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The paper presents an iterative procedure for the time domain deconvolution in nonlinear elastoplastic materials. The approach is intended for the generation of input motions for dynamic soil–structure interaction (DSSI) numerical analyses when the desired earthquake is specified at the surface of a nonlinear soil deposit. The main advantage is that the same constitutive model (or models) to be used in the DSSI simulation to characterise the soil deposit is also employed in the deconvolution procedure. Therefore, the desired surface motion is recovered from the free-field propagation of the resulting input motion at the base of the numerical model, accounting for the assumed constitutive behaviour of the ground. An application example is also presented, where the potential of the proposed approach is shown., Peer Reviewed, Postprint (published version)

El uso de procedimientos y metodologías estandarizadas para realizar análisis dinámico no lineales (ADNL) está en aumento. En este tipo de análisis, varios de los criterios pueden ser definidos de forma arbitraria o seleccionados a criterio del experto, tal es el caso de la selección de los acelerogramas a ser utilizados como dato de partida para el ADNL. Es evidente que una selección inadecuada de los parámetros de entrada, incluyendo las acciones sísmicas, generaría resultados poco realistas y sin sentido físico. En este sentido, el presente estudio tiene como objetivo analizar la influencia de la intensidad de Arias (IA) y la duración significativa (Da5-95) en la selección de registros de aceleración compatibles con un espectro de diseño objetivo para la realización de ADNL. De forma particular, se estudia la variación del daño estructural de un edificio a partir de cuatro acelerogramas, con diferentes IA y Da5-95, ajustados al mismo espectro de diseño. Los resultados demuestran diferencias significativas en el daño esperado. Los registros con mayor intensidad de Arias y duración significativa produjeron un daño estructural mayor a pesar de disponer de espectros de respuesta equivalentes. Se concluye que es relevante considerar estos parámetros sísmicos en la selección de acelerogramas para su uso en ADNL, Peer Reviewed, Postprint (published version)

In this paper, a new seismic site classification for the Costa Rican Strong-Motion Network (CRSMN) is proposed. The soil profile classification of the Costa Rican Seismic Code based on the average shear-wave velocity of the top 30 m (VS30) is used as a reference. The site fundamental period (Tf) is included as a parameter to complement the existing characterization. For this, the VS30 measurements from 52 accelerometric stations are related to the site fundamental period obtained through horizontal-to-vertical spectral ratios (HVSR) using ground motion records from the Costa Rican Strong-Motion Database. The H/V ratios are estimated with 5% damped acceleration response spectra and with traditional Fourier amplitude spectra from the S-wave window. From the relation between VS30 and Tf, different ranges of Tf are assigned to the existing soil profile classification and a graph with three-lines and four-areas is proposed to classify the stations of the CRSMN., This research was partially funded by the National Emergency and Risk Prevention Law N° 8933 from Costa Rica and the UCREA funds from the University of Costa Rica through the project referenced as B9780., Peer Reviewed, Postprint (published version)

