Álvaro González | Centre de Recerca Matemàtica (original) (raw)
Papers by Álvaro González
The Munébrega Plio-Quaternary half-graben is a NW-SE trending neotectonic depression located in t... more The Munébrega Plio-Quaternary half-graben is a NW-SE trending neotectonic depression located in the central sector of the intraplate Iberian Range (NE Spain). The master fault of the half-graben offsets an Upper Pleistocene pediment deposit, forming an upslope-facing scarp. A trench dug across the fault scarp exposed a 25-m wide deformation zone consisting of graben and horst fault blocks with fissures in the upper part of the scarp, and a monoclinal flexure affected by normal and reverse faults in the lower part of the scarp. We infer a minimum of three faulting events over the past 72 ka, yielding an average (maximum) recurrence interval of 24 ka. The oldest event (72-41 ka) produced an antislope scarp on the relict pediment surface, confining deposition to the downthrown block. Cross-cutting faults affecting sedimentary units deposited in the sediment trap produced by the first event provide evidence for at least two younger events (33-19? ka). The measured cumulative vertical displacement (7.4 m) yield a minimum vertical slip rate of 0.10 ± 0.01 mm/year (2r error) for the past 72 ka. If the paleoearthquakes ruptured the whole mappable length of the fault (ca. 20 km), they probably had moment magnitudes ca. 6.9 (Stirling et al. Bull Seismol Soc Am, 2002). Such earthquakes would have been more than a magnitude unit larger than the largest ones recorded historically in the Iberian Range. These results suggest that the official seismic hazard assessments, based solely on the historic and instrumental record, may underestimate the seismic hazard in the area.
Seismological Research Letters, 2013
We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an ... more We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an isotropic atmospheric airburst. The lack of sharp wave arrivals for this event hampers
This work presents an original seismogenic source-zones model at the scale of the Iberian Peninsu... more This work presents an original seismogenic source-zones model at the scale of the Iberian Peninsula to be used in seismic hazard calculations at either national or regional levels. The model has resulted from an interactive process among a group of experts in active tectonics and seismotectonics and an expert in seismic hazard analysis who acted as a data integrator. The process included the making of new models specifically developed for this work, as well as literature search for published models, and the presentation of all them in a common format from which the experts at each region were asked to give their opinion. The final model integrates all the experts’ opinions but keeping a common coherency level and, specifically, the applicability of the model for subsequent seismic hazard calculations. However, it is highlighted that the zone model presented here needs to be completed in some areas with the inclusion of active faults that could be modelled as individual seismogenic s...
Tectonophysics, 2006
Numerical models are starting to be used for determining the future behaviour of seismic faults a... more Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models. The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.
Nonlinear Processes in Geophysics, 2003
Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a re... more Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a onedimensional numerical exploration of the loss function. This first strategy is then refined by considering a classification of the seismic cycles of the model according to the presence, or not, of some factors related to the seismicity observed in the cycle. These factors, statistically speaking, enlarge or shorten the length of the cycles. The independent evaluation of the impact of these factors in the forecast process leads to two-dimensional numerical explorations. Finally, and as a third gradual step in the process of refinement, we combine these factors leading to a three-dimensional exploration. The final improvement in the loss function is about 8.5%.
Journal of Seismology, 2006
The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significa... more The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significantly increased the mean and aperiodicity of the series of time intervals between mainshocks in this segment of the San Andreas fault. We use five different statistical distributions as renewal models to fit this new series and to estimate the time-dependent probability of the next Parkfield mainshock. Three of these distributions (lognormal, gamma and Weibull) are frequently used in reliability and time-to-failure problems. The other two come from physicallybased models of earthquake recurrence (the Brownian Passage Time Model and the Minimalist Model). The differences resulting from these five renewal models are emphasized.
Journal of Iberian Geology, 2012
Europhysics Letters (EPL), 2004
A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of... more A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of anticipated synchronization between pairs of chaotic oscillators, recently developed in the area of Dynamical Systems, and by the earthquake forecasting algorithms in which different pattern recognition functions are used for identifying seismic premonitory phenomena. In the new strategy, copies (clones) of the original system (the master) are defined, and they are driven using rules that tend to synchronize them with the master dynamics. The observation of definite patterns in the state of the clones is the signal for connecting an alarm in the original system that efficiently marks the impending occurrence of a catastrophic event. The power of this method is quantitatively illustrated by forecasting the occurrence of characteristic earthquakes in the so-called Minimalist Model.
![Research paper thumbnail of Erratum: “The occupation of a box as a toy model for the seismic cycle of a fault” [Am. J. Phys. 73 (10), 946–952 (2005)]](https://attachments.academia-assets.com/89297058/thumbnails/1.jpg)
](American Journal of Physics, 2007
We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large e... more We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around 6 that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.
