Gutenberg-Richter B-value Research Articles

Earthquake Magnitude Correlations Expose Short-Term Catalog Incompleteness

Abstract The independence of earthquake magnitudes is a fundamental assumption and limitation in earthquake forecasting. To assess its validity, we examine correlations between the magnitude of successive earthquakes. We first investigate the 2019 Ridgecrest foreshock sequence and find a significant magnitude correlation as well as an unusually low Gutenberg–Richter b-value (≈0.7 using moment magnitudes). We demonstrate that these anomalous features are not indicative of a precursory phase, but a consequence of short-term incompleteness (STI) that is not detected by conventional methods to estimate catalog completeness. Synthetic simulations of this sequence support this explanation: imposing STI leads to significant magnitude correlation and biased b-value estimates. Expanding our investigation to seismicity across southern California reveals pervasive magnitude correlation due to STI, not limited to sequences with large earthquakes. Our findings suggest that magnitude correlation is the most effective indicator of STI, rather than a characteristic of the underlying earthquake-generating process.

Seismicity and fractal analysis in Aswan region, southern Egypt

Seismic activity in Aswan is influenced by the complex interactions of tectonic plates, the accumulation of stress, and the presence of geological fault systems. It revealed that epicenters are well distributed along four fault segments in a conjugate pattern, indicating a prominent E-W compressional stress. This research aims to explore the characteristics of seismicity and seismotectonics, with a focus on assessing their implications for risk reduction and disaster management in this densely populated region. A data review from the Egyptian National Seismological Network (ENSN) identified 464 earthquakes occurred between 2000 and 2021, with local magnitudes ranging from 0.3 to 4.4, and depths up to 25 km. The calculated Gutenberg-Richter b-value is approximately 0.87 ± 0.05, indicating a gradual stress accumulation. The current analysis shows a more consistent level of moderate seismic activity, unlike previous studies in Aswan region that reported a wide range of b-values from 0.554 to 1.07. This suggests that while earlier research captured a wider range of seismic behaviors, recent data indicates a stabilization in earthquake frequency and intensity. Additionally, the fractal dimension (Dc) calculated at 1.57 ± 0.04 shows an intermediate level of complexity and reflecting a clustering pattern of earthquakes. The variations in the b-value with different magnitudes and depths signify the involvement of active smaller faults, responsible for earthquakes up to magnitude 2.2, which then transition to fractured zones inducing earthquakes up to magnitude 2.5. This transition is followed by a decline in seismic activity, indicating regions that are potentially more likely to experience larger earthquakes. Moreover, stress disparities at various depths contribute to smaller earthquakes within the 5–10 km depth range. Return period analysis suggests that the earthquakes of magnitude 3.7 or higher are expected to occur approximately once every decade in Aswan. These findings are of utmost importance for earthquake risk reduction, hazard assessment, and the sustainable development of Aswan area.

Inference of the Gutenberg-Richter b-value: New insights and results

The size-frequency distribution of many geological and geophysical variables, in relation to fractures, faulting and seismicity, is well described by a statistical distribution of the power law type which is characterized by its exponent. For earthquake magnitudes, the exponent is the well-known b-parameter of the Gutenberg-Richter scaling law. In this paper we:•provide a strict statistical derivation of the distribution law of earthquake magnitudes,•show that the maximum likelihood estimator of the b-parameter is unbiased,•demonstrate that the maximum likelihood estimator is invariant to the value chosen as the minimum magnitude threshold in so far as it is larger than the magnitude of completeness of the earthquake catalogue, and•provide a new estimator based on the minimization of the Kolmogorov-Smirnov statistic and provide a strategy for detecting and mapping the spatio-temporal variation of the b-parameter in seismic swarms.The findings are illustrated with simulated data and a case study with real data.

A statistical framework for detection of b-value anomalies in Italy

SUMMARY This 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.

