Probabilistic Seismic Hazard Assessment of Lisbon (Portugal)

Abstract

The 1755 Lisbon earthquake holds significant historical importance in Portuguese history. The subsequent tsunami resulted in extensive destruction and damage, affecting not only Lisbon but also other regions of Portugal, Spain, and North Africa. This significant and hazardous event led to an increase in awareness about earthquake and tsunami risks, not only within Portugal but throughout Europe. This heightened awareness facilitated advancements in scientific developments, including design codes, standards, and earthquake engineering. However, recent studies focusing on hazard assessment for Lisbon are limited. For this reason, this paper aims to present a comprehensive probabilistic seismic hazard analysis (PSHA) for the Lisbon metropolitan area. The first stage of PSHA involves defining applicable and active seismic source models (area and line sources) within the study area. Subsequently, historical and instrumental earthquake records are collected to build a homogenized earthquake catalog, utilizing both global and local earthquake databases. Following this, the completeness level of the earthquake catalog is tested. By incorporating suitable ground motion models to the region and local soil characteristics, seismic hazard maps for various return periods and hazard curves in terms of peak ground acceleration (PGA) are developed. The findings based on the area source model agree with existing literature, indicating PGA values ranging from 0.3 g to 0.9 g, 0.2 g to 0.7 g, 0.2 g to 0.5 g, and 0.1 g to 0.3 g for return periods of 2475, 975, 475, and 50 years, respectively.

1. Introduction

Earthquakes are natural phenomena occurring in diverse geographical areas, distinguished by varying magnitudes determined by stress levels within the tectonic plates. Various regions, especially subduction zones like the Pacific Ring of Fire, the Andes Mountains in South America, the Japan Trench in the Pacific Ocean, and the Mariana Trench in the Western Pacific, are prone to experiencing devastating earthquakes. These events pose a threat not only to communities but also to historical buildings and heritage sites worldwide. Therefore, it is crucial to understand seismic vulnerability, potential hazard levels, and damage scenarios. This perspective leads to taking certain steps to minimize the damage and impact caused by earthquakes on both human lives and cultural heritage.

The initial stage of seismic risk assessment studies is the estimation of seismic hazard levels. To estimate hazard levels at any region, seismic hazard assessment is performed, which can be broadly classified into two main types: deterministic seismic hazard analysis (DSHA) and probabilistic seismic hazard analysis (PSHA) [1,2,3]. These methods aim to evaluate the potential seismicity of active seismic sources using a deterministic or probabilistic framework. The main difference between PSHA and DSHA regards their approach to analyzing the uncertainty about future earthquake occurrences [4]. DSHA considers a single scenario, whereas PSHA interprets all earthquakes with the available seismic source models by weighting the various models according to stochastic and statistical approaches. In a probabilistic framework, the probability of exceeding the level of any intensity measure in a given time interval at the selected site or structure can be assessed [5,6]. As a result of PSHA, hazard curves and, consequently, hazard maps can be obtained for any return period for the selected site of interest. Findings from PSHA provide useful information for national codes, design standards, and construction methods against earthquakes. Numerous studies in existing literature address either DSHA or PSHA in various global locations [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26].

As it is well known, there is always uncertainty in the time, location, and magnitude of the earthquakes in PSHA. For this reason, seismologists cannot estimate exactly where and when an earthquake will happen. However, predictions regarding the expected earthquakes can be made using scientific methods such as investigation of the fault traces, behavior, and type of the underground rocks, analysis of seismic waves, and measuring the deformation at the ground level.

Portugal experiences moderate seismic activity due to the Azores–Gibraltar Transform Fault and the Eurasian–African Plate Boundary. A seismic hazard assessment study is essential to evaluate the impact on historic masonry buildings, which hold cultural significance and unique architectural styles. Understanding local soil effects and structural vulnerabilities can help predict how these structures will respond to earthquakes. There are only a few studies focused on PSHA in Portugal [15,16,17,18,19,20,21,22,23,24]. The project that was initiated in 1992 and concluded in 1999 was the Global Seismic Hazard Assessment Program (GSHAP), reported by [15]. The primary aim of this project was to develop seismic hazard models for various regions worldwide, including Portugal. The novelty of that study is releasing the first global hazard map depicting PGA for a return period of 475 years. In 2002, the study by [16] employed a hybrid approach that combines both zonified (area sources) and non-zonified (smoothed seismicity) probabilistic methods to assess seismic hazards. This methodology integrates seismic sources within homogeneous zones, similar to zonified methods, while also considering earthquakes across the entire region, as in non-zonified approaches. Originally designed for seismic hazard mapping in the United States, this methodology has been adapted to address the unique seismic characteristics of the Iberian Peninsula and its surrounding areas. The results of this study reflect both historical seismicity and current seismic clusters, revealing significant regional variations in seismic hazards. Notably, the highest seismic hazard is observed in the southwestern Peninsula, particularly around Cape St. Vincent and Lisbon. The study also highlights that while the overall uncertainty is relatively stable, the results are sensitive to parameters such as the relative likelihood of large and small earthquakes (often called the b-value) and maximum magnitude of an earthquake (m_max) of the Gutenberg–Richter relation. The study by [17] conducted PSHA by considering two seismic scenarios, using two seismogenic area source models that align with these earthquake scenarios. Meanwhile, these authors performed catalog completeness and evaluation of earthquake activity parameters by considering the size of source models to minimize the uncertainty of large amounts of the dataset. They used the ground motion models (GMMs) of Ambraseys et al. [27], Toro et al. [28], and Atkinson and Boore [29], by incorporating a logic tree framework. Finally, they developed a mean hazard map for the return period of 475 years in terms of peak ground acceleration (PGA), which varies from 0.05 g to 0.20 g. Later, the study by [18] examined two scenarios in the development of seismic zonation for mainland Portugal. The first scenario considers offshore epicenters of earthquakes, while the second scenario focuses on inland epicenters. Two GMMs, namely Carvalho et al. [30] for the first scenario and Ambraseys et al. [27] for the second scenario, were utilized. The results in PGA for the return period of 475 years were presented with a range of 0 to 0.25 g and 0 to 0.18 g for earthquake scenarios one and two, respectively. There is also another project, which is the SHARE project (Seismic Hazard Harmonization in Europe) [19,20,31] developed to provide a harmonized seismic hazard model for Europe. The project classifies seismic zones based on a combination of geological, seismological, and geophysical data. Each zone is assigned a specific number for easy reference and consistency across different datasets and studies. For a detailed explanation of the classification methodology and zone numbering, readers are referred to refs. [19,20,31]. Finally, the most recent study by [24] addresses five key gaps in previous earthquake risk assessments for Portugal by developing a new probabilistic seismic risk model. It updates exposure data with the 2021 national housing census and includes commercial and industrial buildings. The study of [24] broadens risk metrics to include not only economic losses but also buildings lost, built-up area lost, fatalities, and homelessness, while extending geographical coverage to the Azores and Madeira. It also incorporates the latest seismic hazard models from the European H2020 SERA project and provides a uniform vulnerability assessment across building classes. The results highlight regions with the highest seismic risk, offering crucial insights for risk management and financial risk transfer.

The SHARE project, initiated in 2009 and concluded in 2013, was developed under the European Union’s Seventh Framework Programme (FP7) to create a consistent and harmonized seismic hazard model for Europe. The primary objective was to provide a common reference for seismic risk assessment and inform the revision of the National Annexes of Eurocode 8 [32], the European standard for earthquake-resistant design. The project involved a consortium of over 20 research institutions, universities, and geological surveys from across Europe, integrating state-of-the-art techniques and methodologies. These included the collection and analysis of extensive seismic data, the development of GMPEs, and the incorporation of geological, geophysical, and seismological information. Key outputs of the SHARE [19,20,31] project included detailed seismic hazard maps indicating the probability of various ground shaking levels, which serve as essential tools for earthquake preparedness, land-use planning, and infrastructure design. In the same year as the SHARE project, the study by [21] conducted PSHA for Portugal. A logic tree approach was utilized to account for epistemic uncertainties arising from various sources, including seismic zonation, earthquake catalogs, magnitude–frequency distribution methodologies, GMPEs, and site conditions. They also introduced two simplified methodologies to incorporate soil amplification effects due to varying soil conditions. Then, probabilistic hazard maps, presenting results for the mean as well as the 16th and 84th percentiles and their averaged results, were provided for rock sites, which shows that the highest seismic hazard is concentrated in the southern region of Portugal, particularly in the Algarve and Alentejo areas, where the PGA exceeds 0.18 g. The central and northern regions exhibit moderate to low seismic hazards, with the lowest values observed in the northeastern part of the country. The 16th percentile map represents a more conservative estimate of seismic hazard, showing lower PGA values across the country compared to the mean hazard map. Conversely, the 84th percentile map reflects a higher estimate, indicating more extensive areas with elevated PGA values, especially in the southern and central regions.

