Gutenberg Richter Magnitude Frequency Relationship Research Articles

A Bayesian Merging of Earthquake Magnitudes Determined by Multiple Seismic Networks

Abstract We introduce a Bayesian algorithm designed to integrate earthquake magnitudes of the same type reported by various seismic networks, aiming to create unified and standardized catalogs suitable for widespread use. The fundamental concept underpinning this algorithm is the utilization of the inherent consistency within each individual network’s magnitude determination process. Assuming that the magnitudes for an earthquake measured by all networks conform to a Gaussian distribution, with a linear function of the unknown true magnitude serving as its mean, we derive the posterior probability distribution of the true magnitude under four different assumptions for the prior distribution: the uninformative uniform distribution, the unbounded Gutenberg–Richter (GR) magnitude–frequency law, the GR magnitude–frequency relationship restricted by the detection rate, and the truncated GR law as priors. We assess the robustness of the method by a test on several synthetic catalogs and then use it to merge the catalogs compiled by five seismic networks in Italy. The results demonstrate that our proposed magnitude-merging algorithm effectively combines the catalogs, resulting in robust and unified data sets that are suitable for seismic hazard assessment and seismicity analysis.

Responding to Media Inquiries about Earthquake Triggering Interactions

AbstractIn the aftermath of a significant earthquake, seismologists are frequently asked questions by the media and public regarding possible interactions with recent prior events, including events at great distances away, along with prospects of larger events yet to come, both locally and remotely. For regions with substantial earthquake catalogs that provide information on the regional Gutenberg–Richter magnitude–frequency relationship, Omori temporal aftershock statistical behavior, and aftershock productivity parameters, probabilistic responses can be provided for likelihood of nearby future events of larger magnitude, as well as expected behavior of the overall aftershock sequence. However, such procedures generally involve uncertain extrapolations of parameterized equations to infrequent large events and do not provide answers to inquiries about long-range interactions, either retrospectively for interaction with prior remote large events or prospectively for interaction with future remote large events. Dynamic triggering that may be involved in such long-range interactions occurs, often with significant temporal delay, but is not well understood, making it difficult to respond to related inquiries. One approach to addressing such inquiries is to provide retrospective or prospective occurrence histories for large earthquakes based on global catalogs; while not providing quantitative understanding of any physical interaction, experience-based guidance on the (typically very low) chances of causal interactions can inform public understanding of likelihood of specific scenarios they are commonly very interested in.

Critical zone of the branching crack model for earthquakes: Inherent randomness, earthquake predictability, and precursor modelling

The branching crack model for earthquakes was developed by Vere-Jones and Kagan in the 1970s and the 1980s, respectively. With some simple and rational assumptions, its simulation results explain the Gutenberg-Richter magnitude-frequency relationship and the Omori-Utsu aftershock decay formula. By introducing the concept of the critical zone, this model can be connected with the asperity model, the barrier model, and the nucleation model through a parameter – criticality. Particularly, the size of the critical zone determines the maximum magnitude of potential earthquakes and the source of their anomalies. The key to earthquake forecasting is to determine whether the concerned area is in a critical state and how large the critical zone is. We discuss what kinds of anomalies are meaningful as candidates of earthquake precursors. Finally, we outline modelling strategies for earthquake precursors with low probability gains that are due to the inherent randomness of earthquake source processes.

Shaking is Almost Always a Surprise: The Earthquakes That Produce Significant Ground Motion

AbstractAlthough small earthquakes are expected to produce weak shaking, ground motion is highly variable and there are outlier earthquakes that generate more shaking than expected—sometimes significantly more. We explore datasets of M 0.5–8.3 earthquakes to determine the relative impact of frequent, smaller-magnitude earthquakes that rarely produce strong ground motion, to rare, large earthquakes that always cause strong shaking. We find that the natural variability of ground motion, combined with the Gutenberg–Richter magnitude–frequency relationship, ensures that most occurrences of any ground motion come from earthquakes of smaller magnitude than expected, often >2 magnitude units smaller. This holds even for very strong shaking (>20%g), suggesting that M<7 earthquakes could be a significant source of damage.

