Frequency-magnitude Distribution Research Articles

Parameters of the Seismic Regime of the Eastern Sector of the Arctic Zone of the Russian Federation

This work constructs a seismic regime model for the eastern sector of the Arctic Zone of the Russian Federation (AZRF) based on a newly developed, comprehensive integral earthquake catalog for the region, using a uniform magnitude scale from 1982 to 2020. The model parameters are calculated using a novel high-contrast mean-position method, where values are determined within large-radius circles but are assigned to the mean position of epicenters. A quantitative verification method, the L-test, based on the likelihood function, demonstrates that the model aligns well with the initial data. The magnitude–frequency distribution reconstructed from the model corresponds well to observations, both in terms of slope and the number of earthquakes. The epicenters of the largest earthquakes (M ≥ 6) from both the 1982–2020 period and the 1900–1981 period, according to the Kondorskaya–Shebalin catalog, are located in areas with high expected recurrence of such earthquakes as calculated by the model.

The Limits of Applicability of the Gutenberg–Richter Law in the Problems of Seismic Hazard and Risk Assessment

The Gutenberg–Richter law establishes a log-linear relationship between the number of earthquakes that have occurred within some spatiotemporal volume and their magnitude. This similarity property presumably reflects fractal structure of the fault system in which earthquake sources are formed. The Gutenberg–Richter law plays a key role in the problems of seismic hazard and risk assessment. Using the Gutenberg–Richter relationship, we can estimate the average recurrence period of strong earthquakes from the recurrence rate of weaker earthquakes. Since the strongest earthquakes occur infrequently, with intervals of a few hundred years or more, it is not possible to directly assess their recurrence. From indirect geologic and paleoseismic estimates it often seems that strong earthquakes on individual faults occur more frequently than expected in accordance with the Gutenberg–Richter law. Such estimates underlie the hypothesis of the so called characteristic earthquakes. This hypothesis is in many cases additionally supported by the form of the magnitude–frequency distributions for individual faults, constructed from the data of modern earthquake catalogs. At the same time, an important factor affecting the form of the magnitude–frequency distribution is the choice of the spatial domain in which the distribution is constructed. This paper investigates the influence of this factor and determines the conditions under which the Gutenberg–Richter law is applicable for estimating the recurrence of strong earthquakes.

Multimodal Non-Extensive Frequency-Magnitude Distributions and Their Relationship to Multi-Source Seismicity

We investigate multimodal seismicity by analyzing it as the result of multiple seismic sources. We examine three case studies: the Redoubt and Spurr regions in Alaska, where volcanic and subduction-related seismicity occur, and the Kii Peninsula in Japan, where shallow and deep earthquakes are clearly separated. To understand this phenomenon, we perform spatial, temporal, and magnitude analyses. Our application of non-extensive statistical mechanics shows that multimodal models provide a significantly better fit than unimodal ones. We identify patterns in the distributions of time between events and distances between events using multimodal Tsallis q-gamma distributions. In addition, we use the multimodal Sotolongo–Costa model to analyze the magnitude distribution, which effectively captures the complex interactions that may explain the observed lack of fractality in multimodal seismicity.

Seismotectonic assessment of the High Atlas orogen: Implications for the 8 September Mw 6.8 El-Haouz earthquake

The Moroccan High Atlas is a slowly deforming intracontinental orogenic belt, characterized by moderate and diffuse seismic activity. The 8 September 2023 Mw 6.8 El-Haouz earthquake, one of the most powerful quakes recorded in North Africa, has intensified investigations into the seismotectonics of the High Atlas. This study examines seismotectonic patterns in the High Atlas using seismological and geodetic data to better understand the mechanisms driving such seismic events. Seismological data indicate active shortening in the region, contributing to ongoing mountain building. Present-day deformation is partitioned between thrust and strike-slip faulting, with NW-SE compression, consistent with the broader stress field in North Africa. Frequency-magnitude distribution analysis indicates that the Western High Atlas exhibited low b-values, slightly lower than 1, in the eight years preceding the El-Haouz earthquake, with an low b-value (∼ 0.8 ± 0.1) near the epicenter, suggesting high stress accumulation in the region. GNSS observations reveal that the High Atlas experiences low geodetic velocities compared with the Rif collision belt, with displacements below 1 mm/year. Notably, the axial zone of the Western High Atlas exhibits an uplift of 1.1 mm/yr. The combination of moderate shortening and relatively higher uplift prior to the El-Haouz earthquake suggests that present-day deformation in the Western High Atlas is predominantly accommodated by the reactivation of inherited faults in the axial zone. This is further corroborated by the distribution of aftershocks, which supports a steeply dipping seismogenic fault manifested by the Tizi n'Test Fault.