Recently, the study by [22] performed pb-PSHA, known as “physical-based PSHA”, which aims to establish a better alternative when seismogenic zones in GMMs are not well known for the regions. These authors generated a PGA map for the return period of 475 years with a range of 0.02 g–0.35 g for the mainland of Portugal. Reis et al. [23] examined the 1755 Lisbon earthquake regarding its cascade seismic and tsunami activity for the Sines deep-water seaport container terminal using DSHA. The findings regarding PGA were obtained as 0.37 g.

The 1755 Lisbon earthquake is a pivotal event in Portuguese history. The resulting tsunami caused widespread devastation, impacting not just Lisbon but also other parts of Portugal. An extensive review of the literature indicates that most of the research has concentrated on mainland Portugal. However, existing literature highlights a gap in comprehensive analysis concerning Lisbon. This gap pertains to an in-depth PSHA that incorporates an up-to-date catalog of seismic events and sources, particularly for the historical center of Lisbon.

This paper aims to conduct a comprehensive PSHA for the Lisbon metropolitan area. The study begins by defining relevant and active seismic source models (area and line sources) within the research region. Next, historical and instrumental earthquake records are compiled to construct a homogenized earthquake catalog from both global and local earthquake databases. A catalog completeness test is then performed to establish the level of completeness of the earthquake data. By integrating appropriate GMMs with local soil characteristics, seismic hazard curves and subsequently hazard maps for various return periods are generated in terms of PGA. The results are ultimately evaluated against existing literature.

2. Study Area: Metropolitan Area of Lisbon (MAL)

The capital of Portugal, Lisbon, is known as the biggest and most crowded city of Portugal and is situated on the western coast of the Iberian Peninsula in Southern Europe (see Figure 1). The city neighbors the Tagus River, which flows into the Atlantic Ocean. Its metropolitan area comprises 18 municipalities and almost 3 million inhabitants [33], with a population density of 950 inhabitants/km² [33]. Next, the seismicity and tectonic activity of Portugal are introduced.

2.1. Historical and Instrumental Seismicity of Portugal

Throughout its history, Portugal has suffered from earthquakes, including some of significant magnitude and devastating consequences [35,36,37,38]. The country exhibits a moderate level of seismic activity, which is characterized by the frequent occurrence of small-magnitude earthquakes with magnitudes below 5.0, as well as occasional moderate-to-large events with magnitudes ranging from 5.0 to 7.8 [39]. Several studies in the literature demonstrate major historical and instrumental earthquakes happened throughout the mainland of Portugal and its adjacent regions [39,40,41,42,43,44,45]. According to seismicity between 1988 and 1997 and the most significant events between 1344 and 1970 in Portugal, the concentration of small events (M < 5) is observed along the Algarve coast and its neighboring parts based on the study by [39]. On the other hand, the southern part of Portugal has experienced and is expected to continue experiencing large-magnitude earthquakes. Conversely, the northern and central parts of the country are characterized by low seismic activity, with the exception of the Lower Tejo Valley. In this region, there are three significant historical records of earthquakes: one with a magnitude of M_s = 6.0 in 1344, another with a magnitude of M_s = 7.1 in 1531, and a third series of events with magnitudes of M_w = 6.0 and M_s = 5.9 in 1909, as also documented in Figure 2 from the study by [39].

Despite the earthquake events, due to the lack of seismic networks, their documentation lacks detail regarding their magnitude, date, and location. As a result, earthquake records remain scarce with incomplete studies on historical seismic activity [46]. One of the most significant earthquakes that caused severe damage and casualties in Portugal is known as the 1755 Lisbon earthquake. This event did not only affect Portugal, but also all of the Iberian Peninsula and Morocco directly. Apart from its destruction, the water waves caused tsunamis on Portugal, Spain, and Morocco’s coasts. This earthquake may have been considered the first recorded event in history that could provide valuable insights into numerous scientific and technical aspects associated with it [47].

The study by [48] proposed a framework to describe the development of the earthquake catalog for the country, and this study revealed the improvements in the Portuguese earthquake catalog over the centuries. The main findings according to [48] are:

• Before the 18th century, the catalog was lacking events, including determination of seismic sources, origin, and identification of seismic proceeding, etc.
• The maximum magnitude of earthquakes within centuries indicates the most destructive earthquake recorded in the 4th century BC with an intensity of IX, then the 1755 Lisbon earthquake happened with an intensity of VIII.
• The distribution of the minimum magnitude of earthquakes by century depicts the improvement of the Portuguese earthquake catalog since there is a remarkable enhancement in the recording of minimum magnitudes of earthquakes after the 16th century.
• The 19th century is the one that registered the lowest intensities of earthquakes.

Later, the study by [42] also identified seismicity, including 175 records in the mainland territory of Portugal over the years between 1300 and 2014 and described the region’s seismicity in terms of hazard level. Additionally, the study of [42] categorized the catalog into two classes, namely, frequent small events with magnitudes of M < 5.0 and infrequent large magnitudes of 5.0 ≤ M ≤ 7.8. The authors developed a maximum observed intensity map (MOI) I0 (with intensity ≥ V) in terms of the Modified Mercalli Intensity scale (MMI) based on the seismicity that happened between 1300 and 2014 within the mainland of Portugal. The regions of Lisbon and Algarve experienced the highest intensity of earthquakes in terms of MMI. It should also be noted that the MOI map does not employ maximum experienced ground motions, and earthquakes are derived from available literature, including historical and instrumental earthquakes, summarized in

Table 1. Earthquakes in Portugal and its adjacent Atlantic Margin between 1300 and 2014, with maximum observed intensity (Modified Mercalli Intensity Scale) I0 ≥ VIII (taken from [42]).

Date	Longitude	Latitude	I0	M
22 February 1309	−11.0	36.0	VIII–IX	-
01 January 1344	−8.8	38.9	VII–VIII	-
1353/-/-	−8.1	37.3	VII–VIII	-
24 August 1356	−10.7	36.0	VIII–X	-
28 January 1512	−9.2	38.7	VIII	-
26 January 1531	−9.0	38.9	IX	-
November 1578	−8.0	37.1	VII–VIII	-
27 December 1722	−7.6	37.2	VIII	-
01 November 1755	−10.5	37.0	X	$M_W=8.5$
12 January 1856	−8.0	37.1	VII–VIII	-
11 November 1858	−9.0	38.2	VIII	$M_s=8.5$
23 April 1909	−8.8	39.0	X	$M_W=6.0$
11 September 1910	−7.8	38.8	VII–VIIl	-
15 March 1964	−7.9	36.1	VII	$M_s=6.2$
23 April1969	−10.9	35.9	VIII	$M_s=8.0$
28 February 1969	−10.84	35.95	VII	$M_W=8.2$
12 February 2007	−10.5	35.9	V	$M_L=5.9$
17 December 2009	−9.9	36.5	V	$M_L=6.0$

. Notably, the 1969 Portugal earthquake (M_w = 8.2) stands as the most significant instrumental record in Portugal since the 1755 Lisbon earthquake.