Fractal analysis of the seismicity of the territory of Azerbaijan

The article examines the distribution of earthquakes occurred in Azerbaijan and the adjacent territories during the instrumental period (1902¾2018) by investigating the self-similarity and fractal properties of the seismicity of the region. Most parts of the territory of Azerbaijan are considered to be seismically active, and seismic events with a wide range of magnitudes (3 ≤ М < 7.3) have been registered in Azerbaijan during the instrumental period. Earthquake distribution has been analysed by means of the fractal theory, which is based on such notions as the detection of statistical self-similarity in the process under study and its quantitative assessment. The composite catalogue serves as a basis for the research and covers the time span of 1902—2018. It has been compiled with the help of seismic data from the Republican Seismic Survey Center of the Azerbaijan National Academy of Sciences and earthquake catalogues of various international seismological centres.As a result, for the distribution of earthquakes registered in the territory of Azerbaijan the fractal dimensions (the quantitative indicators of self-similarity) of earthquake energy distribution and epicentre distribution have been calculated. The fractal dimension of earthquake epicentre distribution (De) is 1.63, whereas the average value of fractal dimension of energy distribution (d) for Azerbaijani seismic events equals 0.54.Also, using the data from the composite catalogue, the Gutenberg—Richter magnitude-frequency relationship and the b-value for the earthquakes of Azerbaijan and the adjacent territories have been estimated. The statistical relationships between the calculated fractal dimensions of the earthquake energy and epicentre distribution (d and De, respectively) have also been examined.

Probabilistic assessment of earthquake hazard in the Andaman–Nicobar–Sumatra region

The Andaman–Nicobar–Sumatra (ANS) region is a very hazardous area on the globe, which has witnessed a megathrust earthquake of Mw 9.2 on 26 December 2004 and several dozen large earthquakes in the past. We estimate earthquake hazard parameters (i.e. seismic a- and b-values, maximum expected earthquake magnitudes, mean return periods and probabilities of earthquakes) in 11 shallow and 4 intermediate to deep depth seismogenic zones of the ANS region using a uniform and comprehensive earthquake data for the duration 1906–2018. The earthquake hazard scenarios for all seismogenic zones are calculated using the Gutenberg–Richter frequency–magnitude relation and the Gumbel’s extreme value theory. The low b-values ( 0.90) for the earthquake of Mw 7.0 in the next 50 years and 100 years are observed in shallow zones 4–11 (the Sumatra and Nicobar Islands), while only intermediate to deep zone 4 (Sumatra) shows high probabilities. The low return periods ( 0.90) for the earthquake of Mw 7.0 are observed in shallow zones 5–11 (the Nicobar Islands and Sumatra regions), which suggest high earthquake hazard in these zones. The spatial variations of earthquake hazard parameters from one zone to another suggest a large grade of crustal heterogeneity and seismotectonic complexity present in this area.

Unified Scaling Law for Earthquakes as Applied to Assessment of Seismic Hazard and Associate Risks

The distribution of the number of seismic events by magnitudes—the Gutenberg–Richter frequency–magnitude relation—is of paramount importance for seismic hazard assessment of a territory. The generalization of the Gutenberg–Richter relation—the Unified Scaling Law for Earthquakes (USLE) proposed in 1988 makes it possible to take into account the pattern of epicentral distribution of seismic events when changing the spatial scale of the analysis. This is extremely important for adequate downscaling of the frequency of occurrence into a smaller area within the territory under study (e.g., in the megalopolis). In 2002, Per Buck suggested a dual formulation of USLE where, instead of the number of earthquakes over a certain period of time, the reciprocal of their frequency of occurrence—the time between seismic events—is used. The same year, the Institute of Earthquake Prediction Theory and Mathematical Geophysics of the Russian Academy of Sciences developed a modified algorithm for robust estimation of USLE parameters referred to as Scaling Coefficients Estimation (SCE) for producing seismic hazard maps of territories prone to seismic effects. This brief review is focused on the use of the USLE approach to the assessment of seismic hazard and associated risk.