Assessing the Adequacy of Earthquake Catalog Sampling for Long-Term Seismicity in Low-to-Moderate Seismic Regions: A Geodetic Perspective

Abstract Seismic hazard assessment in low-to-moderate seismicity regions can benefit from the knowledge of surface deformation rates to better constrain earthquake recurrence models. This, however, amounts to assuming that the known seismicity rate, generally observed over historical times (i.e., up to a few centuries in Europe), provides a representative sample of the underlying long-term activity. We here investigate how this limited sampling can affect the estimated seismic hazard and whether it can explain the disagreement between the seismic moment loading rate as seen by nowadays Global Navigation Satellite Systems (GNSS) measurements and the seismic moment release rate by past earthquakes, as is sometimes observed in regions with limited activity. We approach this issue by running simulations of earthquake time series over very long timescales that account for temporal clustering and the known magnitude–frequency distribution in such regions, and that those are constrained to a seismic moment rate balance between geodetic and seismicity estimates at very long timescales. We show that, in the example of southeastern Switzerland, taken here as a case study, this sampling issue can indeed explain this disagreement, although it is likely that other phenomena, including aseismic deformation and changes in strain rate due to erosional and/or glacial rebound, may also play a significant role in this mismatch.

Analysis of Magnitude–Frequency Distribution of Earthquakes in the Sichuan Basin, Southwest China

Abstract The Sichuan basin is characterized by underdeveloped active geological structures and low seismic activities. In recent years, an increase in seismicity has been observed in the southern Sichuan basin, which includes small earthquakes induced by water injection during shale gas exploitation and M ≥ 5.0 earthquakes, causing unexpected damage and casualties. This necessitates a comprehensive analysis of the magnitude–frequency distribution of the current seismicity. In this study, we examined the current seismicity using instrumental earthquake records at different periods and estimated the temporal and spatial variations in b-value. We found that the b-values widely vary in the Sichuan basin and analyzed the spatial differences in b-value in seven different earthquake clusters. The results show that the intense fault movement on the western boundary of the Sichuan basin might be the main controlling factor of the increased seismicity in the southern basin instead of being induced by water injection. Furthermore, earthquakes in the Sichuan basin follow the same size distribution as the events on the boundary faults and the Sichuan–Yunnan rhombus active block. Thus, it is appropriate to consider the magnitude–frequency distribution of earthquakes for the Sichuan basin and the Sichuan–Yunnan rhombus block together rather than separately. These results may help improve the recurrence models in probabilistic seismic hazard assessment of the region.

A Benchmarking Method to Rank the Performance of Physics-Based Earthquake Simulations

Abstract Physics-based earthquake simulators are an increasingly popular modeling tool in earthquake forecasting for seismic hazard as well as fault rupture behavior studies. Their popularity comes from their ability to overcome completeness limitations of real catalogs, and also because they allow reproducing complex fault rupture and interaction patterns via modeling the physical processes involved in earthquake nucleation and propagation. One important challenge of these models revolves around selecting the physical input parameters that will yield the better similarity to earthquake relationships observed in nature, for instance, the frictional parameters of the rate-and-state law—a and b—or the initial normal and shear stresses. Because of the scarcity of empirical data, such input parameters are often selected by trial–error exploration and predominantly manual model performance analyses, which can overall be time consuming. We present a new benchmarking approach to analyze and rank the relative performance of simultaneous earthquake simulation catalogs by quantitatively scoring their combined fit to three reference function types: (1) earthquake-scaling relationships, (2) the shape of the magnitude–frequency distributions, and (3) the rates of the surface ruptures from paleoseismology or paleoearthquake occurrences. The approach provides an effective and potentially more efficient approximation to easily identify the models and input parameter combinations that fit more closely to earthquake relations and behavior. The approach also facilitates the exhaustive analysis of many input parameter combinations, identifying systematic correlations between parameters and model outputs that can potentially improve the overall understanding of the physics-based models. Finally, we demonstrate how the method results agree with the published findings in other earthquake simulation evaluations, a fact that reinforces its overall usefulness. The model ranking outputs can be useful for subsequent analyses, particularly in seismic hazard applications, such as the selection of appropriate earthquake occurrence rate models and their weighting for a logic tree.