2.2. Tectonic Activity of Portugal

According to the study of [49], the mainland of Portugal is characterized by three significant geological units, including the primordial Iberian Tableland, the western and southern Meso–Cenozoic margins, and the Neogenic basin of the rivers Tagus and Sado (see Figure 3). The complexity of the region is associated with the interaction between the Atlantic Ocean, which contributes to the formation of basins and horsts through the presence of openings. Furthermore, submergence is still observed in the territory [49]. It is also worth noting that the country lies in a continental margin where there is an interaction between the Eurasian and Nubian (located in northeastern Africa) plates, which directly affects its tectonic activity, leading to the formation of both intraplate and interplate earthquake zones [41]. While a continental margin, specifically the southern part of the region, is linked with a North-Atlantic opening that moves north-south, another boundary, namely the Azores–Gibraltar fault zone, runs towards east-west [50]. In literature, several studies, including [50,51], focused on the Azores islands in terms of their tectonic setting, focal mechanism, and seismic activity. According to the study of [50], the Azores–Gibraltar region, which passes through the Eastern-North Atlantic Ocean, is particularly characterized by a thrust-type faulting mechanism. This region is influenced by a compressive plate boundary. On the other hand, the intersection between Eurasian–African plates is considered the formation of subduction zones at Gorringe and Guadalquivir submarine banks, which is perhaps the convergence of those plates based on the study of [52]. Additionally, Ref. [53] proposes that the continental margin towards the western part of the Iberian Peninsula may be undergoing a transition from a passive state to an active state, which indicates the potential initiation of subduction from the south to the north in the offshore regions of Portugal.

It is also worth mentioning that the epicenter of the 1755 Lisbon earthquake could potentially be associated with this plate boundary, particularly in close proximity to Gorringe Bank. Moreover, according to the study of [39], there is a significant fault called the Messejana fault (MJ) that spans 500 km across the entire southern region of Portugal, exhibiting a northeast–southwest (NE–SW) orientation. This fault is likely connected to the Azores–Gibraltar fault. Furthermore, the Lower Tagus Valley (LTV) is renowned for its ability to generate a substantial seismic hazard, as stated by [54]. Situated in the SW Iberia region, which has a significant population, the LTV rests on a passive continental margin. However, due to the convergent relative motion between Africa and Eurasia, the region becomes susceptible to earthquakes, as highlighted by [45]. Three significant earthquakes, namely Setúbal in 1858 and two earthquakes in 1722 and 1856 that occurred in Algarve and Ribatejo, are believed to be associated with nearby faults or fault segments, namely the Alcochete Fault, Vila Franca Fault, Azambuja Fault, and Asseca Fault. The study of [45] partially mapped the Alcochete and Vila Franca faults using seismic reflection data. However, the exact extension of faults such as Azambuja and Asseca remains uncertain. Nevertheless, the study of [45] proposes a length of 100 km for these faults. LTV lies in a transitional zone between interplate and intraplate activity, which has the potential to generate large offshore earthquakes with large magnitudes.

Another noteworthy seismic zone is situated in the Algarve, which is characterized by a compressive tectonic regime. The Algarve region involves several important faults, namely the north–south-oriented Portimão Fault, Monchique Fault, north–south-oriented Albufeira Fault, São Marcos–Quarteira Fault [55], and the Loulé fault (LF), located with an approximately WE orientation [39]. Also, the western coastal area of Algarve has consistently witnessed the highest levels of seismic intensities. However, as one moves northward or north–eastward, these intensities noticeably decrease [52].

The Lower Sado Valley has another seismic source zone on mainland Portugal that exhibits moderate seismicity, with the occurrence of small to moderate earthquakes. Although larger-magnitude events are less common in this region compared to the southern part of Portugal, there is still observable seismic activity. The precise characteristics, such as historical records, magnitudes, and frequency of earthquakes in the Lower Sado Valley, may vary. Finally, the city of Évora, located in the central part of Portugal in the region of Alentejo, includes a main tectonic structure known as the Moura–Vidigueira fault, characterized by a WNW–ESE strike.

3. Probabilistic Seismic Hazard Analysis

3.1. Methodology and Definition of Input Parameters

The first numerical formulation of PSHA was developed in 1968 by [6], and the methodology has been followed by many studies such as [56,57,58,59]. In PSHA, all potential earthquakes are interpreted, taking into account their resulting ground motion levels and the likelihood of their occurrences. Instead of searching for a worst-case scenario, PSHA estimates the probability of different levels of ground motion intensity being exceeded within a certain time frame and at specific locations. In order to provide an overview of the PSHA process and its outcomes, a framework is depicted in Figure 4, and the main steps of PSHA used in this study are outlined as follows:

(a)

Definition of seismicity: The first step of PSHA requires a collection of events occurring within a specific timeframe and location, along with their associated information, such as magnitude, time, location, depth, etc. These events may include both instrumental and historical records.

In this stage, seismic activity data are gathered from several earthquake catalogs, including Instituto Português do Mar e da Atmosfera (IPMA) [60], Instituto Geográfico Nacional (IGN) [61], United States Geological Survey (USGS) [34], International Seismological Centre (ISC) [62], National Earthquake Information Center (NEIC) [63], and Global Centroid Moment Tensor (GCMT) [64]. IPMA [60], considering the beginning of the instrumental era for Portugal (since 1961). Due to varied magnitude scales across earthquake catalogs, one of the challenges is in the process of homogenization of earthquakes. The IGN [61] in Spain employs different magnitude types, further complicating catalog construction. A study by [65] divides the earthquake catalog into three sub-periods, each linked to specific magnitude types, including L_g magnitude and body wave magnitude m_bLg(MMS), m_bLg(L), and m_b(VC). For this study, the M_w scale is chosen as the primary magnitude scale, with all data converted accordingly using formulas adapted from [65] (see

Table 2. The IGN [61] catalog including earthquake magnitude scale, along with their corresponding notation and periods of use adapted from [65].

Size Parameter	Definition	Period
$m_{bLg\left(MMS\right)}$	Lg magnitude	1962–2002
$m_{b\left(VC\right)}$	Body wave magnitude	1998 to date
$m_{bLg\left(L\right)}$	Lg magnitude	2002 to date
$M_W\left(IGM\right)$	Moment magnitude (calculated by IGM)	2002 to date

and

Table 3. Empirical magnitude conversion equations adapted from [65].

$\mathit{Y}=\mathit{a}+\mathit{b}\mathit{x}$	Magnitude Range
$M_W=0.290+0.973m_{bLg\left(MMS\right)}$	3.1–7.3
$M_W=-1.528+1.213m_{b\left(VC\right)}$	3.7–6.3
$M_W=0.676+0.836m_{bLg\left(L\right)}$	3.0–5.4

).

The earthquake catalogs from USGS [34], ISC [62], NEIC [63], and GCMT [64] is harmonized using the provided equations as given in Table 3. For the magnitude scales, including surface wave magnitude and local magnitude ($M_S$ and $M_L)$, the following formulas are employed [66,67]:

$$log{M}_0=24.66-1.083M_s+0.192{M_s}^2 for M_s\ge 3.6,$$

(1)

$$log{M}_0=1.5M_L+16 for 3.0\le M_L\le 7.0,$$

(2)

$$M_W={\displaystyle \frac{2}{3}}log{M}_0-10.7,$$

(3)

The conversion of magnitude methodology aligns with a prior PSHA study [45] for mainland Portugal. In summary, this approach ensures a standardized seismic catalog for PSHA in mainland Portugal, aligning with established practices. Herein, it is important to note that a minimum threshold magnitude of 3.5 has been assigned for the PSHA framework. Figure 5 presents 3047 instrumental records corresponding to all earthquakes that occurred between 1961 and 2023, along with historical records before 1961. It is worth noting that the literature on historical earthquakes in Portugal predominantly provides information in terms of intensity level.

