The probabilistic seismic hazard assessment of Germany—version 2016, considering the range of epistemic uncertainties and aleatory variability
Abstract
The basic seismic load parameters for the upcoming national design regulation for DIN EN 19981/NA result from the reassessment of the seismic hazard supported by the German Institution for Civil Engineering (DIBt). This 2016 version of the national seismic hazard assessment for Germany is based on a comprehensive involvement of all accessible uncertainties in models and parameters and includes the provision of a rational framework for integrating ranges of epistemic uncertainties and aleatory variabilities in a comprehensive and transparent way. The developed seismic hazard model incorporates significant improvements over previous versions. It is based on updated and extended databases, it includes robust methods to evolve sets of models representing epistemic uncertainties, and a selection of the latest generation of ground motion prediction equations. The new earthquake model is presented here, which consists of a logic tree with 4040 end branches and essential innovations employed for a realistic approach. The output specifications were designed according to the user oriented needs as suggested by two review teams supervising the entire project. Seismic load parameters, for rock conditions of \(v_{S30}\) = 800 m/s, are calculated for three hazard levels (10, 5 and 2% probability of occurrence or exceedance within 50 years) and delivered in the form of uniform hazard spectra, within the spectral period range 0.02–3 s, and seismic hazard maps for peak ground acceleration, spectral response accelerations and for macroseismic intensities. Results are supplied as the mean, the median and the 84th percentile. A broad analysis of resulting uncertainties of calculated seismic load parameters is included. The stability of the hazard maps with respect to previous versions and the crossborder comparison is emphasized.
Keywords
Seismic hazard Germany DIN EN 19981/NA Seismic load parameters1 Introduction
Probabilistic seismic hazard assessments (PSHA) represent the most resilient means to calculate seismic load parameters for seismic building codes or other antiseismic design provisions, presupposing that the input models are carefully chosen and related parameters accurately derived. Still challenging with respect to modern PSHA in general is the comprehensive incorporation of all uncertainties in the models and their corresponding parameters into a probabilistic approach, one which has the advantage of providing a rational framework for integrating uncertainties in a transparent way.
The seismicity of Germany, the target area of the study, and the related seismic hazard is elevated in certain regions of the country, when compared to other parts of central Europe, particularly along the course of the river Rhine. In general, the seismicity is indeed low in relation to the plateboundary regions of the Mediterranean; however, it is not so low that earthquake resistant design provisions are negligible. Extremely low geodetic movements near their own confidence limits, in conjunction with the low seismic activity make it in particularly difficult to assess where strong ground shaking might occur in future. Quite simply, low seismicity regions do not necessarily make seismic hazard assessments any easier, and such complexity requires adequate treatment of uncertainties.
A significant portion of Germany’s industry, infrastructure and regions of high residual density are located in areas of elevated seismicity and, hence, exposed to a certain degree of seismic risk (Grünthal et al. 2006; Tyagunov et al. 2006). Although earthquakes with moment magnitudes M_{ w } > 6 are not known to have occurred within Germany in the historical past, they have struck the immediate surroundings (cf. Sect. 3) and could be expected within the country as well. Though the probability of the occurrence of M_{ w } > 6 earthquakes within Germany is comparatively low, the impacts of such events could be dramatic if critical regions like conurbations or specific industrial plants were to be affected.
The first buildingcode related seismic zonations of Germany were based on maps of generalized maximum observed intensities (DIN^{1} 4149 1955a, b; DIN 4149 1957; DIN 4149 1981), which was subsequently updated for the DIN 4149 (1992) with the extension to the new federal states of Germany by the first author. The first country wide seismic zonation by means of a probabilistic approach was provided by Grünthal and Bosse (1996) and is used as national seismic zoning map since the introduction of the DIN 4149:200504 (Grünthal 2005). A corresponding web portal has been in operation since 2005 (http://gfzpotsdam.de/DIN4149_Erdbebenzonenabfrage). Here one can find the assignment of each German settlement to one of the three seismic zones of the DIN 4149, with the corresponding geological underground class (rock R, soil S, transitional T) and related design spectra, which still has some 100 hits daily. A much more advanced PSHA was accomplished for the needs of the safety regulation of hydraulic structures DIN 19700 (Grünthal 2008; Grünthal et al. 2009a), where uniform hazard spectra (UHS) on rock or soil conditions for four different hazard levels for any site in Germany are provided via a webservice (http://gfzpotsdam.de/DIN19700), which has been operational since 2007. These webbased seismic hazard results are used intensively for a wide variety of applications, not only for safety assessments of dams or other hydraulic structures. The latter approach included epistemic uncertainties and aleatory variabilities of input parameters and models already to a considerable extent.
Other probabilistic seismic hazard maps cover at least parts of Germany but were not prepared for national standardization purposes. These include, e.g. those by Ahorner and Rosenhauer (1978) for SW Germany, who apply the generalized Gumbel distribution of magnitudes on the basis of MonteCarlo simulations (Ahorner and Rosenhauer 1975), which was later updated with the focus on western Germany (Ahorner and Rosenhauer 1986) and modified for the Lower Rhine embayment (Rosenhauer and Ahorner 1994). For the latter area, Grünthal et al. (2004, 2006) calculated PSHA with an advanced consideration of uncertainties by applying logic trees and distributions of aleatory variability as our standard approach since Grünthal and Wahlström (2001) and Wahlström and Grünthal (2000, 2001).
In addition to the aforementioned national PSHA by the authors, their activities have been integrated into panEuropean models by achieving crossborder harmonization in all steps of their procedures. The first of those projects was the Global Seismic Hazard Assessment Program GSHAP (Giardini et al. 1999), where the map from Grünthal and Bosse (1996) was updated and extended to Switzerland and Austria, i.e. the DACH countries, (Grünthal et al. 1998a) which served as test case for the European part of the GSHAP map north of 44° N (Grünthal et al. 1996; Grünthal and GSHAP Region 3 Working Group 1999). While the hazard map according to the project SESAME (Jiménez et al. 2003) north of 44° N coincides with the GSHAP map, an innovative hybrid zoneless approach was applied for the Europeanwide seismic hazard map of the EU project NERIES (Chan and Grünthal 2010). Another harmonized EuroMediterranean seismic hazard map was calculated on behalf of the Global Earthquake Modeling Project GEM1 (Grünthal et al. 2010). The most recent and most elaborated harmonized European seismic hazard map is the one produced in the framework of the EUFP7 project SHARE (Seismic hazard harmonization in Europe) (Woessner et al. 2015).
After the SHARE project as a milestone, further updated PSHA projects have recently been finished in Europe, e.g. for Switzerland the model SUIhaz2015 (Wiemer et al. 2016), Spain (IGNUPM Working Group 2013; GasparEscribano et al. 2015), Portugal (Carvalho and Albarello 2016), Iceland (D’Amico et al. 2016), Turkey (Sesetyan et al. 2016) or are just under preparation, e.g. in Italy (Meletti et al. 2016), Belgium (indicated in Vanneste et al. 2014), in Norway (C. Lindholm, pers. comm.), or in France (P. Labbé, pers. comm.). Such new projects provide opportunities for harmonization and at least comparisons of achieved results at state boundaries, as it will be discussed at the end of the paper.
It is commonly understood that PSHA requires updates from time to time when novel data, better constrained models and improved approaches become available (Frankel 1995). Amongst the innovations motivating the new seismic hazard analysis for Germany are: (1) updated and extended seismicity data, (2) the adoption of a range of seismic source zone concepts (areal based, fault based and zoneless), (3) a comprehensive treatment of uncertainties of seismicity rates in relation to probability density functions of maximum magnitudes, (4) consideration of varying fitting rules for seismicity rate estimations, (5) improved implementation of parameters like focal depths and tectonic regimes in superzones, and (6) use of the latest generation of ground motion prediction equations (GMPEs) suitable for the target area.
The PSHA project described herein was accomplished on behalf of the Deutsches Institut für Bautechnik (DIBt; German Institute for Civil Engineering) and was launched by the respective national committee on standardization of the DIN. Two review panels have been established to provide critical review of all steps of the work in the frame of this project. The panellists for one of these control groups were selected by the DIBt, while the second reviewing group represents the task force for performance based design of the respective committee of standardization. The panellists are composed of representatives of ministries, other authorities, universities, research institutions, technical control boards and consulting engineers.
The paper describes the approach for deriving the new version of the national PSHA, including uniform hazard spectra (UHS) for any site within Germany for the hazard levels of 10, 5 and 2% exceedance probability within 50 years, hazard maps for spectral response accelerations, peak ground accelerations, and deaggregations for selected sites. As agreed upon by the project partners, all hazard calculations have been performed for rock site conditions in terms of a shear wave velocity of \(v_{S30}\) = 800 m/s; i.e. the average shearwave velocity of the upper 30 m. The shear wave velocity of 800 m/s defines the transition from subsoil class A (unweathered rock with high strength, \(v_{S}\) > 800 m/s) to class B (moderately weathered rock with lower strength, 350 m/s < \(v_{S}\) < 800 m/s) of the DIN 4149:200504 or later in the NA to the EC8 (DIN EN 19981/NA:20111), respectively. Moreover, the approach is based on natural tectonic earthquakes. Additionally, the UHS were fitted according to the control parameters of the design spectra of the Eurocode 8 (CEN 2004). All results, including the maps and, in particular, the UHS with the corresponding Eurocode 8 related control parameters, are accessible for the three hazard levels via a webportal for any site within the target area Germany.
