Risk assessment at Puerto Vallarta due to a local tsunami

The Jalisco region in western Mexico is one of the most seismically active in the country. The city of Puerto Vallarta is located at Bahía de Banderas on the northern coast of Jalisco. Currently there exists a Seismic Gap in the Northern coast of Jalisco (Vallarta Gap). Historically seismogenic tsunamis have affected the coast of Jalisco. In this work, we assess the risk due to a local tsunami in the city of Puerto Vallarta as a function of the interaction between hazard and vulnerability. We model the tsunami hazard, generation and propagation, using the initial conditions for a great earthquake (Mw ≥ 8.0) similar to those that occurred in 1787 at Oaxaca and in 1995 at Tenacatita Bay, Jalisco. Vulnerability is estimated with available data for the years 2010–2015 with sociodemographic variables and the location of government, commercial or cultural facilities. The area with the highest vulnerability and risk is between the valleys of the Ameca and Pitillal Rivers, extending to a distance greater than 5.1 km from the coastline and affecting an area of 30.55 km2. This study does not consider the direct damage caused by the tsunamigenic earthquake and aftershocks; it assumes that critical buildings in the region, mostly hotels, would not collapse after the earthquake and could serve as a refuge for its users. The first (It) tsunami wave arrives to Puerto Vallarta (Cuale) 19 min after the earthquake with a height (Hi) of 3.7 m; the run-up (At) arrives 74 min after earthquake with a height (Hr) of 5.6 m.


Introduction
The Jalisco region, in western Mexico (Fig. 1), is one of the most seismogenic regions in Mexico, with many past destructive earthquakes of great magnitude, some of which generated important tsunamis. The largest instrumentally recorded historic earthquake in the twentieth century in Mexico was an M = 8.2, on June 3, 1932, and located off the coast 1 3 of Jalisco. A few days later, on June 18, 1932, a magnitude M = 7.8 earthquake struck the region again. Sánchez and Farreras (1993) have proposed both earthquakes were tsunamigenic. Nevertheless, the most destructive tsunamigenic event in the region was initiated by a probable submarine slump landslide involving sediments provided by the meandering Armería river system accumulated throughout time on the continental shelf that took place on June 22, 1932 (Pacheco et al. 1997;Corona and Ramírez-Herrera 2015). It was responsible for destroying a resort at Cuyutlán (Colima state), causing a maximum water layer height of 15 m and an estimated flooding extent of 1 km along 20 km of coast.
In 1995, an M W = 8.0 earthquake occurred off the coast of Jalisco, caused a tsunami that affected a 200-km-long coastline with damage limited to low-lying coasts (Ortiz et al. , 2000Trejo-Gómez et al. 2015). The 1995 earthquake ruptured only the southern half of the area proposed for the 1932 events (Singh et al. 1985), suggesting that the northern coast of Jalisco, including Bahía de Banderas (BdB) (Fig. 1), presents a seismic gap (Vallarta Gap) that might rupture and generate a local tsunami.
The BdB region ( Fig. 1) could be affected by tele-, regional and local tsunamis. To date, there is no historical report for significant damages caused by tele-tsunamis or regional  Table 1. Modified from Núñez-Cornú et al. (2018) tsunamis at BdB. In the case of tele-tsunamis, the waves reported historically are less than one meter; however, the hazard exists because of the possibility that bay resonance could amplify tsunami waves and generate a seiche that could cause much damage. Dressler and Núñez-Cornú (2007) calculated the bay's eigen-period (resonance period) at T = 2,726 s (45 min 30 s) using a hydropneumatic method and a preliminary bathymetric model of the BdB. Specific sites such as Boca de Tomatlán, Marina Vallarta, Plaza Genovesa and Playa de Los Muertos regions in Puerto Vallarta were evaluated for an incoming wave to BdB of 10 cm amplitude and different arrival periods, and the results vary at different sites with amplitudes higher than 100 cm and oscillations of different periods.