Once different magnitude scales are converted into $M_W$, a composite earthquake catalog is created by eliminating duplicates from different earthquake catalogs. Herein, it is important to note that different earthquake catalogs may provide the same earthquake with varying locations and magnitudes due to several factors related to the data collected by seismographs and the methodologies used to process that data. The variations in reported earthquake locations and magnitudes across different catalogs are a result of differences in seismograph network density and distribution, data processing algorithms, velocity models, magnitude estimation methods, and the availability of data. These differences highlight the importance of using multiple sources to get a comprehensive understanding of seismic events. The algorithm developed for this study prioritizes the selection of the $M_W$ scale for earthquakes when it is available. In cases where $M_W$ is not provided, the algorithm converts other magnitude scales to $M_W$ using the previously mentioned empirical equation. To determine the final magnitude, the algorithm selects the highest converted value. For the earthquake’s location, the algorithm evaluates the latitude and longitude coordinates provided by different catalogs. When the coordinates from different catalogs are in close proximity, the algorithm assigns the earthquake’s location based on the most frequently repeated coordinates among the various catalogs. The next step involves performing a declustering analysis, which consists of two steps: pre-processing and magnitude-dependent filtering. The pre-processing step focuses on eliminating fore/aftershocks by applying a declustering process based on time and space windows determined by the methodology proposed by [68]. This methodology incorporates time and space window approaches derived from previous studies [69,70]. The second step involves considering all events with magnitudes larger than 6.0 as main shocks. It should be noted that a certain level of uncertainty is involved in distinguishing between fore/aftershocks using the approach developed by [68], which identifies 2049 mainshocks. Finally, Figure 6 presents all the mainshocks in the study area.

Historic seismic data often suffer from incomplete records due to limited observational technology and sparse data collection practices. This lack of comprehensive seismicity information can lead to gaps in understanding the true earthquake activity of a region. Stepp’s completeness test [71], developed in 1972, plays a crucial role in addressing these limitations by assessing the reliability and thoroughness of earthquake catalogs. By analyzing the magnitude–frequency distribution of recorded earthquakes, Stepp’s method [71] identifies the point at which the catalog becomes complete for earthquakes of a certain size. This allows researchers to validate whether the historical data accurately reflects the region’s seismic activity or if smaller events may be underrepresented. Consequently, Stepp’s test helps adjust for historical data gaps and improves the reliability of seismic hazard assessments. For this reason, to determine the completeness level of the earthquake catalog, the algorithm by [71] is adopted. The main goal of the completeness test is to determine whether the catalog includes all significant earthquakes within a given time period and region. To do this, the test analyzes the magnitude–frequency distribution of earthquakes, looking at how many earthquakes of different sizes are recorded. By plotting these data, the test identifies a completeness threshold (the smallest earthquake size that is consistently recorded). This threshold helps to ensure that the catalog is accurate and that all relevant earthquakes are included. As a result of this approach, the findings reveal that the number of earthquakes ranging from 3.5 to 4.0 magnitude exhibited a noticeable peak after 2001, while the 4.0–4.5 magnitude range experienced similar behavior in 1998. Furthermore, the cumulative number of earthquakes in the 4.5–4.9 and 5.0–5.4 magnitude ranges has shown consistent increases since 1985 and 1973, respectively. Conversely, the remaining magnitude classes do not display any discernible peak response, suggesting they are relatively complete datasets. This is also depicted in the graph provided by Figure 7.

The mean rate of occurrence is defined by the Poisson process as follows:

$$\lambda ={\displaystyle \frac{1}{n}}\sum _{i=1}^n{k}_i$$

(4)

where $k_1$, $k_2, k_3$,… $k_i$ are the number of earthquakes per unit time interval ($n$). $\lambda$ represents the mean rate of occurrence, which is computed through dividing the number of earthquakes by the interval years.

The variance of the mean rate of occurrence, ${{\sigma }_{\lambda }}^2$ is evaluated by the following equation based on the study of [71]:

$${{\sigma }_{\lambda }}^2=\lambda /T,$$

(5)

The unit time interval of one year provides the standard deviation of the estimate of the mean ${\sigma }_{\lambda }$, as follows:

$${\sigma }_{\lambda }=\sqrt{\lambda /T},$$

(6)

where $T$ represents sample length in years.

Finally, Figure 7 presents the stability of the mean rate of occurrence for each magnitude class. The y axis refers to ${\sigma }_{\lambda }$(standard deviation of the estimated mean of the cumulative number of events), which is calculated using Equation (6). The graph includes fitting lines that are plotted based on the defined years for each magnitude class’s level of completeness. The mean rate of the magnitude class within that time interval is fixed to establish the trendline. Figure 8 shows that the magnitude classes of 3.5–3.9 and 4.0–4.5 begin to align with the trendline within the last 30 years. Similarly, the magnitude class of 4.5–4.9 starts conforming to the fit line within the last 40 years. The magnitude class of 5.0–5.4 shows a fit with trend line 4 over the past 50 years. On the other hand, the remaining magnitude classes, including 5.5–6.0, 6.0–6.5, 6.5–6.9, and 7, are considered complete and maintain consistency over the past 59 years. It should be noted that the magnitude class ≥ 7 overlaps with the 6.5–6.9, which implies the same behavior.

(b)

Definition of seismic sources: Identifying all potential seismic sources within a chosen site, which can be in the form of point, area, or line sources (faults). The goal is to characterize their mechanism types, slip rates, dip angles, and other relevant attributes. Additionally, the process involves eliminating inactive seismic sources, known as “dead” seismic sources, which are no longer capable of generating tectonic activity within the study area.

For the scope of PSHA, a comprehensive literature review is conducted for the mainland of Portugal, and several seismic sources, including area source models and line source models, are found in the literature [15,41,72,73]. These source models partially or entirely cover the study area. Therefore, seismogenic zones that fall entirely within the study area are directly taken for this research. In contrast, those that partially cover or exceed the study area boundaries are adjusted based on seismic activity to determine each activity parameter.

A total of 16 zones are involved in the SHARE source model [19,20,31], which is plotted in Figure 9a. The required adjustments, including rescaling of Source Nos 262, 255, 254, 250, 254, 253, 248, 247, 244, 243, and 0, were made in this model to make the Share model [19,20,31] compatible with the study area. The final form of the SHARE Model [19,20,31] consists of 15 areal sources, as shown in Figure 9b, which depicts that most of the seismicity occupies zones 253, 247, and 254.

The study of [41] identified and correlated some significant historical and instrumental earthquakes with the geographical and tectonic features of the region. The line source model is shown in Figure 10a. These faults and fault traces are also described in the QAFI Database [73] with related information about their associated parameters: geometric, kinematic, quaternary activity, slip rate, paleo earthquakes, and seismic parameters. For this study, the line source models by [41,73] were adapted. Also, Figure 10b shows the line sources model with assumed potential area sources (PASes) within the region along with the past earthquakes. A PAS is employed in PSHA for regions with seismic activity without specific information about faults or tectonic regimes. A polygon is modeled based on the area’s observed seismic activity and considered a potential area source in such cases. This study defines six PASes within the region where no active faults have been identified. While modeling these polygons, the mechanism types of the seismogenic sources are considered to be aligned with the tectonic regime.

To sum up, two types of seismic source models are employed in PSHA analysis. The first model is the areal model, adapted from the area sources model. This model assesses seismic hazards from distributed sources over an area. The second model is the line sources combined with the defined six PASes. This model accounts for seismic hazards associated with specific fault lines with their characteristics and for unspecified regions without information regarding faults. Combining these two models achieves a more comprehensive and accurate assessment of seismic hazard, considering both distributed area sources and specific fault lines within the region. In order to provide a more detailed account of the geological and physical characteristics of the source models,

Table 4. Instrumental and historical earthquakes within the area sources of SHARE model [19,20,31].

Source	Mechanism	Max-Mw-Instrumental	Max-Mw-Historical
247 *	Interplate	6.6	1722-6.5
253 *	Intraplate	7.8	1755-8.5
246 *	Interplate	5.0	-
245 *	Intraplate	5.2	-
242 *	Intraplate	5.3	1858-6.8
251 *	Intraplate	5.0	1531-6.5
249 *	Intraplate	4.7	-
0 *	Intraplate	5.0	-
244 *	Interplate	5.6	1724-7.0
250 *	Intraplate	4.7	-
255 *	Intraplate	5.3	-
243 *	Interplate	5.4	1857-6.5
262	Interplate	5.1	-
254 *	Intraplate	6.4	1773-6.1
248 *	Interplate	4.9	-

* The sources located within a 300 km radius from the center of the selected site. Bold: These specific sources are highlighted in bold in Table 4 and Table 5.

and

Table 5. Overview of fault mechanisms in the region and predicted maximum earthquake magnitudes, based on instrumental and historical data, and the magnitude empirical equations proposed by [75].