Although the PSHA was performed for \(v_{S30}\) = 800 m/s, different underground conditions are prevalent in most parts of Germany. A corresponding research project aiming at modifications of the here derived \(v_{S30}\) rock UHS has been conducted in parallel at the Bauhaus University Weimar (Schwarz et al. 2017) for the combination of classes of subsoil and geological underground conditions defined in the national building code and in the NA to the EC 8, respectively.
The study is based on the assumption of stationarity of seismicity and is therefore restricted to the timeindependent seismic hazard approach, which considers a constant average occurrence frequency of earthquakes in their source regions and does not include the hazard due to aftershocks or foreshocks. Cases of foreshocks or aftershocks of economic concern in the target area are extremely rare. Applications of timedependent approaches to PSHA in the study area are strongly limited due to the short observation time of earthquakes with respect to the low level of seismicity. Similarly, induced seismic events in the target area (Grünthal 2014) are not considered here, since they are related to human activities in the underground and follow other principles than the natural tectonic earthquakes.
We use here the probabilistic approach based on Cornell (1968), subsequently extended by Esteva (1969, 1970) to incorporate the aleatory variability of ground motion relationships. Quantitative analysis of epistemic uncertainty, in the form of logic trees (LT), was first introduced into to PSHA by Kulkarni et al. (1984). Concerning the probabilistic methodology of PSHA in its current understanding we are referring McGuire (2004).
A specific goal of our regional study is to consider epistemic uncertainties in a comprehensive way; to a degree that is usually applied rather to site specific analyses. The employment of LTs requires that their branches must be mutually exclusive and collectively exhaustive. Pitfalls in applying LTs are discussed in Bommer and Scherbaum (2008). Epistemic uncertainties are accounted for here in several components of the model: (1) in form of five models of seismic source zones (SSZ) and two models to handle the zoneless approach in one logic tree, and (2) via the variability of all parameters qualifying the SSZs. These topics are the subjects of the following sections: the models of seismic sources (including the zoneless models), in Sect. 4 and the parameters characterizing the source zones of all models, in Sect. 5. The strategy to consider the epistemic uncertainties of ground motion models in form of a selection of a set of suitable GMPEs is described in Sect. 6. A comprehensive presentation of the logic tree to define the epistemic uncertainties of our models with the parameters of their elements is presented in Sect. 7. The parameters characterized by aleatory uncertainties are derived as respective density functions and are subject to the integration procedure. This part of the seismic hazard model is described in Sect. 8. The presentation of the results is subject of Sect. 9.
The comprehensive incorporation of epistemic uncertainties into the approach enables the calculation of mean and any required quantile, typically given in the form of the median and the 84th percentile. As a check on plausibility, the input model is also used to calculate an intensity based hazard map.
The results of the PSHA are discussed and compared with former national PSHA data and those of neighbouring countries (Sect. 10). Whilst it is our intention to make available the entire range of input parameters and results, this would go far beyond the scope of this paper. Therefore, reference is made to accompanying material summarized in a related technical report (Grünthal et al. 2017), which is publicly available in a direct way from the web portal of the library of the GFZ Potsdam. The results of the hazard calculations are accessible to the public via an interactive web portal (http://www.gfzpotsdam.de/EqHaz_D2016).
2 Seismicity
Well established seismicity data on natural, tectonic earthquakes are the prerequisite for reliable determination of seismicity rates of SSZ and hence for trustworthy PSHA. In low seismicity areas especially, the record of available sufficiently complete data should be as long as possible. The data source for this study is primarily the EuropeanMediterranean Earthquake Catalogue (EMEC) (Grünthal and Wahlström 2012), which is available from http://www.gfzpotsdam.de/EMEC. Compilation and harmonisation of the catalogue is described very detailed in the preceding catalogue version; i.e. the CEntral, Northern and northwestern European earthquake Catalogue (CENEC) (Grünthal et al. 2009b). These catalogues use harmonized moment magnitudes M_{ w } throughout. The catalogue EMEC (Grünthal and Wahlström 2012) represents the southern expansion of CENEC (south of the study area of this paper) and the temporal extension by 2 years up to 2006. The generally high degree of harmonization achieved in CENEC, which holds for the de facto identical data of EMEC as well, is analysed in Grünthal et al. (2009c). The specificity and transparency of descriptions in Grünthal et al. (2009a), how these catalogues for the study area were created, enable users to produce further temporal extensions as well as those with respect to lower magnitude thresholds where local sources provide such data. We employ here the temporal extension up to 2014 and the lower threshold of M_{ w } = 2.0 as already applied and described in Grünthal (2014) and Stromeyer and Grünthal (2015).
To estimate the completeness times of bins of larger magnitudes with few data, the statistical method by Hakimhashemi and Grünthal (2012) was employed, as well as an assessment from a historical perspective in combination with the cumulative number of events with time. The former is based on statistical interpretation of temporal changes in variances of interevent times. The results of both approaches are very similar. In case of differences, standard deviations of maximum likelihood estimates of GutenbergRichter bvalues decide which datum to use. For the west and southwest of our target area, i.e. in the regions of elevated seismicity of Germany, the completeness time of M_{ w } of 3.5–4.5 is about 1870, of M_{ w } 4.5–5 1800, M_{ w } 5–5.5 1650, M_{ w } 5.5–6 1450 and M_{ w } 6–6.5 1250 (cf. Grünthal et al. (2017)).
3 Regional tectonic setting and seismicity
3.1 Principal tectonic architecture
The crustal basement of Germany, in the range of the focal depths of most of the observed seismicity, is built mainly by the central European Variscides, and only in the northwest and most northern parts by the central European Caledonides. Both form the West European Platform (WEP). It is embedded between the AlpidicCarpathian orogen in the south and the Fennoscandian shield in the north, as well as the EEC in the northeast and the Bohemian massif in the east. The latter is acting as a rigid indenter into the WEP, as it was modelled by Grünthal and Stromeyer (1992).
Figure 3 shows a tectonic sketch map illustrating the major tectonic features. Since the present day seismicity occurs in the clear majority of cases along preexisting faults and fractures, the sketch map includes tectonic elements that originate in different geological eras. Also depicted is the current tectonic regime within larger areas (cf. Sect. 8.5), which allows for the identification of the most likely orientations under which faults might be active for each style of faulting. Additional information represents lineaments interpreted according to Earth and Space Research (ERS) radar mosaics of large parts of the target area and surroundings (Fig. 4).
The WEP was heavily affected by the Apulian continent–continent collision from the midCretaceous onset of Alpine orogeny onwards (Sissingh 2006; Schmid and Kissling 2000). This continent–continent collision is still ongoing as active uplift of external Alpine basement massifs and is connected with remarkable seismicity. It coincides to a large extent with increased uplift gradients (Ustaszewski and Pfiffner 2008).
The Apulian indentation into the relatively ductile WEP, in conjunction with the rigid lithospheric shields that bound the WEP from north to east, created a system of Cenozoic rifts (Ratschbacher et al. 1991; Cloetingh et al. 2005). They appear as grabens and subgrabens (e.g. Lower Rhine, Upper Rhine, Eger, Bresse), activated during the late Eocene with more pronounced rifting starting in late Oligocene and filled with Cenozoic sediments (Ziegler 1994; Geluk et al. 1994; Ziegler and Dèzes 2006, 2007; Bourgeois et al. 2007). Additionally, a system of horsts, blocks and tilted blocks was formed under a still present NWdirected compressional stress field, emerging in the early Miocene and accelerated in the Pliocene (Ziegler and Dèzes 2006, 2007). These processes lead to a considerable level of neotectonic activation of the WEP, manifest in the geomorphologic features, and is still ongoing, as demonstrated in the current observed seismicity (Cloetingh and Cornu 2005).
Volcanism accompanied this fragmentation of the upper crust of the WEP at different spots (Bourgeois et al. 2007). The last volcanic eruptions occurred in the Eifel (midwest of Germany) about 11,000 years ago at the Maar of Ulmen and 12,900 years ago at the Lake of Laach volcano (Schmincke 2010). Volcanic and magmatic activities are still present in different areas, but to a substantially diminished extent. This holds also for intraplatefaulting and block movements. Accordingly, Scholz et al. (1986) classify not only the Alpidic region but also the Rhine Graben structure as a plateboundary related area; however, the Alpine foreland, west of the URG, are classed as an intraplate related area.
The presentday crustal stress field governs the tectonic regime of an area, which reveals the proportion of strike slip faulting, normal faulting and thrust faulting (Fig. 3). The maximum horizontal stress (\(S_{Hmax}\)) orientation is, according to more than 750 data points for Germany (Reiter et al. 2015; Heidbach et al. 2016), predominantly in NW–SE direction in the seismically most active parts of Germany. Since the tectonic regime parameters are a direct input in PSHA, its derivation on the basis of observed stress data is subject of the respective Sect. 8.5 of the elaboration of the earthquake model. Vertical and horizontal displacement data exist only according to a few subregional areas of Germany. These data do not yet provide a coherent picture on strain accumulation or strain release.
Much of the seismicity of Germany is connected with distinct elements of the fragmented character of the upper crust in the area, which proves that the tectonic processes within the WEP connected with the Alpidic collision did not at all come to a standstill. Although the WEP can in general be seen as “stable continental region” (e.g. Johnston 1994; Kanter 1994), it clearly presents features of ongoing crustal activities, even though they are comparatively weak.
