Introduction
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 β values to seismic sources (e.g.
Bungum, 2007) or propose a simple way of distributing the seismic potential
based on a uniform magnitude value, Mc, assigning events with a magnitude
lower than Mc to the zone and events with magnitude higher than Mc to the
faults (Frankel, 1995; Woessner et al., 2015). The question is, how is this
Mc value determined? Why can the fault not generate events with a magnitude
below the Mc value? In a study region such as southern Spain, with slow
faults and maximum magnitudes around 6.5–7.0, it is difficult to choose an
Mc in a non-arbitrary manner.
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.
Source (zones and faults) hybrid approach to hazard estimation
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 (a) shows the
(normalized) cumulative number of earthquakes per year for different magnitude
intervals. Solid circles indicate the inflection point that marks the lower
limit of the completeness period for the respective magnitude interval CP(m).
Panel (b) shows the CP(m) corresponding to each magnitude interval. Note
that the CP(m) is not well constrained for magnitudes above the MMaxC value
(note dashed and dotted curves in both figures).
![]()
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(m). This period is defined for a given magnitude M as the period
during which a catalogue of events of magnitudes M and higher is complete. This
is comparable to assuming that all events of a given magnitude, M, that have
actually occurred are effectively contained in the catalogue within the
period CP(m=M) (and not outside of this period).
The completeness periods, CP(m), for different magnitudes up to a maximum-completeness magnitude value, MMaxC, are lower than the observation
period (OP) of the catalogue.
Magnitude values above MMaxC present recurrence periods higher than
the catalogue OP. These values usually constitute a sample that does not
include a high enough number of records to clearly establish the recurrence
period, as this makes it increasingly difficult to constrain rates for rarer events.
By representing the number of recorded events for different magnitude
intervals as a function of time it is possible to identify the reference
years, RY(m), for different magnitude intervals using the slope method
(Hakimhashemi and Grünthal, 2012), also known as the temporal course of
earthquake frequency (TCEF) (Nasir et al., 2013). This method consists of
plotting the cumulative number of earthquakes of a given magnitude range
over time and estimating the year, presenting a significant gradual change
in slope (Fig. 2). Consequently, CP(m) and MMaxC values can be
calculated for m<=MMaxC. It is then possible to estimate
seismicity rates (Eq. 1) and the seismic moment in each magnitude interval
(Eq. 2) as follows:
n˙(m)=n(m)CP(m),
where n˙(m) is the annual rate of events
with magnitude (m) and n(m) is the number of recorded events with
magnitude (m) in the catalogue in the completeness period, CP(m).
M˙o(m)=(m)⋅Mo(m),
where Mo(m) is the seismic moment
released by events of magnitude m, obtained using the equation proposed by
Hanks and Kanamori (1979) (log(Mo)=1.5⋅Mw+16.1).
Finally, the cumulative rates in the interval [MMin, MMaxC] can be
estimated, where MMin is the minimum-magnitude value used to compute
seismic hazard, as shown in Sect. 2.1. This is illustrated with an example
in Fig. 2, with [MMin, MMaxC]=[4.0, 5.9].
Although faults are capable of generating earthquakes with magnitude
m>MMaxC, the distribution of seismic potential is carried
out in the completeness period [MMin, MMaxC]. In this way, we
avoid using magnitudes with long recurrence periods that have not been
recorded in the catalogue within the completeness periods. The computation
of the seismic potential of the fault in the interval [MMaxC,
MMax(fault)], where MMax(fault) is the maximum-magnitude value of
events that can be generated in a fault, is constrained with other
geological criteria (see below).
The seismic potential is represented by the total rate of earthquakes (N˙min)
and the cumulative rate of seismic moment (M˙o), for the
magnitude range [MMin, MMaxC], in the completeness period CP(m).
Details on how to determine N˙min and M˙o for the entire region,
the corresponding zone and faults are explained in the following section.
Seismic potential of the region
The N˙min and M˙o values representing the seismic potential of
the region are derived from the seismic catalogue of the magnitude interval
[MMin, MMaxC] for the completeness periods, CP(m).