Physical Review E, Dec 3, 2019
Power-law type distributions are extensively found when studying the behaviour of many complex sy... more Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult to establish power-law behaviour unambiguously. In this work we present a statistical procedure to merge different datasets with the aim of obtaining a broader fitting range for the statistics of different experiments or observations of the same system or the same universality class. This procedure is applied to the Gutenberg-Richter law for earthquakes and for synthetic earthquakes (acoustic emission events) generated in the laboratory: labquakes. Different earthquake catalogs have been merged finding a Gutenberg-Ricther law holding for more than eight orders of magnitude in seismic moment. The value of the exponent of the energy distribution of labquakes depends on the material used in the compression experiments. By means of the procedure exposed in this manuscript, it has been found that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent.
Earth and Space Science, 2019
The size or energy of diverse structures or phenomena in geoscience appears to follow power law d... more The size or energy of diverse structures or phenomena in geoscience appears to follow power law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially important in these cases, given that they may be used to assess long-term hazard. After reviewing the theoretical background for power law distributions, we improve an objective statistical fitting method and apply it to diverse data sets. The method is described in full detail, and it is easy to implement. Our analysis elucidates the range of validity of the power law fit and the corresponding exponent and whether a power law tail is improved by a truncated lognormal. We confirm that impact fireballs and Californian earthquakes show untruncated power law behavior, whereas global earthquakes follow a double power law. Rain precipitation over space and time and tropical cyclones show a truncated power law regime. Karst sinkholes and wildfires, in contrast, are better described by truncated lognormals, although wildfires also may show power law regimes. Our conclusions only apply to the analyzed data sets but show the potential of applying this robust statistical technique in the future.
Geophysical Journal International, 2014
A spatially localized seismic sequence originated few tens of kilometres offshore the Mediterrane... more A spatially localized seismic sequence originated few tens of kilometres offshore the Mediterranean coast of Spain, close to the Ebro river delta, starting on 2013 September 5, and lasting at least until 2013 October. The sequence culminated in a maximal moment magnitude M w 4.3 earthquake, on 2013 October 1. The most relevant seismogenic feature in the area is the Fosa de Amposta fault system, which includes different strands mapped at different distances to the coast, with a general NE-SW orientation, roughly parallel to the coastline. However, no significant known historical seismicity has involved this fault system in the past. The epicentral region is also located near the offshore platform of the Castor project, where gas is conducted through a pipeline from mainland and where it was recently injected in a depleted oil reservoir, at about 2 km depth. We analyse the temporal evolution of the seismic sequence and use full waveform techniques to derive absolute and relative locations, estimate depths and focal mechanisms for the largest events in the sequence (with magnitude mbLg larger than 3), and compare them to a previous event (2012 April 8, mbLg 3.3) taking place in the same region prior to the gas injection. Moment tensor inversion results show that the overall seismicity in this sequence is characterized by oblique mechanisms with a normal fault component, with a 30 • low-dip angle plane oriented NNE-SSW and a subvertical plane oriented NW-SE. The combined analysis of hypocentral location and focal mechanisms could indicate that the seismic sequence corresponds to rupture processes along shallow low-dip surfaces, which could have been triggered by the gas injection in the reservoir, and excludes the activation of the Amposta fault, as its known orientation is inconsistent with focal mechanism results. An alternative scenario includes the iterated triggering of a system of steep faults oriented NW-SE, which were identified by prior marine seismics investigations.
Seismological Research Letters, Nov 1, 2013
We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an ... more We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an isotropic atmospheric airburst. The lack of sharp wave arrivals for this event hampers
These are the selected, high-quality displacement seismograms (28 vertical and 6 radial) of the C... more These are the selected, high-quality displacement seismograms (28 vertical and 6 radial) of the Chelyabinsk meteor, recorded at 28 broadband seismic stations. They are shown, with normalized amplitude, in order of increasing epicentral distance. Recorded seismograms are in red, and modeled ones in blue. Each caption indicates the epicentral distance in km, network code (e.g., II), station code (e.g., ARU), "Z" for vertical seismograms and "R" for radial ones. The bottom axis shows the recording time (hours and minutes UTC). The origin time of the meteor's terminal explosion is indicated by red triangles.