Fault Name	Mechanism	Length (km)	Max-Mw-Instrumental	Max-Mw-Historical	Mw-W&C
CPR	R	83	5.3	1915-6.3	7.3
CW	RLSS	66	5.5	-	7.2
HO *	R	109	7.8	1755-8.5	7.5
SWIM-1	RLSS	282			7.9
GoB *	R	161	5	-	7.7
SWIM-2	RLSS	130	4.6	-	7.5
PT *	LLSS	150	4.9	-	7.6
SL *	R	95			7.4
PRV *	LLSS	220			7.8
MVB *	LLSS	205			7.7
NCRV *	LLSS	160			7.6
MP *	R	66	4.9	-	7.2
PBT	R	100	4.7	-	7.4
Po *	LLSS	34	5.2	-	6.9
EsO *	RLSS	30			6.8
La *	LLSS	13			6.4
Alb *	R	20			6.6
AST *	R	89			7.4
Qu *	R	65			7.2
SE *	RLSS	40			7.0
NJ	N	5	5.2	-	5.8
Ma	N	11			6.2
AP *	LLSS	138	4.4	-	7.6
VM *	R	55	5.2	-	7.1
TL *	N	15	4.3	-	6.4
Be	LLSS	31	5.3	-	6.8
GBT *	R	72	6.6	1722-6.5	7.3
Ne	LLSS	160	5.2	-	7.6
TXBT	R	67	6.4	-	7.2
Ub	RLSS	60	4.1	-	7.2
MM1/2	R	21	5.5	-	6.6
Ca	N	8			6.1
MM2/2	R	22			6.6
Mi	R	19			6.6
EC	N	5			5.8
LR	N	12			6.3
SLN	N	11			6.2
CG	N	9	4.8	-	6.1
PA *	N	12	5.3	1858-6.8	6.3
PNS *	LLSS	36			6.9
LTV *	R	160			7.7
OT *	R	20			6.6
PO *	R	130	4.8	-	7.6
PAS1 *	Area source	-	5.6	1724-7.0	-
PAS2	Area source	-	4.9	-	-
PAS3	Area source	-	5.2	1773-6.1	-
PAS4	Area source	-	5.6	-	-
PAS5 *	Area source	-	5.3	-	-
PAS6 *	Area source		4.7	-	-

Note—R: reverse; LLSS: left lateral strike slip; RLSS: right lateral strike slip; N: normal. * The sources located within a 300 km radius from the center of the selected site. Bold: These specific sources are highlighted in bold in Table 4 and Table 5.

are provided. The source segmentation proposed by [46] is adopted for identifying the area source model regarding source mechanism. Historical and instrumental records are used to correlate with the area sources. Herein an additional note is that as part of the evaluation process in PSHA, seismic sources located within a 300 km radius of the chosen site are considered, which is proposed by [1]. Therefore, the area covers a radius of 300 km, which is shown in Figure 11. These specific sources are highlighted in bold in Table 4 and Table 5. Among these sources, Source No. 253 stands out as it experienced the Lisbon earthquake in 1755 and recorded a maximum magnitude of 7.8 in 1969. This high activity rate and its involvement in devastating events designate Source No 253 as an active tectonic feature. In the region, HO and SWIM-1 are the closest faults to the potential epicenter of the significant Lisbon earthquake. Notably, the most prominent instrumental record with a magnitude of 7.8 also occurred near these faults (see Figure 12). Another observation is that HO has the reverse type of mechanism, whereas SWIM-1 has a strike-slip mechanism despite their coinciding location, as shown in Figure 11. This variation in fault mechanism can have significant implications for seismic activity in the region. According to the methodology of Wells and Coppersmith, 1994 [74] utilized in the study, both Fault SWIM-1 and Fault HO have the potential to generate earthquakes with a maximum magnitude of up to 8.5. The approach by [74] considers the fault dataset, including the fault mechanism and their rupture length, to estimate the potential earthquake magnitude. The fact that both faults can generate high-magnitude earthquakes further emphasizes their significance in SHA for the area. The coexistence of reverse and strike-slip mechanisms at the exact location might imply complex tectonic processes in the region, warranting careful consideration in assessing potential seismic risks. By incorporating this information into the seismic hazard analysis, the study ensures a more comprehensive understanding of the potential earthquake scenarios in the region.

Finally, to choose an appropriate maximum magnitude for use in PSHA for the associated faults or area sources, the study compares the instrumental, historical, and W&C magnitudes (only for the line source model) [74]. The highest value among these three estimates is selected as the input for PSHA, considering it the potential maximum magnitude for SHA.

(c)

Description of the magnitude recurrence relationship: This task involves the definition of a mathematical or statistical model used to evaluate the likelihood of earthquakes of different magnitude levels occurring over a specific time.

The magnitude recurrence relationship, also called magnitude–recurrence distribution or Gutenberg–Richter law introduced by [75], is a key concept that describes the relationship between the magnitude of earthquakes and their frequency of occurrence within a period of time and region for each seismic source in PSHA. The Gutenberg–Richter law [75] assumes that the distribution of earthquake magnitudes in a given region and period follows an exponential pattern. This relationship is mathematically represented as follows:

$$logN\left(m\right)=a-bm,$$

(7)

where $logN$ is the logarithm of the number of earthquakes exceeding a certain magnitude m within a specific time period and a specific region, $a$ and $b$ are constants that depend on the seismicity characteristics of the region, and m is the magnitude of the earthquake. The “a” parameter describes the expected number of earthquakes of magnitude equal to or larger than m. The parameter “b” is a slope that represents the rate at which the number of earthquakes decreases with increasing magnitude in the magnitude–frequency distribution.

In PSHA, the minimum value of magnitude, denoted as $m_0$, represents the expected intensity level or magnitude that could potentially cause damage. For this particular study, it is assumed that $m_0$ is equal to 3.5. On the other hand, there is an upper limit, denoted as $m_1$, which represents the maximum magnitude earthquake that is likely to occur in the region of interest. This upper limit can be determined either by analyzing historical earthquake catalogs or by estimating it through empirical relationships between rupture dimensions and magnitude. Because of the constraints imposed by both the lower and upper magnitude limits, the probability density function of earthquake magnitudes can be expressed as shown below [76]:

$$f_M\left(m\right)=k\beta e^{-\beta \left(m-m_0\right)}, k={\left[1-e^{-\beta \left(m_1-m_0\right)}\right]}^{-1},$$

(8)

where $\beta$ is a seismotectonic parameter that is utilized to describe the relative frequency of large earthquakes in comparison to smaller ones. It helps to characterize the distribution of earthquake magnitudes. The parameter $k$ serves as a normalizing constant, which adjusts the cumulative distribution function in such a way that it reaches unity at the upper magnitude limit $m=m_1$.

To reduce uncertainty, instead of relying on an estimated value for the seismicity parameter λ, the average annual number of earthquakes with a magnitude equal to or higher than $m_0$ is considered. The $\beta$ for each seismic source zone is determined using two alternative algorithms: the least squares regression (LSR) and the maximum likelihood (MLH) approaches. The LSR aims to minimize the sum of squares of the differences between observed and estimated values, while the MLH seeks to maximize the likelihood of the estimated function fitting the observed data. The $\beta$ value of the incomplete catalog is assessed based on the approach of Aki-Utsu [77] as follows:

$$\beta ={\displaystyle \frac{1}{\overline{m}-m_{min}}},$$

(9)

where, $\overline{m}$ is the average magnitude, and $m_{min}$ corresponds to the minimum magnitude of the incomplete catalog.