Based on the hypothesis of an earthquake that fills the Vallarta Gap (M W = 8.0), Núñez-Cornú et al. (2006) estimate tsunami run-up height (H r ) and analyze the effects in four places in Puerto Vallarta, and they concluded that a tsunami would enter at Pitillal river´s valley as a 2 m ≤ H r ≤ 4 m and in the area of the Ameca river's valley as a 5 m ≤ H r ≤ 7 m. The estimated run-up was imprecise in shallow waters (depth < 50 m), due to the resolution of the information used, because it does not discriminate between different beaches in Puerto Vallarta. For this scenario, a specialized study is required to generate more datasets that characterize the shallow water marine relief in Puerto Vallarta because in these areas the tsunami´s wave is refracted, and hazard level could be increased.
An example of flood damage at Puerto Vallarta was a storm surge generated by Hurricane Kenna in October 2002. The waves produced by this hurricane entered land up to a distance of 1 km approximately. Three hotels suffered intense non-structural damage, and the tourist strip was affected with different levels of damage depending on the proximity to the beach, or due to flooding and sand deposition. There were no reported direct victims associated with this event.
The coastal community at Puerto Vallarta faces the challenge of mitigating the local tsunami hazard from major earthquakes. This fact requires developing accurate risk reduction measures based on thorough tsunami hazard, vulnerability and risk assessments. Núñez-Cornú and Carrero-Roa (2012) suggest that land managers with an adequate perception of risk could make decisions to prevent a disaster by reducing vulnerability through design actions based on scientific data and risk assessment theory. Risk assessment consists of three phases: evaluation, management and perception. Reducing vulnerability requires mitigation actions such as sustainable land uses, possible civil works and population preparation (knowing how to take shelter to stay safe, etc.). Civil Defense Authorities need to generate contingency response protocols, determine the recovery and reconstruction actions in the affected area and evaluate economic losses in the community due to a false alert.
Risk perception is a critical phase of risk assessment, all kinds of factors intervene, starting with the academic level, personal experience and perception, and others such as collective memory and intuition. This occurs at all levels, both in the possible affected and in the authorities. A wrong perception in decision-making can cause a disaster worse than the highest of the proposed scenarios. One such example is the catastrophe caused by Hurricane Katrina in 2005 in New Orleans, USA (Dixon 2015), with more than 1800 fatalities. Katrina remains the costliest disaster in the US history. Another example occurred as a result of the 1985 eruption of Nevado del Ruiz Volcano, Colombia, where a lahar destroyed the city of Armero causing more than 24,000 fatalities, despite the scientific efforts of INGEOMINAS to obtain an accurate volcanic risk map of the Nevado del Ruiz Volcano and the efforts of the Colombian Civil Protection to disseminate it and implement an alert system. "It was difficult for nongeologists (Congress and local officials) (Mileti et al. 1991). Such a disaster occurs after a catastrophic chain of hazard and social events (Smith 2013). For Núñez-Cornú and Carrero-Roa (2012), it is not the lack of information or misperception of hazard that causes the disaster, rather a disaster results from the inadequate management of socially acceptable risk, based on three factors: (a) denying the hazard, (b) maintain the inertia of territory without planning and (c) transfer the costs of risk to others.
An assessment of the tsunami risk of a coastal community is the primary initial information required for the design of civil defense education programs to society, and the implementation of protocols by local emergency institutions and the civil defense both in public and private buildings (Hebenstreit et al. 2003). Currently, Puerto Vallarta has the highest population density on the Jalisco coast and the second largest urban area in the state and plays an essential role in the regional economic development, mainly through tourism. The 2020 population census results counted 291,839 (Instituto de Información Estadística y Geográfica de Jalisco INEGI 2020). More than 90% of Puerto Vallarta inhabitants live in our study area (Fig. 2), and there is an average floating population of approximately 50,000 people during the high tourist season, from October to April.
The objective of this work is to carry out a first evaluation of the risk that a local seismogenic tsunami represents for the city of Puerto Vallarta. Hazard is modeled from potential tsunami inundation zones based on numerical simulations of a major thrust earthquake occurring in the Vallarta Gap. The vulnerability is obtained with data from public databases. This study does not consider direct damages caused by that earthquake; it assumes that critical buildings in the region, mostly hotels, would not collapse after the earthquake and could serve as a refuge for its users.