Study of seismicity in the NW Himalaya and adjoining regions using IMS network

The Reviewed Event Bulletin (REB) of the International Data Center (IDC) has been used in order to investigate the seismicity of the Northwest Himalaya and its neighboring region for the time period June 1999 to March 2015 within the geographical coordinates 25–40° N latitude and 65–85° E longitude. We have used a very precisely located earthquake dataset recorded by the International Monitoring System (IMS) Network containing 7,583 events with body wave magnitudes from 2.5 to 6.3. The study area has been subdivided into six regions based on the Flinn-Engdahl (F-E) seismic and geographical regionalization scheme, which was used as the region classifications of the International Data Center catalog. The examined region includes NW India, Pakistan, Nepal, Xizang, Kashmir, and Hindukush. For each region, Magnitudes of completeness (Mc) and Gutenberg-Richter (GR) recurrence parameters (a and b values) have been estimated. The Gutenberg-Richter analysis is preceded by an overview of the seismotectonics of the study area. The obtained Mc values vary from 3.5 to 3.9. The lower value of Mc was found mainly in Xizang region whereas the higher Mc threshold is evident in Pakistan region. However, the b values vary from 1.19 to 1.48. The lowest b value is recorded in Xizang region, which is mostly related to the Main Karakoram Thrust (MKT) fault, whereas the highest b values are recorded in NW India and Kashmir regions, which are mostly related to the Main Frontal Thrust (MFT) fault. The REB for the selected period has been compared to the most renowned bulletin of global seismicity, namely that issued by the National Earthquake Information Center (NEIC) of the United States Geological Survey (USGS). A study of 4,821 events recorded by USGS in the study region indicates that about 36 % of seismic events were missed and the catalog is considered as complete for events with magnitudes ≥4.0. However, both a and b values are obviously higher than those of IMS catalog. The a and b parameters in the Gutenberg-Richter magnitude–frequency relationship have been utilized to forecast the probability of future earthquakes of different magnitudes and returned periods (recurrence intervals).

Joint Determination of Event Epicenter and Magnitude from Seismic Intensities

Characteristic features of seismicity with long recurrence intervals can be deduced from analysis of historical earthquake records that inherently suffer from uncertainty in the event locations and magnitudes. A novel method to determine the event epicenters and magnitudes jointly from seismic intensities is proposed. The probability for a set of event epicenter and magnitude is assessed by accounting the fitness between the observed and reference seismic intensities, spatial‐occurrence probability based on seismicity density distribution, and temporal‐occurrence probability from the Gutenberg–Richter magnitude–frequency relationship. A set of event epicenter and magnitude yielding the peak probability is chosen. The validity of the method is tested for both synthetic and instrumental seismic‐intensity data, confirming high accuracy. The method is applied effectively to historical events with written seismic damage records. It is found that the errors generally decrease with increasing number and azimuthal coverage of seismic‐intensity data, and increase with epicentral distances. The method appears to be promising for historical earthquakes of which source properties are poorly known. The method is applicable for assessment of the properties of long‐period seismicity, which is crucial for assessment of potential seismic hazards.

Earthquake hazard analysis for East Anatolian Fault Zone, Turkey

The aim of this study was to investigate the earthquake hazard of the East Anatolian Fault Zone by determining the a and b parameters in a Gutenberg–Richter magnitude–frequency relationship. For this purpose, the East Anatolian Fault Zone is divided into five different source zones based on their tectonic and seismotectonic regimes. We calculated the b value, which is the slope of the frequency–magnitude Gutenberg–Richter relationship, from the maximum likelihood method (ML). Also, we estimated the mean return periods, the most probable maximum magnitude in the time period of t years and the probability for an earthquake occurrence for an earthquake magnitude ≥M during a time span of t years. We then produced a and b value maps using the ML. We obtained the lowest b value in Region 1 covered Karliova triple junction. This conclusion is strongly supported from the probability value, which shows the largest value (90 %) for an earthquake with magnitude greater than or equal to 6.0. The mean return period for such a magnitude is the lowest in this region (43 years). The most probable magnitude in the next 100 years was calculated, and we determined the highest value around Karliova triple junction. According to these parameters, Region 1 covered the Karliova triple junction and is the most dangerous area around the East Anatolian Fault Zone.

An investigation of seismicity for the Central Anatolia region, Turkey

The aim of this study is to investigate the seismicity of Central Anatolia, within the area restricted to coordinates 30–35° longitude and 38–41° latitude, by determining the “a” and “b” parameters in a Gutenberg–Richter magnitude–frequency relationship using data from earthquakes of moment magnitude (Mw) ≥ 4.0 that occurred between 1900 and 2010. Based on these parameters and a Poisson model, we aim to predict the probability of other earthquakes of different magnitudes and return periods (recurrence intervals). To achieve this, the study area is divided into six seismogenic zones, using spatial distributions of earthquakes greater than Mw ≥ 4.0 with active faults. For each seismogenic zone, the a and b parameters in the Gutenberg–Richter magnitude–frequency relationship were calculated by the least squares method. The probability of occurrence and return periods of various magnitude earthquakes were calculated from these statistics using the Poisson method.