3.2 Areal distribution of seismicity and its relation to tectonic elements
The seismicity of the study area (Fig. 1) can be related to tectonic elements as they are compiled in Fig. 3. The seismicity shows highest activity along the Alpine belt, spanning parts of northern Italy, the western and eastern Alps through to the transition to the Dinarides. The Alpine belt continues further northeast in form of the MurMürz zone in eastern Austria continuing as seismicity chain along the Carpathians, which encircles the Pannonian basin.
North of the Alpine belt, the seismicity is remarkably elevated along the course of the river Rhine up to The Netherlands and into the adjoining parts of Belgium. Outside Germany, diffuse seismicity occurs in several different regions: western and southeast France along the Bresse Graben, in the LondonBrabant massif, in western and central Great Britain (extending to the westernmost part of the Doggerbank with the remarkable 1931 M_{ w } 5.8 earthquake), in the central Graben of the North Sea, in the southern Fennoscandian Shield (i.e. western Norway and southwest Sweden) flanked by the Kattegat and Skagerrak, representing lowered southern margins of the Fennoscandian Shield, as well as in the northeastern rim of the Bohemian massif, the Lugicum.
The pronounced seismicity zone along the river Rhine north of the epicentre of the Basel earthquake consists of, from south to north, the URG, the Middle Rhine area and the LRG. The latter shows well defined NW–SE striking normal faults, which can be well associated with most of the seismicity there. They are used here as a composite fault model for the hazard calculation. The border faults of the URG are seismically not noticeable, as the seismicity occurs mainly along north–south striking fault elements (cf. related material in Grünthal et al. 2017). Likewise, the seismicity is also relatively elevated both west and east of the southern part of the URG; towards the west in the French Vosges region and towards the east in the Black Forest. It is also elevated further east in the local seismicity spot of the Hohenzollernalb (HZA) with the 1911 quake as the historically strongest event. Here, the seismicity is connected with subparallel lamellar north–south striking sinistral en echelon segments (Reinecker and Schneider 2002), which manifest in form of fissures with at least Pleistocene openings (Illies 1982). These fault information is represented as lineaments according to Earth and Space Research (ERS) radar mosaics in Fig. 4.
A singular area of elevated activity ranges basically E of 12°E and N of 50°N in the middle east part of Germany, covering western Saxony, eastern Thuringia, and extending southeastward to the mostwestern part of the Czech Republic and further to Bavaria. This area of seismic activity was so far not generating earthquakes with M_{ w } > 5 in historical times. Tectonically, it is connected with a system of almost north–south directed faults, which are most pronounced from the Vogtland swarm quake area in the south up to the area of Leipzig, where the seismicity fades out. These north–south striking tectonic features of the VogtlandLeipzig zone (VLZ) (Fig. 4) are clearly traceable as photo lineations of satellite imasges (Grünthal et al. 1985; Bankwitz et al. 2003; Pohl et al. 2006). At the southern edge, in the Vogtland region and immediate surroundings, seismicity occurs mainly in form of intensive earthquake swarms with events no larger than M_{ w } 4.7 within each individual swarm. There and directly south, a remarkable amount of mantlederived gas exhalations are interpreted as indications of ongoing magmatic activities (Bräuer et al. 2011). The immediate surroundings of the swarm quake region and the easterly adjacent Eger Graben have experienced remarkable Cenocoic volcanism (cf. Fig. 3).
A diffuse seismicity arises, besides of the described seismicity zones within Germany, de facto in all parts. This means, no part can be regarded as aseismic; i.e. economically significant seismic events can be expected, in principle, everywhere. This issue, which is typical for many, if not most smalltomoderate seismicity regions, we are considering in our PSHA approach, as it is described below.
4 Models of seismic sources
 1.
two large scale areal seismic source zone models (LASZ) based solely on the principal geological structure and tectonic regime and architecture as basically outlined in Fig. 3. Such a model predicts that large earthquakes may occur in areas where no earthquakes have been observed yet and far from known faults or past seismic events,
 2.
three seismicity data driven small scale areal seismic source zone models (SASZ) considering numerous photo lineations of small scale tectonic features (cf. Fig. 4) and including composite seismic fault zones,
 3.
two versions of a zoneless approach. These are taking into account the fact that earthquakes may be clustered in stable continental interiors (Calais et al. 2016). Higher probability is then given to earthquake occurrences close to earthquakes that have been observed (smoothed seismicity models) or known fault lineations (SASZ).
Each of them represents an element of the first branching level of the seismic source zone logic tree, described below. This differentiation into five areal source zone models; i.e. the above mentioned basic principles (1) and (2), follows the concept of Grünthal et al. (2009a). A new addition in the current model is the incorporation of composite seismic fault zones, the use of a zoneless approach and the areal extension of the models in order to include areal source zones (ASZ) at distances of up to 250 km around the target area. The calculation of seismicity parameters characterizing each seismic source is treated in Sect. 5.2.
4.1 Models of tectonically based large scale areal seismic source zones—models A and B
The 31 large scale areal seismic source zones (LASZ) of model A numbered from N to S (column 1) with the corresponding tectonic units and superzone numbers of \(b\)values, \(M_{max}\), kernels and depths, tectonic regime parameters and description of tectonic terranes
LASZ Model A  Tectonic units or regions  Corresponding superzone numbers of  Tectonic terranes  

\(b\) values  \(M_{max}\)  Kernels and depths  Tectonic regimes  
A01  Baltic Shield S  4  5  1  1  Nonextended 
A02  Skagerrak and Kattegat  3  4  1  1  Nonextended 
A03  Central Graben  2  2  1  1  Extended 
A04  SorgenfreiTornquist zone east  4  5  1  1  Nonextended 
A05  Danish Embayment  2  3  1  1  Nonextended 
A06  Baltic Belarus Syneclise  4  5  1  1  Nonextended 
A07  Great Britain  1  1  9  9  Nonextended 
A08  Doggerbank W  1  1  9  9  Nonextended 
A09  Central European basin zone  2  3  1  1  Nonextended 
A10  Rønne Graben, TornquistTheisseyre zone, Polish trough  4  6  1  1  Extended 
A11  Lower Saxonian tectogene, Thuringian basin, Franconian line  7  10  5  5  Nonextended 
A12  Lower Rhine Graben, Ardennes massif E  5  8  3  10  Extended 
A13  Saxony  8  11  5  5  Nonextended 
A14  VogtlandLeipzig zone N  8  11  5  5  Nonextended 
A15  London Brabant massif  1  7  2  2  Nonextended 
A16  Eger Graben N  8  12  5  5  Extended 
A17  Middle Rhine zone  6  9  3  11  Extended 
A18  Lugicum  4  5  5  5  Nonextended 
A19  VogtlandCheb basin  8  12  5  5  Magmatic 
A20  Bohemian massif  4  5  5  5  Nonextended 
A21  WestRhenish Massif, Lorraine, Paris Basin E  9  13  2  2  Nonextended 
A22  Upper Rhine Graben  10  14  3  3  Extended 
A23  South German block  11  15  5  5  Nonextended 
A24  Pfahl line  11  15  5  5  Nonextended 
A25  Eastern Alps, MurMürz zone, Western Carpathians  12  16  6  6  Alpidic A 
A26  Western Pannonian basin  13  17  8  8  Alpidic A 
A27  Extern Alps  14  18  4  4  Alpidic A 
A28  Central Alps  15  19  4  4  Alpidic A 
A29  Internal Alps  17  21  4  4  Alpidic B 
A30  Bresse Graben S  16  20  2  2  extended 
A31  Po Plain and Apulian promontory  18  22  7  7  Alpidic B 
The LRG is subdivided in this model to indicate a crossing area (B16) of the NW trending active faults of the LRG with the SWNE faults of the adjacent most easterly Ardennes, respectively the LondonBrabant massif. This area is the transitional zone from the active Middle Rhine zone towards the LBM. Since the basic and large scale tectonic architecture is, in general, well constrained, the modelling of the LASZ does not leave much freedom to modellers. Thus, our model A in combination with modifications in form of model B seems to be sufficient to cover the uncertainties related to a basic tectonic zonation.
4.2 The concept of superzones as derivatives of SSZ model A
The tectonically reasoned LASZ model A is also used in our approach as basis for the determination of superzones to ascertain parameters and distribution functions based on sufficiently large data sets; i.e. these superzones are all derivatives of model A. Therefore, the five superzones are already introduced in this subsection, although their detailed treatment will be the subject of later parts of this paper.
The derivation of probability density functions (PDF) of maximum magnitudes M_{ max }, as described in Sect. 5.1, requires the introduction of two superzone models, one defining tectonic terranes and the other the superzones for the calculation of their PDF. The applied tectonic terranes differentiate between nonextensional (terrane number 1) and extensional earth crust (2), where different prior functions of M_{ max } are used. The usage of different truncations of the PDFs necessitates the further distinction of a seismically active magmatic region (3) and of the Alpine region into the external, central and eastern Alps (4, Alpidic A) and the internal Alps with the adjacent Po Plain and Apulian promontory (5, Alpidic B). Figure 7b and Table 1 show which of the modelA zones belong to which of the five different tectonic terranes.
The M_{ max }superzone model itself is based on that described for the bvalues, where those require a division according to different tectonic terranes. This applies to four of the bvalue superzonemodels, resulting in 22 M_{ max } superzones (Fig. 7c and Table 1).