The $\widehat{\beta }$ values corresponding to the artificially completed earthquake catalogs are calculated by taking into consideration the time interval, which can be explained by the difference in the observed mean activity rate (λ). The algorithm for the MLH approach is proposed by [78], which estimates $\widehat{\beta }$ values by dividing an incomplete earthquake catalog into sub-catalogs to define the level of completeness of each catalog separately (i.e., sub-catalog 1, sub-catalog 2, …, sub-catalog n), as shown below:

$$\widehat{\beta }={\left({\displaystyle \frac{r_1}{{\widehat{\beta }}_1}}+{\displaystyle \frac{r_2}{{\widehat{\beta }}_2}}+\dots +{\displaystyle \frac{r_n}{{\widehat{\beta }}_n}}\right)}^{-1},$$

(10)

where ${\widehat{\beta }}_i$ is the Aki-Utsu [77] estimator and $r_i$ denotes the rate of events that have a magnitude equal to or greater than the level of completeness which is calculated as follows:

$$r_i={\displaystyle \frac{n_i}{\sum _s^i{n}_i}},$$

(11)

where $n_i$ corresponds to the total number of events at a specific magnitude level for sub-catalog i, and in the denominator, the total number of events across all magnitude levels is defined, symbolized by $s$.

Finally,

Table 6. Seismicity parameters of area sources model.

	MLH				LSR
NO	Not Corrected		Corrected		Not Corrected		Corrected		Mmax
	$\mathit{\lambda }$	$\mathit{\beta }$	$\mathit{\lambda }$	$\mathit{\beta }$	$\mathit{\lambda }$	$\mathit{\beta }$	$\mathit{\lambda }$	$\mathit{\beta }$
247	4.29	2.50	10.68	6.10	4.60	2.09	5.09	2.05	6.6
253	5.25	2.68	10.72	6.36	5.65	1.58	9.65	1.78	8.5
246	0.35	2.62	1.31	6.30	0.37	2.16	0.57	2.21	5.0
245	0.41	2.21	1.04	6.02	0.43	2.09	0.52	2.03	5.2
242	0.94	1.88	2.17	5.96	1.00	1.87	1.00	2.01	6.8
251	0.56	2.57	1.43	5.74	0.59	2.30	0.30	1.53	6.5
249	0.32	1.94	0.85	6.14	0.33	2.15	0.35	2.16	4.7
0	0.60	1.67	1.42	5.13	0.60	1.85	0.83	1.97	5.0
244	0.68	3.01	1.76	6.17	0.79	1.74	1.52	2.26	7.0
250	0.81	3.47	2.14	7.56	0.87	3.05	0.74	3.19	4.7
255	1.57	3.65	3.98	7.43	1.62	2.41	1.09	1.92	5.3
243	0.95	1.04	1.99	4.91	0.97	1.96	1.35	1.98	6.5
262	0.46	1.45	1.35	5.93	0.49	1.77	0.74	1.98	5.1
254	11.37	2.13	26.09	5.44	11.90	2.35	11.96	2.46	6.4
248	2.05	2.56	5.37	5.60	2.30	3.09	4.30	3.62	4.9

and

Table 7. Seismicity parameters of line source model.

	MLH				LSR
	Not Corrected		Corrected		Not Corrected		Corrected
	$\mathit{\lambda }$	$\mathit{\beta }$	$\mathit{\lambda }$	$\mathit{\beta }$	$\mathit{\lambda }$	$\mathit{\beta }$	$\mathit{\lambda }$	$\mathit{\beta }$	Mmax
CPR	0.29	2.04	1.09	6.72	0.30	1.91	0.25	2.34	7.3
CW	0.22	1.90	0.65	8.16	0.24	1.30	0.11	1.55	7.2
HO	0.74	2.45	1.46	5.88	0.79	1.24	0.46	1.47	8.5
SWIM-1	1.44	2.45	2.86	5.88	1.54	1.24	0.89	1.47	8.5
GoB	2.33	2.85	6.06	6.75	2.59	2.85	1.79	3.33	7.7
SWIM-2	0.33	2.75	0.97	5.93	0.37	2.73	0.22	2.56	7.5
PT	0.25	2.91	0.63	6.44	0.27	2.93	0.09	2.66	7.6
SL	0.20	2.91	0.49	6.44	0.21	2.93	0.07	2.66	7.4
PRV	0.42	2.91	1.05	6.44	0.45	2.93	0.15	2.66	7.8
MVB	0.41	2.91	1.02	6.44	0.43	2.93	0.14	2.66	7.7
NCRV	0.30	2.91	0.74	6.44	0.32	2.93	0.11	2.66	7.6
MP	1.06	3.40	2.82	7.58	1.11	2.88	0.57	3.00	7.2
PBT	0.60	2.31	1.60	7.30	0.67	2.78	0.37	3.60	7.4
Po	0.12	2.80	0.30	6.07	0.13	2.24	0.05	2.33	6.9
EsO	0.11	2.80	0.27	6.07	0.11	2.24	0.04	2.33	6.8
LA	0.05	2.80	0.12	6.07	0.05	2.24	0.02	2.33	6.4
Alb	0.07	2.80	0.18	6.07	0.07	2.24	0.03	2.33	6.6
AST	0.32	2.80	0.80	6.07	0.33	2.24	0.13	2.33	7.4
Qu	0.43	2.80	1.09	6.07	0.46	2.24	0.18	2.33	7.2
SE	0.14	2.80	0.36	6.07	0.15	2.24	0.06	2.33	7.0
NJ	0.46	2.86	1.16	5.92	0.48	2.60	0.14	2.38	5.8
Malaha	1.00	2.86	2.49	5.92	1.03	2.60	0.29	2.38	6.2
AP	0.11	2.77	0.29	5.02	0.13	2.43	0.03	2.10	7.6
VM	0.67	1.90	1.58	5.62	0.70	2.07	0.25	2.36	7.1
TL	0.16	3.96	0.63	6.29	0.17	3.58	0.08	3.59	6.4
Be	0.52	2.70	1.36	6.79	0.54	1.76	0.11	1.22	6.8
GBT	1.78	2.52	4.51	7.04	1.90	1.72	0.86	1.77	7.3
Ne	1.08	2.12	2.61	6.29	1.13	1.78	0.33	1.78	7.6
TXBT	1.14	1.84	2.80	6.71	1.21	1.35	0.52	1.45	7.2
Ub	0.17	4.28	0.48	7.18	0.17	3.42	0.05	2.41	7.2
MM1/2	0.30	3.16	0.73	7.10	0.33	2.16	0.06	1.67	6.6
Ca	0.12	3.16	0.28	7.10	0.12	2.16	0.02	1.67	6.1
MM2/2	0.32	3.16	0.77	7.10	0.34	2.16	0.06	1.67	6.6
Mijas	0.27	3.16	0.66	7.10	0.30	2.16	0.06	1.67	6.6
EC	0.07	3.16	0.17	7.10	0.08	2.16	0.01	1.67	5.8
LR	0.17	3.16	0.42	7.10	0.19	2.16	0.03	1.67	6.3
SL Nieves	0.16	3.16	0.38	7.10	0.17	2.16	0.03	1.67	6.2
CG	0.38	1.91	0.97	6.13	0.41	2.17	0.17	2.39	6.1
Porto Alto	0.04	2.20	0.09	5.74	0.04	2.12	0.01	1.80	6.3
PNS	0.11	2.20	0.27	5.74	0.12	2.12	0.03	1.80	6.9
LTV	0.48	2.20	1.18	5.74	0.52	2.12	0.15	1.80	7.7
OT	0.11	2.20	0.27	5.74	0.12	2.12	0.03	1.80	6.6
PO	0.14	1.39	3.87	5.66	0.14	1.21	0.10	1.99	7.6
PAS1	2.35	1.48	5.41	5.02	2.51	2.10	1.48	2.37	7.0
PAS2	1.59	2.52	4.21	5.71	1.76	3.22	1.13	3.77	4.9
PAS3	0.54	2.12	1.29	6.36	0.54	2.09	0.25	2.18	6.1
PAS4	3.92	1.74	8.93	4.86	4.03	2.40	1.67	2.73	5.6
PAS5	1.84	2.30	4.95	6.41	1.97	2.36	0.67	2.01	5.3
PAS6	0.76	4.05	1.98	8.01	0.81	3.01	0.24	2.61	4.7

present the results in terms of activity rates of the area sources model and line sources model, respectively, for both complete and incomplete catalogs. Note that the activity rates labeled as “corrected” in Table 6 and Table 7 refer to values calculated using only the complete earthquake catalog obtained through the methodology described by [71], as outlined previously. Despite the LSR method mostly tending to estimate higher activity parameters than MLH, the parameters from both approaches generally show a close agreement for the incomplete earthquake catalog. LSR may lead to larger activity parameters compared with MLH, particularly if there are large earthquakes, which can disproportionately affect the estimated parameters. However, for the case of the completed catalog, a noticeable variation is observed between the methods, along with larger values compared to the estimators for the incomplete earthquake catalog. According to the results obtained from both MLH and LSR methods, it is evident that the activity parameters of the line source model tend to overestimate the seismicity in the region, while the parameters from the area model lead to underestimation of seismicity in the region. For instance, sources of 247, 253, and 254 display higher λ values, implying that the past seismicity has a major composition of small earthquakes. On the other hand, the presence of lower $\beta$ values such as in sources 242, 0, 243, and 262, indicated a larger proportion of large earthquakes relative to small earthquakes in the region. In the case of the line source model, most of the faults exhibit lower values of λ and $\beta$ that can be attributed to the occurrence of larger magnitude earthquakes in close proximity to the faults, while only a few smaller magnitude earthquakes are observed.