In this work, the directionality effects during the MW 7.8 earthquake, which occurred in Muisne (Ecuador) on 16 April 2016, were analyzed under two perspectives. The first one deals with the influence of these effects on seismic intensity measures (IMs), while the second refers to the assessment of the expected damage of a specific building located in Manta city, Ecuador, as a function of its azimuthal orientation. The records of strong motion in 21 accelerometric stations were used to analyze directionality in seismic actions. At the closest station to the epicenter (RRup = 20 km), the peak ground acceleration was 1380 cm/s2 (EW component of the APED station). A detailed study of the response spectra ratifies the importance of directionality and confirms the need to consider these effects in seismic hazard studies. Differences between IMs values that consider the directionality and those obtained from the as-recorded accelerograms are significant and they agree with studies carried out in other regions. Concerning the variation of the expected damage with respect to the building orientation, a reinforced concrete building, which was seriously affected by the earthquake, was taken as a case study. For this analysis, the accelerograms recorded at a nearby station and detailed structural documentation were used. The ETABS software was used for the structural analysis. Modal and pushover analyses were performed, obtaining capacity curves and capacity spectra in the two main axes of the building. Two advanced methods for damage assessment were used to obtain fragility and mean damage state curves. The performance points were obtained through the linear equivalent approximation. This allows estimation and analysis of the expected mean damage state and the probability of complete damage as functions of the building orientation. Results show that the actual probability of complete damage is close to 60%. This fact is mainly due to the greater severity of the seismic action, This research has been partially funded by the Ministry of Economy and Competitiveness (MINECO) of the Spanish Government and by the European Regional Development Fund (ERDF) of the European Union (EU) through projects with references CGL2015-65913-P (MINECO/ERDF, EU) and EFA158/16/POCRISC (INTERREG/POCTEFA. EU). R.E.A. holds a PhD fellowship from the Consejo Nacional de Ciencia y Tecnología (CONACyT) in México., Peer Reviewed, Postprint (published version)

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Earthquake Engineering on 2019, available online at: http://www.tandfonline.com/10.1080/13632469.2019.1597783, Recent research have proven the importance of considering the directionality effect on the expected seismic damage of structures. However, it demands a high computational effort if the nonlinear dynamic analysis (NLDA) is used to estimate the seismic response. This paper presents a simplified approach to obtain peak response parameters for a building subjected to bi-directional ground motions considering the directionality effect. To do so, the maximum and median response spectra, considering all the non-redundant response spectra, of several ground motion pairs are calculated. Afterwards, a spectral matching technique is applied to these spectra and new acceleration components are obtained. A series of NLDA are performed with these new components and the roof displacement and base shear values are calculated. These results are compared with the maximum and median values, calculated by performing a series of NLDA, after rotating the earthquakes records by considering increments of 1° in the interval 0°–180°. The results agree with both approaches validating the efficiency of the simplified proposed approach., This research was partially funded by the Spanish Government’s Ministry of Economy and Competitiveness (MINECO) and by the European Regional Development Fund (ERDF) of the European Union (EU) through the project referenced as CGL2015-65913-P (MINECO/ERDF, EU). The first author is supported by a Ph.D. scholarship grant from the Institute for the Training and Development of Human Resources (IFARHU) and the Government of Panama’s National Secretariat of Science, Technology, and Innovation (SENACYT)., Peer Reviewed, Postprint (author's final draft)

Estimations of seismic risk in urban areas should include quantifications of the expected damage to civil structures subjected to earthquakes. In buildings, this quantification depends on the maximum inter-story drift (MIDR), among other aspects. In this study, the correlation between several intensity measures (IMs) and the maximum inter-story drift of steel structures was investigated. Three steel frame buildings of 3, 7 and 13 stories were used as a testbed. These buildings were modelled as 2D framed structures. For the seismic hazard, forty strong ground motion pairs were selected (80 individual horizontal components) from the Italian database. These records were scaled to a specific peak ground acceleration (PGA) and matched to a design spectrum from Eurocode 8. Nonlinear dynamic analysis was used to estimate the seismic response of the structures. Thus, 720 nonlinear dynamic analyses (NLDA) were performed [3 structures × (80 as recorded accelerograms + 80 scaled records + 80 matched records)]. Preliminary results indicate that PGA and MIDR show the worst correlation. A higher correlation was observed for peak ground velocity, root-mean-square velocity and specific energy density intensity-based measures. Finally, a new IM, which is highly correlated with MIDR, is proposed. This IM is called IΔ-PGV and considers both the PGV and the significant duration., Peer Reviewed, Postprint (author's final draft)