Tectonic setting and local Tsunamis
In western Mexico, three tectonic plates interact, the Rivera Plate (RP) and the Cocos Plate, which are subducted along the Mesoamerican trench (MAT) under the North American Plate (NOAM). This interaction has generated an active fragmentation process (Bourgois and Michaud 1991) of the NOAM in this region, giving rise to a tectonic unit known as the Jalisco Block (JB), proposed by Luhr et al. (1985) that is drifting away the Mexican mainland (Fig. 1). The JB is defined to the north by the extensive structure known as the Tepic-Zacoalco Rift Zone (TZR), which continues east with the Chapala Rift Zone (ChZ) and the Pacific coast, and continues south to the Pacific coast by Colima Rift Zone (CRZ). The CRZ is similar in structure and age to the TZR and is defined on land and offshore by recent seismic activity (Pacheco et al. 1997). The TZR consists of several tectonic depressions with extensional and right lateral movements, which also indicate deep crustal failures between the JB and NOAM. The western border of JB is defined by the MAT.
Recent geophysical studies Núñez-Cornú et al. (2016); Carrillo de la Núñez et al. 2019;Madrigal et al. 2021) found that to the north of the Marias Islands, there is no clear evidence of an active subduction zone. Instead, faulting is observed to the west of the Marias Islands, while to the south between the María Magdalena and María Cleofas islands, the subducted slab of the Rivera Plate is delineated by regional seismicity. They also report the existence of a 100-km-long tectonic structure south of Maria Cleofas Island, Sierra de Cleofas (SC). The SC is oriented N-S and marks the boundary between RP and JB, possibly as a result of compression of RP against JB. It establishes the beginning of the current subduction and associated seismic activity. Urías et al. (2016) propose that the existence of Ipala Canyon (IC) is related to extension produced by the abrupt change in RP convergence and that IC may be the southeast limit of a major forearm block (Fig. 1), called Banderas Forearc Block.
The Jalisco region has experienced numerous destructive earthquakes of great magnitude with epicenters along the coast and inland. The historical macroseismic data for the region date back to 1544 (Núñez-Cornú 2011). Núñez-Cornú et al. (2018) reported that at least 22 major earthquakes with M ≥ 7.0 took place in the past 474 years. Suter (2019) studied and concluded that the 1563, May 27, M I = 8, earthquake took place offshore Puerto de Navidad (now named as Barra de Navidad), and the estimated rupture area to be similar to the 1932 and 1995 earthquakes. Suter (2018) analyzed the

Fig. 2
Study area with population density distribution using AGEBs macroseismic data of the October 2, 1847, Jalisco Earthquake, and concluded that there were two earthquakes the same day. The first one, a subduction type earthquake, took place at 07:30 am offshore Tecomán, Colima with an estimated magnitude of M W = 7.4 ( Fig. 1); the second, a shallow intraplate type earthquake with an estimated magnitude M I = 5.7, took place at 09:30 am and affected the western part of the ChR, destroying the city of Ocotlán and other towns nearby.
Although no strong earthquake has been reported in the region on March 12, 1883, Orozco y Berra (1888) reports the occurrence of a tsunami in Las Peñas (currently Puerto Vallarta): "It was observed that the sea withdrew its ordinary beaches to a considerable extent and at a considerable distance from the coast, revealing some mountains and valleys in the background... It is not known with certainty what the ocean brought about in its withdrawal, but after some time, it reoccupied its box with enough noise and impulse".
To date, thirteen big destructive earthquakes (M > 7.0) ( Table 1, Fig. 1) associated with the subduction process of RP below NOAM along the Jalisco coast region have been identified. Only for seven of these, are there local data of relevant damage caused by the tsunamis generated. It is necessary to add to this seven tsunamigenic earthquakes, two tsunamis (1883 and 1932-06-22) probably generated by submarine landslides. However, no geological studies have been conducted for Puerto Vallarta to identify damage and/or effects of historical tsunamis.  Aida (1978) describes a numerical experiment for tsunami generation based on a seismic fault model, using seismic parameters, and shows that the calculated tsunamis agreed reasonably well with the tsunami records observed at several stations along the coast. The author proposes the existence of a correction factor K to adjust the results.