(d)

Selection of Ground Motion Models (GMMs): GMMs predict the intensity of shaking during an earthquake based on various factors, such as earthquake size and distance from the site. Choosing models that are well suited for the specific region improves the accuracy of the predictions, as models are often developed based on regional seismic data and conditions. It is important to review existing literature, compare different models, and seek expert recommendations to select the most suitable ones. This step involves choosing GMMs by considering various factors such as the region’s tectonic setting, geological conditions, and the available data on ground motion recordings to predict the potential ground shaking level at a particular site.

Numerous researchers have developed GMMs for the purpose of estimating ground motion intensity on a global scale [27,79,80,81,82,83,84]. The process of selecting the most suitable GMMs for the mainland of Portugal involves several important steps. These steps include identifying seismic sources relevant to the region, considering the soil conditions and insights from local experts, and adhering to past studies that were conducted for the same region. The selection of GMMs for this study was meticulously considered to ensure their relevance to the seismic characteristics of Lisbon. According to recommendations by [18], who conducted PSHA for Portugal, the model of [27] is suggested for seismic sources located in inland areas with rock sites. This GMM is widely used across Europe and is based on data from highly active regions like Italy, Greece, and Turkey, as demonstrated by [17]. Additionally, local experts for mainland Portugal endorse using the GMM of [29] for SHA in the region. The mentioned GMMs are employed in the calculation process of PSHA to estimate PGA values at selected sites for this study. The reason for their utilization is their suitability and compatibility with the seismic characteristics of the region under investigation.

(e)

Identification of Soil Class: This step involves the classification and characterization of different types of soil materials in the region. The seismic response of the ground under seismic load can differ according to the type of soil where seismic waves pass. Local soil characteristics play a critical role in how seismic waves are amplified. Soft soils can significantly amplify shaking compared to firmer soils or bedrock, affecting the intensity of ground motion at the surface. Incorporating site-specific soil data, such as soil density, stiffness, and layering, allows for adjustments to the GMMs to account for these amplification effects. It is noted that local soil characteristics are incorporated as the Vs30 value, which is used as an input for the GMMs.

For the soil model, the study conducted by [85] is adopted. The study focuses on the LTV region, including MAL, which is densely populated with approximately 3.5 million inhabitants and has a history of devastating historical earthquakes resulting in significant economic and human losses. In response to this concern, the researchers investigated creating detailed average shear wave velocity in the top 30 m (Vs30) and soil classification maps for the LTV region. They achieved this by utilizing in situ shear-wave velocity measurements, along with P- and S-wave seismic velocities from seismic refraction data and some cross-hole datasets. Additionally, the mapping process incorporated lithostratigraphic studies and analyses of boreholes drilled for water supply and geotechnical investigations. They identified 82 soil profiles within Lisbon in terms of their geological, lithological features, age, and soil classes according to Eurocode 8 [32].

Figure 12 shows the Vs30 map of the surrounding region of LTV, developed using the natural neighborhood interpolation method in ArcGIS PRO [86]. The Vs30 map of the region depicts that the resolution of values is higher in the western part of LTV, which can be attributed to exhibiting a more precise spatial distribution of sites with known Vs30 in the region. Overall, the region is predominantly occupied by B soil type according to Eurocode 8 [32]. In addition, the location of the National Museum of Archeology (MNA) in Monastery of Jerónimos, a monument with great importance in Portuguese history, is shown in Figure 13 to assess its soil class and then calculate its hazard level later in PSHA.

(f)

Utilized Logic Tree Algorithm: Figure 14 shows the utilized logic tree algorithm, consisting of five branches: seismic zonation, earthquake catalog, seismicity models, Mmax, and GMMs. The first branch of the framework displays two seismogenic models, which are employed to assess seismicity levels within the region. Furthermore, in the context of PSHA, the analysis exclusively focuses on mainshocks, as indicated in the catalog branch. This is because the rate of ground motion intensity measure exceedance at the specific location is determined by the largest magnitude of an earthquake within each cluster of events, as explained by [6]. Subsequently, two statistical techniques are employed to estimate seismicity parameters for input into the PSHA. The initial method is the MLH, which seeks to maximize the likelihood of the estimated function aligning with the observed data. The second approach is the LSR, which aims to minimize the sum of squares of the discrepancies between the observed and estimated values. The next step involves determining the maximum magnitude of an earthquake for each seismic source, which can be achieved through instrumental or historical records. In the case of the line source model, the estimation by [75] is employed, taking into account the rupture length of the faults. The highest obtained value is then considered as M_max within the logic tree framework. Finally, the appropriate GMMs for Portugal, namely those proposed by refs. [27,29], are employed in PSHA.

3.2. Results

Once completing all the essential steps of PSHA, the analysis yields valuable outputs for evaluating seismic hazard at selected locations. These results are typically presented through hazard curves, hazard maps, and site-specific response spectra. In this study, single-site PSHA is performed at various return periods, including 2475, 975, 475, and 50 years, to estimate PGA values at selected sites. The PGA values obtained for various return periods provide critical insights into the seismic hazard levels at selected site/sites. These values help in understanding the likelihood of experiencing certain levels of ground shaking over different time spans, which is essential for designing buildings and infrastructure that can withstand potential earthquakes. The spatial distribution of PGA levels within the study area is determined using the natural neighborhood interpolation method, and hazard maps are developed for each return period. Both area source and line source models are used to generate PGA maps, allowing for a comparison of the variations between these models. The obtained PGA results revealed that the line source model yields higher seismicity in terms of PGA compared to the area source model, as evidenced by the findings of activity parameters of seismic sources in Section 3.1 (see Figure 15, Figure 16, Figure 17 and Figure 18 for the generated PGA maps within the region). Our results show that the PGA values from the line source model are significantly higher compared to those from the area source model. Line sources can sometimes overestimate hazard compared to area sources [18]. The main reason is that area source models spread activity rates across larger regions, while fault line models concentrate on specific fault lines [87,88,89]. Therefore, in regions near fault planes, line sources are typically preferred. Furthermore, the sites with softer soil conditions demonstrate higher PGA levels. This highlights the significant influence of soil characteristics on the seismic hazard levels experienced at different sites. In general, these observations provide useful insights into the SHA for the study area and imply the importance of considering both source models and soil conditions in PSHA. It is finally noted that the PGA resolution is higher in the western part of the region due to the predominant utilization of soil information for the sites in that area.

Particularly, the location of MNA demonstrates the following PGA levels for area sources model:

• 0.3–0.4 g for the return period of 2475 years,
• 0.2–0.3 g for the return period of 975 years,
• 0.1–0.2 g for the return period of 475 years,
• 0.0–0.1 g for the return period of 50 years.

On the other hand, for line source model, the PGA levels at the same location are:

• 1.1–1.2 g for the return period of 2475 years,
• 0.9–1.0 g for the return period of 975 years,
• 0.7–0.8 g for the return period of 475 years,
• 0.3–0.4 g for the return period of 50 years.

Considering both source models, the average PGA levels at MNA are as follows for the respective return periods:

• 0.7–0.8 g for the return period of 2475 years,
• 0.5–0.6 g for the return period of 975 years,
• 0.4–0.5 g for the return period of 475 years,
• 0.2–0.3 g for the return period of 50 years.