The calculation of discretized focal depth density functions (cf. Sect. 8.3) requires a sufficient number of catalogued earthquakes with the information on their focal depths. Tectonically related modelA zones were combined in a way that usually more than 25 events are assembled in a respective focaldepth superzone. The resulting depth superzone model is shown in Fig. 7d and tabulated concerning the association of combined LASZs of model A in Table 1.
Also the determination of the parameters of kernel function for the application of a zoneless approach (cf. Sect. 4.4) necessitates a sufficient number of earthquakes. It proved to be suitable to apply the superzone model for this approach, which was derived already for the focal depth density functions; i.e. there holds also Fig. 7d for the different kernel functions.
Finally, a superzone model is needed for the derivation of tectonic regime parameters (cf. Sect. 8.5). Concerning this model we could also proceed from the depth superzone model, which required a partition of the depth superzone of the Rhine chain into three tectonic regime superzones, since a sufficiently large volume of tectonic regime data constrains such a differentiation into Upper Rhine Graben, Middle Rhine and Lower Rhine Graben. The resulting eleven superzones of the model for the tectonic regime are shown in Fig. 7e and their relation to LASZs of model A in Table 1.
4.3 Models of small scale areal seismic source zones: models C to E
Our principle of the delineation of small scale areal seismic source zones (SASZ) is quite different from the one that is applied for the LASZ models. For the definition of SASZ, we consider the detailed pattern of both the fault lineations and the historically observed seismicity, presuming areal stationarity of the latter. The SASZ models can be connected with large uncertainties in areas of diffuse seismic activity, which can lead to greater variability. Therefore we employ three SASZ models, which were originally derived independently from each other.
SASZ model C is based on Burkhard and Grünthal (2009), which was extended by Grünthal et al. (2009a) and later provided for the project SHARE (Woessner et al. 2015) as model for Germany. For its application in SHARE, it needed simplifications concerning those SASZs with too small seismic activity because of a higher magnitude threshold used in the SHARE project. Model D is basically that of the DACH study (Grünthal et al. 1998a) with simplifications in larger distances from the target area. It benefited much from advice by G. Schneider (Stuttgart). Finally, we employ model E, which largely corresponds to the model by Ahorner and Rosenhauer (1986). These models have been used already in Grünthal et al. (2009a), albeit without the slight areal extension to include SSZ up to distances of 250 km around the target area, which were added for this study. Their SW parts for the most seismically active parts of Germany are shown in Fig. 6. All these models are depicted in full in the accompanying report together with coordinates of their respective polygon traces. The areal differences in their variability, as an expression of uncertainties in modelling, are small along the boundaries of the URG, but large in northern Germany, where the dissimilarity of the models can be seen as an expression of large model uncertainties. The seismicity spot of the HZA, as mentioned above, is modelled in the SASZ in form of the SSZ C55, D54, E52 (cf. Fig. 6).
There is one basic difference in model C as it is used here in comparison with its earlier applications since Grünthal et al. (2004). This concerns the area of the LRG, where we modelled so far the fairly well known seismogenic normal faults by a set of SASZ as proxies to these faults. They are modelled now as composite seismic faults, described in the following subsection.
4.4 Model of composite seismic fault sources as part of the SASZ model C
Tectonic faults are used as seismic sources for the analysis, in particular as part of our SASZ model C, inasmuch as respective reliable information is available for the target area. This is solely the case for the LRG (Vanneste et al. 2014). Other areas of enlarged seismicity, such as the region of the HZA or the URG, could not yet be incorporated as fault source models as their respective data are incomplete. However, the data available for the LRG allow at least the construction of 15 composite seismic sources (CSS) (Vanneste et al. 2013) combining an unspecified number of individual sources according to Haller and Basili (2011). We make direct use of the fault geometry including dip, rake and depth range of the NW–SE striking CSS model by Vanneste et al. (2013), except for the two most northwestern ones. They have the largest distance to the target area and show very low seismicity. The determination of rates for the CSS requires a related catchment area of seismicity covering the region of the LRG or basically the largest part of the LASZ A12. This area is subdivided into two catchment subareas C15 and C22.
4.5 Zoneless models
An alternative to a SSZ based approach is a pure zoneless approach. These zoneless approaches use seismicity models based on smoothed epicentral locations of past earthquakes (Beauval et al. 2006; Stock and Smith 2002; Zechar and Jordan 2010) and require neither any definition of source zones nor earthquake recurrence models. But there are intrinsic uncertainties resulting from the choice of the smoothing functions and the impossibility to account for the occurrence of magnitudes larger than the observed maximum. Zoneless approaches are, according to Beauval et al. (2006), particularly useful for PSHA in low seismicity areas and can contribute to stabilize the results. Our basic motivation for its usage was to consider an antagonist view with respect to the large scale source zone concept, where the precise location of historically observed seismicity does not play any or even a very minor role. With the parallel use of zoneless approaches, we extend and round off the range of models to define sources of expected future earthquakes.
The resulting hazard according to the zoneless approach is very similar to that of the zonebased models for about 80% of the target area. Concerning the LASZ approach, as an antagonistic view with respect to the zoneless method, the latter yields significantly higher values in the localized parts of increased seismicity (up to 30% or 0.4 m/s^{2} for the level of the mean return period RP = 475 a). Concerning the SASZ model, the effect with respect to the resulting hazard is opposite. Here, the hazard according to the zoneless technique is about 10–20% lower (with the highest differences of about 0.2 m/s^{2}) in seismically exposed areas, but a little higher in rims surrounding areas of locally increased activity. This is due to the smearing effect of the bandwidth function.
4.6 Logic tree of seismic source models
The next branching level in Fig. 9 describes the bifurcation of the LASZ approach into the two variants, the models A and B. We found both to be equally important, resulting in equal weights of 0.5. Equal weighting for a branching level is not explicitly indicated as such in Fig. 9. The following branching level concerns the breakdown of the SASZ models. The most modern model C with the composite seismic fault modelling is assigned the highest weight of 0.5, which is the same as the other two SASZ models combined, each having a weight of 0.25. Finally, the two kernel smoothing models have the same weights of 0.5 each, since both were estimated as equally significant.
5 Parameters with epistemic uncertainties characterizing each seismic source
The parameters and models with epistemic uncertainties which characterize each source zone include (1) the parameters of the GutenbergRichter relation, which control the rates of seismicity and depend on (2) maximum magnitudes. The final branching level of the logic tree is that of the ground motion prediction equations (GMPE), discussed further in Sect. 6.
5.1 Maximum magnitudes M _{ max }
5.1.1 Probability density functions of M _{ max } in respective superzones and areal seismic source zones
The definition of a magnitude describing the largest possible earthquake within a certain region, i.e. \(M_{max}\), has been introduced into PSHA by Cornell and Vanmarcke (1969). Based on Cornell (1971), Algermissen and Perkins (1976) related \(M_{max}\) to specific source zones. The enigmatic nature of \(M_{max}\), due to obvious limitations of its observability, associates this parameter with a considerable epistemic uncertainty. This holds especially for regions with low to moderate seismicity, where the historical record of about a millennium is usually too short to constrain the largest possible earthquake. Consequently, we prefer methods to describe \(M_{max}\) with respective density functions ranging over a broad span of magnitudes.
A considerable number of methods are in use that attempt to extend the conceivable range of \(M_{max}\) up to its possible upper range. We employ here, as in all our previous studies on PSHA in Europe north of the Mediterranean region since Grünthal and Wahlström (2001) and Wahlström and Grünthal (2000, 2001), a Bayesian approach based on the ergodic principle; i.e. the substitution of temporal limitations in the observational record using observations of the same phenomenon taken from a larger spatial domain. Such an approach was proposed by Cornell (1994) in the frame of the analysis of the largest globally observed earthquakes in stable continental regions (SCR) (Johnston 1994). Coppersmith (1994) gave the description of the elements in implementing this approach, which makes use of the multiplication of one of two types of a priori distribution of \(M_{max}\) according to the global data and a likelihood distribution function derived from the seismicity features of the source zone to which the approach is applied. The likelihood distribution function is zero below the largest observed magnitude of a respective source. This considers the unarguable fact that \(M_{max}\) has to be larger than or equal to the largest observed earthquake in a source zone. The multiplication yields the a posteriori probability density function (PDF) of \(M_{max}\). We truncate this a posteriori PDF of a source zone according to suitable constraints as described below. For implementing the a posteriori PDF into PSHA, it is discretized by five sample values of \(M_{max}\), i = 1…5, of equal weights, according to the approach described by Miller and Rice (1983). The two a priori normal distributions characterize extended and nonextended crustal terranes. Since we described the basics of the respective approach in detail in Grünthal et al. (2009a), we can generally be brief and will highlight here those elements which are new with respect to our previous procedures.
The application of the Bayesian approach requires the subdivision of the crustal domains into extensional and nonextensional terranes for the use of one of the two a priori functions (Kanter 1994; Johnston 1994; Cornell 1994). Here, we follow our scheme, as it is described in Grünthal et al. (2009a) or in Burkhard and Grünthal (2009), with the Cenozoic graben structures as extended terranes and the regions north of the Alpidic parts of the study area as nonextensional terranes. The Alpidic parts are, according to the recommendation for the PEGASOS project by Coppersmith (pers. communication; cf. Burkhard and Grünthal 2009), treated with the extensional type of the a priori function. The basic scheme for the construction of respective superzones of crustal domains follows the LASZ of our model A. The association of the types of crustal terranes to certain LASZ of model A has been described already in Sect. 4.2.
