Consequences of large earthquakes affect all aspects of human life , both by direct and indirect effects . Characterization of seismic hazard allows us to prevent and mitigate the devastating effects of earthquakes. The development of a Probabilistic Seismic Hazard Assessment (PSHA) through a statistical analysis of the occurrence of earthquakes, leads to the determination of exceeding probabilities for different ground motion levels . The results derived from a PSHA are used in the definition of seismic actions in building codes e.g., which makes them of crucial importance in the protection of human lives and the limitation of damages.

Recorded seismicity is the fundamental input data of PSHA, in which the so-called Gutenberg-Richter relationship and the maximum magnitude of the earthquake catalogue describe the seismic activity of a region. Gutenberg-Richter relationship is calculated fitting to a log-linear equation the cumulative magnitude distribution of an earthquake catalogue (Eq. ). 1log10N(M)=a-b⋅M where N(M) represents the number of earthquakes with magnitude equal to, or higher than M, a is the annual activity rate of earthquakes and b is slope of the function, which depends on the relationship between the number of large and small events.

The probability density function associated with the Gutenberg-Richter relationship (fM(M), Eq. ) describes a dependence with the minimum magnitude. This magnitude can be considered as the magnitude of completeness, Mc, from which all seismicity is assumed to have been recorded. 2fM(m)=1-e-β(M-Mc)Mc≤M≤∞ In Eq. (), β represents another way of expressing the slope of the Gutenberg-Richter relationship (Eq. ). 3β=b⋅ln⁡(10)

Most of the implementations of the Gutenberg-Richter equation on PSHA are by means of the truncated, or modified, relationship , in which probability density function (fMt(M), Eq. ) depends also on Mmax. In this case, Mmax is considered to be the maximum possible value of the earthquake magnitude. This approximation avoids the overestimation of the mean return period of the largest earthquakes of the general Gutenberg-Richter exponential relationship.

4fMt(m)=1-e-β(M-Mc)1-e-β(Mmax-Mc) At slow-moving fault systems, with tectonic deformation rates of less than 2 mm yr⁻¹ and seismic cycles of thousands of years, recorded seismicity is usually moderate . An example is the case of SE Spain. In this region, seismicity is low to moderate, even though the EBSZ fault system has the potential to generate large earthquakes .

Paleoseismological studies have shown that the time interval between major earthquakes at the EBSZ single faults is of the order of several thousands of years . Meanwhile, the historical and instrumental record used in hazard studies at SE Spain, barely covers a thousand years: from 1048 to the present . This period is shorter than the seismic cycle of the faults. For example, in the case of the Carrascoy fault, the interval between large earthquakes is estimated to be of three thousand years . Consequently, historical and instrumental record covers just one-third of the seismic cycle at this fault. Meaning a narrow part of the seismic cycle, earthquake catalogues neither may record the entire seismogenic potential of faults nor changes in their behaviour. An example of the latter is the study carried out by in which fault slip rate variability has been proposed during the last 210 kyr in the case of the Carrascoy fault at the EBSZ. This variability can be related to accelerations of the system and interactions between adjacent faults, which can lead to the coexistence of short seismic cycles with large ones .

Characterization of slow-moving fault systems uses geological data to complement the scarce information about seismic activity. A better understanding of fault systems has turned into the inclusion of them as independent seismogenic sources in hazard studies around the world . According to , at cities located near active faults with recurrence intervals of 2 kyr, the inclusion of faults as seismogenic sources may represent a contribution of 10 %–30 % of hazard for return periods of 500 yr. Another approach has modeled the EBSZ as seismogenic source zone. To include the contribution of its main faults to a classical PSHA, a hybrid approach was used by defining an area source formed by the fault system .

Synthetic seismicity appears as another tool to address the limitations of seismic record . Computer models based on earthquake physics allow the creation of synthetic catalogues with the same characteristics as the instrumental ones but extended in time. Time expansion makes it possible to reproduce several seismic cycles and to evaluate different models of seismogenic processes . By using rate- and state- dependent friction numerical approach , it is also possible to simulate the physics of rupture processes of earthquakes . All of these features make synthetic seismic models useful for gaining a better understanding of earthquake occurrence, as illustrated in this study.