Hazard
Since the time of that publication, several different methods to model the seismic source of an earthquake using seismic and geodetic data observed from the earthquake have been proposed (Johnson 1999;Ratnasari et al. 2020;Gusman et al. 2014), as well as different methods to model the displacement of water generated by the seismic source. (Geist 1999;Bryant 2001). In this study, we applied the methodology used in a previous study in Oaxaca, Mexico , as described below, to model the 1787 earthquake tsunami effects, as in this case, there was no seismic model of the source. A seismic source based on the local tectonics was proposed; the theoretical tsunami waves modeled fit fairly well with the description of historical damage.
In this case, we assume the rupture will occur on the plate interface and assume dimensions consistent with an M w ~ 8.0, which for the Vallarta Gap is an inverse fault plane of L = 150 ± 30 km, W = 60, km, dipping 11° toward the coast at a depth of 10 km on the interplate region, according to the standard relation: where A is the area in km 2 (Utsu and Seki 1954;Wyss 1979;Singh et al. 1980). The total area was integrated from segments of individual subareas, A i = 30 × 30 km 2 . Twelve segments were used (Fig. 3).
The seismic moment Mo i of each of the segments was adjusted individually by varying the coseismic dislocation (d i ) from to the relationship to fit the moment magnitude of the earthquake (M W ) (Hanks and Kanamori 1979). Moment estimates assume a rigidity modulus which has been used previously for this region by various authors: The coseismic vertical deformation of the seafloor as produced by the buried fault plane is computed by using the dislocation model of Mansinha and Smylie (1971) by prescribing a reverse fault mechanism on each one of the segments. Increasing the d i value will increase the value of the Mo i and the M W. For the initial tsunami condition, the sea-level change is taken to be the same as the seafloor uplift calculated from the dislocation model.
The propagation of the tsunami is simulated by the vertically integrated long-wave equations (Pedlosky 1982): In these equations, t is time, η is the vertical displacement of the water surface above the equipotential level, h is the depth of the water column, g is gravitational acceleration, and M is the vector of the discharge fluxes in longitudinal and latitudinal directions. These equations are solved in a spherical coordinate system by the method of finite differences with the Leap-Frog scheme (Goto et al. 1997). For computation, the step time was set to 1 s, and the grid spacing of 27 s was used for the whole region, whereas a grid spacing of 3 s was used to describe the shallow areas. For nearshore bathymetry in the study region, from 1000 m depth to the coast, we used data from local navigational charts (SEMAR 2011). No detailed bathymetry of BdB was available (scale 1:4,000 or higher). For depths greater than 1000 m, we used data from the ETOPO-2 data set (Smith and Sandwell 1997).
This model generated theoretical tsunami waveforms and arrival times, which were computed along the coast in 24 virtual gauge sensors (theoretical pressure sensors or VTG) off the coast of the Nayarit, Jalisco and Colima states, at depths of 10 m (Fig. 3).  Table 4 The tsunami amplification factor because of shoaling from 10 m depth up to the coast is practically negligible and ranges from 1 to 2%. To measure the maximum flood area due to run-up, a digital terrain elevation model (DTM) was generated on land, with cells of 4 m 2 , that was interpolated from the DTM obtained by photogrammetry at the year 2000 (Núñez-Cornú et al. 2006). This DTM allows us to map elevation values equivalents to the run-up model. The tsunami hazard was calculated for a scenario of maximum flooding at high tide with the theoretical tsunami obtained. Different zones were delimited to match the altitude values on the coast of Puerto Vallarta with the synthetic waveforms of tsunami and the variation in the local tide around + 1 m, based on tidal forecasts by Centro de Investigación Científica y de Educación Superior de Ensenada, Baja California (CICESE 2016) for Puerto Vallarta for the years 2012, 2013 and 2016.

Vulnerability
We follow the same methodologies used by Núñez-Cornú et al. (2006) and Suárez-Plascencia et al. (2008) for the previous city's vulnerability studies, natural hazard's atlas and disaster's reports in México (Guzman et al. 2003;Simioni 2003;Rosales Gómez et al. 2004;García Arróliga et al. 2014). Due to the importance of Puerto Vallarta, there are enough databases on people, homes and facilities in our study area on different online platforms, whether government or private. Data used, such as people and housing, are from different platforms such as those maintained by Consejo Nacional de Población (CON-APO 2012), Instituto Nacional de Estadística y Geografía (INEGI 2010;2013;. Some facilities data in the studied area were updated using Google (2015) application.
