This paper presents a methodological approach to seismic hazard assessment based on a hybrid source model composed of faults as independent entities and zones containing residual seismicity. The seismic potential of both types of sources is derived from different data: for the zones, the recurrence model is estimated from the seismic catalogue. For fault sources, it is inferred from slip rates derived from palaeoseismicity and GNSS (Global Navigation Satellite System) measurements.

Distributing the seismic potential associated with each source is a key
question when considering hybrid zone and fault models, and this is normally
resolved using one of two possible alternatives: (1) considering a
characteristic earthquake model for the fault and assigning the remaining
magnitudes to the zone, or (2) establishing a cut-off magnitude,

The proposed approach is applied in southern Spain, a region of low-to-moderate seismicity where faults move slowly. The results obtained are contrasted with the results of a seismic hazard method based exclusively on the zone model. Using the hybrid approach, acceleration values show a concentration of expected accelerations around fault traces, which is not appreciated in the classic approach using only zones.

Active faults are the main earthquake sources in the crust. However, their incorporation in seismic hazard assessment is not straightforward since there are not enough data available to adequately model them. This leads to a limited use of faults as independent sources in seismic hazard analyses and to an extended use of seismic zones that cover a significant portion of the crust, assuming uniform seismic characteristics within each source.

This situation has begun to change in recent years, as more studies on active tectonics, palaeoseismicity and fault deformation rates derived from GNSS and other measurements become available. These recently available studies constrain fault parameters such as rupture plane geometry, predominant sense of slip, slip rates, etc. (e.g. Dixon et al., 2003; Langbein and Bock, 2004; Papanikolaou et al., 2005; Walpersdorf et al., 2014; Metzger et al., 2011).

Taking fault type rather than zones into consideration in seismic hazard studies requires addressing two factors: the 3-D geometry of the source and the data required to characterize its seismic potential. In most practical cases, the seismic potential of faults is characterized based on the slip rate using characteristic earthquake models proposed by Wesnousky (1986) (for instance, Field et al., 2014; Akinci and Pace, 2017) instead of Gutenberg–Richter recurrence models (Parsons and Geist, 2009). Other approaches such as extracting the seismic parameters of every single fault from the earthquake catalogue are not always viable, especially in areas with slow-moving faults. Additionally, the period considered in the catalogue may be too short compared with the recurrence time of the fault to provide an unbiased estimation of fault seismic parameters.

In principle, modelling all existing active faults as independent entities could be conceived as the most accurate source model for seismic hazard assessment. However, this vision is still rather idealistic. A more realistic view would include only a limited number of active faults (those with the highest seismic activity) as independent sources. Accordingly, small faults that generate low-magnitude events or slow faults that produce rare events cannot be properly characterized. To prevent a possible deficit in the seismic source model for a given region, the use of faults as seismic sources may be completed with zones that account for the seismic potential associated with these small or slow faults or simply with unknown faults that cannot be characterized independently. Hence, we propose considering a hybrid source model composed of faults and zones: the first modelled as independent sources and the second including residual seismicity.

Adequately establishing the distribution of seismic potential using a model that combines zones and faults poses a challenge, since these are derived from different data sources. For zones, the recurrence model is calculated based on the seismic catalogue, whereas for faults, the recurrence model is derived from fault geometries and slip rate estimates based on GNSS-measured deformation rates. The problem is that some of the events contained in the catalogue may be associated with the faults and may have already been included when calculating the seismic potential of the faults based on the slip rate estimates. If all events are assigned to the zone, the events associated with the faults would be counted twice, leading to an overestimation of the total seismic potential (for both faults and zones).

Some authors assign initial

The approach presented in this paper addresses the challenging question of how to estimate the anticipated ground motion exceedance rate using a short period of earthquake observations and limited geological data (with significant uncertainties). This challenge is common to all probabilistic seismic hazard models (Kijko et al., 2016). The purpose of this study is to approach this challenge proposing a model that contains different types of seismic sources (faults and zones) and adequately distributes the seismic potential, preventing double counting and taking completeness periods into account.

Diagram showing the distribution of the seismic potential of a region, expressed as the sum of the seismic potential of the faults and the seismic potential of the zone.

An application of the approach presented is carried out in SE Spain, the area with the highest seismic hazard in Spain. Most of the previous work that partly or wholly addresses this area includes zones only (García-Mayordomo et al., 2007; Benito et al., 2010; Mezcua et al., 2011; IGN-UPM working group, 2013; Salgado-Gálvez et al., 2015) or is based on zoneless methods (Peláez and López-Casado, 2002; Crespo et al., 2014). A first attempt to combine faults and zones was carried out by García-Mayordomo (2005), who developed a zone model for the area taking into account the use of the characteristic earthquake model for faults.