Seismic variations before Eastern Anatolian catastrophic events in February 2023

AbstractThe East Anatolian Fault System has been intensively studied over the years due to its potential to generate strong earthquakes and the high exposure of the economy and population in the region. This interest intensified even more after the strong earthquakes in the area at the beginning of February 2023, leading to a focused search for features and precursors that might suggest such an upcoming event. We analyze certain characteristics of seismicity within the East Anatolian Fault System before the earthquakes of February 6, 2023, with magnitudes Mw = 7.8 and Mw = 7.5, over the time period between 1983 and 2022. The earthquake catalog from January 1983 to September 2023, created by Turkish Bogazici University KOERI, is used. Processing of the data is performed by the ZMAP 7.1 software used in the MATLAB environment. Events with a magnitude greater than 2.5 are considered in four time periods: 1983–1992, 1993–2002, 2003–2012, and 2013–2022, totaling 29,346 events. The b-value of the magnitude-frequency distribution of earthquakes (slope of the recurrence graph) is determined; the parameter β, indicative of the increase or decrease in the rate of anomalous seismicity, and parameter Z, associated with anomalous seismic quiescence, is evaluated. A significant decrease in the value of b (from 1.07 to 0.84) is observed when comparing the two periods (2013–2017/2018–2022), indicating accumulated stress in the Earth’s crust. Furthermore, the Z parameter analysis for the period July 2021 to December 2022 shows evidence of relative seismic quiet in the examined area compared to the period from January 2020 to the end of June 2021. Those results suggest that the spatiotemporal variations of the studied seismic parameters could serve as predictors of the two very strong seismic events in the southern part of the Eastern Anatolian region of Turkey.

The role of heterogeneous stress in earthquake cycle models of the Hikurangi-Kermadec subduction zone

Summary Seismic and tsunami hazard modelling and preparedness are challenged by uncertainties in the earthquake source process. Important parameters such as the recurrence interval of earthquakes of a given magnitude at a particular location, the probability of multi-fault rupture, earthquake clustering, rupture directivity and slip distribution are often poorly constrained. Physics-based earthquake simulators, such as RSQSim, offer a means of probing uncertainties in these parameters by generating long-term catalogues of earthquake ruptures on a system of known faults. The fault initial stress state in these simulations is typically prescribed as a single uniform value, which can promote characteristic earthquake behaviours and reduce variability in modelled events. Here, we test the role of spatial heterogeneity in the distribution of the initial stresses and frictional properties on earthquake cycle simulations. We focus on the Hikurangi-Kermadec subduction zone, which may produce Mw > 9.0 earthquakes and likely poses a major hazard and risk to Aotearoa New Zealand. We explore RSQSim simulations of Hikurangi-Kermadec subduction earthquake cycles in which we vary the rate and state coefficients (a and b). The results are compared with the magnitude-frequency distribution (MFD) of the instrumental earthquake catalogue and with empirical slip scaling laws from global earthquakes. Our results suggest stress heterogeneity produces more realistic and less characteristic synthetic catalogues, making them particularly well suited for hazard and risk assessment. We further find that the initial stress effects are dominated by the initial effective normal stresses, since the normal stresses evolve more slowly than the shear stresses. A heterogeneous stress model with a constant pore-fluid pressure ratio and a constant state coefficient (b) of 0.003 produces the best fit to MFDs and empirical scaling laws, while the model with variable frictional properties produces the best fit to earthquake depth distribution and empirical scaling laws. This model is our preferred initial stress state and frictional property settings for earthquake modelling of the Hikurangi-Kermadec subduction interface. Introducing heterogeneity of other parameters within RSQSim (e.g. friction coefficient, reference slip rate, characteristic distance, initial state variable, etc) could further improve the applicability of the synthetic earthquake catalogues to seismic hazard problems and form the focus of future research.

