Análisis estadístico y comportamiento fractal de las réplicas sísmicas del Sur de California

Mediante el análisis estadístico y utilizando diversas técnicas fractales en esta tesis se estudia el comportamiento temporal y espacial de tres series de réplicas sísmicas ocurridas en el Sur de California, que tuvieron lugar después de los terremotos de Landers (Mw=7.3, 1992), Northridge (Mw=6.7, 1994) y Hector Mine (Mw=7.1, 1999) Se plantean tres objetivos principales en este trabajo: 1) Caracterizar y analizar el proceso de ocurrencia de las réplicas sísmicas, en particular el comportamiento temporal que presentan. De acuerdo con la hipótesis que proponen CORREIG et al. (1997) y MORENO et al. (2001), el análisis de este comportamiento temporal muestra que la producción de las réplicas sísmicas se puede describir como una superposición de dos procesos de relajación de los esfuerzos tectónicos. 2) Simular el comportamiento temporal de las tres series de réplicas sísmicas mediante una versión modificada del modelo del Fiber Bundle, el cual describe el proceso de ruptura de un material heterogéneo previamente fracturado, como la corteza terrestre. El análisis de las réplicas sísmicas simuladas con este modelo modificado, que se introduce en el trabajo de MORENO et al. (2001), (FBMdp), nos permitirá encontrar las similitudes y las diferencias con respecto a las series de réplicas reales. Además, nos proporcionará una interpretación y una posible relación entre la dinámica presente en el modelo y el proceso de ruptura que originan las réplicas sísmicas. 3) Analizar y caracterizar el comportamiento fractal de las tres series de réplicas sísmicas mediante dos series temporales, la de distancia, Δ, y la de tiempo, τ, entre réplicas consecutivas. Para realizar este análisis se aplican diversas técnicas fractales como el análisis de rango reescalado, el posible comportamiento de las series como fractales auto-afines y el análisis de la lacunaridad. Además, se utiliza el teorema de Reconstrucción para caracterizar la predictibilidad del sistema y su posible comportamiento caótico. El análisis fractal que se aplica a estas dos series, Δ y τ, se repite para diferentes valores de magnitud umbral, para poder interpretar la influencia que tiene este parámetro en los resultados. De las diversas conclusiones que se obtienen en este estudio, a modo de resumen, se destacan los siguientes: 1) A partir del análisis de la cinemática que presenta la producción de las réplicas sísmicas, se detecta una superposición de dos procesos de relajación del esfuerzo tectónico. El primer proceso describe el decaimiento temporal a largo plazo de las réplicas sísmicas, el cual queda bien descrito por la ley de Omori Modificada, OM. Las réplicas sísmicas que satisfacen este proceso se les denomina leading aftershocks. El segundo proceso describe que existen episodios de réplicas que se producen a un ritmo mayor, alejándose del comportamiento descrito por la ley de OM. Las réplicas sísmicas que se producen de forma súbita se les denominan cascades. El gran número de réplicas que tienen las tres series sísmicas (LND, HM y NOR) permite que, a diferencia de los trabajos de CORREIG et al. (1997) y MORENO et al. (2001), se puedan realizar más análisis estadísticos y aplicar más técnicas fractales a las cascades. De los resultados que se desprenden de estos análisis se concluye que las cascades muestran características destacables y comunes a las tres series de réplicas sísmicas. 2) El FBMdp es un modelo adecuado para describir el proceso de producción de las réplicas sísmicas. La comparación que se realiza entre las series de réplicas simuladas y las series reales muestra que las simulaciones permiten reproducir las características principales que se observan en las secuencias empíricas, en particular, el comportamiento temporal que indica un doble proceso de relajación de los esfuerzos tectónicos. En base a la similitud de las series de réplicas simuladas con las reales, es posible relacionar la dinámica intrínseca de este modelo con el proceso físico subyacente a la producción de las réplicas sísmicas. Por ejemplo, es posible interpretar el fenómeno de las cascades, que se observan en las secuencias de réplicas sísmicas reales y en las simuladas, en base a las características que presentan los sistemas de auto-organización críticos, SOC (self-organized criticality). Cabe mencionar que algunas características de la sismicidad no se pueden reproducir con este modelo, como por ejemplo, la magnitud de las réplicas sísmicas. Es por esto que algunas leyes clásicas como la ley de Gutenberg-Richter o la ley de Båth no se pueden verificar con este modelo. 