The hybrid model proposed is composed of fault-type sources and zone-type sources. In addition, the term “region” is defined as the geometric container for both source types. Thus, the region presents the same geometry as the zone and its seismic potential (seismicity rate and seismic-moment rate) is the sum of the potentials of the two types of sources (faults and zone). The zone is used to represent the seismic potential of events that cannot be associated with specific faults. Although there is a geometrical equivalence between region and zone, their seismic potential is very different, as the seismic potential of the region equals the seismic potential of the zone plus the seismic potential of the faults contained within the region (Fig. 1).

Completeness analyses of the seismic catalogue. Panel

The problem is then how to distribute the seismic potential of the region
between the zone and the faults without counting some faults twice. The
following considerations were taken into account:

The seismicity rate of the region is derived from the seismic catalogue
after excluding the events that lie outside their respective completeness
periods, CP(

The completeness periods, CP(

Magnitude values above

Finally, the cumulative rates in the interval [

Although faults are capable of generating earthquakes with magnitude

The seismic potential is represented by the total rate of earthquakes (

The

The cumulative-moment rate of the faults is estimated assuming that the
fault planes are accumulating energy evenly and using the equation proposed
by Brune (1968):

The slip rate

This moment rate represents the average annual seismic moment accumulated in
each fault that will be released by earthquakes of different magnitudes

Substituting the previous relations in Eq. (6), solving the integral and
reordering the equation for

The total seismic-moment rate for each fault (

In this approach it is considered that all faults included in the same
region will present the same

The parameters representing the zone are initially unknown. They can be
calculated for the interval [

Regarding the faults,

COV coefficient associated with seismic-moment rate obtained using synthetic catalogues.

Graph extrapolating the recurrence model of the fault up to the maximum expected magnitude value, as deduced from geological criteria.

With this third equation, it is possible to solve the system and obtain a
new

Considering that the faults may generate events with magnitudes larger than

Regarding the

The proposed approach strongly relies on computing seismicity, earthquake
rates and moment rates, within the magnitude interval [

In order to capture the variability of seismic-moment rates calculated from
the earthquake catalogue, a sensitivity analysis of three key factors is
conducted. These factors are (1) the number of records used to compute
moment rates, (2) the magnitude range covered by the complete catalogue and
(3) the proportion of earthquakes of different magnitude (

Three-dimensional view of the seismic sources considered for hazard calculation, including faults (red) and zones (brown).

Synthetic catalogues derived from GR-modified recurrence models are
generated for this purpose. Earthquake rates are computed using different
numbers of events, magnitude intervals and

The procedure consists of five steps:

generating 2000 synthetic catalogues for different combinations of
earthquake rates, magnitude intervals and

calculating earthquake rates for different magnitude values for each synthetic catalogue (Eq. 6);

calculating moment rates for different magnitude values for each synthetic catalogue;

calculating the sum of moment rates for different magnitude values in order to obtain the cumulative-moment rate for each synthetic catalogue (Eq. 7);

computing the mean and the standard deviation of the distribution of calculated seismic-moment rates.

It is also important to consider the uncertainty associated with the slip
rate and the area of the fault, as these are propagated into the
distribution of seismic-moment rates of the fault in proportion to the
deviation of the area or slip rate value. The uncertainty of the slip rate
value is more relevant for low slip rate values than for large slip rate
values (a similar trend can be deduced for low and high area values). For
instance, a deviation of

The approach described above is applied in south-eastern Spain, the most
seismically active area in the country. The tectonic deformation and
seismicity is related to the north-western boundary between the Eurasian
and African plates (e.g. Kiratzi and Papazachos, 1995), with an approximate
shortening rate of about 4 mm yr

Assigning earthquakes to specific faults is not an easy task, partly due to
errors in earthquake location and to the existence of blind, unknown faults:
whereas earthquakes can be clearly associated with a rupture, such as the
2011

The seismogenic source model considered for SE Spain is composed of
12 regions that contain a total of 95 faults (Supplement) Active fault data are
taken from the QAFI database (v2.0) (García-Mayordomo et al., 2012),
which includes information about fault segmentation, geometry and slip rate
(see Fig. 5). The maximum expected magnitude in each fault is derived from
the rupture length using Stirling et al. (2002) equations derived from the
instrumental data set. These equations are chosen because they are also the
ones used in the QAFI database and ensure consistency with said
database. Moment rates accumulated in the faults are estimated using the
fault plane area and the slip rate value according to the formula proposed
by Brune (1968). A value of

Seismic rate and seismic-moment rate recorded in the different regions
for two magnitude intervals (

The zone model proposed by García-Mayordomo et al. (2010) is used to obtain the geometries of the 12 regions (and thus of the zones) that account for the seismicity that cannot be ascribed to faults (see Fig. 5). All the regions considered in this model contain fault sources, with the exception of regions 28, 29, 33 and 40. In these cases, the seismic potential of the corresponding region is assigned to the zones.