The analysis in this study consisted of determining population attributes and locations of government offices or facilities that indicate Puerto Vallarta´s vulnerability in the affected area by the local tsunami hazard. We included census information of 214 Basic Geostatistical Areas (Area GeoEstadística Básica [AGEB] as defined by INEGI) and of five rural localities (less than 2500 inhabitants, Fig. 2) for the whole of Puerto Vallarta Municipality.
According to Guzman et al. (2003), it is necessary to estimate the population affected if the hazard occurs, for that reason the population projection in the affected area to the year 2015 was calculated; assuming that the growth was natural, the following equation was used: where C is the exponential growth of the population susceptible to hazard, P is the number of inhabitants registered in the last census, e is Euler's number, r is the population growth rate and t is the time in a year, concerning the last available census.
Initially in this study, a projection of the affected population was calculated using Eq. 7 for the hazard area, according to the 2010 census data, assuming that the population grows continuously and slowly, the latter assuming that there are no massive migratory movements after the census records available. This is a frequent calculation in risk management studies, using data from the last census.
We used a vectorial geographical information system (GIS) to calculate z statistic in population data (Wheater and Cook 2000;Mendenhall et al. 2013); with these values, it was possible to compare different AGEBs per vulnerabilities (attributes) in the affected area. Furthermore, the vulnerability of the population was analyzed according to the age (7) C = P e r•t range (Table 2) with different factors or criterion scores (Gómez Delgado and Barredo Cano 2006) for prioritizing the vulnerability age group. Only for this information layer and before z statistic was calculated, different experiments were carried out to observe which values highlighted the most vulnerable age groups. The highest value was for the population less than six years old, followed by older adults and populations with special needs (limited mobility or cognitive impairment), with the assumption that in these population categories, support would be needed for transport or with precise instructions to facilitate their movement to a shelter.
Other population attributes are also observed as the type of housing and availability of services such as electricity and potable water services, Internet and computer availability, these do not represent significant differences in affected AGEBs, and therefore, they are not used in the final maps.
We also located within the county the vulnerable facilities that in case of contingency, it is necessary to keep them in operation, like bridges, shopping centers (supply of food), schools, communications and transportation. Facilities were located in GIS and then were reclassified as high vulnerability. In the same way, we added a layer for overall average damages to household goods for affected tsunami areas. The total vulnerability in each AGEB is evaluated in eight information layers or vulnerability criteria, which are reclassified as very high, high, medium and low. In this way, a vulnerability is obtained as a basis for calculating risk (Fig. 4). The study area is divided into eight micro-basins by natural boundaries in the vulnerability map.
Then, we observed results in each AGEB and then we reclass vulnerability ratings as low, mean or high for local tsunami for Puerto Vallarta (Fig. 4). Layers with z statistic can be viewed as a density distribution, age ranges, education level, range of motion or learning, occupied population and housing.

Risk
According to Smith (2013), risk is based on probability and simply stated as probability times loss. When the analysis is undertaken, risk (R) is taken as some product of probability and loss. Tobin and Montz (1997) define a hazard as a potential threat to humans and their welfare 1 3 and suggest that the risk is expressed as the product of the probability of occurrence (hazard) and vulnerability.
To evaluate the risk in Puerto Vallarta, we estimate from the modeling of one earthquake with the initial condition for a tsunami and the vulnerability information previously described, according to the relation: where R is the risk, H the hazard and V the vulnerability.
Moreover, the following functions are used (Fig. 4): also, the probability factor or dislocation factor is related to the Mo or Magnitude, according to logarithmic Gutenberg-Richter relation (Gutenberg and Richter 1944): Vulnerability information's layers are reclassified in each AGEB (Fig. 4): where v1 is the education, v2: housing, v3: occupied population, v4: age, v5: population density, v6: the range of motion or learning, v7: facilities and, v8: debris cleaning.