N˙minregionMMinMMaxC=∑MMinMMaxCn˙(m)M˙oregionMMinMMaxC=∑MMinMMaxCn˙(m)⋅Mo(m),
with n˙(m) the annual rate of events with magnitude (m) recorded in
CP(m) and Mo(m) the seismic moment for magnitude m. The notation
X|MiMj represents the magnitude interval (Mi, Mj) in
which variable X is computed.
Seismic potential of faults
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):
M˙ofault=υ⋅μ⋅A,
where υ is the slip rate, μ is the shear modulus and A is
the area of the fault plane.
The slip rate υ and the area of each fault plane can be derived
from specific studies based on paleoseismic analyses and GNSS measurements.
There are also some databases available to search for these data, including
the EDSF for Europe (Basili et al., 2013), the DISS for Italy (DISS Working
Group, 2018) and the QAFI for Spain and Portugal (Garcia-Mayordomo et al.,
2012). The shear modulus may be estimated from values close to
μ=3.2×1010 Pa (Walters et al., 2009; Martínez-Díaz et al.,
2012).
This moment rate represents the average annual seismic moment accumulated in
each fault that will be released by earthquakes of different magnitudes
m=0 up to the maximum magnitude of the fault, MMax(fault). The value
MMax(fault) can be evaluated from a geometrical aspect of the fault
planes using empirical relationships proposed in the literature, such as Wells
and Coppersmith (1994), Stirling et al. (2002) and Leonard (2010). Thus, M˙ofault can be expressed as follows (Eq. 6):
M˙ofault=∫Mm=0MMax(fault)n˙(m)⋅Mo(m)dm,
where n˙(m) can be estimated applying a recurrence model, for
instance, the modified GR model shown in Eq. (7).
n˙(m)=N˙minfault⋅βe-βme-βMm=0-e-βMMax(fault),
and the seismic moment Mo(m), can be estimated from the Hanks and
Kanamori (1979) relation expressed in exponential terms, Mo(m)=edm+c
with c=16.1⋅ln(10) and d=1.5⋅ln(10), where m is the moment
magnitude Mw (Anderson and Luco, 1983).
Substituting the previous relations in Eq. (6), solving the integral and
reordering the equation for N˙minfault, we get Eq. (9).
N˙minfault=M˙ofault⋅(dβ)⋅e-βMm=0-e-βMMax(fault)β⋅e-βMMaxMoMMax(fault)-e-βMm=0MoMm=0,
where Mm=0 is the minimum magnitude that may be generated at a
fault rupture (here taken as m=0), MMax(fault) the maximum
magnitude, and M˙ofault the seismic-moment rate
accumulated in the fault (Eq. 5).
The total seismic-moment rate for each fault (M˙ofault) and
seismicity rate (N˙minfault) can be formulated
as the sum of the seismic-moment rate released at different magnitude
intervals; thus, it follows
N˙minfault=N˙minMM=0MMin+N˙minMMinMMaxC+N˙minMMaxCMMax(fault)
M˙ofault=∑MM=0MMinn˙(m)⋅Mo(m)+∑MMinMMaxCn˙(m)⋅Mo(m)+∑MMaxCMMax(fault)n˙(m)⋅Mo(m).
By implementing a recurrence model, it is possible to derive the seismicity
rate and the moment rate in the interval [MMin, MMaxC] (see
example in Fig. 3 with [MMin, MMaxC]=[4.0, 6.9]).
In this approach it is considered that all faults included in the same
region will present the same β value and different seismicity rates
(N˙minfault), as this parameter depends on the
seismic-moment rate of each fault (M˙ofault).
(a) Seismicity rate (cumulative number of events per year vs. magnitude)
and (b) moment rate (cumulative seismic moment per year vs. magnitude)
plots. The different magnitude intervals mentioned in the text are marked.
![]()
Seismic potential of the zone
The parameters representing the zone are initially unknown. They can be
calculated for the interval [MMin, MMaxC] given that
SeismicPotentialzone=SeismicPotentialregion-SeismicPotentialfaults,
or specifically,
N˙minzoneMMinMMaxC=N˙minregionMMinMMaxC-∑N˙minfaultMMinMMaxC
M˙ozoneMMinMMaxC=M˙oregionMMinMMaxC-∑M˙ofaultMMinMMaxC.
In principle, there are two equations with two unknowns related to the zone:
N˙minzoneMMinMMaxC,
and
M˙ozoneMMinMMaxC.