On the effect of background seismicity in physics-based earthquake simulations

Physics-based simulations have been extensively employed to generate synthetic earthquake catalogs over the past decade. In this kind of simulation, primary known faults are typically modeled, while smaller and intermediate faults are often neglected. As a result, the location of earthquakes in the simulation is confined to the modeled faults. Furthermore, due to the elimination of off-fault seismicity, a complete match of the frequency-magnitude distribution of the synthetic catalog with observed data is not achieved. This paper presents an approach to include off-fault seismicity (or background seismicity) within the simulation. First, background earthquakes are separated from the primary faults’ earthquakes, and a fault section is assigned to each event. By employing a scaling relationship, the dimensions of these fault sections are determined according to the magnitude of the corresponding event. The fault section’s slip rates are estimated based on the observed frequency-magnitude distribution. Combining the background fault model with the primary fault model results in a comprehensive model that accounts for all stress interactions between fault elements within the simulator in actual locations. As a result, a broader range of frequency-magnitude distribution in the synthetic catalog can be matched to the observations. A case study using one of the available simulators, Virtual Quake, on a sample area is presented. The results demonstrate that eliminating off-fault seismicity could lead to an underestimated assessment of the earthquake probabilities for the whole region and a biased estimation of earthquake rates in individual faults.

Seismotectonics-Driven Estimation of b-Value: Implications for Seismic Hazard Assessment

Abstract Taking full advantage of good-quality historical earthquake and seismogenic source data available for Italy (Catalogo Parametrico dei Terremoti Italiani [CPTI15] and Database of Individual Seismogenic Sources [DISS] databases), we tested the regional variability of the b-value of the Gutenberg–Richter law, focusing on the dominantly extensional, nearly 1200-km-long seismogenic corridor straddling the Apennines chain; an 18,200 km2 area generating about 45% of the seismic moment released countrywide. We carefully chose and tested the most appropriate completeness interval and completeness magnitude (Mc), and used the Lilliefors method, the Utsu test, and a bootstrap technique to verify the quality of our results and inferences. The 0.65 b-value we obtained is substantially lower than b-values used in Italian seismic hazard models, often close to 1.0; yet it predicts more accurately the observed Apennines earthquake record, suggesting that most currently adopted magnitude-frequency distributions underpredict events in the Mw range 6.0–7.1 and overpredict those in the range 5.2–5.5. We also highlight that the time, space, and magnitude distribution of the largest Italian earthquakes hardly follows the Gutenberg–Richter law: it rather favors a characteristic behavior. We contend that the b-value is too critical of a parameter for being calculated using statistically weak data sets, such as those resulting from overly detailed area-source models: one may end up characterizing low-hazard areas more accurately than high-hazard areas. Conversely, we advocate the use of fewer, larger area sources that fully exploit the current understanding of regional seismotectonics, as a way of obtaining more realistic regional hazard models.

Precise relative magnitude measurement improves fracture characterization during hydraulic fracturing

SUMMARY Microseismic monitoring is an important technique to obtain detailed knowledge of in-situ fracture size and orientation during stimulation to maximize fluid flow throughout the rock volume and optimize production. Furthermore, considering that the frequency of earthquake magnitudes empirically follows a power law (i.e. Gutenberg–Richter), the accuracy of microseismic event magnitude distributions is potentially crucial for seismic risk management. In this study, we analyse microseismicity observed during four hydraulic fracture treatments of the legacy Cotton Valley experiment in 1997 at the Carthage gas field of East Texas, where fractures were activated at the base of the sand-shale Upper Cotton Valley formation. We perform waveform cross-correlation to detect similar event clusters, measure relative amplitude from aligned waveform pairs with a principal component analysis, then measure precise relative magnitudes. The new magnitudes significantly reduce the deviations between magnitude differences and relative amplitudes of event pairs. This subsequently reduces the magnitude differences between clusters located at different depths. Reduction in magnitude differences between clusters suggests that some attenuation-related biases could be effectively mitigated with relative magnitude measurements. The maximum likelihood method is applied to understand the magnitude frequency distributions and quantify the seismogenic index of the clusters. Statistical analyses with new magnitudes suggest that fractures that are more favourably oriented for shear failure have lower b-value and higher seismogenic index, suggesting higher potential for relatively larger earthquakes, rather than fractures subparallel to maximum horizontal principal stress orientation.