What Is the Effect of Seismic Swarms on Short-Term Seismic Hazard and Gutenberg-Richter b-Value Temporal Variation? Examples from Central Italy, October–November 2023

A seismic hazard can be quantified by using probabilities. Modern seismic forecasting models (e.g., Operational Earthquake Forecasting systems) allow us to quantify the short-term variations in such probabilities. Indeed these probabilities change with time and space, in particular after strong seismic events. However, the short-term seismic hazard could also change during seismic swarms, i.e., a sequence with several small-/medium-sized events. The goal of this work is to quantify these changes, using the Italian Operational Earthquake Forecasting system, and also estimate the variations in the Gutenberg–Richter b-value. We focus our attention on three seismic swarms that occurred in Central Italy in October–November 2023. Our results indicate that short-term variations in seismic hazard are limited, less than an order of magnitude, and also that b-value variations are not significant. Placing our findings in a more general context, we can state that according to currently available models and catalogs, the occurrence of seismic swarms does not significantly affect the short-term seismic hazard.

Injection-induced fault slip and associated seismicity in the lab: Insights from source mechanisms, local stress states and fault geometry

Probing source mechanisms of natural and induced earthquakes is a powerful tool to unveil associated rupture kinematics. The source processes of failure and slip instability driven by stress loading are affected by fault geometry, but the source ruptures of injection-induced seismicity in relation to fault structures and local stress states remain poorly understood. We have conducted a series of fault reactivation and slip experiments on sandstone samples containing faults with different surface roughness (smooth saw-cut fault and fractured rough fault). We impose progressive fluid injection to induce fault slip, and simultaneously monitor the associated acoustic emission (AE) activity. Using high-resolution AE recordings, we perform full moment tensor inversion of all located AE sources, and investigate the changes of AE source characteristics associated with induced fault slip and their relation to fault roughness. For the complex and rough fault, we observe significant non-double-couple components of AE sources and a high degree of focal mechanism heterogeneity. The temporal changes of AE mechanisms associated with injection-induced fault slip on the smooth fault reveal increasing proportions of double-couple components and decreasing variability of AE focal mechanisms when approaching the onset of slip events. The observed inconsistency between the nodal planes of AE sources and the macroscopic fault plane orientation is attributed to the development of secondary fracture networks surrounding the principal slip surface. We analyze changes in the magnitude-frequency characteristics and source mechanisms of AEs with fault-normal distance, showing that for the smooth (mature) fault, Gutenberg–Richter b-value of on-fault seismicity is lower and focal mechanisms are less heterogeneous, compared to off-fault seismicity. Our results emphasize the important role of roughness-related changes in local fault geometry and associated stress heterogeneity for source mechanisms and rupture kinematics of injection-induced seismicity.

Regional Multifractal Variability of the Overall Seismic Activity in Pakistan from 1820 to 2020 via the Application of MDFA on Earthquake Catalogs

The overall seismicity of Pakistan from 1820 to 2020 is analysed in terms of its multifractal behaviour. Seismic events of magnitude ML = 3.0 and above are spatially clustered into four distinct groups, each one corresponding to a different region of high seismic activity. The Multifractal Detrended Fluctuation Analysis (MFDA) method applied on each cluster reveals pronounced inter-cluster heterogeneity in terms of the resulting generalised Hurst exponent and fractality spectrum, possibly due to the particular tectonic characteristics of the regions under investigation. Additional results on the variability of the Gutenberg–Richter b-value across the defined clusters further corroborate the uniqueness of the seismic profile of each region.

Spatial mapping of b-value and fractal dimension prior to November 8, 2022 Doti Earthquake, Nepal.