Analysis of the b-values before and after the 23 October 2011 Mw 7.2 Van–Erciş, Turkey earthquake

The b-values from the Gutenberg–Richter frequency–magnitude relation are investigated in the Lake Van region in eastern Turkey where accommodated the 23 October 2011 Mw 7.2 Van–Erciş earthquake. Earthquake catalog is provided by the Kandilli Observatory and Earthquake Research Institute (KOERI). The catalog consists of 6709 well-located events with local magnitudes (ML) from 2.6 to 5.8. The time span of the catalog covers the period 2002 and 2012. The b-values were significantly lower at the Van–Erciş mainshock area prior to 23 October 2011. The mainshock occurred near to the high stress (low b-value) asperity in the east of Lake Van. The decrease in b-values supports “low b-value-high stress hypothesis” prior to the Van–Erciş earthquake. The temporal change of b-value before the mainshock exhibits a strong trend of decreasing which could be used as an indicator of the approaching mainshock. This b-value analysis provides an evidence for significant difference that exist between pre-seismic and post-seismic periods of the mainshock area. Distribution of low b-values for Van–Erciş aftershock sequence relates the termination of the mainshock rupture to the east may be the precursory phenomena for the future moderate or large magnitude earthquakes in the Lake Van region.

Historical seismicity and dynamic rupture process of the 2011 Tohoku-Oki earthquake

A number of studies have documented the complex rupture process of the M w 9.0 March 11, 2011 Tohoku-Oki earthquake, which is characterized by different stages of rupture, including a large delayed slip near the trench and multiple high-frequency ruptures along the down-dip edge of the seismogenic zone. In this study, a multiscale circular patch model was used to represent the spatial heterogeneity of fracture energy inferred on the plate interface, with spontaneous dynamic rupture simulated by solving the elasto-dynamic equation with a slip-weakening friction law. Historical seismicity, recorded over the past 100 years, was used to determine the spatial heterogeneity of seismic events, with an additional large patch used to model large slip movements near the trench. Dynamic rupture processes qualitatively consistent with observations were successfully modeled during this study, although slight adjustments, including the introduction of foreshock-related stress concentrations, were needed to accomplish this. The delayed failure of the shallow largest patch, representing the main rupture stage, was only achieved by a dynamic nucleation process comprising cascading ruptures within small and moderately sized patches near the down-dip edge of the seismogenic zone; this failure was followed by successive ruptures along the down-dip edge of the zone. This study confirms that a free surface significantly increases fault slip and released seismic moment during an earthquake. In addition, we found that the largest patch occupies the area where the b-value of the Gutenberg–Richter magnitude–frequency relationship is much smaller than 1, while the hypocenter corresponds to a local maximum b-value of about 1.5. This research also suggests that seismicity catalogs can be used to constrain the spatial segmentation of plate boundaries and to propose possible scenarios for the dynamic rupture processes of future earthquakes. ► Historical seismicity data are used to model plate interface heterogeneity. ► Simple model explains complex rupture processes during the Tohoku-Oki earthquake. ► Cascading ruptures of smaller patches work as a dynamic nucleation process.

Footprints of nonextensive Tsallis statistics, selfaffinity and universality in the preparation of the L’Aquila earthquake hidden in a pre-seismic EM emission

Fracture induced physical fields allow a real-time monitoring of damage evolution in materials during mechanical loading. We investigate the preparation of the recently occurred L’Aquila earthquake in terms of a detected precursory electromagnetic anomaly. The precursor is well described by a recently introduced model for earthquake dynamics, which has been rooted in a nonextensive Tsallis framework starting from first principles. The analysis in terms of nonextensivity implies that the well established aspect of self-affine nature of faulting and fracture is hidden into the precursor, namely, the activation of the L’Aquila fault is a reduced self-affine image of the regional seismicity covering many geological faults. The Gutenberg–Richter magnitude–frequency relationship, the best known scaling relation for earthquakes, verifies the results based on nonextensivity. The latter suggests that the activation of the L’Aquila fault is a magnified image of the laboratory seismicity by means of acoustic and electromagnetic emissions. Finally, we present evidence for universality in magnetic storm, earthquake, and electromagnetic precursor occurrence by means of complexity and nonextensivity.