3) El análisis fractal que se realiza a las series de distancia, Δ, y de tiempo, τ, entre réplicas consecutivas proporciona múltiples resultados. A modo de resumen, se destaca que las series de Δ presentan una ligera persistencia temporal, ya que el exponente de Hurst es ligeramente superior a 0.5. Esta característica es independiente de la magnitud umbral que se utilice. Además las series de Δ se pueden describir como un fractal auto afín del tipo filtered fractional gaussian noise. El teorema de reconstrucción indica que las series de Δ muestran un comportamiento complejo y caótico con una alta inestabilidad predictiva debido a la aleatoriedad que se observa en el mecanismo dinámico. También es interesante destacar que la distribución estadística de la series de Δ muestran que, independientemente de la magnitud mínima de análisis que se utilice, todas quedan bien descritas por una única función de distribución acumulada que es la de Pareto Generalizada. El análisis fractal que se realiza a las series de τ muestra resultados destacables, en particular, cuando se realiza la comparación entre las series de τ y algunas series de tiempo teóricas, τteo, las cuales obedecen estrictamente la ley de OM. Esta comparación pone en evidencia que el comportamiento de las series de τ está alterado por la presencia de las cascades. Por lo tanto, se reafirma la hipótesis que indica que, aunque la ley de Omori Modificada describe el proceso general de decaimiento de las réplicas sísmicas, existe otro proceso físico simultáneo que da pie a que ocurran aceleraciones súbitas en la producción de algunas réplicas sísmicas.In this PhD thesis we are interested in the time and spatial behavior of seismic aftershock sequences. Through statistical analyses and several fractal techniques we intend to analyze three aftershocks sequences occurred at Southern California, after the Landers (Mw = 7.3, 1992), Northridge (Mw = 6.7, 1994) and Hector Mine (Mw = 7.1, 1999) mainshocks. There are three main objectives in this thesis: 1) To characterize and analyze the process of occurrence of aftershocks, particularly the time behavior they exhibit. 2) To simulate the time behavior of the three aftershocks series through a modified version of the Fiber Bundle model, describing the rupture process in heterogeneous and fractured materials, like the Earth crust. 3) To analyze and characterize the fractal behavior of the three aftershock series through two time series, the elapsed distance, ¿, and the elapsed time, t, between consecutive aftershocks. As a summary, the main conclusions are listed below: 1) The kinematic analysis of the aftershock sequences shows a superposition of two different processes of tectonic stress release. The first process describes a long-term time decay of aftershocks, which is well described by the modified Omori law, MO. The aftershocks that satisfy this process are called leading aftershocks. The second process describes the aftershock production at a higher rate, which departs from the behavior described by MO law. These groups of seismic aftershocks are called cascades. Unlike the study by CORREIG et al. (1997) and MORENO et al. (2001), the much larger number of aftershocks belonging to the three sequences (LND, HM and NOR) allows the implementation of additional statistical analyses and fractal techniques to the cascades. The results derived from these analyses lead to conclude that cascades show remarkable features common to the three aftershock series. 2) The FBMdp is a suitable model to describe the process of aftershock generation. The comparison between simulated and real aftershock sequences shows that this model can reproduce features observed in aftershock sequences, in particular, the time behavior suggesting a double process of tectonic stress release. The similarity of simulated and real aftershock sequences make possible to relate the intrinsic model dynamics with the physical process leading the aftershock generation. For example, it is possible to interpret the phenomenon of cascades, which are observed in the simulated and real aftershocks sequences, in the theoretical framework of the self-organized critical (SOC) systems. 3) The fractal analyses applied to the elapsed distances, ¿, and time, t, series show different results. As a summary, it can be noted that the series of ¿ depict slight time persistence as the Hurst exponent is slightly higher than 0.5. This feature is independent of the magnitude threshold. Furthermore, the series of ¿ may be described as a self affine fractal, in particular, as a fractional filtered gaussian noise. The reconstruction theorem states that the ¿ series are complex and show a chaotic behavior with high predictive instability due to randomness in the observed dynamic mechanism. Independently of the minimum magnitude used in the analysis, the statistical distribution of all ¿ series is well described by the Generalized Pareto cumulative distribution function. The fractal analyses were applied to t series and also to some theoretical elapsed time series, tteo, fully satisfying the MO law. Remarkable differences are found between the empirical, t, and theoretical, tteo, series. These differences support that the empirical t series are perturbed by the presence of the cascades. Therefore, the hypothesis that, although Modified Omori law describes the general process of aftershock decay, it is confirmed the existence of another physical process leading to sudden accelerations in the aftershock generation