An earthquake of magnitude 5.6 mb (6.6 ML) hit western Nepal (Doti region) in the wee hours of wednesday morning local time (2:12 AM, 2022.11.08) killing at least six people. Gutenberg-Richter b-value of earthquake distribution and correlation fractal dimension (D2) are estimated for 493 earthquakes with magnitude of completeness 3.6 prior to this earthquake. We consider earthquakes in western Nepal Himalaya and adjoining region (80.0-83.5°E and 27.3-30.5°N) for the period of 1964 to 2022 for the analysis. The b-value 0.68±0.03 implies a high stress zone and the spatial correlation dimension 1.81±0.02 implies a highly heterogeneous region where the epicenters are spatially distributed. Low b-values and high D2 values identify the study region as a high hazard zone. Focal mechanism styles and low b-values correlate with thrust nature of earthquakes and show that the earthquake's occurrence is associated with the dynamics of the faults responsible for generating the past earthquakes.

Source characteristics of icequakes caused by surface crevasses on Urumqi Glacier No. 1, Tianshan, China

SUMMARYIcequakes associated with crevassing provide key information on stress fields and water flow pathways inside glaciers, conditions which are sensitive to temperature and precipitation. In this study, we analyse seismic data from 321 days recorded by five broad-band seismometers on Urumqi Glacier No. 1, Tianshan, China, to investigate the source characteristics of icequakes. We first apply a multidimensional autoregressive maximum-likelihood algorithm to detect 12 template events from 62 days of continuous waveform data. The centroid locations of the 12 template events are located using a grid-search approach. We then obtain a catalogue of 41 895 icequakes by compiling all seismic data through a template-matching method. The local magnitudes of all icequakes range between −3.3 and 0.5, with a completeness magnitude of −2.95 and Gutenberg–Richter b-value of 1.08. The particle motion and frequency contents of the 12 template events show that the dominant phases on the vertical component are Rayleigh waves at 5–40 Hz, suggesting that these icequakes were generated by near-surface crevasses. The average daily icequake number for each month and diurnal icequake variations show clear seasonal features. The icequakes may be related to growth of the surface crevasses due to additional melting water and precipitation in summer and to the thermal contraction of the ice body in winter.

Probabilistic seismic hazard assessment for Western Mexico

An updated probabilistic seismic hazard analysis in terms of peak ground acceleration and spectral acceleration values, for B, B/C, and C NEHRP site classes, for a 5% and 10% probability of exceedance in 50 years, has been conducted for Western Mexico. To achieve this assessment, a unified and updated declustered earthquake catalog (1787–2019), as well as an updated focal mechanism database (1963–2016), was compiled, prepared, and processed specifically for this work. Two alternative source models (area sources and a spatially smoothed seismicity model) were considered in the assessment, within a logic tree scheme. A characteristic earthquake model has been also implemented for some of the defined sources. The designed logic tree has additionally included other parameters: the possible uncertainty related to the Gutenberg-Richter b-value way of estimation, the maximum expected magnitude value, as well as two-alternative GMPEs selected for the subduction seismic sources. The obtained ground-motion results have been presented as seismic hazard isoacceleration maps, as well as uniform hazard spectra and hazard curves for 15 selected cities, for the three considered site conditions. A comparison between the obtained hazard values and the current seismic design regulations, as well as previous studies, has been also performed, and a new design response spectrum has been proposed. Finally, some regression fitting relationships between the obtained ground-motion values have been achieved. Concerning the most significant results, it is worth noting that the southwestern coast (in the perimeter of the Middle America Trench of the Mexican Subduction Zone) presents the highest hazard values. For instance, the cities of Apatzingán, Autlán, Colima, Lázaro Cárdenas, and Manzanillo exhibit the largest observed PGA values among all the studied cities. Our approach and results are supported by the fact that the recent September 19, 2022, Mw 7.6 earthquake has been located in this highest seismic hazard area.

Visibility Graph Analysis of Reservoir-Triggered Seismicity: The Case of Song Tranh 2 Hydropower, Vietnam.

In this study, the visibility graph analysis of seismicity triggered by Song Tranh 2 hydropower (Vietnam) is performed. The relationship between the seismic (the Gutenberg-Richter b-value) and topological (the k-M slope) parameters of seismicity is analysed. Our findings indicate that the relationship between the Gutenberg-Richter b-value and the k-M slope of the investigated seismicity is in agreement with that characterising the tectonic seismicity. The results obtained from analysing the reservoir-triggered seismicity of Song Tranh 2 area could contribute to better characterisation of the relationship between the seismological and topological parameters of seismicity, strengthening the universal character of the relationship between the b-value and the k-M slope.