Regarding the faults, N˙minfault|MMinMMaxC and
M˙ofault|MMinMMaxC are derived using an initial
(not definitive) β value. Regarding the region, N˙minfregion|MMinMMaxC and
M˙oregion|MMinMMaxC are known, as they were
extracted from the catalogue (Eqs. 1 and 2). A new additional equation is
obtained relating N˙minzone|MMinMMaxC and
M˙ozone|MMinMMaxC using Eq. (8) for the
interval [MMin, MMaxC] in the zone, resulting in the
following:
N˙minzoneMMinMMaxC=M˙ozoneMMinMMaxC⋅d-βzone⋅e-βzoneMMin-e-βzoneMMaxCβzone⋅e-βzoneMMaxCMoMMaxC-e-βzoneMMinMoMMin..
Notice that Eqs. (8) and (14) are similar: they differ in the type of source
and computation interval. Equation (8) is for faults and it is computed in the
magnitude interval [Mm=o, MMax]. Equation (14) is for zones, and the
magnitude interval is restricted to [MMin, MMaxC]. Also note that
the β value of the zone in this equation can be equal to the β value
of the region, as both sources present similar seismic natures.
COV coefficient associated with seismic-moment rate obtained using
synthetic catalogues.
M(4.0–5.0)
M(4.0–6.0)
M(4.0–7.0)
b
b
b
Records
0.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
0.5
1.0
1.5
2.0
200
0.00
0.09
0.10
0.09
0.19
0.30
0.39
0.31
0.36
1.00
1.17
0.43
180
0.09
0.10
0.10
0.09
0.20
0.29
0.33
0.28
0.35
0.87
1.21
0.42
140
0.10
0.11
0.11
0.10
0.21
0.31
0.33
0.25
0.39
0.92
1.17
0.31
120
0.11
0.13
0.13
0.13
0.25
0.40
0.47
0.34
0.49
1.12
0.87
0.36
100
0.11
0.13
0.13
0.12
0.25
0.39
0.50
0.36
0.48
1.16
1.15
0.43
60
0.16
0.15
0.17
0.15
0.32
0.47
0.57
0.40
0.58
1.37
1.12
0.44
40
0.18
0.20
0.21
0.21
0.39
0.64
0.79
0.59
0.71
1.73
1.40
0.62
20
0.27
0.31
0.33
0.32
0.61
0.91
1.18
0.79
1.08
2.60
2.21
0.91
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 β value for the faults (second iteration) that balances the three
equations. The result is the distribution of seismic potential between the
zone and the faults in the interval [MMin, MMaxC].
Considering that the faults may generate events with magnitudes larger than
MMaxC, the corresponding distribution of seismic potential in the
interval (MMaxC , MMax(fault)] is calculated by extrapolating the
recurrence model with the last adjusted β value (Fig. 4).
Regarding the MMax value expected for the zone (MMax(zone)), this
can be considered equal to MMaxC or extended to a higher-magnitude
value if it is assumed that bigger events can occur in other unidentified
sources (such as blind faults).
Analysis of uncertainty
The proposed approach strongly relies on computing seismicity, earthquake
rates and moment rates, within the magnitude interval [MMin,
MMaxC] of the seismic catalogue that contains the complete record of
events that have occurred in the entire region.
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 (b value).
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 b values that could be
representative of areas of low-to-moderate seismic activity.
The procedure consists of five steps:
generating 2000 synthetic catalogues for different combinations of
earthquake rates, magnitude intervals and b values;
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.
Table 1 shows the coefficient of variation (COV; the standard deviation/mean)
associated with each combination: number of events, magnitude
interval and b value. As can be seen, the greater the number of records in
the sample and the lower the magnitude range, the lower the uncertainty
associated with the rate of seismic moment calculated. The b value presents
a different trend, recording the greatest variability for b values
between 1.0 and 1.5. This table is useful for estimating the uncertainty of the seismic-moment rate calculated from the seismic catalogue as a function of the
number of earthquakes, magnitude interval and b value.
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 ±1 mm yr-1 in a slip rate of ±2 mm yr-1
represents an uncertainty of 50 %, leading to a COV value of 0.5
at the moment rate of the fault. However, the same deviation (±1 mm yr-1)
for a fault with a slip rate of ±10 mm yr-1 represents an
uncertainty of 10 %, leading to a COV coefficient moment rate of only 0.1 for the fault.