For the inhabited homes in the tsunami flood area, costs for the loss of household, cleaning and debris transportation were calculated for each micro-basin. For this, a program is used to budget costs and control civil engineering work. The damage costs do not estimate the structural damages to buildings or bridges caused by a great earthquake. Nor do we include the costs associated with the cessation of day-to-day operations for an international airport, international maritime terminal and regional bus station, which we excluded from this study. Also we excluded the costs for the loss of cultural heritage, such as Museo del Cuale (sometimes unrecoverable as an archaeological site) or costs such as the loss of documents in cadaster, special equipment or computer in hospitals, government offices and schools.
The risk and vulnerability maps were generated in a raster image manager, for which values for Puerto Vallarta were entered at different points in each AGEB and interpolated with a spline method.

Earthquake, fracture area, magnitude and dislocation
In this study, different tests were performed for the proposed tsunami by changing the initial earthquake conditions by varying the dislocation while keeping the fracture plane constant. In this work, five hazard scenarios were evaluated with dislocation values d i = 2, 3, 4, 5, and 6 m ( Table 3) for Puerto Vallarta. Pitillal riverside (VTG 5, Fig. 3 and Fig. 5) was the site of the highest run-up calculated along Puerto Vallarta coast, 2.7 m ≤ H r ≤ 8 m, and I t = 20 min (arrival time of first tsunami wave after earthquake), A t = 72 min (H r arrival time). We analyze, in particular, the case for d i = 5 m.

Sea level and arrival times
The tsunami hazard was obtained from run-up values that affected Puerto Vallarta. We calculated a scenario for maximum flooding assuming the Mw 8.0 earthquake occurred at high tide, and run-up would affect coastal communities in our study region. The synthetic tsunami waveforms outputs generated for the first 10 h after the earthquake for 24 VTG distributed on the southern coast of Nayarit, Jalisco, and north of Colima, heights and arrivals times of tsunami for coastal communities for the studied region are plotted in Fig. 5 and listed in Table 4.
In Jalisco coast, the calculated first Tsunami wave (H i ) had an arrival time (I t ) of 11 min after the earthquake and corresponded to the municipality of Cabo Corrientes for the 1 3 VTG near communities Aquiles Serdán (H i = 5.8 m, It = 11 min) and Ipala (H i = 9.0 m, I t = 13 min). At Ipala, the run-up wave (H r ) is 10.9 m and the arrival times (A t ) 37, 60, 96, and 120 min (in this case four "big" waves were generated), other localities see Table 4.

Flood by a local tsunami
The H r and the most ocean water inland penetration (x) were calculated for our region. Five of eight micro-basins tsunami hazard scenarios were at the maximum, with a runup of 5 m ≤ H r ≤ 9 m and an inland penetration of 0.6 km (Cuale) ≤ x ≤ 5.1 km (Ameca), resulting in a total flood area of 30.55 km 2 . The tsunami flood, Hr and inland penetration comparison between micro-basins Ameca, Salado, Pitillal, Camarones and Cuale is shown

Housing and public facilities vulnerability
In 2020, in Puerto Vallarta 96% of the population is concentrated in the study area. The remaining people for the municipality live in ≥ 100 rural towns whose elevations are ≥ 20 m. For that reason, the rural towns were not considered in the risk assessment because they are outside the areas directly affected by the local tsunami hazards. By the year 2015, this study calculated that the population in the flood area increases to include 47 AGEB as shown in Fig. 8. By equation C = P(e r•t ) projected 88,316 inhabitants inside the adverse effects of the tsunami hazard area, but data from the 2020 census indicate 83,400 inhabitants. The relative error corresponds to 10% less than the projected values. Land use in Puerto Vallarta has favored the establishment of tourist services, commerce, and high-density housing close to the beach. For the year 2010, there were 33,942 dwellings in the affected area. The services available such as potable water, electricity and drainage between the tourist strip and the rest of the community were compared. It is observed that the indexes are similar in the all municipalities, even in zones of height greater than 20 m; the reason is that there is an acceptable comparable coverage of these services. In the case of a disaster, it is assumed that the first attention would be given to re-establish At the time of this study, there were 320 vulnerable public facilities in the municipality, of which 33% are vulnerable to flooding if a local tsunami occurs. Table 5 shows the number of public facilities and the volume of debris per micro-basin to estimate cleaning costs. The number of vulnerable facilities observed by micro-watersheds is as follows: 45 in Salado, 27 in Pitillal, 14 in Cuale, 12 in Ameca-Mascota and 6 in Camarones. The percentages of vulnerable facilities for the total municipality considering their primary use are the following: schools 15%, government and emergency care 5%, health units 2% and for various uses 11% (such as the distribution of electric energy, fuel storage, shopping malls, entertainment, museums, roads, transportation and bridges).
