe such as the Lower Rhine Embayment (Fig. 12; Vanneste et al. 2013). Not all faults mapped and included in the EDSF could be used, however. For example, we excluded all mapped faults that represent only a small portion of a large background zone, thereby assuming that the fault coverage is not complete. The resulting earthquake rate forecast model for the cumulative annual rate [log10
≥ 4.5)/km2] is shown in Fig. 12 together with the tectonic association of the background zones and maximum slip rates of the fault sources.
Comparing the total rate forecasts for crustal seismicity
To obtain a global overview of the three crustal seismicity rate forecasts we calculated the total expected average annual earthquake rates and compared them with the cumulative frequency–magnitude distribution of the declustered earthquake catalogue using the superzone catalogue completeness (Fig. 13). For the AS- and the FSBG-models this involves summing up the rates of all individual zones. In contrast, by construction the SEIFA-model uses the combined maximum likelihood fit to the entire declustered catalogue (Hiemer et al. 2014).
Compared to the observed seismicity, Fig. 13 illustrates that the AS-model (blue) fits well the observed seismicity up to magnitude M
= 7, shows a slight overestimate up to M
= 8, and falls in between the rates of the largest magnitudes. The SEIFA-model forecasts a smaller total earthquake rate compared to the observed seismicity in the magnitude range M
= 4.5–7.5, while it is qualitatively in good agreement with the observed rates in the uppermost magnitude range (dark yellow). In contrast, the FSBG-model forecasts higher rates from M
= 4.5–7.2 and lower rates for the magnitude range above 7.5. The variability of the total rate forecasts illustrates the epistemic uncertainty in the source models and has several implications:
The frequency–magnitude distribution of the declustered earthquake catalogue (cut at the completeness levels) shows increased rates starting at M
= 6.5 as compared to what is expected when extrapolating from smaller magnitudes. Reasons for this increased rate may arise from the completeness intervals, the declustering procedure and the different approaches used to determine magnitudes—or a combined effect.
The activity rates calculated from slip rates on fault sources (FSBG-model) show an underestimation of M
≥ 7.5 events, while events of M
≤ 7.0 are overestimated; the range in between is matched qualitatively well. We assume a Gutenberg–Richter type behaviour of faults constraining the maximum magnitude based on a weighted combination of scaling relations—the weighted M
are smaller compared to those used in the area source model. From an overall perspective this leads to an overestimation of small events, however, with considerable heterogeneity between slow-slipping and fast-slipping faults. The overestimation of smaller events could be reduced by considering a larger M
, which is however not supported by the current data. An alternative could be to consider characteristic type earthquake rate distributions such as in Schwartz and Coppersmith (1984). While it remains to be tested whether this would lead to a better representation of observed earthquake rates (e.g. Kagan et al. 2012), a combination of a Gutenberg–Richter type and a characteristic model might comprise a viable alternative.
The SEIFA-model forecasts a slightly lower activity rate compared to the observed data (Fig. 13, dark yellow line). The power-law fit considers the space–time history for catalogue completeness from all completeness superzones (Stucchi et al. 2012; Hiemer et al. 2014). The visual comparison in the upper magnitude range is qualitatively satisfying. The forecasts are consistent with the SHEEC catalogue as well as with data from the Global CMT catalogue as shown in quantitative retrospective and pseudo-prospective tests (Hiemer et al. 2014).
The mean cumulative rate forecast of the AS-model (Fig. 13, blue line) obtained from individual area sources shows a good agreement with the observed data for the magnitude range 4.5 ≤ M
≤ 6.5 and slightly higher rates in the magnitude range 6.7 ≤ M
≤ 7.7. Qualititatively the model matches well the uppermost range of magnitudes.
Combining the three source models within the logic-tree according to the assigned weights (0.5 for the AS-model, 0.3 for the SEIFA-model and 0.2 for the FSBG-model: Fig. 6; Table 1) we obtain a good qualitative match with the observed data (Fig. 13, red line). The three source models therefore generate forecasts that describe well the epistemic uncertainty of earthquake activity for crustal seismicity in Europe. Spatial variability in matching observed seismicity with the different models obviously exists across the study region. However, these are not established well enough to modify weights on a regional basis.
Modelling subduction zones and deep seismicity in Vrancea
We separately modelled the deep seismicity of the Calabrian, Hellenic, and Cyprus Arcs subduction zones as well as the non-subduction deep seismicity of the Vrancea Region (Romania). The activity rates of the three subduction zones has been jointly computed for interface and in-slab seismicity as depth uncertainties did not allow for a separation.
The subduction interface is modelled as a complex fault as defined by depth contours in the EDSF. Seismicity on the interface is concentrated between 20 and 50 km depth for the Hellenic and 10–50 km depth for the Cyprus Arcs. The surface projection of the subduction interface is shown in Fig. 14, coloured according to the assigned maximum magnitudes. Activity rates are taken to be uniform across the complex structure. In-slab seismicity is modelled in depth volumes located at 40–160 km depth in all subduction zones. In both instances seismicity is homogeneously distributed throughout the area. Maximum magnitudes as well as the b-value are the same for subduction interface and in-slab seismicity. Maximum magnitudes are estimated to range between M
= 8.3 and M
= 8.9 with increments of 0.2 and decreasing weights (0.5, 0.2, 0.2, 0.1). The estimated b-value is 0.9 with no difference for in-slab and interface events.
The SEIFA-model uses the same structure for interface and in-slab events. However, in contrast to the model used in combination with the crustal AS-and FSBG-model, the SEIFA-model uses a heterogeneous distribution of the activity rate parameters determined from a combined probability density function determined from smoothing the earthquake density and the moment release on the subduction interface (see Hiemer et al. 2014 for details). Within this model, both the maximum magnitude (M
= 9.0) and the b-value (b = 0.95) are the same for subduction interface and in-slab seismicity.
In the Vrancea region, situated beneath the southern Carpathian Arc, the most hazardous seismicity falls in the depth range 70–150 km with earthquakes occurring in the intervals 70–90 and 110–150 km. Lacking a well-defined structural description of the seismogenic processes of the area, we model the deep seismicity with four volumes at depth. The shape differs from the delineation of the crustal area sources (Fig. 14). This specific model is used in combination with all crustal seismicity models.
Earthquake density, depth levels and maximum magnitudes vary within these zones as well as the parameterisation of the preferred rupture orientation. The maximum magnitude expected for Vrancea earthquakes was assigned based on observed seismicity. We allowed for larger magnitudes by adding four magnitude increments with decreasing weights as we did for crustal sources. The M
values in the 70–90 km depth range are 7.5 and 7.8; the seismicity between 110 and 150 km is limited to M
values of 7.8–8.1 (Fig. 14).
Attenuation of seismic wave amplitudes exhibits azimuthal dependence—a characteristic that is likely due to the rupture characteristics of the deep events and wave propagation effects rather than amplification effects. This characteristic has been implemented in intensity attenuation relations (Sokolov et al. 2009; Sørensen et al. 2010) but is not considered in GMPEs that consider several spectral ordinates, as required for a harmonised European assessment. To overcome this limitation the deep seismicity is modelled to mimic the azimuthal dependence with a set of sources at depth, a scheme similar to that adopted by Sokolov et al. (2009).