Anomalies and transient variations of b-value in Italy during the major earthquake sequences: what truth is there to this?

SUMMARY The Gutenberg–Richter b-value is thought to be a proxy of stress conditions in the crust and therefore able to locate asperities as zones of stress concentration responsible for the nucleation of strong events. The scientific literature contains a broad range of case studies showing precursory drops of b, just before the occurrence of strong events, and subsequent rises, during the early part of aftershocks sequences. Translating these results into hazard assessment, the b-value has assumed the status of a candidate precursor to the occurrence of an imminent large event. This issue is analysed here for three major seismic sequences that occurred recently in Italy. In comparison to previous studies, this investigation indicates that the variability of b may not be a reliable indicator of stress or a significant precursor in these examples, and instead may be assigned to a combination of chance, inhomogeneities in the data and inefficiencies in estimation methodologies. Consequently, extreme caution is required when we interpret b-values both as a proxy of physical processes involved in a seismic sequence and as a precursor to the occurrence of imminent strong events.

The effect of magnitude uncertainty on the Gutenberg–Richter b-value estimation and the magnitude–frequency distribution: ‘what hump?’

Summary The uncertainties on magnitudes of the earthquakes have a negligible effect on the estimation of the Gutenberg–Richter b-value if these uncertainties have a homogeneous distribution, that is, the magnitude error is the same for all the earthquakes. Here, we show that a non-uniform error distribution can have a significant impact on the b-value estimation, and it generates a hump in the magnitude–frequency distribution. Through a simulation approach, we show when the bias in the estimation is large, when it can be neglected, and how it is possible to avoid it.

A Retrospective Analysis ofb-Value Changes Preceding Strong Earthquakes

AbstractEarthquake precursors have long been sought as a means to predict earthquakes with very limited success. Recently, it has been suggested that a decrease in the Gutenberg–Richter b-value after a magnitude 6 earthquake is predictive of an imminent mainshock of larger magnitude, and a three-level traffic-light system has been proposed. However, this method is dependent on parameters that must be chosen by an expert. We systematically explore the parameter space to find an optimal set of parameters based on the Matthews correlation coefficient. For each parameter combination, we analyze the temporal changes in the frequency–magnitude distribution for every M ≥ 6 earthquake sequence in the U.S. Geological Survey Comprehensive Earthquake Catalog for western North America. We then consider smaller events, those with a foreshock magnitude as small as 5, and repeat the analysis to assess its performance for events that modify stresses over smaller spatial regions. We analyze 25 M ≥ 6 events and 88 M 5–6 events. We find that no perfect parameter combination exists. Although the method generates correct retrodictions for some M 5 events, the predictions are dependent on the retrospectively selected parameters. About 80%–95% of magnitude 5–6 events have too little data to generate a result. Predictions are time dependent and have large uncertainties. Without a precise definition of precursory b-value changes, this and similar prediction schemes are incompatible with the IASPEI criteria for evaluating earthquake precursors. If limitations on measuring precursory changes in seismicity and relating them to the state of stress in the crust can be overcome, real-time forecasting of mainshocks could reduce the loss of lives.