For the vulnerability categories, the z statistic was used; they classified as NULL for the case that in the AGEB, the data are equal to zero or data not available. The low vulnerability group corresponds to the values z ≤ -− 0.5, medium for values − 0.5 < z < 1 and high for values of z > 1. Different ranges of z-score values were established in layers of education level, occupied population and housing by observing in the study area those values that reflect the conditions of hypothesis.
High vulnerability values due to population variables such as age or special needs (learning disabilities or cognitive impairment), educational condition and population density were observed at the El Salado, Pitillal and Ameca micro-basins (Las Juntas). The total occupied population of the municipality of Puerto Vallarta in 2010 was 47,676, of which 18,592 are in the tsunami impact zone, and are concentrated in the El Salado basin. We use a raster GIS for the image to show the vulnerability map of Puerto Vallarta for the local tsunami hazard as far as an elevation of 30 m. Map was obtained from 539 points with all the municipality´s information, of which 219 points correspond to AGEB with data for population and housing data and 323 points for the vulnerable facilities (Fig. 9).

Risk
We estimated the cost of property damage in each dwelling inhabited in the affected area under the assumption that the minimum damage was $1,200 US dollars (which includes damage to some household goods as living room, breakfast room, bed and kitchen), so the total cost calculated for this concept was $27,925,200 US dollars.
Cleaning and transporting debris costs depend on the volume calculation. The affected areas were measured in each micro-basin, assuming a debris height of 0.1 m. The condition established that the debris was vegetation, sand and mud and that people should do the cleaning without the use of special equipment. For debris moving and unloading costs, the conditions were to use a dump truck and to transit by road up to a distance of 1 km. The cost calculated for this concept was $6,457,899 US dollars (Table 5).
We used a raster GIS for imaging to show the risk in Puerto Vallarta for a local tsunami, and focused in five of eight micro-basins: Ameca, Salado, Pitillal, Camarones and Cuale, where the observed land uses were the hotel zone with medium risk, the housing area and the vital facilities with high and very high risk. We present two maps of Risk: in the first (Fig. 10), we consider the total flood area due to a 5 m coseismic slip; in the second (Fig. 11), an empirical probability factor based on the magnitude (coseismic slip) was considered; a smaller slip is more likely than a large slip; in this case, a probability factor between 1.0 and 0.1 (Fig. 4) was applied to the vulnerability.

3 5 Discussion
Puerto Vallarta is located in a seismic region, in which great magnitude earthquakes and local tsunamis have occurred. In this city, the impact due to historical tsunamis is unknown due to a lack of evidence because to date no specific studies have been carried out. We calculated H r and A t for local tsunami to assess the hazard on Jalisco's and southern Nayarit´s coasts using a theoretical seismic source based on the local tectonics. Values used for the coseismic slip or dislocation range from two to six meters (8.0 < Mw < 8.2). Pacheco et al. (1997) propose a maximum slip of 4 m for the 1995 earthquake. Quintanar et al. (2011) propose a maximum slip of 3.2 m for the 2003 earthquake, however, there is no reported tsunami for this earthquake. Trejo- Gómez et al. (2015) used the same method to model the effects of the 1995 earthquake tsunami, but use different slips in some segments of the rupture area to adjust the reported data . The H r estimated in five places of Puerto Vallarta agrees with the studies of Núñez-Cornú et al. (2006). The scales   of the data do not allow for the estimation of a tsunami due to the slipping of sediments in the deltas of the rivers in Puerto Vallarta, as happened in Coyutlan, 1932. For this type of tsunami, we estimated more significant destruction because the H r was ≥ 10 m because of the earthquake's impulse due to the collapse of the sediment fringe of the Armeria River. The vulnerability assessment for tsunamis and the methodology used in this study is similar to that used for floods and earthquakes, for the population and facilities affected at the time the hazard occurs (Guzman et al. 2003). These studies are based on the information available for the city of Puerto Vallarta and published by government agencies. The estimated vulnerability of the municipality of Puerto Vallarta due to tsunami flooding would be useful for both the local and regional types after a major local or distant earthquake in the event that the tsunami entered the bay with an amplitude equal to the natural frequency of BdB which could then generate seiches. The results provide some preliminary answers for this particular city, and we did not consider the floating population due to tourism because it varies by the time of year and the characteristics of the lodgings, quality and service costs.