Application of the approach in south-eastern Spain
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-1 (Argus et al., 1989) in a roughly NNW–SSE
direction. Crustal deformation is accumulated over a broad area in which
seismicity is diffuse (Benito and Gaspar-Escribano, 2007).
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 M 5.2 Lorca event generated in the Alhama de Murcia fault system
(Cabañas et al., 2011), other events have occurred in areas where there
are no mapped active faults, for instance the 2007 Mw=4.7 Pedro Muñoz
and 2015 Mw=4.7 Ossa de Montiel earthquakes, both located in central Spain
(QAFI database, García-Mayordomo et al., 2012).
Source input data
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 μ=3.2×1010 Pa is
assumed for the shear modulus (Walters et al., 2009; Martínez-Díaz et al., 2012).
Seismic rate and seismic-moment rate recorded in the different regions
for two magnitude intervals (MMin–MMax) and (MMin–MMaxC)
obtained from the seismic catalogue. The table includes the ratio of seismic-moment rate of the two intervals, indicating what percentage of the seismic
movement rate liberated from Mmin to Mmax is contemplated
in the magnitude intervals over which hazard is distributed (MMin–MMaxC).
Note that no faults have been catalogued within regions 28, 29, 33 and 40, which
is why no values have been assigned (–).
Region
MMin
MMax
MMaxC
MMin–MMax
MMin–MMaxC
% M˙o recorded in
N˙ (4.0)
M˙o
N˙ (4.0)
M˙o
complete periods
(Nm yr-1)
(Nm yr-1)
28
4.0
5.4
–
0.211
1.90×1022
–
–
–
29
4.0
6.2
–
0.176
7.90×1022
–
–
–
30
4.0
4.6
4.6
0.053
1.86×1021
0.053
1.86×1021
100 %
31
4.0
6.5
5.7
0.241
7.88×1022
0.239
4.70×1022
60 %
33
4.0
5.4
–
0.082
1.41×1022
–
–
–
34
4.0
6.3
5.5
0.219
3.28×1022
0.218
2.56×1022
78 %
35
4.0
6.5
5.5
0.574
8.73×1022
0.570
7.09×1022
81 %
36
4.0
6.2
5.4
0.142
2.21×1022
0.141
1.41×1022
64 %
37
4.0
6.0
5.7
0.442
1.01×1023
0.440
9.07×1022
90 %
38
4.0
6.5
5.4
0.527
6.75×1022
0.525
5.70×1022
84 %
39
4.0
6.6
5.4
0.313
6.00×1022
0.308
4.30×1022
72 %
40
4.0
6.0
–
0.135
4.06×1022
–
–
–
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 Mw (IGN-UPM Working Group, 2013;
Cabañas et al., 2015). This catalogue contains 1,496 earthquakes, with
magnitudes ranging from 4.0 to 6.6. The uncertainty assessment of the
catalogue used in this study is explained in Gaspar-Escribano et al. (2015).
According to the completeness analysis, a MMaxC of 5.9 is estimated for
SE Spain (although not every region reaches this maximum-magnitude value).
The recurrence periods for magnitudes higher than 6 are too long to
allow us to establish completeness periods for these magnitude ranges (see Fig. 2).
Table 2 shows the seismic potential for each region, calculated in the
magnitude intervals [MMin, MMaxC] and [MMin,
MMax(region)]. It is observed that the seismic potential in the first
interval up to MMaxC, constitutes at least a 60 % of the seismic
potential in the second interval, up to MMax(region).
Subsequently, a recurrence model (GR-mod) is assigned to all regions,
obtaining the corresponding b values and COV coefficients (see Table 3).
Note that zone 30 lacks a COV estimate because the sample of records (only 7)
is very limited, and the [MMin, MMaxC] interval is very narrow,
resulting in increased uncertainty in the hazard estimates for this
region. A GR-mod recurrence model is also assigned to the faults. Finally,
the distribution of seismic moments among all seismic sources is carried out
(Table 4). As may be observed, the seismic-moment rate associated with the
zone has a strong influence on the estimated seismic hazard of the region.