Analysis of the b-Values Before the July 21 th, 2017 Mw 6.6 Bodrum-Kos, Turkey Earthquake

In this study, a statistical analysis of regional and time-dependent changes of earthquake activity in Bodrum and its vicinity before the Bodrum-Kos earthquake (Mw 6.6) that occurred on 21 July 2017 was performed and the Gutenberg-Richter b-value change was investigated. The earthquake catalog used in the calculations was taken from Boğaziçi University, Kandilli Observatory and Earthquake Research Institute. This catalog contains 16947 earthquakes with M>2 between 2004 and the time until the Bodrum-Kos earthquake of 21.07.2017. The completeness magnitude for these earthquakes was calculated as 2.6. The b-value was calculated as 1.25 ±0.01 using the maximum probability method. Considering that tectonic earthquakes have b-values between 0.5-1.5, it is seen that the b-value obtained by Gutenberg-Richter law for the vicinity of Bodrum in this study is a good fit. In addition, it was observed that b-value took high values in the north of Bodrum before the Bodrum-Kos earthquake occurred. Low values are observed in the southeast of Bodrum. Stress accumulation was correlated with b-values for the region.

Seismicity and seismic hazard assessment in West Africa

No in-depth seismic hazard study for West Africa (WA) has ever been conducted, as the regional earthquake catalogues are incomplete. Such lack of comprehensive seismic hazard study for the region has negatively affected the planning and development of critical infrastructure and disaster risk management. Therefore, this study aims to bridge the knowledge gap by applying modern techniques to updating the existing catalogues and assessing the seismic hazards for the region. We updated the current earthquake catalogue for WA using information from the International Seismological Centre, published information, and data from seismic stations in the region. The seismotectonic setting of WA is considered stable continental crust despite several recorded earthquakes occurring in the region, the largest being the June 22, 1939 earthquake of magnitude M6.8 with epicentre in Ghana. However, WA has also been classified as a region of shallow crustal seismicity. Therefore, we investigated both these research schools of thought and compared their results. For each scenario, three different ground-motion models (GMMs) were applied and combined to produce each hazard map using logic tree formalism with equal weights. The region was divided into five seismic source zones for computation of the earthquake recurrence parameters, with the same parameters computed for the entire WA region. The computed Gutenberg–Richter b-value, activity rates λ, and regional maximum possible magnitudes mmax for the five zones ranged from 0.84 to 1.0, 0.3–2.1, and 5.2–7.0, respectively. The calculated b-value, λ, and mmax for the entire region were 0.77, 4.1, and 7.2, respectively. The estimated b-value of 0.77 falls within the generally accepted range for tectonic seismicity. The seismic hazard predicted by GMMs for stable continental areas was higher than that predicted for shallow crustal seismicity in the investigated region. Therefore, our results confirmed that WA is characterised by stable continental crust. The highest hazard levels were observed in parts of Ghana, Togo, Guinea-Bissau, Guinea, and the Cameroon Volcanic Line region (CVL), ranging between 0.02 g and 0.03 g.

Reservoir-Triggered Earthquakes Around the Atatürk Dam (Southeastern Turkey)

Reservoir-triggered seismicity has been observed near dams during construction, impoundment, and cyclic filling in many parts of the earth. In Turkey, the number of dams has increased substantially over the last decade, with Atatürk Dam being the largest dam in Turkey with a total water capacity of 48.7 billion m3. After the construction of the dam, the monitoring network has improved. Considering earthquakes above the long-term completeness magnitude of MC= 3.5, the local seismicity rate has substantially increased after the filling of the reservoir. Recently, two damaging earthquakes of Mw5.5 and Mw5.1 occurred in the town of Samsat near the Atatürk Reservoir in 2017 and 2018, respectively. In this study, we analyze the spatio-temporal evolution of seismicity and its source properties in relation to the temporal water-level variations and the stresses resulting from surface loading and pore-pressure diffusion. We find that water-level and seismicity rate are anti-correlated, which is explained by the stabilization effect of the gravitational induced stress imposed by water loading on the local faults. On the other hand, we find that the overall effective stress in the seismogenic zone increased over decades due to pore-pressure diffusion, explaining the enhanced background seismicity during recent years. Additionally, we observe a progressive decrease of the Gutenberg-Richter b-value. Our results indicate that the stressing rate finally focused on the region where the two damaging earthquakes occurred in 2017 and 2018.