In this article, we present a strong-motion database from earthquakes recorded by the Earthquake Engineering Laboratory at the University of Costa Rica. The database consists of 2471 three-component accelerograms from 155 digitally recorded events. It covers the last 20 yr of measurements, including records from the 5 September 2012 Mw 7.6 Nicoya earthquake. The engineering and seismological communities can use this data either to conduct new research or to improve seismic hazard studies in the region. A catalog is also available with metadata of each record containing several intensity measures from the ground-motion time histories., This research was partially funded by the National Emergency and Risk Prevention Law Number 8933 from Costa Rica, the Espacio Universitario de Estudios Avanzados (UCREA) funds from the University of Costa Rica through the project referenced as B9780, and the Spanish Government’s Ministry of Economy and Competitiveness (MINECO) through the project referenced as CGL2015-65913-P. L. A. P. is supported by a Ph.D. Scholarship Grant from the Government of Panama’s Institute for the Training and Development of Human Resources (IFARHU) and the National Secretariat of Science, Technology, and Innovation (SENACYT)., Peer Reviewed, Postprint (author's final draft)

The paper investigates directionality effects of ground motions in the context of dynamic soil-structure interaction (DSSI) analyses. The problem addressed corresponds to a nonlinear soil deposit, overlaying firm ground, where the input motion was derived from an acceleration time history recorded at a rock outcrop. A simplified procedure is proposed to incorporate directionality effects. The main objective is to identify in advance the incidence angle producing the maximum response of a structure for a given earthquake. Results from the simplified procedure were evaluated by comparison with what is called here the complete rotational approach, where the behaviour of the structure, as a function of the incidence angle of the input motion, is derived through a large number of nonlinear dynamic soil-structure interaction analyses. The obtained results show the importance of considering directionality effects in DSSI analyses. The maximum response of the system was reasonably captured with the simplified approach., Peer Reviewed, Postprint (author's final draft)

Aplicat embargament des de la data de defensa fnis al 31 de desembre de 2021, Premi a la millor tesis doctoral en l'àmbit de la geofísica, a la XXVI Convocatòria dels Premis de Geofísica de la fundació José García-Siñeriz., Earthquakes are defined as a "violent shaking of the Earth's crust and mantle, caused by forces acting inside the Earth". In most cases, these forces are caused by an energy release process generated from the contact of the Earth's tectonic plates. Other less common causes are the human-induced earthquakes or those generated through volcanic activity. In either case, the energy is released in the form of multi-directional waves, which reach the surface, causing different effects. However, the intensity of an earthquake is not uniform in all its propagating directions. Many times, the motion is polarized due to the type of fault and/or the proximity to it, causing higher intensities in specific directions, depending on the dynamics and geometry of the rupture. This is what is known as the directivity effect. Furthermore, both the intensity and the shape of the wave vary depending on the propagation medium. Ground motion prediction models deal with the spread of the released energy from source to site. Local site effects, both soil effects and topographical effects, are also important. Rigid media, such as rocky and stiff soils, do not tend to amplify the seismic motion, while soft soils amplify specific frequencies depending on local sub-soil geology and on the motion characteristics. Directionality effects refer to the strong motion in a specific site. This thesis deals with two important issues related to directionality. The first one refers to the orientation of the sensors recording the seismic actions; the second one refers to the expected damage in buildings depending on the directions of their strong and weak main axes. It is worth to mention that nowadays, directionality effects are not considered in most structural regulations. In this thesis, special attention is paid to the directionality and soil effects. Since 2008, around 360,000 earthquake fatalities have been reported. This evidence demonstrates the need to develop more and better ways to assess and t, Els terratrèmols es defineixen com una "sacsejada violenta de l'escorça i el mantell, produïda per forces que actuen a l’interior de la Terra". En la majoria dels casos, aquestes forces són causades per processos relacionats amb l’alliberament d'energia, produït pel contacte entre plaques tectòniques. Altres terratrèmols menys freqüents, són els induïts per activitats antròpiques o els d’origen volcànic. En qualsevol cas, l'energia s'allibera en forma d'ones multidireccionals, que arriben a la superfície, causant efectes diversos. Les intensitats causades per un terratrèmol però, no són uniformes en totes les direccions de la seva propagació. Tot sovint, el moviment fort està polaritzat, degut al tipus de falla i/o a la proximitat a l’hipocentre, de forma que, depenent de la geometria i dinàmica de la ruptura, les acceleracions són més intenses en determinades direccions. Aquest fenomen es coneix com l’efecte de directivitat. D’altra banda, la intensitat i la forma de l'ona varien depenent del medi de propagació. En aquest sentit, els models predictius del moviment fort del sòl tenen en compte, també, el efectes deguts a la propagació, des de la font al lloc d’interès, de l'energia alliberada. Els efectes locals, principalment els deguts a la topografia i a la geologia locals, també són importants. Els medis rígids, com els sòls rocosos i compactes, no tendeixen a amplificar el moviment sísmic, mentre que els sòls tous sí que amplifiquen freqüències específiques, depenent de les propietats del subsòl i de les característiques del moviment. Els efectes de direccionalitat fan referència al moviment fort en un lloc específic. Aquesta tesis aborda dos temes importants en relació a aquests efectes. El primer es refereix a l’orientació dels sensors que enregistren les accions sísmiques; el segon està relacionat amb el dany esperat en edificis concrets, depenent de l'orientació dels seus eixos principals. Val a dir que, avui en dia, la major part de les normatives sísmique, Award-winning, Postprint (published version)