The Munébrega Plio-Quaternary half-graben is a NW-SE trending neotectonic depression located in t... more The Munébrega Plio-Quaternary half-graben is a NW-SE trending neotectonic depression located in the central sector of the intraplate Iberian Range (NE Spain). The master fault of the half-graben offsets an Upper Pleistocene pediment deposit, forming an upslope-facing scarp. A trench dug across the fault scarp exposed a 25-m wide deformation zone consisting of graben and horst fault blocks with fissures in the upper part of the scarp, and a monoclinal flexure affected by normal and reverse faults in the lower part of the scarp. We infer a minimum of three faulting events over the past 72 ka, yielding an average (maximum) recurrence interval of 24 ka. The oldest event (72-41 ka) produced an antislope scarp on the relict pediment surface, confining deposition to the downthrown block. Cross-cutting faults affecting sedimentary units deposited in the sediment trap produced by the first event provide evidence for at least two younger events (33-19? ka). The measured cumulative vertical displacement (7.4 m) yield a minimum vertical slip rate of 0.10 ± 0.01 mm/year (2r error) for the past 72 ka. If the paleoearthquakes ruptured the whole mappable length of the fault (ca. 20 km), they probably had moment magnitudes ca. 6.9 (Stirling et al. Bull Seismol Soc Am, 2002). Such earthquakes would have been more than a magnitude unit larger than the largest ones recorded historically in the Iberian Range. These results suggest that the official seismic hazard assessments, based solely on the historic and instrumental record, may underestimate the seismic hazard in the area.
Seismological Research Letters, 2013
We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an ... more We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an isotropic atmospheric airburst. The lack of sharp wave arrivals for this event hampers
This work presents an original seismogenic source-zones model at the scale of the Iberian Peninsu... more This work presents an original seismogenic source-zones model at the scale of the Iberian Peninsula to be used in seismic hazard calculations at either national or regional levels. The model has resulted from an interactive process among a group of experts in active tectonics and seismotectonics and an expert in seismic hazard analysis who acted as a data integrator. The process included the making of new models specifically developed for this work, as well as literature search for published models, and the presentation of all them in a common format from which the experts at each region were asked to give their opinion. The final model integrates all the experts’ opinions but keeping a common coherency level and, specifically, the applicability of the model for subsequent seismic hazard calculations. However, it is highlighted that the zone model presented here needs to be completed in some areas with the inclusion of active faults that could be modelled as individual seismogenic s...
Tectonophysics, 2006
Numerical models are starting to be used for determining the future behaviour of seismic faults a... more Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models. The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.
Nonlinear Processes in Geophysics, 2003
Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a re... more Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a onedimensional numerical exploration of the loss function. This first strategy is then refined by considering a classification of the seismic cycles of the model according to the presence, or not, of some factors related to the seismicity observed in the cycle. These factors, statistically speaking, enlarge or shorten the length of the cycles. The independent evaluation of the impact of these factors in the forecast process leads to two-dimensional numerical explorations. Finally, and as a third gradual step in the process of refinement, we combine these factors leading to a three-dimensional exploration. The final improvement in the loss function is about 8.5%.
Journal of Seismology, 2006
The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significa... more The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significantly increased the mean and aperiodicity of the series of time intervals between mainshocks in this segment of the San Andreas fault. We use five different statistical distributions as renewal models to fit this new series and to estimate the time-dependent probability of the next Parkfield mainshock. Three of these distributions (lognormal, gamma and Weibull) are frequently used in reliability and time-to-failure problems. The other two come from physicallybased models of earthquake recurrence (the Brownian Passage Time Model and the Minimalist Model). The differences resulting from these five renewal models are emphasized.
Journal of Iberian Geology, 2012
Europhysics Letters (EPL), 2004
A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of... more A new forecasting strategy for stochastic systems is introduced. It is inspired by the concept of anticipated synchronization between pairs of chaotic oscillators, recently developed in the area of Dynamical Systems, and by the earthquake forecasting algorithms in which different pattern recognition functions are used for identifying seismic premonitory phenomena. In the new strategy, copies (clones) of the original system (the master) are defined, and they are driven using rules that tend to synchronize them with the master dynamics. The observation of definite patterns in the state of the clones is the signal for connecting an alarm in the original system that efficiently marks the impending occurrence of a catastrophic event. The power of this method is quantitatively illustrated by forecasting the occurrence of characteristic earthquakes in the so-called Minimalist Model.
American Journal of Physics, 2007
We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large e... more We illustrate how a simple statistical model can describe the quasiperiodic occurrence of large earthquakes. The model idealizes the loading of elastic energy in a seismic fault by the stochastic filling of a box. The emptying of the box after it is full is analogous to the generation of a large earthquake in which the fault relaxes after having been loaded to its failure threshold. The duration of the filling process is analogous to the seismic cycle, the time interval between two successive large earthquakes in a particular fault. The simplicity of the model enables us to derive the statistical distribution of its seismic cycle. We use this distribution to fit the series of earthquakes with magnitude around 6 that occurred at the Parkfield segment of the San Andreas fault in California. Using this fit, we estimate the probability of the next large earthquake at Parkfield and devise a simple forecasting strategy.