In this study, a classical PSHA methodology has been applied to 100 different 1 kyr long seismic catalogues extracted randomly from a 1 Myr synthetic catalogue of the EBSZ . Depending on the time interval of analysis, each catalogue is supposed to cover a different part of the seismic cycle of faults. To compare the results obtained, a PSHA is also carried out with data from the historical and instrumental catalogue. The results derived from these analyses will show how the calculation of seismic hazard depends on the time interval in which the seismic catalogue is recorded.

Southeastern Spain is characterized by weak to moderate seismicity . Nevertheless, it is considered the most seismically active region of the Iberian Peninsula , due to the convergence between the African and Eurasian plates . This study focuses on the Eastern Betic Shear Zone (EBSZ), located at the Betic Cordillera, specifically, at its Internal Zones. Betic Cordillera conforms the northern termination of the Rif-Betic Alpine orogenic belt . The EBSZ is an active deformation zone that conforms mainly left-lateral strike-slip faults oriented N-S to ENE-WSW . The main faults that constitute the system are (Fig. , Table ), from south to north: the Carboneras Fault (CF), the Palomares Fault (PF), the Alhama de Murcia Fault (AMF), the Los Tollos Fault (LTF), the Carrascoy Fault (CAF) and the Bajo Segura Fault (BSF). The mean slip rate of the system is estimated to be 1.5 ± 0.3 mm yr⁻¹ unevenly distributed across different faults.

The EBSZ is characterized by a moderate seismic activity, although it has produced many damaging earthquakes (Mw≥6.0) in historical times: 1048 Orihuela , 1482 OHerrerorihuela , 1487 Almería , 1518 Vera , 1522 Alhama de Almería , 1673 Orihuela , 1674 Lorca , 1804 Dalías , 1829 Torrevieja and 1910 Adra . The most recent damaging earthquake was the Lorca event of 2011, with Mw=5.1, which claimed nine fatalities and huge economic losses . All these major earthquakes have been associated with the faults of the area . For producing a PSHA of the region, the EBSZ has been modeled previously as a seismogenic zone which gathers the seismic features of the fault system.

In order to gain insight into the influence of the observation time interval on seismic hazard results at the EBSZ, we have resorted to the use of synthetic seismic catalogues. From a 1 Myr-long computed catalogue , we randomly selected ten thousand 1 kyr sub-catalogues to characterise the seismic hazard within a classical PSHA framework. These 1 kyr sub-catalogues were extracted to match the duration of the historical catalogue (spanning from 1048 AD and therefore approximately 1 kyr long). Each sub-catalogue represents a possible realisation of the long-term seismic process, allowing us to compare the hazard estimated from multiple stochastic 1 kyr realisations with that derived from the observed historical and instrumental seismicity, which can likewise be interpreted as a single realisation.

Synthetic seismicity consists of a million-year catalogue generated using RSQSim earthquake simulator. RSQSim simulations require a fault system model that includes a representation of the geometry, kinematics and frictional parameters of the fault segments. The implementation of the EBSZ in RSQSim is based on a fully-interacting 3D model built externally to the simulator. This model is composed of triangular cells of 1 km² resolution, allowing the simulation of events with magnitudes greater than Mw=3.0 and approximating some geometric complexities. Rate- and state-dependent friction parameters control the sliding resistance and are selected in this model following realistic relations between rupture area and earthquake magnitude. Seismic cycles are divided into several states (healing, nucleation and seismic rupture) that are passed by fault elements throughout the simulation. The evolution of stress, slip variation and state variable are controlled by analytical expressions that use event-driven steps. Mean slip rates of faults are used by the simulator to apply tectonic loading to the faults by the backslip method . The result of the simulations applied to this model is an earthquake catalogue characterized by a Magnitude Frequency Distribution (MFD) that tends to fit well with the historical and instrumental features. For more details on the physics-based model and the validation procedure of the best-fit catalogue, see , , and .