In this paper, remote and in situ techniques to estimate the dynamic response of a building to ambient vibration are reported: data acquired through a real-aperture radar (RAR) interferometer and conventional accelerometers are analyzed. A five-story reinforced concrete housing building, which was damaged during the May 11th 2011 Lorca (Spain) earthquake, is used as a case study. The building was monitored using both types of instruments. The dynamic properties of the building are estimated first taking acceleration measurements using a set of 10 high-precision accelerometers installed on the roof of the building. Further, the displacement–time histories, recorded with the RAR device pointing to a corner of the building, are analyzed. Then, the ability and shortcomings of RAR measurements to deal with the fundamental frequencies of vibration of the structure are investigated. The advantages and limitations of from-inside (accelerometric) and from-outside (RAR) measurements are highlighted and discussed. A relevant conclusion is that, after strong earthquakes, RAR may be an interesting and useful tool, as it allows surveying the structural response of mid-rise buildings remotely, without the need to enter the structures, which may be dangerous for inspectors or technicians in cases of severely damaged buildings. Given that the instrumented building suffered significant damage, the ability of these kinds of measurements to detect damage is also discussed., This research has been partially funded by the Ministry of Economy and Competitiveness (MINECO) of the Spanish Government and by the European Regional Development Fund (ERDF) of the European Union (EU) through projects with references CGL2015-65913-P (MINECO/ERDF, EU) and EFA158/16/POCRISC (INTERREG/POCTEFA. EU). R.E.A. holds a PhD fellowship from the Consejo Nacional de Ciencia y Tecnología (CONACyT) in México. L.A.P. is supported by a Ph.D. scholarship grant from the Institute for the Training and Development of Human Resources (IFARHU) and the Government of Panama’s National Secretariat of Science, Technology, and Innovation (SENACYT)., Peer Reviewed, Postprint (published version)