4. Comparison of the Results with the Literature

The existing body of research on PSHA for Portugal, as documented in previous studies [17,18,90], provides valuable insights into the seismic hazard level of the region. These studies have contributed significantly to understanding the seismic risks in mainland Portugal. In particular, the study by [18] focuses on establishing seismic zonation for mainland Portugal, the Azores, and the Madeira Archipelagos, which incorporates two seismic scenarios consistent with the definitions outlined in the previous Portuguese Code [91]. Under type 1 seismic action, earthquakes with epicenters primarily offshore are considered, while type 2 seismic action encompasses earthquakes with epicenters primarily inland. They employed the area source model of Eurocode 8 [32] and applied two GMMs: the first, by [30], valid for seismic action type 1; and the second, by [27] model, referring to seismic action type 2. The PGA map corresponding to Eurocode 8 [32] is depicted in Figure 19a. Notably, the results of this study align with those of seismic action 2 (0.08–0.18 g) when the area sources are employed, where the range is within 0.10–0.20 g in this work. This alignment underscores the reliability of the area source model used in both studies. However, it is essential to note that slight variations in the hazard estimations might be attributed to soil effects. Unlike this study, ref. [18] did not consider local soil information in the PSHA, which could influence ground motion and ultimately impact hazard assessments. The choice of GMMs within the logic tree also plays a pivotal role in shaping hazard estimations. This study incorporated different GMMs with equal weights, acknowledging that this selection process significantly influences the overall robustness of the hazard estimations regarding areas.

Figure 19b shows the PGA map for the return period of 475 years generated by [17]. Two area source models, namely SA and SB models, according to [17], were once again employed to classify earthquakes based on their location, distinguishing between offshore and onshore events. They employed three GMMs, which are refs. [27], [28], and [29] with their respective weights. Their findings reveal that the region has the potential to encounter a PGA range spanning 0.15 g to 0.19 g. Remarkably, these results closely align with those derived from the area source model and particularly with the estimations provided by [17]. This alignment underscores the reliability and consistency of the seismic hazard assessments conducted by different research groups. It is noteworthy that the estimations presented by [17] appear to have a much closer correspondence to this study’s findings compared to those of [18]. While both studies incorporated rock sites into their PSHA analyses, the alignment of the results by [17] with this research suggests a higher level of agreement in seismic hazard assessments, potentially attributed to similarities in modeling approaches or other factors.

Subsequently, the most recent hazard assessment was conducted by the Global Earthquake Modal Foundation (GEM) [90], as presented in Figure 19c. This assessment depicts the study area with a PGA range of 0.08 g to 0.035 g. Consistent with prior studies, the area source model remains in agreement with the findings of [90]. Notably, this PGA range exhibits variations that deserve attention. The lower limit of the PGA range aligns more closely with the findings of [18], whereas it tends to underestimate seismic hazard levels when compared to the study conducted by [17]. Conversely, the upper limit of the PGA range demonstrates a closer alignment with the results derived from the area source model and, to some extent, [90]’s assessment. This upper limit suggests a higher potential for seismic ground motion, which corresponds more closely to the estimations provided by these models.

The observed variations in the PGA range highlight the inherent complexities and uncertainties in seismic hazard assessment, particularly within this specific region. These variations may stem from differences in modeling assumptions, geological conditions, or other site-specific factors. The findings of the area source model in this study are, in general, consistent with previous studies conducted on the mainland of Portugal. This alignment can be attributed to the utilization of area source models in the available studies for PSHA. However, it is essential not to overlook the uncertainty surrounding the choice of the seismic source model used, especially considering that the line source model indicates a higher level of hazard for the region.

5. Conclusions

This study performs PSHA to develop seismic hazard maps for varying return periods within the MAL. Seismic activity spanning the time frame from 1961 to 2023 has been meticulously compiled from diverse earthquake catalogs. A collective count of 3047 instrumental earthquakes was gathered, with a designated threshold magnitude of 3.5 (M_w). Furthermore, declustering was performed to eliminate foreshocks and aftershocks, leading to a total of 2534 mainshocks identified. Notably, the highest magnitude recorded for an earthquake within this instrumental era was 8.2, observed within the defined region. In contrast, the 1755 Lisbon earthquake is renowned as the most destructive seismic event in historical times.

The various magnitude scales were converted into the M_w scale to obtain a homogenized earthquake catalog. For this purpose, the regionally compatible and most recently available empirical equations were employed. A completeness analysis method, as suggested by [71], was incorporated for accurate computation of activity rates attributed to each seismic source. It facilitated the determination of the magnitude completeness level of earthquakes. This consideration is particularly crucial, given the historical limitations of seismic stations in recording small magnitude events. The results of the completeness analysis have revealed that earthquakes ranging between magnitudes 3.5 and 4.0 have been deemed complete after 2001, whereas the 4.0–4.5 magnitude range attained completeness after 1998. Furthermore, the 4.5–4.9 and 5.0–5.4 magnitude ranges were recognized as complete data records since 1985 and 1973, respectively. Conversely, the remaining magnitude range, greater than 5.4, represents a relatively complete dataset.

Two distinct seismic source models were employed in PSHA: the area source model and the line source model. These models were applied to PSHA, considering a 300 km radius for each site. The prevailing fault mechanism within the study region was identified as a combination of reverse, normal, and strike-slip mechanisms, predominantly situated in an interplate subduction zone. Then, a magnitude–frequency relationship was built for each seismic source to determine the activity rates. In this study, two statistical approaches, namely, LSR (least squares regression) and MLH (maximum likelihood), were employed to minimize uncertainty. The outcomes revealed that while the LSR method typically yields higher activity parameter estimates than MLH, both methods generally exhibit close agreement for the incomplete earthquake catalog. However, significant variation arises between the methods in the completed catalog, accompanied by higher values relative to the estimations for the incomplete catalog.

The soil map for the region was created using an interpolation method. The soil data utilized in this process was derived from the investigation conducted by [85], which identified 82 distinct soil profiles in Lisbon. The Vs30 map of the area showed a higher resolution of values in the western part of LTV, reflecting a more accurate spatial distribution of Vs30 in that region. Generally, the region is mainly characterized by B-type soil. As anticipated, softer soil conditions are evident near riverside areas. To perform PSHA, two specific GMMs [27,29] were utilized in the PSHA process, aligning with their suitability for the relevant seismic source mechanism.

Subsequently, the logic tree algorithm, comprised of five branches including seismic zonation, earthquake catalog, seismicity models, M_max, and GMMs, was employed in PSHA to assess the level of hazard within the region. PSHA results were presented through hazard maps for various return periods regarding PGA. When the results of PSHA from each seismic source model are individually considered, the line source model overestimates seismic activity within the region compared to the area source model. Another noteworthy observation was the association of softer soil conditions with elevated hazard values. To facilitate a comparison with existing literature, the same regions studied in previous hazard assessment research were examined, highlighting the alignment of area source model results with past findings. This consistency can be attributed to utilizing area source models in the existing research conducted for PSHA.

Finally, this research is an initial attempt to integrate up-to-date seismic data, employ robust statistical methods for completeness analysis, incorporate soil models, and compare different seismic source model results specific to Lisbon. It provides valuable insights into the seismic hazard levels in Lisbon, contributing to a more nuanced understanding of regional seismic risks. Differences in GMMs, seismic source characterization, and soil conditions can lead to variations in hazard estimates. The variations observed in the PGA values, particularly between different models and compared with literature, highlight the inherent uncertainties in seismic hazard assessments. The findings have significant implications for urban planning and engineering in Lisbon. It is noted that the uncertainties in this study must be considered when using the results for earthquake-resistant design and planning. Future studies should aim to refine models and incorporate additional data to reduce these uncertainties and improve the accuracy of hazard assessments. This study reinforces the need for careful selection of seismic models and the incorporation of local data to ensure accurate hazard assessments. Also, the limitations, notably concerning the uncertainty surrounding the utilization of GMMs, should be addressed. Future research endeavors aimed at exploring suitable, region-specific GMMs would enhance our comprehension of hazard estimates in a more precise manner.