Physical Review E, Dec 3, 2019
Power-law type distributions are extensively found when studying the behaviour of many complex sy... more Power-law type distributions are extensively found when studying the behaviour of many complex systems. However, due to limitations in data acquisition, empirical datasets often only cover a narrow range of observation, making it difficult to establish power-law behaviour unambiguously. In this work we present a statistical procedure to merge different datasets with the aim of obtaining a broader fitting range for the statistics of different experiments or observations of the same system or the same universality class. This procedure is applied to the Gutenberg-Richter law for earthquakes and for synthetic earthquakes (acoustic emission events) generated in the laboratory: labquakes. Different earthquake catalogs have been merged finding a Gutenberg-Ricther law holding for more than eight orders of magnitude in seismic moment. The value of the exponent of the energy distribution of labquakes depends on the material used in the compression experiments. By means of the procedure exposed in this manuscript, it has been found that the Gutenberg-Richter law for earthquakes and charcoal labquakes can be characterized by the same power-law exponent.
Earth and Space Science, 2019
The size or energy of diverse structures or phenomena in geoscience appears to follow power law d... more The size or energy of diverse structures or phenomena in geoscience appears to follow power law distributions. A rigorous statistical analysis of such observations is tricky, though. Observables can span several orders of magnitude, but the range for which the power law may be valid is typically truncated, usually because the smallest events are too tiny to be detected and the largest ones are limited by the system size. We revisit several examples of proposed power law distributions dealing with potentially damaging natural phenomena. Adequate fits of the distributions of sizes are especially important in these cases, given that they may be used to assess long-term hazard. After reviewing the theoretical background for power law distributions, we improve an objective statistical fitting method and apply it to diverse data sets. The method is described in full detail, and it is easy to implement. Our analysis elucidates the range of validity of the power law fit and the corresponding exponent and whether a power law tail is improved by a truncated lognormal. We confirm that impact fireballs and Californian earthquakes show untruncated power law behavior, whereas global earthquakes follow a double power law. Rain precipitation over space and time and tropical cyclones show a truncated power law regime. Karst sinkholes and wildfires, in contrast, are better described by truncated lognormals, although wildfires also may show power law regimes. Our conclusions only apply to the analyzed data sets but show the potential of applying this robust statistical technique in the future.
Geophysical Journal International, 2014
A spatially localized seismic sequence originated few tens of kilometres offshore the Mediterrane... more A spatially localized seismic sequence originated few tens of kilometres offshore the Mediterranean coast of Spain, close to the Ebro river delta, starting on 2013 September 5, and lasting at least until 2013 October. The sequence culminated in a maximal moment magnitude M w 4.3 earthquake, on 2013 October 1. The most relevant seismogenic feature in the area is the Fosa de Amposta fault system, which includes different strands mapped at different distances to the coast, with a general NE-SW orientation, roughly parallel to the coastline. However, no significant known historical seismicity has involved this fault system in the past. The epicentral region is also located near the offshore platform of the Castor project, where gas is conducted through a pipeline from mainland and where it was recently injected in a depleted oil reservoir, at about 2 km depth. We analyse the temporal evolution of the seismic sequence and use full waveform techniques to derive absolute and relative locations, estimate depths and focal mechanisms for the largest events in the sequence (with magnitude mbLg larger than 3), and compare them to a previous event (2012 April 8, mbLg 3.3) taking place in the same region prior to the gas injection. Moment tensor inversion results show that the overall seismicity in this sequence is characterized by oblique mechanisms with a normal fault component, with a 30 • low-dip angle plane oriented NNE-SSW and a subvertical plane oriented NW-SE. The combined analysis of hypocentral location and focal mechanisms could indicate that the seismic sequence corresponds to rupture processes along shallow low-dip surfaces, which could have been triggered by the gas injection in the reservoir, and excludes the activation of the Amposta fault, as its known orientation is inconsistent with focal mechanism results. An alternative scenario includes the iterated triggering of a system of steep faults oriented NW-SE, which were identified by prior marine seismics investigations.
Seismological Research Letters, Nov 1, 2013
We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an ... more We determined the parameters of the Chelyabinsk seismic source, modeling it for simplicity as an isotropic atmospheric airburst. The lack of sharp wave arrivals for this event hampers
These are the selected, high-quality displacement seismograms (28 vertical and 6 radial) of the C... more These are the selected, high-quality displacement seismograms (28 vertical and 6 radial) of the Chelyabinsk meteor, recorded at 28 broadband seismic stations. They are shown, with normalized amplitude, in order of increasing epicentral distance. Recorded seismograms are in red, and modeled ones in blue. Each caption indicates the epicentral distance in km, network code (e.g., II), station code (e.g., ARU), "Z" for vertical seismograms and "R" for radial ones. The bottom axis shows the recording time (hours and minutes UTC). The origin time of the meteor's terminal explosion is indicated by red triangles.