The PDFs of \(M_{max}\) were derived, as in our previous works, for respective superzones. LASZs of model A are combined according to tectonic constraints (cf. Grünthal et al. 2009a and Burkhard and Grünthal 2009) to build the 22 \(M_{max}\) superzones for this study (cf. Sect. 4.2). PDFs of \(M_{max}\) of superzones are applied to the areal source zones of the LASZ models A and B and to those of the SASZ models C, D and E as they are covered by respective superzones.
Differentiation of tectonic terranes for the upper truncation of the \(M_{max}\) distribution
Tectonic terranes  LASZ  Max. observed magnitude  Magnitude increment 

Nonextended  A01, A02, A04, A05, A06, A07, A08, A09, A11, A13, A14, A15, A18, A20, A21, A23, A24  5.7  1.3 
Extended  A03, A10, A12, A16, A17, A22, A30  6.1  1.3 
Magmatic active  A19  4.8  1.3 
Alpidic A  A25, A26, A27, A28  6.6  0.8 
Alpidic B  A29, A31  6.9  0.7 
5.1.2 M _{ max } of composite seismic sources CSS
Each of the CSS was associated with the mean values of \(M_{max}\) within the range of 6.3 ≤ \(M_{max,mean}\) ≤ 7.1 with standard deviations σ of 0.3 according to Vanneste et al. (2013). We assume normal distributions on \(M_{max}\) and cut these at their lower bounds at the respective \(M_{max}\) − σ and at their upper bounds always at \(M_{max,trunc}\) = 7.4, which is the above described truncation applied for the LRG. We use also here the method by Miller and Rice (1983) for discretization into five values of \(M_{max}\) of equal weights.
5.2 Seismicity rates of seismic source zones depending on M _{ max }
The estimation of the seismicity rates based on catalogued earthquake data is an essential step within a PSHA. It requires the consideration of the uncertainties associated with the observed annual seismicity rates to quantify the resulting uncertainties in the hazard (Abrahamson and Bommer 2005; Bommer et al. 2005).
5.2.1 The methodology
Optimal sampling point positions and corresponding weights of the standard normal distribution for \(k\) = 4
Sample points \(z_{i}\)  \( \sqrt {3 + \sqrt 6 }\)  \( \sqrt {3  \sqrt 6 }\)  \(\sqrt {3  \sqrt 6 }\)  \(\sqrt {3 + \sqrt 6 }\) 
Weights \(w_{i}\)  \(\frac{3  \sqrt 6 }{12}\)  \(\frac{3 + \sqrt 6 }{12}\)  \(\frac{3 + \sqrt 6 }{12}\)  \(\frac{3  \sqrt 6 }{12}\) 
5.2.2 Seismicity parameters in superzones of commonb values
Parameters \(a\) and \(b\) of the magnitude frequency relation for the 18 common \(b\) superzones
Common \(b\) superzones  \(b\)value  \(a\)value  Normalized \(\nu \left( {4.0} \right)\)value  Number of events for fit 

1  0.80 ± 0.04  2.85 ± 0.17  0.054  185 
2  0.95 ± 0.08  2.49 ± 0.24  0.004  88 
3  0.83 ± 0.05  2.45 ± 0.14  0.130  120 
4  1.01 ± 0.03  3.52 ± 0.09  0.012  305 
5  0.78 ± 0.03  2.27 ± 0.09  0.454  223 
6  1.05 ± 0.06  2.96 ± 0.17  0.440  135 
7  0.93 ± 0.07  2.06 ± 0.20  0.020  98 
8  0.92 ± 0.03  2.71 ± 0.09  0.198  546 
9  1.16 ± 0.05  3.70 ± 0.12  0.004  369 
10  1.07 ± 0.04  3.34 ± 0.12  0.415  304 
11  1.02 ± 0.03  3.59 ± 0.07  0.128  718 
12  0.81 ± 0.02  3.10 ± 0.07  0.608  638 
13  0.73 ± 0.03  2.74 ± 0.13  0.492  366 
14  0.98 ± 0.02  3.53 ± 0.05  0.623  902 
15  1.06 ± 0.01  4.34 ± 0.03  0.836  3752 
16  0.81 ± 0.04  2.32 ± 0.10  0.238  188 
17  0.80 ± 0.04  3.35 ± 0.18  2.099  93 
18  0.89 ± 0.04  4.34 ± 0.19  3.779  210 
5.2.3 Differentiation of the minimum magnitude for fit for the calculation of frequencymagnitude parameters
Barth et al. (2015) described that difference for the URG as well. Both papers discuss possible reasons. As illustrated in the figure, the smaller magnitude events reflect basically the frequency of occurrence of more modern instrumental earthquakes, while the larger ones represent mainly historical earthquakes. Maximum likelihood estimates are driven by the numerous smaller magnitude events, which would lead to an underestimate of the rate of larger magnitude events with respect to the catalogued data, in case their rates do not fit with those of the many small magnitude events. Assuming an exclusive loglinear relation of the rates also for these SSZs these uncertainties are treated as two logic tree branches: one branch takes into account all data and another one uses a fit to the data for the larger magnitudes. As it is clearly shown in Fig. 14, the uncertainty in fitting all data is much smaller than for the case when the minimum for the fit is set at larger magnitudes. About 35% of the SSZ allow the described differentiation in performing the fit to the data. Otherwise, the minimum magnitude for the fit at small M is used for both branches of the LT. The example in Fig. 14 shows one of the most striking differences in the fit to small and larger magnitudes. With respect to the explicit parameters a and b for each SSZ and for both types of fit, we refer to the accompanying report. There both values are provided together with the parameters of the covariance matrix as a measure of uncertainty for the different M_{ max i } per zone for all five models and for the two different versions of the minimum for fit.
5.2.4 Seismicity rates of composite seismic sources (CSS)
The slip rates at the different fault segments of the CSS model were derived by Vanneste et al. (2013) from geologically based longterm vertical displacements. They are rather low and connected with relatively large uncertainties. As we do not know which portion of the slip is released aseismically and which portion in the form of seismic events, we did not convert slip rates to activity rates. Instead, we relate the seismicity of events with \(M_{w}\) ≥ 5.3 to the 3D planes of CSSs according to the observed rates of the corresponding catchment subareas. The calculation of the seismicity rates is performed also according to the method by Stromeyer and Grünthal (2015). The distribution of the seismicity rates to the individual faults is assumed to be proportional to their length while preserving the overall rate. This approach combines each of the five \(M_{max}\) dependent areal rates with the respective set of maximum magnitudes of the faults that means the \(M_{max,i}\) of the catchment area with the \(M_{max,i}\) of the respective CSS. The occurrence of smaller magnitude earthquakes is assumed as equally distributed seismicity within the respected catchment subareas.
6 Challenges and strategy to select a set of GMPEs
The prediction of groundmotion in lowtomoderate seismicity areas like Germany and the consideration of the epistemic uncertainty is challenging due to the lack of strongmotion data (PEER 2015). This leaves us with two options: the development of stochastic groundmotion models derived from weak motion analysis (e.g. Drouet and Cotton 2015; Edwards et al. 2016) or the selection of models calibrated on data from other regions of the world (Cotton et al. 2006). The second option was, however, the only possible choice since highquality weakmotion databases are not available yet in Germany. The selection of GMPE calibrated on data from other regions was driven by three motivations: the consistency between the GMPE host regions and the German tectonic regime, the results of recent GMPE testing and the particular needs of our hazard approach.
The tectonic context, as described in Sect. 3, is complex with active structural elements mainly along the chain of the Rhine up to rather stable parts towards the north and northeast. While formerly such regionalization processes were mainly based on hardly reproducible expert judgements (e.g. Delavaud et al. 2012), we employ more objective and replicable datadriven methodologies (Chen et al. 2016). The results of these datadriven regionalization schemes corroborate the suggestion that the area of Germany displays attenuation properties that are similar to those of active crustal regions. However, the seismic activity is low, which makes it difficult to predict future properties of major earthquakes. The key parameter in this context then is the stress drop, which controls the highfrequency content of ground motions (Cotton et al. 2013). Stressdrop analyses of earthquakes within or close to the target area are rare because of the scarce seismicity. Some quakes recorded in Western Europe, like Saint Dié (2003, \(M_{w}\) = 4.8, eastern France) or Market Rasen (2008, \(M_{w}\) = 4.5, UK) have, however, shown stressdrop values (Scherbaum et al. 2004a; Rietbrock et al. 2013) that are larger than the average observed in active parts of Europe. This analysis then favours the use of models from active crustal regions (in terms of attenuation) with the need to take into account a large epistemic uncertainty associated to future stressdrops.
The number of recordings of smalltomoderate earthquakes has increased in northwest and western Central Europe in the last decade. Several authors have then been taking advantage of these weak motions to test and select respective GMPEs (Beauval et al. 2012; Drouet and Cotton 2015; Rietbrock et al. 2013; Edwards and Fäh 2013). These testing results confirm that groundmotion models according to active crustal regions should be considered for hazard evaluations in Germany.

The hazard computed at a given location depends on both the seismic source model and on the ground motion model. Preliminary deaggregation results and earlier German seismic hazard projects have shown that the hazard results are mainly controlled by groundmotion due to moderate earthquakes 4.5–5.5 located at short distances (below 25 km). Regional variations of groundmotions are mostly observed for distances larger than 50–60 km (e.g. Boore et al. 2014; Kotha et al. 2016). The deaggregation results show that the magnitude scaling of groundmotion in the magnitude range 4.5–6.5 is critical—a criterion that was part of the GMPE selection process.