The historical and instrumental earthquake catalogue in SE Spain is compiled by the Instituto Geográfico Nacional (IGN, National Geographic Institute). It can be downloaded freely online . The earthquake catalogue provides information on the date, the location, and the magnitude of earthquakes. To conduct this study, it has been necessary to process the catalogue collected until 2022, since the last hazard studies were carried out in 2012. Originally, earthquakes were reported on heterogeneous magnitude scales. In order to obtain the size of earthquakes on the same magnitude scale, a homogenization process is needed. Using the equation proposed by , from a Reduced Major Axis Regression (RMA), the magnitudes mbLg and mb are converted to moment magnitude, Mw. Then, earthquakes with magnitudes smaller than Mw=3.0 are removed from the catalogue, since the equations of do not work in this range of values and the completeness of the catalogue cannot be guaranteed. In addition, earthquakes occurring at depths greater than 35 km are removed as they do not impact the seismic hazard .

According to the Poisson hypothesis , earthquakes must be considered as independent phenomena that occur randomly in time. For this purpose, a declustering process has been applied to the earthquake catalogue using a set of equations developed ad-hoc for the region (Eqs. , , and ). 5log(T)=0.6⋅Mw-0.7 for Mw<5.9 6log(T)=0.04⋅Mw+2.6 for Mw≥5.9 7log(L)=0.2⋅Mw+0.4 where T represents the time interval between earthquakes; Mw, the maximum magnitude of each cluster and L the linear distance that separates two earthquakes. Mw is determined by means of an iterative process in which the largest earthquake is selected from a cluster of related events. The declustering process allows differentiation between mainshocks and fore- after-shocks. Mainshocks are selected as independent events with information that is representative of the cluster. This procedure has been applied to both historical-instrumental and synthetic catalogues as is the common procedure on classical PSHA analyses.

The characterisation of the EBSZ as a seismogenic source is represented by the Gutenberg-Richter relationship and the maximum magnitude of each catalogue. Different scenarios for seismic hazard assessment have been generated using the Mersenne-twister random number generator and selecting intervals of 1 kyr from the general synthetic catalogue of 1 Myr. Each sub-catalogue is subjected to a PSHA, which results in an individual hazard curve for the selected sites.

The input data for the hazard calculation consist of the annual earthquake rate, the slope of the Gutenberg-Richter relationship and the maximum magnitude of each catalogue at the EBSZ. The seismic parameters of the seismogenic zones adjacent to the EBSZ zone are also required for the model. These data have been adopted from the ZESIS database (Table ). These parameters were obtained within the framework of the National Seismic Hazard Map project, following a process of declustering and magnitude homogenization of the earthquake catalogue . In that work, different zoning models and procedures for calculating the Gutenberg-Richter parameters were tested and eventually incorporated into the hazard calculations through a logic-tree approach. The maximum magnitude parameter was modelled using a normal probability distribution. The mean maximum magnitude and its standard deviation were derived for each zone based on criteria that balanced the available information on the presence and size of active faults and the magnitude of the largest historical events. Active fault parameters were obtained from the QAFI database which at that time was version 2. Several procedures were evaluated to convert fault-size parameters into moment magnitude using empirical relationships from the literature . Table shows the values referenced for the ZESIS model , which we adopt here.

For each scenario, a MFD has been created and adjusted to a Gutenberg-Richter power relationship using the maximum likelihood fitting technique (Eq. , ). 8b=log⁡10e(M‾-Mc) where M‾ describes the mean magnitude of earthquakes with a magnitude at least Mc, representing the magnitude of completeness of the catalogue.

The magnitude of completeness has been calculated using the Goodness-of-fit test (GMF, ). Maximum magnitude has been calculated, following the procedure of , as an average between the geological maximum and the maximum magnitude of each catalogue.