The estimation of b-value of the frequency–magnitude distribution and of its 1σ intervals from binned magnitude data

SUMMARY The estimation of the slope (b-value) of the frequency–magnitude distribution of earthquakes is based on a formula derived by Aki decades ago, assuming a continuous exponential distribution. However, as the magnitude is usually provided with a limited resolution, its distribution is not continuous but discrete. In the literature, this problem was initially solved by an empirical correction (due to Utsu) to the minimum magnitude, and later by providing an exact formula such as that by Tinti and Mulargia, based on the geometric distribution theory. A recent paper by van der Elst showed that the b-value can be estimated also by considering the magnitude differences (which are proven to follow an exponential discrete Laplace distribution) and that in this case the estimator is more resilient to the incompleteness of the magnitude data set. In this work, we provide the complete theoretical formulation including (i) the derivation of the means and standard deviations of the discrete exponential and Laplace distributions; (ii) the estimators of the decay parameter of the discrete exponential and trimmed Laplace distributions and (iii) the corresponding formulas for the parameter b. We deduce (iv) the standard 1σ intervals for the estimated b. Moreover, we are able (v) to quantify the error associated with the Utsu minimum-magnitude correction. Furthermore, we have discussed the formulas to produce statistically independent magnitude differences. We tested extensively the b-value estimators on simulated synthetic data sets including complete catalogues as well as catalogues affected by a strong incompleteness degree such as aftershock sequences where the incompleteness is made to vary from one event to the next. We have also analysed the real aftershock sequence of the 30/10/2016 Norcia (central Italy) to integrate the finding of the simulations. To judge the performance of the various estimators we have introduced an index p that can be seen as a non-parametric extension of the Student's t index. The main outcomes of this paper are that (1) the b-value estimators devised for continuous magnitude data are not adequate for binned magnitudes, (2) for complete data sets, estimators based on magnitudes and on magnitude differences provide substantially equivalent results, (3) for incomplete magnitude data sets, estimators based on magnitude differences provide better results and (4) for incomplete aftershock sequences there is no evidence that methods based on positive magnitude differences are superior than other methods using differences. This conclusion is further confirmed by our analysis of the above-mentioned Norcia seismic sequence. This last finding contrasts with the van der Elst's claim that the so called ${{b}_ + }$ method is the most adequate to treat real aftershock sequences.

Probabilistic estimation of the source component of seismic hazard in North-Eastern Brazil

Stable continental regions pose unique challenges for conducting Probabilistic Seismic Hazard Analysis because the earthquake activity driving mechanisms are poorly understood. For instance, the lower seismicity (hence the paucity of data) and the absence of well-defined active fault systems complicate accurately determining seismic source parameters. Northeastern Brazil is a stable continental region exhibiting moderate-size events recorded with significant seismic intensities and provoking the collapse of poorly constructed buildings in the last century. Thus, assessing the seismic hazard is critical for seismic risk mitigation. The seismic hazard depends on three components: source, path, and site, and here, we present the probabilistic seismic hazard analysis of the source component for NE Brazil. Spatial aggregation of earthquake sources outlined four areal seismic zones. A goodness-of-fit test rejected the Gutenberg-Richter model of magnitude frequency distribution in one of the studied seismic zones. For this reason, we estimated the magnitude probability distribution function in that zone using a nonparametric adaptive kernel estimator. In other zones the Gutenberg-Richter magnitude frequency model was applied. In either way of the magnitude probability distribution modelling we considered the upper bound for magnitude equal to 6.6 mR, based on the upper bound of a 95 % confidence interval for the standard normal distribution of palaeoearthquake sizes. Our findings suggests that potentially damaging events are likely to occur, and we cannot neglect chances for the occurrence of earthquakes exceeding 5.2 mR. The calculated mean return periods indicate significantly shorter intervals between consecutive large events than palaeoseismic records.