Puerto Vallarta is a medium-sized city, and we did not assess the vulnerability of buildings (Simioni 2003;Santos et al. 2014;Voulgaris and Murayama 2014) only the surface area affected by tsunami flooding. In our case study, land use is mostly designated for buildings, hotels, tourist services and commerce and these are closest to the coast. Considering that most hotels have 4 or more levels (susceptible to respond to vibration by the earthquake energy), two assumptions were made: (a) the tsunami generated is of low speed and does not generate too much turbulence like the one that occurred in October 1995 in Tenacatita Bay and (b) buildings are seismic resistant, so they would not collapse. Given these conditions, in some places in Puerto Vallarta, multi-story hotels could serve as vertical evacuation and shelter for the guests themselves and other people in the case of a tsunami.
In other places, moving to a safe area is more feasible. Walking to a safe area is feasible in 11 min or 16 min if walking speed (v) is 1.1 m/s or if under faster, more extreme walking conditions v = 0.751 m/s (Ashar et al. 2018), because our model estimated that the first tsunami arrival would be at ≥ 19 min (Table 4 and Fig. 6). It is important not to forget that a family emergency plan is essential for people with special needs (transportation or precise instructions are needed as support to facilitate their movement to a shelter).
One factor that increases the risk created by a local tsunami in the Puerto Vallarta coastal strip is the current land use. It has allowed a reduction in protective zones, and high population density construction close to the beach, and in the zones of mangroves in the Ameca and Salado micro-basins.

Conclusions
The risk area in Puerto Vallarta Municipality affected by flooding due to a local tsunami for an earthquake M W = 8.2 (d i = 5 m) was measured to be 30.55 km 2 approximately. The highest risk was found in the northern study area, between the valleys of the Ameca and Pitillal rivers (calculated area 26.5 km 2 ), because this area contains the highest population density in Puerto Vallarta and at a distance of 0.8 km from the coastline, there are also the regional bus station, the international airport and the international port. We consider that the northern hotel zone could be a vertical evacuation zone for tourists and local people, following such an earthquake and tsunami. Some hotels in Puerto Vallarta could function 1 3 as a refuge; these seismically resistant structures should have more than four levels, while in the south study zone, from Boca de Tomatlán community to Playa Camarones, the risk area is 1.5 km 2 , and it is feasible for people to walk to a safe area from some points. In the area of Puerto Vallarta, the arrival time (I t ) of the first waves (H i ) is between 19 and 23 min after the earthquake with H i between 3.2 and 4.3 m; then, the tsunami warning is the earthquake itself. The run-up (A t ) arrives between 69 and 74 min after the earthquake with a height (H r ) between 4.6 and 6.8 m.
The results presented in this work are basic in the design of protocols and action plans for Civil Defense in Jalisco (as escape routes and safe places during the phenomenon). Also, it provides essential information for the territorial managers of the province, who design the Partial Development Plan. A preliminary evaluation of essential cost damage for a simplified house and for the cleaning of debris was also calculated. Maps for tsunami hazard and local vulnerability in Puerto Vallarta were made.
The perception of the risk in the minds of the authorities of the Jalisco State will guarantee that economic and social activities are sustainable. The next partial plans of county development must be reviewed, specifically the strip of coastline of up to 20 m elevations in Jalisco State, such that land use favors very low population density and the implementation of a construction standard for seismic-resistant buildings throughout this county.