The seismic moment released in the region is estimated from the seismic
catalogue of Spain homogenized to

Table 2 shows the seismic potential for each region, calculated in the
magnitude intervals [

Subsequently, a recurrence model (GR-mod) is assigned to all regions,
obtaining the corresponding

Parameters extracted from the seismic catalogue for each region used to estimate the COV coefficient for Table 1, regions 28, 29, 33 and 40 have been excluded because they contain no faults.

The seismic hazard calculation is carried out using the software CRISIS2012
(Ordaz et al., 2013), considering the strong motion equation of Campbell and
Bozorgnia (2014), which makes it possible to include the fault geometry and
the faulting style. The ground motion parameters predicted include peak
ground acceleration (PGA) and 15 spectral accelerations within the period
range (0.05–10 s), all obtained in hard soil (

Seismic potential distribution of faults and zones. The last column includes the percentage of regional seismic potential assigned to each source within the region.

Seismic hazard results obtained with the proposed hybrid model (HM) and with the classical method based in zone (CM) are shown in Fig. 6a and b. Only the geometry of the zone model differs in the two analyses: the ground motion prediction equation (GMPE) and the other calculation parameters are the same in both approaches. The definition of seismic zones applied in the classic method is explained with detail in IGN-UPM Working Group (2013).

PGA estimates for the return period of 475 years using the zone approach (CM) reach maximum values in Granada, Almeria and the Murcia region, around 0.20 g. Minimum PGA values are obtained in Jaén, with values as low as 0.06 g.

Figure 6a shows the seismic hazard map resulting from applying our approach (HM). It can be seen that the largest accelerations are estimated around the Carboneras Fault and the fault set of Granada, (0.38 g), followed by the Alhama de Murcia and La Viña faults systems (0.30 g) and, to a lesser extent, by the Venta de Zafarraya, Carrascoy, Bajo Segura, Baza, Mijas and Cartama fault systems.

The seismic hazard map obtained using the HM displays more spatial variability than the one obtained with the CM, showing maximum values along fault sources that decrease sharply away from the faults. This trend reflects a source proximity effect, implying higher acceleration values for the surface projection of the fault rupture plane that rapidly decrease away from the fault (by one half at a distance of about 15 km).

The differences between the expected maximum acceleration obtained with the
two methods, CM and HM, for return periods of 475 and 4975 years appear in
Fig. 7a and b. The trend presented in both maps is very
similar for the two return periods. A different case is found in region 30
(Case Lietor Fault), a very complex region with scarce seismic activity and
large faults with low slip rates (see Supplement). Here, the HM gives higher
seismic hazard than the CM only for long return periods. For this region,
the magnitude range [

To clarify how faults are conditioning the final seismic hazard in our model, the seismic hazard curves showing a partial contribution of different sources in Murcia, Almeria and Granada are shown in Fig. 9 for PGA and SA (1.0 s). For each city, black lines show the total seismic hazard curve and coloured lines show the seismic hazard curve associated with different sources (zone and faults) for each city.

In Murcia, seismic hazard for short return periods is associated with multiple sources (zone and faults), but for return periods exceeding 475 years (an exceedance probability of 0.1 or lower in 50 years) the seismic hazard is dominated by the Carrascoy Fault. This effect is very similar for PGA and SA (1.0 s).

In Almeria, only two sources, zone 38 and the Carboneras Fault, contribute significantly to seismic hazard. In PGA both sources combine equally to give the seismic hazard for the city, but, for SA (0.1 s), the Carboneras Fault predominates, especially for return periods of more than 475 years.

In Granada, there are many sources contributing to seismic hazard for the city. This is because there are many known faults in its vicinity. Seismic hazard is controlled by zone 35 for PGA and SA (1.0 s) and shorter return periods. This trend changes for return periods greater than 975 years.

PGA for return period of 475 years derived from

Figure 10 shows the uniform hazard spectra obtained for four cities in the study area. These graphs can be used to compare the maximum accelerations predicted with the CM and HM in different spectral ordinates, evidencing that the trend observed in PGA persists throughout the entire spectrum.