In the development of seismic hazard studies, a set of Ground Motion Prediction Equations (GMPE) is often used in combination with a logic tree. In this case, in which we are interested in the variation of results linked to the observation time window, we use a single GMPE, to avoid including more parameters that might condition the variability of the results. GMPE has been selected as the one derived by because it includes parameters that describe the behaviour of a fault system, such as the style of faulting and the depth of nucleation of earthquakes. Other studies of seismic hazard on the Iberian Peninsula had also chosen as GMPE .

Hazard curves reveal the estimated return period for different ground motion levels. Using three types of seismic parameters for the EBSZ: the ones that came from (1) synthetic seismicity, (2) historical and instrumental seismicity updated to the present and (3) ZESIS database, this study conducts a PSHA for six of the most populous cities in SE Spain (Fig. , Table ). Hazard curves have been computed using R-CRISIS software , which calculates seismic hazard using a fully probabilistic approach. Using seismic and geometric features of seismic sources, R-CRISIS performs a spatial integration by subdividing the original source. This procedure is based on the assumption that seismicity is evenly distributed over the area source . Considering the selected GMPE, R-CRISIS evaluates the exceedance probability at different values of ground motion at the selected sites. The probabilities of all the magnitudes and seismic sources are summed to obtain the total exceedance values. Exceedance values have been transformed into return periods. The results obtained consist of 100 curves from 100 synthetic catalogues, one curve for the historical and instrumental catalogue updated to the present, and one curve for ZESIS data. A hundred synthetic scenarios have been considered enough to show whether the variability within the time interval of analysis exists and to quantify it.

The main objective of this work is to examine the variability between subcatalogues with analogous characteristics derived from a single synthetic catalogue. This approach ensures that the epistemic uncertainties associated with their generation are common to all subcatalogues, making the differences observed in their comparison independent of those uncertainties. Since our study focuses specifically on the variability introduced by the observation time window, we have deliberately decided not to address other sources of epistemic uncertainty. These uncertainties have been previously explored in , from which the synthetic seismic catalogue used here originates.

Seismic hazard estimates depend strongly on the characterization and parametrization of the seismogenic sources model used. When the source model characterization relies entirely on the historical earthquake catalogue, the incompleteness of the data becomes a major limitation, as fault seismic cycles are usually longer. On slow-moving fault systems, such as the EBSZ, the historical and instrumental record only represents a small part of the seismic cycle and the occurrence of large earthquakes could have not been recorded yet. In this study, we have shown how the variability of the time interval of analysis leads to different results in seismic hazard assessment. For the selected calculation sites, the return period for different PGA values showed a strong dependency on the time window in which the catalogue has been recorded. The variation coefficient ranges from 11 % to 21 % for a PGA=0.04 g, and from 25 % to 58 % for a PGA=1 g. Using synthetic seismicity, this study evidences that there is a dependence in the quantification of seismic hazard with the time interval in which the earthquake catalogue spans.

The evaluation of a statistically representative set of 10 000 sub-catalogues reveals the recurrent appearance of large-magnitude events (Mw>7.2) associated with multi-fault ruptures. Although infrequent, these events reflect the long-term seismogenic behaviour emerging from the synthetic fault system, typically nucleating on the AMF and CF, which exhibit the highest slip rates within the EBSZ. Rather than implying a systematic dominance of large earthquakes in seismic hazard at engineering return periods, their presence highlights how rare events may significantly influence hazard variability when different observation time windows sample the seismic cycle unevenly.

At places where the geometry and behaviour of faults are well-known, synthetic models of seismicity can be built with confidence. This approach is especially useful in cases where systems have slow rates of deformation and seismicity is just low or moderate. In these cases, synthetic catalogues can reveal the inner variability of such systems and clarify the seismogenic potential of faults. Nevertheless, they are constrained to the quality of the geological knowledge available for the active faults present in the region. To better understand the models and their impact on seismic hazard, further investigations should focus on issues such as fault segmentation, structural development, frictional properties, and degree of coupling (aseismic deformation and secondary faulting).