A problem often encountered in the application of recent GMPEs based on complex functional forms (e.g. NGAWest 2) is also related to the availability of suitable metadata in the target region. In low to moderate seismic regions the source and site characterizations are generally not as detailed as in the data set used to derive the GMPE (host region). In such cases, the GMPEs are applied in simplified forms, where one or more variables (e.g. basin depth, hanging wall foot wall effects) are constrained to default values. This operation should be accompanied by either a proper handling of the epistemic uncertainty introduced when fixing some variables, or by propagating the uncertainty to the aleatory component (Bommer et al. 2005). Both choices imply some additional work and tricky expert decisions. We therefore have chosen to favour models derived with simple functional forms and to develop a new model calibrated on the NGAWest 2 database since such simplified “NGAWest 2” functional form was not available (Bindi et al. 2017).
6.1 A logic tree built to capture three types of uncertainties: dataset, functional form and stressdrop

empirical models are dependent on the selected databases used to calibrate the models;

empirical models depend on the developers functional form choices;

average stressdrops may be larger in the stable (noncratonic) part of Europe compared to active regions where the models have been developed.
6.2 New highquality groundmotion datasets
During the course of this national hazard project, several high quality strongmotion datasets became available: the RESORCE European and Middle East Reference database for seismic groundmotions in Europe (Akkar et al. 2014; Douglas et al. 2014a) and the NGAWest2 dataset (Ancheta et al. 2014; Gregor et al. 2014). A major update of the broadband (mainly Japanese based) model of the Cauzzi and Faccioli (2008) model was also published (Cauzzi et al. 2015).
Key improvements of these recent databases are the increase in the number of records from moderatemagnitude events (\(M\) < 5), the high quality of the metadata associated with these earthquakes and the homogeneous processing of both large and moderate earthquakes. These new datasets offer a new opportunity to capture the magnitude scaling of groundmotion for \(M_{w}\) between 4.5 and 6.5, which is precisely the magnitude target of seismic hazard assessments of countries like Germany. This better datacoverage of moderate magnitude earthquakes is important since several studies (e.g. Cotton et al. 2008) have shown that groundmotion models derived from largemagnitude datasets will tend to overestimate the ground motion from small and moderate earthquakes.
Recent analyses (Boore et al. 2014; Kotha et al. 2016) have shown that regional variations of groundmotions of active shallow earthquakes may be significant only for distances larger than 50–60 km. Most of the hazard in Germany is driven by events in shorttomoderate distances and, therefore, models derived from these three databases are acceptable. They have different strengths: the European RESORCE records may be more representative of future German groundmotion because of a closer tectonic similarity. The NGAwest database is, however, more complete at short distances (\(R\) < 20 km). Japanese stations have all measured soil \(v_{S30}\). Soil and rock stations have been correctly identified which may contribute to a better evaluation of site responses at the \(v_{S30}\) = 800 m/s target. We then have chosen to select models based on these three databases and give half of the total weight (0.5) to the European (RESORCE) branch. Equal weights (0.25) were assigned to the Japanese and NGAwest2 branches.
6.3 Taking into account functional form variations
Despite all the developers having started with a same common strongmotion archive, the predicted spectral accelerations from the models usually show significant differences, which can be related to varying data selection criteria but also modellers choices. For example and as discussed by Bindi et al. (2017), some NGAWest 2 models have chosen functional forms with a magnitude hinge around \(M_{w}\) = 5.5. Such choice has a low impact on hazard computations in high seismicity regions but a larger one in moderate seismicity regions. Selecting models based on multiple approaches is, however, a way towards more effectively capturing epistemic uncertainty in terms of the centre, the body and the range of technicallydefensible interpretations of the available data (USNRC 2012). The main “European” branch of the logic tree includes for this reason two models based on the classical randomeffects approach (Akkar et al. 2014; Bindi et al. 2014) but also a model based on the neuralnetwork, datadriven and calibration method (Derras et al. 2014). Equal weights were assigned to these three.
6.4 Taking into account stressdrop uncertainties
The final stage of developing our logictree concerning groundmotions was to apply scaling factors to the selected equations in order to capture epistemic uncertainty due to stressdrop. Such final logictree branches have been adopted by the recent groundmotion logic trees developed in moderate seismicity region like Switzerland (Edwards et al. 2016) and South Africa (Bommer et al. 2015).
It could be shown by Bommer et al. (2015) that changing of stress drop results in relatively constant changes in the groundmotion amplitudes across ranges of magnitude and response periods. The only departures from this constant scaling occur for long response periods and small earthquakes. Given that the dominant scenarios identified in deaggregation of the hazard at longer response periods are typically associated with larger magnitudes, it seems reasonable to adopt constant scaling factors across all periods. This assumption renders the amplitudescaling process transparent, simple and predictable.
Bommer et al. (2015) have also selected «host» models from active crustal regions and they have considered that the stressdrops of these «host» regions were around 8–10 MPa. Such a value is consistent with our recent analysis (Bora et al. 2017) of European stressdrops. For the target region (South Africa), the values were inferred from an extensive literature review of values used for the development of hybridempirical and stochastic GMPEs in SCRs, which are generally higher. As discussed above, the potential for higher values of stressdrop in the stable part of Europe (noncratonic and cratonic) is consistent with stressdrop analyses (Scherbaum et al. 2004a; Rietbrock et al. 2013) of a couple of European earthquakes like Saint Dié (2003) and Market Rasen (2008). However, our recent analysis of the European, large stressdrops of \(M\) > 4 crustal earthquakes (Bora et al. 2017) does not indicate clear regional variations of stressdrops in Europe. The origin of “energetic” earthquakes (Baltay et al. 2011) is then still unclear.
We finally have chosen scaling factors greater than unity (1.0, 1.25 and 1.5) similar to the one chosen by Bommer et al. (2015). A branch was also added for potentially lower values (with a scaling factor of 0.75) given that part of Germany, unlike most stable continental regions, is under an extensional tectonic regime. The amplitude scaling factors of 1.25 and 1.5 roughly correspond to factors related to the stress drop of about 1.5 and just over 2, respectively. Starting with nominal native stress drops of around 8–10 MPa for the models means that the amplitude scaled models represent median stress drop levels from around 6 MPa to just over 20 MPa. This LT scheme is considering a slightly larger epistemic uncertainty compared to the one adopted recently by Edwards et al. (2016) in Switzerland. Their logic tree branches show values between 5 and 9 MPa for deep (\(H\) > 6 km) events located in the foreland. Lower stressdrop values and larger ranges of uncertainty have been chosen for shallow events (values between 1 and 7.5 MPa).
The chosen weighting is symmetric and reflects the belief that stressdrops (and associated groundmotions) may be higher in Germany than in the more active tectonic regions from which the groundmotion models were selected: weights of 0.36 have been given to the factors 1.00 and 1.25, smaller weights (0.14) to the outer branches representing the factors 0.75 and 1.5.
6.5 Selected GMPEs and their model parameters
Parameters of selected GMPE
References  Range of \(M_{w}\)  Range of \(R\) (km)  Distance metric^{a}  Tectonic regime^{c}  Component  Range of \(T\) (s)  PGA 

Akkar et al. (2014)  4.0–7.6  up to 200  epi, JB, hypo  N, R, S  geometric mean  0.01–4.0  given 
Bindi et al. (2014)  4.0–7.7  up to 300  JB, hypo  N, R, S, U  geometric mean  0.02–3.0  given 
Derras et al. (2014)  4.0–7.0  5–200  JB^{b}  N, R, S  geometric mean  0.01–4.0  given 
Bindi et al. (2017)  3.0–7.9  4–300  JB, hypo  U  RotD50^{d}  0.01–4.0  given 
Cauzzi et al. (2015)  4.5–7.9  up to 150  rup  N, R, S  geometric mean  0.01–10.0  0.01 s 
The main use of areal sources in our approach requires the preference of the hypocentral distance \(r_{hypo}\) as distance metric. Three of the five selected GMPE can consider \(r_{hypo}\) as distance metric. The parameters \(r_{JB}\) and \(r_{rup}\) of the other two GMPEs were transformed into \(r_{hypo}\) according to a procedure of Scherbaum et al. (2004b), which had to be modified for a better numerical handling. This modification is described in Grünthal et al. (2009a).
7 Logic tree for epistemic model parameters characterizing seismic source zones
The next branching level concerns the discretization of the PDF of \(M_{max}\) into five values \(M_{max,i}\) of equal weight of 0.2. Each \(M_{max,I}\) is combined with the four discretized distributions of seismic rates, with the weights derived in Sect. 5.2.
The following set of branching levels considers the handling of GMPE, whose selection is described above in Sect. 6. First, we differentiate the principle data source of GMPEs with EuropeanMiddle East data with the weight of 0.5. Global and Californian recordings, specifically the NGA2West data (Ancheta et al. 2014), were represented by the GMPE of Bindi et al. (2017) and given a weight of 0.25. The same weight is given to the other global data set with the focus on Japanese recordings with the respective GMPE by Cauzzi et al. (2015). Concerning the EuropeanMiddle East data we have selected the GMPEs of Akkar et al. (2014), Derras et al. (2014) and Bindi et al. (2014) as additional branches with equal weights of 0.167 each. In the final branching level, each of the five selected GMPEs is then connected with a variation of expected stress drop, which is modelled in form of four branches representing respective factors and weights as already described above in Sect. 6.