This is due to the limited number of known active faults that can be
modelled as independent sources, a common situation in areas with low and
moderate seismic activity. However, it is worth noting that the seismic
potential of regions 35, 36 and 38 is dominated by the seismic potential of faults.
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.
Region
MMin
MMaxC
β-value
Record
COV
region
30
4.0
4.6
1.800
7
–
31
4.0
5.7
1.980
66
0.4
34
4.0
5.5
2.345
35
0.6
35
4.0
5.5
2.242
117
0.3
36
4.0
5.4
2.400
25
0.7
37
4.0
5.7
1.917
83
0.3
38
4.0
5.4
2.240
85
0.3
39
4.0
5.4
1.750
61
0.3
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 (Vs30=760 m s-1) conditions.
Seismic potential distribution of faults and zones. The last column
includes the percentage of regional seismic potential assigned to each source
within the region.
Region
Source
β value
N˙min
M˙o
(Nm yr-1)
30
Σ fault
1.700
0.0078
2.76×1020
15 %
zone
1.800
0.0451
1.58×1021
85 %
Total
0.0529
1.86×1021
31
Σ fault
1.950
0.0372
7.37×1021
16 %
zone
1.980
0.2017
3.97×1022
84 %
Total
0.2389
4.70×1022
34
Σ fault
2.250
0.0244
2.92×1021
11 %
zone
2.345
0.1932
2.27×1022
89 %
Total
0.2176
2.56×1022
35
Σ fault
2.186
0.3474
4.33×1022
61 %
zone
2.242
0.2227
2.77×1022
39 %
Total
0.5701
7.09×1022
36
Σ fault
2.330
0.0804
8.02×1021
57 %
zone
2.400
0.0603
6.08×1021
43 %
Total
0.1407
1.41×1022
37
Σ fault
1.900
0.1247
2.57×1022
28 %
zone
1.917
0.3152
6.50×1022
72 %
Total
0.4399
9.07×1022
38
Σ fault
2.180
0.3269
3.55×1022
62 %
zone
2.240
0.2131
2.15×1022
38 %
Total
0.5400
5.70×1022
39
Σ fault
1.820
0.1005
1.35×1022
31 %
zone
1.750
0.2077
2.96×1022
69 %
Total
0.3082
4.30×1022
Results
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 [MMin, MMaxC] is very small and it is
necessary to extrapolate the model to a larger scale, given the high
uncertainty shown in Table 3. However, the results reflect that, for longer
periods, these slow faults play a relevant role in the seismic hazard of the
region (see Fig. 8), where the HM hazard curve reflects a substantial
increase in hazard for long return periods.
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 (a) the
proposed hybrid approach and (b) classic zone methodology. Note the
fault proximity effects in (a) for these faults: (1) Carboneras Fault,
(2) Alhama de Mucia Fault, (3) Carrascoy Fault, (4) Bajo Segura Fault,
(5) Mijas and Cartama faults, (6) Zafarraya Fault and (7) Baza Fault.
![]()
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.
Discussion
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 Mc that separates the magnitude range in which faults and
zones produce earthquakes, as in the works of Frankel et al. (1996).
Comparison of seismic hazard results from the two models (HM and CM) for
return periods of (a) 475 and (b) 4975 years.
![]()
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 MmaxC is crucial
for adequately limiting this distribution: a low MmaxC value leads to a notable
extrapolation of the recurrence model for faults with large rupture planes;
a high MmaxC value may not ensure the complete record of all events of that
magnitude. In applying the method to SE Spain the MmaxC value identified is 5.9,
which may seem too low. However, this value is consistent with the
low–moderate level of seismicity in the study area. In fact,
the IGN seismic catalogue (http://www.ign.es/web/ign/portal, last access: 20 October 2018)
does not contain any shallow event with magnitude equal to or higher than 6.0
in the instrumental period.
In addition, for the purposes of hazard calculations, the distribution of
seismic potential for the entire magnitude interval (between the Mmin and
the Mmax values expected for each source) requires and is dependent on the
selected recurrence models to represent fault and zone activities. In this
regard, different types of recurrence models may be used: modified
Gutenberg–Richter, truncated Gutenberg–Richter (Gutenberg and Richter,
1944), or the models proposed by Main and Burton (1981), Chinnery and
North (1975) and others. The use of one model versus another depends on
each application and on the available data.
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).
Conclusions
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 β value.
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.