In this study, previous microzonation studies in Barcelona (Spain) were revisited, and available data on the predominant periods of soils in the city were compiled to develop an updated microzonation map of the city. In addition, the building database was updated and used to create a map of building fundamental periods. The crossing of soil predominant period and building fundamental period maps led to the detection of areas in which resonance phenomena and, indeed, increased amplification of the structural response are expected. Thus, zones of Barcelona were identified in which the seismic hazard is probably greater due to resonance effects. The improved microzonation maps and the detection of soil-building resonance areas contribute significantly to enhanced precision and awareness of seismic hazard and risk in Barcelona., We thank Lucille Banham for her assistance in the preparation of the English manuscript. This research was partially funded by the Spanish Government’s Ministry of Economy and Competitiveness (MINECO) and by the European Regional Development Fund (ERDF) of the European Union (EU) through the project referenced as CGL2015-65913-P (MINECO/ ERDF, EU). The first author is supported by a Ph.D. scholarship grant from the Government of Panama’s Institute for the Training and Development of Human Resources (IFARHU) and the National Secretariat of Science, Technology, and Innovation (SENACYT)., Peer Reviewed, Postprint (author's final draft)

Se evalúa el comportamiento sísmico esperado de un edificio mixto, con una sección de hormigón armado y otra sección de estructura metálica. El edificio es un inmueble situado en el municipio costero GAD-M-Manta de Ecuador, de uso comercial y residencial. El edificio sufrió daños durante el terremoto ocurrido el 16 de abril de 2016. Se efectuará una análisis estructural y sísmico detallado, orientado principalmente a evaluación del daño esperado, en caso de terremoto.

In this study, a simplified approach to account for directionality effects on twodimensional (2D) dynamic soil-structure interaction analyses (DSSI) is proposed. When an earthquake is recorded, the direction with the maximum intensities rarely corresponds with the orientation of accelerometers and, therefore, the maximum response of a system generally takes place at an intermediate unknown orientation. A straightforward approach is to perform DSSI analyses with a number of linear combinations of the horizontal as-recorded components to obtain the peak response parameters for each orientation. Nevertheless, DSSI analyses are computationally expensive especially when the nonlinear behavior of the soil is considered. Here, three hypotheses are evaluated for predicting the angle that generates the maximum response of a building. By determining this angle in advance, only one DSSI analysis would be required to obtain the maximum response of a system for a given earthquake. Here, a particular case is analyzed where a ground motion recorded at a rock outcrop is used to derive the input motion for a finite element model, including a soil deposit and a surface structure. A series of 2D dynamic finite element analyses were performed to assess the proposed approach where input motions were obtained from the linear combination of the horizontal as-recorded components of the 1976 Friuli earthquake. The obtained results show the importance of considering directionality effects in DSSI analyses. The maximum response of the system was reasonably captured with the orientation obtained through the simplified approach., This research has been partially funded by the Ministry of Economy and Competitiveness (MINECO) of the Spanish Government and by the European Regional Development Fund (FEDER) of the Eu-ropean Union (UE) through the project reference CGL2015-65913-P (MINECO/FEDER, UE). Alva RE, the first author of the study, is the holder of a PhD fellowship from the Centro Nacional de Ciencia y Tecnología (CONACyT) in México., Postprint (published version)

The equal displacement approximation is a well-known procedure for estimating the non-linear behavior of structures subjected to earthquake ground motions. This procedure plays a significant role in current seismic design, since it constitutes the basic assumption for defining strength reduction factors. In this paper, calculation of the performance point based on this rule is used to estimate engineering demand parameters such as those obtained by advanced probabilistic non-linear dynamic analysis, NLDA. We present a modification to the classic approach, to improve the predictability of the equal displacement rule. Uncertainties in seismic action and structural properties are considered. Mid-rise reinforced concrete buildings will be used as a testbed. To obtain a representative sample of buildings for statistical analysis, we describe the development through implementation of a numerical tool for calculating probabilistic NLDA. This tool, which is expected to evolve into interoperable software for assessing the seismic risk of structures, is developed within the framework of the KaIROS project. The results presented in this paper could be used to estimate the seismic risk of structures in a very simplified manner., Postprint (published version)