High-Definition Mapping of the Gutenberg–Richter b-Value and Its Relevance: A Case Study in Italy

Abstract The spatial variability of the magnitude–frequency distribution is important to improve earthquake forecasting capabilities at different time scales. Here, we develop a novel approach, based on the weighted maximum-likelihood estimation, to build a spatial model for the b-value parameter of the Gutenberg–Richter law and its uncertainty, also for earthquake catalogs with a time-varying completeness magnitude. Then, we also provide a guideline based on the Bayes factor to measure the importance of the b-value spatial variability with respect to a model having a spatially uniform b-value. Finally, we apply the procedure to a new Italian instrumental earthquake catalog from 1960 to 2019 to investigate the b-value spatial variability over the Italian territory.

A comprehensive spatiotemporal evaluation of the current earthquake activity in different parts of the Frakull-Durrës fault zone, Albania

This study presents a detailed spatiotemporal analysis for the Frakull-Durrës (F-D) fault zone at the beginning of 2020. For this purpose, the most frequently used statistical seismicity parameters such as magnitude completeness, Mc-value, Gutenberg-Richter b-value, recurrence times, annual probabilities and standard normal deviate, Z-value, were mapped. The F-D fault zone was divided into two seismogenic subregions, and Mc-value was taken as 2.5 for both the south and north parts. The b-value was estimated as 0.83 ± 0.06 for the south part and 0.85 ± 0.06 for the north part. b-values for both zones are smaller than 1.0 and these values may be considered to be a larger stress accumulation to build up over time and to be released by the next possible earthquakes. Clear decreasing trends were observed in time variations of b-values before the occurrences of several strong main shocks. Analyses of annual probabilities and recurrence times suggest that the study region has an intermediate/long-term earthquake hazard in comparison to occurrences of strong/destructive earthquakes in the short term. Some anomaly regions of a small b-value and a large Z-value were found along the F-D fault zone at the beginning of 2020: i) among Lushnje-Tirana-Durrës including the middle part of the F-D fault zone, ii) in and around Lezha including the north end of the F-D fault zone. Thus, the combination of regions with the lowest b-value and largest Z-value may supply preliminary results for earthquake hazard, and these regions may be considered to be the most likely regions for future strong/large earthquakes in the F-D fault zone.

High-Resolution Imaging of the ML 2.9 August 2019 Earthquake in Lancashire, United Kingdom, Induced by Hydraulic Fracturing during Preston New Road PNR-2 Operations

AbstractHydraulic fracturing (HF) at Preston New Road (PNR), Lancashire, United Kingdom, in August 2019, induced a number of felt earthquakes. The largest event (ML 2.9) occurred on 26 August 2019, approximately three days after HF operations at the site had stopped. Following this, in November 2019, the United Kingdom Government announced a moratorium on HF for shale gas in England. Here we provide an analysis of the microseismic observations made during this case of HF-induced fault activation. More than 55,000 microseismic events were detected during operations using a downhole array, the vast majority measuring less than Mw 0. Event locations revealed the growth of hydraulic fractures and their interaction with several preexisting structures. The spatiotemporal distribution of events suggests that a hydraulic pathway was created between the injection points and a nearby northwest–southeast-striking fault, on which the largest events occurred. The aftershocks of the ML 2.9 event clearly delineate the rupture plane, with their spatial distribution forming a halo of activity around the mainshock rupture area. Across clusters of events, the magnitude distributions are distinctly bimodal, with a lower Gutenberg–Richter b-value for events above Mw 0, suggesting a break in scaling between events associated with hydraulic fracture propagation, and events associated with activation of the fault. This poses a challenge for mitigation strategies that rely on extrapolating microseismicity observed during injection to forecast future behavior. The activated fault was well oriented for failure in the regional stress field, significantly more so than the fault activated during previous operations at PNR in 2018. The differing orientations within the stress field likely explain why this PNR-2 fault produced larger events compared with the 2018 sequence, despite receiving a smaller volume of injected fluid. This indicates that fault orientation and in situ stress conditions play a key role in controlling the severity of seismicity induced by HF.