Carbon Loss from Earthquake Induced Landslides in Fiordland

Landslides triggered by two earthquakes in Fiordland, New Zealand, were mapped using Google Earth Pro retro satellite imagery (eye altitude of 1.5-2.5 km, enabling ± 50 m precision), then catalogued and classified in a GIS inventory. Ground acceleration during the 2003 Mw 7.2 Secretary Island Earthquake resulted in at least 1852 landslides, but the larger Mw 7.8 2009 Dusky Sound Earthquake had lower accelerations and produced only 313. Both events dislodged large swaths of native forest, grassland vegetation and soil from Fiordland’s steep slopes in similar proportions, some landing in rivers and fiords. The landslide maps and magnitude-frequency distributions show close similarity to a published Global Forest Loss dataset derived from 2001-2022 satellite imagery. Assuming forest loss in this wilderness is predominantly landslide-related, it enables the more-precise earthquake-induced landslide mapping to be placed in a longer-term context of other vegetation loss, mostly rainfall-induced landslides, during the past two decades. The total area of forest loss during the 2003 earthquake was anomalous, whereas during 2009 the earthquake losses were similar to areas of forest loss assumed to be rainfall-induced landslides throughout Fiordland each year. Carbon concentrations of landslide vegetation and soil were calculated by defining vegetation types from a published Land Cover Database, and soil organic carbon concentration from a 1 km resolution raster dataset. Total carbon loss from earthquake-induced landslides amounts to 2.05E+06 tonnes for the 2003 Mw7.2 and 2.17E+05 tonnes for the 2009 Mw 7.8. By way of comparison, New Zealand’s total annual carbon sequestration was 6.3E+06 tonnes in 2020. Earthquake-induced and rainfall-induced landslides are shown to account for significant changes in stored carbon and available carbon sequestration, especially in areas of densely vegetated land, such as Fiordland. Processes of landscape disturbance should be included in carbon accounting and estimates of national greenhouse gas emissions.
 
 Supervised by: Caroline Orchiston
 Scholarship Project Funded by: Centre for Sustainability

Relation between earthquake swarm activity and tides in the Noto region, Japan

The Noto region in Japan has been experiencing earthquake swarm activity since mid-2018, with repeated rises and falls in activity. Crustal deformation (expansion and uplift) observed there since the end of 2020 has been connected to crustal fluids. Studies in other regions have suggested that tides are related to earthquake swarm activities associated with crustal fluids. Therefore, we investigated whether tides are also involved in the Noto earthquake swarm activity. Our results suggest a tidal correlation only at greater depths in the southern part of the analyzed area (‘region Sd’). There, we inferred that an increase in pore fluid pressure caused by the inflow of deep fluids may have led to a decrease in fault fracture strength, making the local seismicity relatively susceptible to the effects of tidal forces. The significantly high value in region Sd of the scaling parameter b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b$$\\end{document} of the Gutenberg–Richter law (describing the earthquake magnitude–frequency distribution) and observed crustal deformation are consistent with this interpretation.Graphical

18-years of high-Alpine rock wall monitoring using terrestrial laser scanning at the Tour Ronde east face, Mont-Blanc massif

Since the end of the 20th century, each decade has been warmer than the previous one in the European Alps. As a consequence, Alpine rock walls are generally facing high rockfall activity, likely due to permafrost degradation. We use a unique terrestrial laser scanning derived rockfall catalog over 18 years (2005–2022) compared with photographs (1859–2022) to quantify the evolution of the east face of Tour Ronde (3440–3792 m a.s.l.) in the Mont-Blanc massif (western European Alps) that is permafrost-affected. Overall, 210 rockfalls were identified, from 1 to 15 500 m3. Forty-five events were >100 m3 while cumulated volume of events <10 m3 represents <1% of the fallen rocks. The rockfall magnitude-frequency distribution of the overall inventory follows a power law, with a mean exponent b of 0.44 ± 0.03, characterizing a high contribution of large rockfalls. The depth of failure ranges from a few centimeters to more than 20 m while 95% of the rockfalls depth is <5 m, highlighting the role of the active layer. The mean rock wall erosion rate is 18.3 ± 0.2 mm yr−1 for the 2005–2022 period and ranks in the top range of reported values in the Alps. It has greatly increased between the periods 2006–2014 and 2016–2022, probably in relation to a series of summer heat waves. The exceptional erosion rate of 2015 is driven by one large rockfall in August. Since 2006, an ice apron that covered 16 100 m2 has now almost vanished, and the surface of the glacier du Géant at the rock wall foot has lowered by several tens of meters. The retreat of these two ice masses contributed to the rock wall instability as more than 35% of the rockfall volume detached from the deglaciated surfaces.