Altogether the combined logic tree contains 4040 final branches; five source zone models, plus the two zoneless models combined with the 20 GMPE branches. Each seismic source is modelled with four rate models in combination with five \(M_{max,i}\) yielding 20 branches, plus two branches of the minimum for fitting the observed yearly rates of magnitudes, five GMPEs combined with four variants characterizing the uncertainties in stress drop, which results in 800 branches. We use the entire LT as it is presented; i.e. we do not allow any pruning of the LT for the hazard calculations.
8 Parameters with aleatory uncertainty: the hazard integral
Features of these integration ranges and density functions are given as follows.
8.1 Magnitude
The density function of seismicity rates (cf. Sect. 5.2) is integrated from a minimum magnitude \(M_{min}\) up to \(M_{max}\) (cf. Sect. 5.1) in increments of 0.05 magnitude units. A pragmatic choice of \(M_{min}\) was often to adapt the lower common validity range of magnitude for the applied GMPE, which was in many cases \(M_{w}\) 4.5.
Our rationale for choosing \(M_{min}\) is, according to McGuire (2004), based on the intensity threshold of engineering relevance, which is \(I\) = 5–6. This is also the lower limit of seismic zones of the current building code (DIN EN 19981/NA 2011). The corresponding magnitude would be \(M_{w}\) = 4.3 according to the master event relation in Grünthal et al. (2009c) under consideration of minus \(1\sigma\) as safety margin. Therefore, \(M_{min}\) = 4.3 is applied in our PSHA.
8.2 Distance
The integration over the areal distribution of randomly distributed seismic activity within each seismic source zone was accomplished according to the validity ranges of distances of the five selected GMPEs (cf. Table 5). Therefore, we use 200 km as upper limit, although one of them has a lower scope of application of 150 km only. We apply 20 steps for integration per area source and a 5 km increment along the faults.
8.3 Discretized focal depth density functions
Sampled depths distribution for each DSZ at three optimally selected depths with their corresponding weights
DSZ  LASZ (model A)  Depths (km)  Weights  

1  A09, A05, A04, A01, A10, A06, A03, A02  9.6  19.5  32.0  0.421  0.376  0.203 
2  A21, A30, A15  5.2  13.4  23.1  0.309  0.470  0.221 
3  A12, A17, A22  7.7  13.7  20.9  0.513  0.338  0.149 
4  A27, A28, A29  6.3  10.6  16.2  0.341  0.446  0.213 
5  A11, A23, A14, A13, A19, A16, A24, A20, A18  8.0  16.4  32.7  0.603  0.333  0.064 
6  A25  7.6  12.4  28.6  0.672  0.306  0.022 
7  A31  6.4  11.7  17.6  0.327  0.490  0.183 
8  A26  7.3  14.4  24.2  0.467  0.442  0.091 
9  A07, A08  8.5  15.5  23.9  0.261  0.486  0.253 
8.4 Limitation of the groundmotion residuals
The integration over the groundmotion residuals of a GMPE requires a truncation of the respective lognormal distribution. It is now common to have groundmotion data points with at least three standard deviations (\(3\sigma\); \(\varepsilon\) = 3) above the logarithmic mean (Bommer et al. 2004). Therefore, this could be one reason for the limitation at \(\varepsilon_{max}\) = 3, as it is used e.g. by Woessner et al. (2015). Another rationale would be tests to check, what values of \(\varepsilon_{max}\) would result in calculated load parameters, which would be sufficiently near to the case that no truncation at all is applied. As it is well known, the transfer from \(\varepsilon_{max}\) = 2 to \(\varepsilon_{max}\) = 3 yields a significant growth of amplitudes. We took then calculations for \(\varepsilon_{max}\) = 6 as a de facto upper bound, where the portion beyond is, with only 1.973 ppb, vanishingly small. In case of a PGA based hazard curve for Cologne, the deviation of the \(\varepsilon_{max}\) = 4 curve from the one for \(\varepsilon_{max}\) = 6 is for PGA ≤ 0.5 m/s^{2} smaller than 0.035% and for PGA = 1.0 m/s^{2} just 0.097%. The corresponding deviation of the \(\varepsilon_{max}\) = 3 curve from the one for \(\varepsilon_{max}\) = 6 is for PGA ≤ 0.5 m/s^{2} in this case smaller than 0.72% and for PGA = 1.0 m/s^{2} only 1.78%. Therefore, we concluded that we have a sufficient saturation already with the usage of \(\varepsilon_{max}\) = 3. To conserve the median of respective GMPE, we perform the truncation symmetrically; i.e. the integration limits are \( \varepsilon_{max}\) and \(+ \varepsilon_{max}\).
8.5 Tectonic regime
Four of the five GMPEs used in this study differentiate the tectonic regime by an appropriate styleoffaulting coefficient. Only Bindi et al. (2017) leaves it unspecified. Our assignment of the tectonic regime to the sources is based on the data of the World Stress Map (WSM) 2016 (Heidbach et al. 2016). 513 data records within the study area provide information on the tectonic regime, where we restrict us on the data with AC qualities according to the latest WSM quality ranking scheme (Heidbach et al. 2016).
Combination of LASZs of model A to build eleven tectonic superzones TSZ
TSZ  LASZ (model A)  Strikeslip  Normal  Thrust 

1  A09, A05, A04, A01, A10, A06, A03, A02  0.632  0.263  0.105 
2  A21, A30, A15  0.571  0.214  0.214 
3  A22  0.500  0.500  – 
4  A27, A28, A29  0.538  0.299  0.167 
5  A11, A23, A14, A13, A19, A16, A24, A20, A18  0.727  0.258  0.015 
6  A25  0.816  0.053  0.132 
7  A31  0.315  0.076  0.609 
8  A26  0.520  0.080  0.400 
9  A07, A08  0.594  0.250  0.156 
10  A12  0.267  0.733  – 
11  A17  –  0.750  0.250 
We are aware that uncertainties of the chosen tectonic regime parameters may be significant. However, variations of the rupture mechanisms of earthquakes of up to 10% have an almost negligible effect on source zone based PSHA, especially in regions of low seismicity.
9 Results of the PSHA
The hazard calculations were accomplished for rock underground conditions, characterized by an average shear wave velocity of the upper 30 m \(v_{S30}\) = 800 m/s for the hazard levels of occurrence, or exceedance probabilities, of 10, 5 and 2% within 50 years, which correspond to the mean return periods RP = 475, 975 and 2475 years. The horizontal 5% damped Uniform Hazard response Spectra (UHS) were computed for the spectral range of periods \(T\) of 0.02–3.0 s, standardly for the weighted arithmetic mean of the logic tree, the median, the 84th and the 16th percentile. Seismic hazard maps were also generated for (1) the mean and the mentioned percentiles for selected horizontal 5% damped spectral response accelerations (SRA) of the UHS, (2) for mean amplitudes of periods in the UHS representing the plateau, and (3) for peak ground accelerations PGA. Hazard maps in terms of (4) macroseismic intensities were also calculated for plausibility checking.
The hazard calculations were performed at nodes with a spacing of 0.1 times 0.1 geographic degrees, which corresponds to a grid of about 7 times 11 km in the middle part of the target area. Altogether, these are 6226 grid points within Germany plus a small belt around for technical reasons to generate the hazard maps. The latter are based on a 2Dinterpolation to receive 0.01 × 0.01 degree spacing. The seismic hazard was assessed with a modified version of the computer code FRISK88M (Risk Engineering 1997) for the seismic source zone based branches of the LT. On the basis of Woo (1996) we developed a code to compute the zoneless part, whose results were incorporated into the LT according to the formerly mentioned code.
9.1 PSHA results at the grid points
For the histogram, the whole range of annual rates resulting from the LT was divided into 100 intervals. The distribution shows the cumulative weight of all end branches resulting in a rate less than or equal to a certain value versus that value. They are shown for PGA and RP = 475a. The skewness of the resulting distributions becomes obvious. It is different for both locations. The positions of the respective values of the mean, median and the 84th percentile are marked. The relatively small difference between mean and median for Aachen is typical for the entire Rhine chain, SW Germany and most of the other areas, except for an area in eastern Thuringia with the centre near to Gera and low seismicity regions in central and northern Bavaria, where the difference between both parameters is particularly large because of remarkably pronounced epistemic uncertainties there.
9.2 Seismic hazard maps
Seismic hazard maps were calculated for the considered SRA, for PGA, for the mean SRA amplitudes at \(T\) = 0.1, 0.15, 0.2 s, as described above, and for the macroseismic intensity—and all these for the three hazard levels used for the study as well as for the median, the mean and the 84th percentile. A selection of them is presented here, additional ones are compiled in the accompanying technical report (Grünthal et al. 2017) and are accessible via our web portal.
Differences in the skewness of the hazard results were already mentioned in connection with Fig. 17, where the spread between median, mean and the 84th percentiles were presented between Aachen (50.8°N, 6.1°E) and a site near Gera (50.9°N, 12.2°E). This behaviour can be followed in detail with the 84th/50th quotient map (Fig. 26 middle part). Aachen is located in an area with the almost lowest quotients, and the site near Gera in a local spot of almost highest ones.