The use of sensors to obtain the dynamic properties of structures by means of ambient vibrations has become a common practice. However, conventional and more extensively used methods require the installation of sensors, which should be in contact with the structure. These methods could be even risky in case of structures weakened by a hazardous event, for which the risk of collapse is unknown. In this study, two main subjects are analyzed and discussed. The former is related to the use of the Real-Aperture Radar (RAR) as a non-invasive, remote sensing interferometric method to measure the vibration response to ambient noise of buildings. As a test bed, two high-rise regular buildings with reinforced concrete frames (8-story) and steel frames (12-story), located in Barcelona, Spain, are analyzed. Notice that the RAR device is a sensor using the principle of interferometry to measure displacements. This type of sensors has exhibited a good performance in urban environments at different atmospheric, meteorological and lighting conditions, compared to other types of remote sensors (e.g. Laser Doppler). Another advantage is that RAR devices have a very good resolution and they can operate at great distances from the object to be measured. However, so far, RAR is rarely used in buildings, being still a poorly studied technique. The latter subject is related to the optimal post-processing of the acquired data. At this respect, the Power Spectral Density (PSD) signal-processing technique is used to process the signals acquired. From this analysis, the predominant periods of the analyzed buildings were obtained and then they were compared with those periods obtained from measurements of accelerometers located inside the structures. The results indicate that the use of RAR can be a reliable alternative to estimate the structural periods in a relatively simple and non-invasive manner., Postprint (published version)

In this paper, the directionality effects of the as recoded ground motions are investigated. The Italian accelerometric archive (ITACA) is used for this purpose. A number of 949 horizontal ground motion records (two components) are used. The following measures, resulting from different ways of combining the maximum values (m1,m2) of the two horizontal components were investigated: Geometric Mean (GMRot), projection (Rot) of the two as recorded components onto all non-redundant azimuths and larger (LRot) value [max(m1,m2)]. The sensor-orientation-independent quantities: GMRotDpp, RotDpp, GMRotIpp and LRotDpp have been obtained. In these quantities, pp means percentile and D and I, respectively, mean dependent and independent of the period. The 50th percentiles values of these intensity measures were compared to the GM of the as-recorded components obtaining differences of 1% for GMRotD50 and in the ranges 2-6%, 1-2% and 15-27% respectively for RotD50, GMRotI50 and LRotD50. The three first ratios show a good agreement with similar studies in other regions. Moreover, the vector combination of the two orthogonal time histories (Root of the Sum of Squares, RSS) presents equal values as RotD100 and LRotD100. The study has also been performed by using the maxima of the time histories combinations; the following quantities are thus investigated: mGMRotDpp and mGMRotIpp, where m indicates peak values of the combined time histories. Our results indicate that the ratios between the 50th percentile of these orientation independent intensities and the GM of the as-recorded components, are in the ranges 0.78-0.85 and 0.79-0.86, respectively, proving that former ones are conservative., This research has been partially funded by the government of Spain (Ministry of Economy and Competitiveness –MINECO, in its Spanish acronym) and by the European Regional Development Fund (FEDER, in its Spanish acronym) of the European Union (EU) through projects referenced as: CGL2011-23621 and CGL2015-65913 -P (MINECO / FEDER, UE)., Postprint (published version)