Real-time Performance of the Virtual Seismologist Earthquake Early Warning Algorithm in Southern California

The Virtual Seismologist (VS) method is a Bayesian approach to regional network-based earthquake early warning (EEW) that estimates earthquake magnitude, location, and the distribution of peak ground motion using observed ground motion amplitudes, predefined prior information, and appropriate attenuation relationships (Cua 2005; Cua and Heaton 2007). The application of Bayes's theorem in earthquake early warning (Cua 2005) states that the most probable source estimate at any given time is a combination of contributions from prior information (possibilities include network topology or station health status, regional hazard maps, earthquake forecasts, the Gutenberg-Richter magnitude-frequency relationship) and a likelihood function, which takes into account observations from the ongoing earthquake. Prior information can be considered relatively static over the timescale of a given earthquake rupture. The changes in the source estimates and predicted peak ground motion distribution, which are updated each second, are due to changes in the likelihood function as additional arrival and amplitude data become available. The potential use of prior information differentiates the VS approach from other regional, network-based EEW algorithms, such as ElarmS (Allen and Kanamori 2003).

Parametric-historic Procedure for Probabilistic Seismic Hazard Analysis Part I: Estimation of Maximum Regional Magnitude m max

—A new methodology for probabilistic seismic hazard analysis (PSHA) is described. The approach combines the best features of the "deductive" (Cornell, 1968) and "historical" (Veneziano et al., 1984) procedures. It can be called a "parametric-historic" procedure.¶The maximum regional magnitude m max is of paramount importance in this approach and Part I of our work presents some of the statistical techniques which can be used for its evaluation. The work is an analysis of parametric procedures for the evaluation of m max, when the form of the magnitude distribution is specified. For each of the formulae given there are notes on its origin, assumptions made of its derivation, and some comparisons. The statistical concepts of bias and variance are considered for each formula, and appropriate expressions for these are also given. Also, following Knopoff and Kagan (1977), we shall demonstrate why there must be a finite upper bound to the largest seismic event if the Gutenberg-Richter frequency-magnitude relation is accepted.

Assessment of Seismicity Model for Hong Kong Region

The seismicity model, the Gutenberg-Richter magnitude-frequency relationship. has been developed for Hong Kong region. Detailed investigation and statistical tests on the completeness of the earthquake catalogue and the regional variation of the seismicity have been carried out. It has been found that in the catalogue compiled in this study the historical records on land since 1895 are likely to be complete for surface-wave magnitude M = 4 % or greater. and that there is no record before 1920 in offshore area about 100 km from coastal lines. Almost all historical records before 1894 are on land. indicating that the historical records may be complete only on land. The earthquake spatial distribution is not uniform on land. The number of earthquakes with M = 6 or greater per year in the last 100 years is much larger than that in the previous historical time (1500–1894). It has also been found that the regional variation of the seismicity is a significant factor likely to affect the seismic hazard in Hong Ko...

Scale invariance for a heterogeneous fault model

A very simple model of fault fracturing is presented. The fault is envisaged as a series of faultlets whose area is randomly distributed and whose strength have a Gaussian distribution. Faultlet slip occurs when the loading stress reaches its strength. Large earthquakes are generated by coalescence of smaller cracks. Theb value of the Gutenberg-Richter frequency magnitude relation is then calculated. Ab equal to 1 (scale invariance) is obtained only for events with magnitudeM greater than 3. At lower magnitude the number of events decreases with decreasing magnitude. A similar result can be explained by the experimental observation of an anomalous scaling law of real earthquakes. Here the suggestion is advanced that a similar observation could be interpreted by a multifractal approach.

On least-squares estimation of b values

Abstract Although the maximum-likelihood estimator of b values is optimal from a certain statistical point of view, given the Gutenberg-Richter frequency-magnitude relation, many researchers have been using least-squares fitting of a straight line to the frequency-magnitude plot. However, ordinary least squares is an inefficient method. A generalized least-squares approach is statistically more satisfactory. The details of this method are given and applied to data from California. The improvement in efficiency is substantial. In addition, the generalized least-squares approach works well also for data from a different frequency-magnitude relation, proposed by Lomnitz-Adler and Lomnitz. The maximum-likelihood estimator (from the Gutenberg-Richter model) has too large a variability in this situation.

On the frequency-magnitude relation logN = a ? bM

This paper is an attempt to study the dependence of constantsb ona, of the Gutenberg-Richter's frequency-magnitude relation logN = a − bM which seems to be linear. Further it is found that the maximum magnitude observed in a particular region can be approximated by the ratioa/b.