9.3 Intensity based seismic hazard map
The earthquake input model for our PSHA was also used to calculate a hazard map in terms of macroseismic intensities, especially for the purpose of a plausibility check, since so few strong ground motion recordings exist for the target area that they can hardly be the basis for a testing of resulting hazard. The same is true with respect to a comprehensive and almost complete macroseismic database for entire Germany. These macroseismic data are solely sufficient to construct a map of maximum observed intensity of the roughly last 500 years. This means that testing of PSHA maps has currently clear limitations for our target region (cf. discussions in Beauval et al. (2008) or Mak et al. (2014)). Our new intensity based hazard map enables especially the comparison with our previous intensity hazard map (Grünthal et al. 1998a), which is still used as basis for the seismic zoning map of the national annex to the current building code.
9.4 Comparisons with our previous PSHA and with the new Swiss earthquake hazard model
Variations of seismic load parameters among different generations of PSHA for respective target regions are of significant relevance for the practice of earthquake engineering. We therefore compare our results with analogous code related ones in terms of the UHS and hazard maps for the DIN 19700 (Grünthal et al. 2009a) and the intensity based hazard map (Grünthal et al. 1998a), which form the basis for the seismic zoning map of the National Annex to the current building code DIN EN 19981/NA (2011).
9.5 The interactive web portal
The web portal http://gfzpotsdam.de/EqHaz_D2016 hosted at GFZ Potsdam provides access to the products of this national hazard project. Seismic hazard maps can be interactively viewed with respect to PGA, SRA at \(T\) = 0.02, 1.0 and 3.0 s as well as for mean SRA amplitudes at \(T\) = 0.1, 0.15, 0.2 s. All results are presented as median, mean and 84th percentile maps for the hazard levels of exceedance probabilities of 10, 5 and 2% within 50 years. The intensity based hazard map is available for mean values of the exceedance probability of 10% within 50 years.
The UHS are important for engineering applications and can interactively be selected by mouse click on the respective hazard map for any point within Germany or by entering a place name into the search control. In this case, the respective UHS is given for the centre of the corresponding settlement. The spectra are shown either as shape preserved splines or as fit to the EC8 elastic spectral shapes. All data of the UHS including the corresponding EC8 parameters are downloadable as CSV or JSON file.
10 Summary, discussion and conclusions
 (a)
the application of a longlasting harmonized historical earthquake database of the last millennium up to 2014;
 (b)
the extensive modelling of sources of future earthquakes as (1) large scale tectonic zones considering the prospective occurrence of significant seismicity in areas which have been quite in the historical past, (2) different small scale models considering seismotectonics, lineations of faults according to remote sensing satellite data, and crustal structure, and (3) zoneless approaches based on welldetermined datadriven kernels;
 (c)
composite finite fault models where sufficiently proved by data;
 (d)
adoption of superzones for the determination of parameters or distributions (\(b\) values, \(M_{max}\), \(h\), \(tr\), kernels) to guarantee a sufficient number of data points; e.g. more than 70 earthquakes per zone to derive rate parameters;
 (e)
considering paleoseismological findings for the modelling of maximum magnitudes with large ranges of uncertainties and a conservative upper bound truncation of their respective probability density functions;
 (f)
the consequent application of our new method to model uncertainties in the seismicity rates in a satisfactory way;
 (g)
the full involvement of relatively higher rates of larger magnitude earthquakes than predicted by the occurrence of modern smaller magnitude events in about one third of the seismic source zones with a relatively high weight;
 (h)
the use of the latest generation of a set of five GMPEs with an additional epistemic uncertainty concerning the variation in stress drop in the target area;
 (i)
the determination of weights in logic trees as a consensus of a larger group of experts;
 (j)
the integration over ± 3σ of the aleatory variabilities of the used GMPEs;
 (k)
the integrating over probability density functions of focal depths and tectonic regimes determined within superzones;
 (l)
no allowance of any pruning of the logic tree for the hazard calculations;
 (m)
plausibility check of the model (except the part on GMPEs) by using the input model to calculate an intensity based hazard map and to compare it with previous respective calculations;
 (n)
output response ground motions for mean values (as arithmetic mean of the outcome of all logic tree branches), median and percentiles for the period range of the UHS of 0.02 s up to 3.0 s;
 (o)
fitting of the UHS additionally to the control parameters of the EC8 design spectral shape;
 (p)
provision of the hazard results on internet portals as well as the entire input model in a transparent way.
The comparison of our results in terms of UHS and seismic hazard maps with previous seismic hazard assessments shows a remarkable persistence, even though the approaches were performed independently and are indeed different. Figure 27 shows an example of one UHS according to our new results and the UHS for the same site according to Grünthal et al. (2009a). The largest amplitudes of both spectra are practically the same; however, there is a shift of the peak of spectrum towards lower periods, which is due to the fact that the site factors of recent GMPEs have changed and are better calibrated for rock conditions.
A similar agreement holds also for our earlier approaches on a national level (Grünthal et al. 2004, 2006) and for the comparison with our European hazard maps too (Grünthal and GSHAP Region 3 Working Group 1999; Grünthal et al. 2010; Chan and Grünthal 2010), where we can compare the PGA data. Of particular interest is the comparison of our new intensity based hazard map with the one of Grünthal et al. (1998a). The resemblances between both are also in this case remarkable (cf. Fig. 29). However, it is obvious that all these similarities in our approaches over the last almost 20 years are not a proof of the reliability of our new results. In this connection we have to stress that it was always a principle of our PSHA approaches to be independent from previous results; i.e. not to be influenced by any anchoring.
Concerning the comparison with results from new PSHA approaches in neighbouring countries, we could make use so far of the Swiss data (Wiemer et al. 2016), which indeed fit remarkably well along the common border (Fig. 30). These two converging, but fully independent approaches can be seen as a proof of concept and of the robustness of modern PSHA.
We would have wished to rigorously test our earthquake model. However, we have to face clear limitations of testing (Mak et al. 2014; Beauval et al. 2008) due to the lack of a sufficient number of strong ground motion records in Germany as well as sufficiently complete macroseismic data for the entire country.
Seismic hazard evaluations in low seismicity areas stay challenging. Because of the low tectonic loading rate, individual faults may stay dormant for a long time and then become active for a short period (e.g. Stein et al. 2017). Intraplate seismicity is also often characterized by clustered and episodic earthquakes and extended aftershock sequences (e.g. Calais et al. 2016). Exactly such features, which are treated in both papers, we had to tackle within our study. Furthermore, the expected maximum magnitudes of future earthquakes are fairly uncertain in low seismicity areas and future earthquakes may be larger than the historically observed ones, or new findings concerning paleoseismic earthquakes with larger magnitudes than assumed so far will come to light. Moreover, because of the lack of sufficient data, groundmotion models have been calibrated on data from other regions of the world and then may not be adequately adapted to source, propagation and rock conditions of our target area. Future efforts for improving the hazard model can benefit from the application of recently developed methods for evaluating the hazard sensitivity (Molkenthin et al. 2017). The availability of computational efficient sensitivity analysis techniques allows for focus to be placed on only on those input models whose variability is mostly controlling the key parameters of the overall hazard assessment, and to discuss the way we capture the CBR (Center, Body and Range) of technically defensible interpretations only on the logic tree branches that matter. It should be recognised, however, that despite the potential insights offered by analyses of this kind, they are difficult with such complete and complex logic tree.
Douglas et al. (2014b) encourage the publication of the uncertainties in hazard studies because this makes studies more transparent. Our model uncertainties have been captured with 4040 LT branches. The areal distribution of quotients of different percentiles have been shown and discussed in the previous section. The uncertainty index (100 × log(85th/15th)), suggested by Douglas et al. (2014b), has also been computed. The obtained values of the uncertainty index (for PGA, RP = 475a) range between 32 (Allgäuer Hochalpen; i.e. region at the border to Austria) and 81 (for the HZA). These values are larger than most of the values reported by Douglas et al. (2014b) for past national hazard studies but similar or even larger than those obtained in modern sitespecific hazard analyses for equivalent tectonic context. This is an expected result as past regional studies have not quantified epistemic uncertainty in a comprehensive way and the uncertainty range of a regional study should be larger than the one obtained in a sitespecific hazard analyses for equivalent tectonics (Pagani et al. 2016). This also confirms that the comprehensive effort we made to capture uncertainties has been reaching a technical and scientific level usually dedicated to sitespecific studies.
It remains difficult to “be certain about uncertainty” (Knight 1921), however. While early PSHA studies came up solely with mean values without any quantification of uncertainties, the abilities in incorporating uncertainties have improved for the better uncertainties in the input models were understood and could become part of a PSHA. When comparing uncertainties in PSHA results, one has to be sensitive concerning limitations in the correct handling of uncertainties in the respective input sets of considered studies. Since we do not know the true hazard, we can hardly be confident what uncertainty range would be sufficient in the resulting hazard. We, at least, followed the goal to consider uncertainties in a comprehensive way inasmuch they are physically, geologicaltectonically, mathematically and logically sound, balanced and justified.
Footnotes
 1.
DIN—Deutsches Institut für Normung, German Institute for Standardisation.
Notes
Acknowledgements
This analysis was partly funded by the Deutsches Institut für Bautechnik (DIBt). In this context, the work has greatly benefited from the discussions und suggestions by the members of the two review teams; i.e. the colleagues C. Butenweg, A. Fäcke, E. Fehling, H. SadeghAzar, F.H. Schlüter, H. Schneider, T. Schmit, J. Schwarz, T. Spies, S. Stöhr. We would also like to express our thanks to our colleagues Oliver Heidbach and Graeme Weatherill, whose comments and insights are gratefully acknowledged. The authors appreciate the useful and constructive suggestions by Hilmar Bungum and one anonymous reviewer.
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