A statistical framework for detection ofb-value anomalies in Italy

SUMMARYThis study presents a new robust statistical framework, in which to measure relative differences, or deviations from a hypothetical reference value, of Gutenberg–Richter b-value. Moreover, it applies this method to recent seismicity in Italy, to find possible changes of earthquake magnitude distribution in time and space. The method uses bootstrap techniques, which have no prior assumptions about the distribution of data, keeping their basic features. Excluding Central Italy, no significative b-value variation is found, revealing that the frequency–magnitude distribution exponent is substantially stable or that data are not able to reveal hidden variations. Considering the small size of examined magnitude samples, we cannot definitively decide if the higher b-values in Central Italy, consistently founded by all applied tests, have a physical origin or result from a statistical bias. In any case, they indicate short-lived excursions which have a temporary nature and, therefore, cannot be associated solely to spatial variations in tectonic framework. Both the methodological issues and the results of the application to seismicity in Italy show that a correct assessing of b-value changes requests appropriate statistics, that accurately quantify the low accuracy and precision of b-value estimation for small magnitude samples.

On the b-value dependency of injection-induced seismicity on geomechanical parameters

Variability in the b-value, which describes the frequency distribution of earthquake magnitudes, is usually attributed to variations in differential stress in the setting of natural and laboratory earthquakes. However, differential stress is unlikely to explain b-value variations on the reservoir scale of injection-induced seismicity cases where significant differential stress variability can hardly be expected. We investigate the responsible geomechanical parameters for the b-value reduction observed in injection-induced seismicity at the Basel EGS field in Switzerland, for which a measured in-situ stress model and fault orientations of numerous microseismic events are available. We estimate the shear and normal stresses along faults, differential stress, pore pressure increase at failure, and the Coulomb failure stress, for each event. Event magnitude and shear stress display the most systematic and clear correlation between each other, while other parameters do not show a clear correlation with event magnitude. We further examine the relationship between the b-value and these geomechanical parameters. We discover that the b-value systematically decreases with increasing shear stress. Again, other geomechanical parameters do not show a clear correlation with the b-value. We conclude that b-value variability is explained by variations in shear stress in the injection-induced seismicity setting, where near constant differential stress conditions are expected. Furthermore, we observe that b-value reduction with time also correlates with an increasing number of events along faults having high shear stress, which strongly supports our conclusions. Thus, we discovered a profound physical mechanism behind b-value variation in injection-induced seismicity beyond general understanding of b-value variation.

Statistical Analysis of Mt. Vesuvius Earthquakes Highlights Pitfalls in Magnitude Estimation

Here, we characterize the statistical behaviour of the Mt. Vesuvius seismicity using distinct available catalogues. Our analysis confirms that for this area, the GR distribution exhibited two scaling regimes of the b-value, not commonly observed for the standard frequency-magnitude distribution of earthquakes. By assuming a physical cause, we tested four different hypotheses for the source of the break in the scaling: finite size effect, depth variations in the b-value, radial dependence in the b-value, and different b-values for swarm and non-swarm events. None of the above reasons are able to explain the observation. Thus, we investigated the possibility of some pitfalls in magnitude estimation. Based on our analysis, we suggest there is a bias in the duration magnitude the catalogues are based on. This is due to the arbitrary extrapolation to smaller magnitudes of a linear regression derived for earthquakes with m≥3.0. When a suitable correction is applied to the estimated magnitude, the GR distribution assumes the usual shape, with a b-value closer to that usually observed in volcanic areas. Finally, the analysis of the time variation of some statistical parameters reveals that the state of the volcano appears to be stationary over the entire analysed period, possibly with only a slight decrease in the b-value, indicating a small reduction in differential stress.