A stochastic rupture earthquake code based on the fiber bundle model (TREMOL v0.1): application to Mexican subduction earthquakes

In general terms, earthquakes are the result of brittle failure within the heterogeneous crust of the Earth. However, the rupture process of a heterogeneous material is a complex physical problem that is difficult to model deterministically due to numerous parameters and physical conditions, which are largely unknown. Considering the variability within the parameterization, it is necessary to analyze earthquakes by means of different approaches. Computational physics may offer alternative ways to study brittle rock failure by generating synthetic seismic data based on physical and statistical models and through the use of only few free parameters. The fiber bundle model (FBM) is a stochastic discrete model of material failure, which is able to describe complex rupture processes in heterogeneous materials. In this article, we present a computer code called the stochasTic Rupture Earthquake MOdeL, TREMOL. This code is based on the principle of the FBM to investigate the rupture process of asperities on the earthquake rupture surface. In order to validate TREMOL, we carried out a parametric study to identify the best parameter configuration while minimizing computational efforts. As test cases, we applied the final configuration to 10 Mexican subduction zone earthquakes in order to compare the synthetic results by TREMOL with seismological observations. According to our results, TREMOL is able to model the rupture of an asperity that is essentially defined by two basic dimensions: (1) the size of the fault plane and (2) the size of the maximum asperity within the fault plane. Based on these data and few additional parameters, TREMOL is able to generate numerous earthquakes as well as a maximum magnitude for different scenarios within a reasonable error range. The simulated earthquake magnitudes are of the same order as the real earthquakes. Thus, TREMOL can be used to analyze the behavior of a single asperity or a group of asperities since TREMOL considers the maximum magnitude occurring on a fault plane as a function of the size of the asperity. TREMOL is a simple and flexible model that allows its users to investigate the role of the initial stress configuration and the dimensions and material properties of seismic asperities. Although various assumptions and simplifications are included in the model, we show that TREMOL can be a powerful tool to deliver promising new insights into earthquake rupture processes.The authors are grateful to two anonymous reviewers and the editor for their relevant and constructive comments that have greatly contributed to improving the paper. M. Monterrubio-Velasco and J. de la Puente thank the European Union’s Horizon 2020 Programme under the ChEESE Project (https://cheese-coe.eu/, last access: 1 May 2019), grant agreement no. 823844, for partially funding this work. M. Monterrubio- Velasco and A. Aguilar-Meléndez thank CONACYT for support of this research project. Quetzalcoatl Rodríguez-Pérez was supported by the Mexican National Council for Science and Technology (CONACYT) (Catedras program, project 1126). This project has received funding from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant agreement no. 777778, MATHROCKS, and from the Spanish Ministry project TIN2016-80957-P. Initial funding for the project through grant UNAM-PAPIIT IN108115 is also gratefully acknowledged.Peer ReviewedPostprint (published version

Multifractal characterization of seismicity: the case of Carterbury region (New Zealand), 2000 -2018

The Multifractal Detrended Fluctuation (MF-DF) algorithm is applied to measure the complexity of two time series, the inter-event hypocentral distance Δδ(t), and the inter-event time series Δτ(t) In particular, we apply this methodology to the seismic sequences produced in the Carterbury region during 18 years (2000-2018). Results indicate a clear multifractal behavior of Δδ(t) and Δτ(t). Moreover, an increses in the complexity is observed when a large event occurs . These results suggest that the MF-DF algorithm could be useful as a seismic precursor index

Evolution of the multifractal parameters along different steps of a seismic activity: The example of Canterbury 2000–2018 (New Zealand)