We present a hybrid method (HM) for determining a seismic source model that
combines zones and faults as independent sources. The HM is based on the
distribution of seismic potential among different sources and does not
impose any restriction with respect to the type of recurrence model assigned
to seismic sources. Moreover, the HM does not require defining a fixed
cut-off magnitude

Comparison of seismic hazard results from the two models (HM and CM) for
return periods of

Seismic hazard curve (with HM and CM) of a site close to the Lietor Fault.

This marks a difference with other approaches that model the seismic potential of faults using two alternatives: (1) single-magnitude rupture models such as Wesnousky's (1986) characteristic earthquake model, as seen in Field et al. (2014) and Akinci and Pace (2017), and (2) models that set a fixed cut-off magnitude and assume that the biggest magnitudes take place in the faults and the smaller ones occur in the zone. In contrast, the formulation of the HM considered above uses a GR-type recurrence model for faults, in line with the proposals made by some other authors (Woessner et al., 2015).

Seismic hazard curve (with HM) of Murcia, Almería and Granada considering all the seismic sources involved. The black lines show the total seismic hazard curve and the coloured lines show the seismic hazard curve associated with different sources (zone and faults).

One strong point of the HM is that it ensures a distribution of seismic
potential between faults and zones that prevents double counting of
seismicity. This is achieved by computing the seismic potential of faults
and zone using the events contained in the completeness period of the
catalogue for different magnitude ranges. Identifying the magnitude interval
used to distribute seismic potential between zone and faults is of
fundamental importance. Specifically, determining

In addition, for the purposes of hazard calculations, the distribution of
seismic potential for the entire magnitude interval (between the

The results of applying the HM are compared with the results of the CM in terms of expected accelerations. A single GMPE is used for both calculations. We have not used any other GMPE (or combination of GMPEs through a logic tree) to simplify the calculations and allow a direct comparison of hazard results.

Uniform hazard spectra obtained in four cities with CM and HM for three return periods.

The results obtained with the HM show an increment of expected accelerations near fault traces (in a factor of 2) in relation to the results of the CM approach. This is consistent with observations of very high ground motions in the epicentral areas of recent earthquakes, such as the 2009 L'Aquila and 2011 Lorca events (Akinci et al., 2010; Cabañas et al., 2014). This increment is achieved at the expense of decreasing expected accelerations in areas located farther away from faults. This is a consequence of the redistribution of seismic potential in the region, which is not increased, but redistributed in several sources (zone and faults).

An approach for combining zones and faults in a seismic source model is formulated in this paper.

It is based on the distribution of seismic potential among different sources
under certain conditions to prevent counting seismicity twice. Two
points of the methodology are critical and must be carefully assessed: the
analysis of completeness and the choice of recurrence model used to
represent the seismic activity of either source. They are determined by the
data available (composition of the seismic catalogue, fault slip rates and
geometries, etc.) in the study region, and hence not easily automatized and
extendible to other areas. Thus, the approach followed for the application in
SE Spain should be reevaluated when it is applied to a different area. For instance,
it is to be expected that implementing this approach in a region with
rapidly moving faults would produce significantly different results, requiring
further adjustments. The higher fault slip rates would imply that the faults
consume a larger proportion of the seismic potential available, compromising
the convergence of the iterative method to obtain the zone

An initial assumption of the approach is that the seismic-moment potential accumulated in active faults is released only seismically. This condition can be easily modified in the formulation presented above. Additional data informing about other ways of releasing seismic energy, such as slow slip events or aseismic transients, would help to constrain this point.

The seismic hazard map obtained with the HM presents a more heterogeneous aspect compared to the CM seismic hazard map, which assigns a uniform seismic potential to each region. In the HM hazard map, the accelerations expected along fault traces increase and decrease farther away from fault traces, thus keeping the seismic potential budget of the region in balance. This effect can be useful for applications in which the effects of being near a fault must be emphasized, such as urban seismic risk studies for cities located atop active fault planes.

As a final conclusion, we identify some points that require further development and are the focus of an interesting line of research. Specifically, these include (1) determining catalogue completeness for different time-magnitude intervals in the study area; (2) selecting the recurrence model assigned to fault sources according to the data available, and (3) determining the proportion of seismic potential accumulated in faults that is released through earthquakes.

The available data of active faults are in the Supplement.

The supplement related to this article is available online at:

All authors contributed to the preparation of this paper.

The authors declare that they have no conflict of interest.

We would like to thank Mario Ordaz Schroeder for his time and support during a research stay carried out by ARM at the Instituto de Ingeniería, UNAM, and we acknowledge financial support from Vicerrectoría de Investigación y Desarrollo (VRID), UdeC, “216.419.003-1.0IN”. Edited by: Maria Ana Baptista Reviewed by: five anonymous referees