Structures with high lateral stiffness and/or with brittle to semi-brittle elements in their lateral resistant system may exhibit a rapid decrease of their shear capacity and a sudden loss of stiffness when lateral cyclic loads, as those produced by earthquakes, are applied. This behavior can be related to damage (partial or complete) of a particular structural element. In this article, the expected seismic damage is analyzed and assessed in two different structures. The first one is a low-rise reinforced masonry structure, with hollow concrete blocks (2 stories); the second one is a high-rise dual reinforced concrete building (18 stories). In both cases, materials are characterized using a proper hysteresis model, which takes into account softening and shear degradation. To quantify the structural damage, the well-known Park and Ang damage index is used. The damage curves shown in this paper, exhibit a quick damage increase for relatively low-intensity values, which is attributed to nonlinear incursions of several structural elements with low ultimate ductility. However, incremental dynamic analyses are time-consuming; therefore, it becomes important to develop simplified methods, also successfully representing this kind of effects. A recently proposed damage index, which can be computed in an easy and straightforward way from capacity curves or capacity spectra, is modified in this work to include this fast strength degradation. Details of the computations of this new damage index are also described here., This research has been partially funded by the Ministry of Economy and Competitiveness (Ministerio de Economía y Competitividad-MINECO) of the Spanish Government and by the European Regional Development Fund (Fondo Europeo de Desarrollo Regional-FEDER) of the European Union (UE) through projects referenced as: CGL2011-23621 and CGL2015-65913-P (MINECO/FEDER, UE). Mr. Juan Jiménez Pacheco, sponsored by the University of Cuenca, obtained a scholarship from the Ministry of Higher Education, Science and Technology, SENESCYT, Government of Ecuador, for doctoral studies in the Earthquake Engineering program of the UPC-Barcelona Tech., Postprint (published version)

In this paper, a simplified non-invasive method to diagnose the safety state of buildings is tested. The method is based in remote sensing measurements of the natural vibrations of actual buildings using an interferometric Real-Aperture Radar (RAR). This non-invasive technique may allow us to detect damage in buildings by means of the change in their modal properties, mainly the fundamental period, which is measured using ambient vibrations. To test the technique, a set of buildings located in Spain were measured by using the remote procedure and the results were compared with the ones obtained with conventional acceleration or velocity sensors. In this paper, the results a building of the campus of the Technical University of Catalonia (UPC) are shown. The fundamental period of the building was successfully obtained by means of remote and easy measurements. The method is more successful for mid-to high-rise buildings where the RAR shows a better performance. The final purpose of these studies is to check for the ability of such remote sensing surveys to detect damaged buildings. The technique may be very useful in post-earthquake inspections as the method may allow us to know the safe/unsafe state of buildings without entering them., This research has been partially funded by the Ministry of Economy and Competitiveness (MINECO) of the Spanish Government and by the European Regional Development Fund (FEDER) of the Eu-ropean Union (UE) through the project reference CGL2015-65913-P (MINECO/FEDER, UE). Alva RE, the first author of the study, is the holder of a PhD fellowship from the Centro Nacional de Ciencia y Tecnología (CONACyT) in México., Postprint (published version)

En esta investigación se han comparado las nuevas medidas de intensidad del movimiento del suelo, propuestas por Boore et al. (Boore et al. 2006), para una base de datos de acelerogramas de Costa Rica, Nicaragua y El Sal-vador. Estas medidas están basadas en una serie de registros de aceleración ortogonales horizontales, rotados por todos los ángulos posibles, de tal manera que se proponen nuevas medidas que son independientes de la orientación de los sensores, asumiendo únicamente la ortogonalidad del sensor. Estas nuevas medidas son: GMRotDpp y GMRotIpp, donde “pp” representa el percentil, comúnmente “50” y D e I indican que es dependiente o independiente del periodo. Para determinar GMRotDpp, es necesario definir el ángulo de rotación requerido para obtener el valor del percentil (pp) deseado, tomando todas las medias geométricas del conjunto de ángulos de rotación no redundantes, esto para cada uno de los periodos considerados, no pudiendo definir un solo ángulo válido para todos los periodos, por lo cual se dice que es dependiente del periodo. Por su parte la otra nueva medida GMRotIpp , requiere el cálculo de GMRotDpp, y define un único ángulo para el cual la medida se aproxima con el menor error posible al valor dependiente del periodo, siendo esta medida independiente del periodo. Estas dos medidas fueron comparadas entre sí, encontrando una relación que permite determinar qué medida es la más adecuada para cada caso de estudio. Al mismo tiempo fueron comparadas con la máxima respuesta espectral esperada definida por la media cuadrática y se obtuvieron relaciones que fueron comparadas con otras obtenidas por diferentes autores.