The multifractal detrended fluctuation algorithm is applied to a series of distances and elapsed times between consecutive earthquakes recorded along the years 2000–2018 in the Canterbury region (New Zealand). The time evolution of several multifractal parameters (Hurst exponent, Hölder central and maximum exponents, spectral amplitude, asymmetry, and complexity index) is analyzed. Peaks of multifractal parameters, with statistical significance exceeding 95%, are associated with three earthquakes of notable magnitude (equaling or exceeding Mw = 5.7). Additionally, some other peaks are also associated with the swarm of earthquakes of moderate magnitude. Possible shortcomings created by this assignment to mainshocks or swarms can be removed by comparing the results corresponding to elapsed times and interevent distances between consecutive events. Additionally, the Buishand test, which is used to verify the statistical significance of the detected peaks, also discriminates between mainshocks of notable seismic magnitude and swarms of earthquakes with moderate magnitude. The obtained results, based on the multifractal structure of the seismic activity, could also represent some advances in predicting, with sufficient time, forthcoming mainshocks of high magnitude and mitigate their destructive effects.The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation program, under Grant Agreement No. 823844, the ChEESE CoE Project.Peer ReviewedPostprint (published version

Comparative analysis of a new assessment of the seismic risk of residential buildings of two districts of Barcelona

There are personal and institutional decisions that can increase the seismic resilience of the buildings in a city. However, some of these decisions are possible if we have basic knowledge of buildings’ seismic risk. The present document describes the main results of a detailed study of seismic vulnerability and seismic risk of residential buildings of Ciutat Vella (the ancient district of Barcelona) and Nou Barris (one of the newest districts of Barcelona). In this study, we assessed seismic risk according to the Vulnerability Index Method-Probabilistic named as VIM_P. Moreover, we analyzed the influence of basic buildings’ features in the final vulnerability and seismic risk values. For instance, we assessed the seismic vulnerability and the seismic risk of groups of buildings defined according to the number of stories of the buildings. Findings of this research reveal that the annual frequency of exceedance of the collapse damage state in Ciutat Vella buildings is, on average, 4.7 times higher than for the buildings in Nou Barris. Moreover, according to the Best vulnerability curve, 70.31% and 2.81% of Ciutat Vella and Nou Barris buildings, respectively, have an annual frequency of exceedance of the collapse damage state greater than 1 × 10–5.The present research has received partial funding from the European Union’s Horizon 2020 research 826 and innovation program (grant agreement Nº 823844, ChEESE CoE Project).Peer ReviewedPostprint (author's final draft

Fractal structure and predictability of distances between consecutive events: an analysis of three seismic aftershock sequences in Southern California

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Analysis of the key features of the seismic actions due to the three main earthquakes of May 11, 2011 in Lorca, Spain

The seismic records are in general valuable information, especially in cases where damage in buildings has occurred. The main purpose of the present document is to describe the principal results of the analysis of features of ground motions due to the main three earthquakes that occurred in Spain on May 11, 2011. In this day the major earthquake had a magnitude of 5.1 Mw. This event triggered different levels of damage in numerous buildings in the city of Lorca located in southern Spain. Unfortunately, 9 persons died due mainly to the collapse of non-structural elements. We describe in the present paper the application of the software Seismograms Analyzer-e (SA-e) to perform the processing and the analysis of the seismic records obtained in five stations during the main three earthquakes on May 11 (the largest earthquake of magnitude 5.1 Mw, the precursor of magnitude 4.5 Mw, and the aftershock of magnitude 3.9 Mw). We also highlight the significant similitudes between the seismograms generated in the LOR station during these three earthquakes. Additionally, we determined the values of acceleration that occurred in the roof of the buildings of Lorca, because these values of acceleration contributed both to the damage of numerous buildings and the collapse of several parapets of some buildings. The analysis of these accelerations is relevant because the collapse of some parapets was the cause of the death of the 9 people that died during the main earthquake. For example, according to our study in the roof of a building with a fundamental period of 0.25 s the acceleration could have reached values near to 1.04 g. We also analyzed the potential of damage in function of the values of CAVSTD. Additionally, we determined hypothetical seismic forces for the design of parapets in buildings of Lorca considering the NCSE-02 normative, and the values of Sa based on the seismic records. We determined a significant difference between the seismic forces that could have been used to design the parapets of the buildings in the Lorca city and the forces determined according to the values of PGA that were proposed in a recent study of seismic hazard for Spain.The first author acknowledges to CONACYT, Barcelona Supercomputing Center, and to the Universidad Veracruzana by their contribution to the development of the present study. Complementary information about Seismograms Analyzer-e is available on the WEB page of SA-e2 . .Peer ReviewedPostprint (published version

The EU Center of Excellence for Exascale in Solid Earth (ChEESE): Implementation, results, and roadmap for the second phase

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