Richter Relation Research Articles

The return period and probabilities of earthquakes occurrence in North-East, India (Eastern-Himalayas) and its vicinity inferred from Gutenberg–Richter relation

The return period and probabilities of earthquakes occurrence in North-East, India (Eastern-Himalayas) and its vicinity inferred from Gutenberg–Richter relation

Spatiotemporal variations in seismic activity in and around the focal region of the 2021 [formula omitted]7.3 and 2022 [formula omitted]7.4 Fukushima-Oki earthquakes, Japan

The spatiotemporal evolution of seismic activity is presented for a broad region surrounding the focal areas of the 2021 M7.3 and 2022 M7.4 Fukushima-Oki earthquakes, which occurred within the subducting slab off the Pacific coast of Fukushima Prefecture, northeastern Japan. This study investigates the spatiotemporal variations in seismic activity during the periods before the 2021 M7.3 earthquake, between the 2021 M7.3 and 2022 M7.4 earthquakes, and after the 2022 M7.4 earthquake using the b-value of the Gutenberg–Richter relation, the aftershock decay rate (p-value), and changes in the seismicity rate (Z-value). The study area is also divided into two depth sections to investigate the depth variations in these seismicity parameters relative to the plate interface. The b-values in the deeper section (intraslab) are generally lower than those in the shallower section (around the plate interface) throughout the entire analysis period, including the hypocentral areas of the M7.3 and M7.4 earthquakes. The aftershock decay rates for the M7.3 and M7.4 earthquakes also show depth-dependent characteristics, with a slower decay rate (p < 1.0) at many grid nodes in the deeper section than in the shallower section. Furthermore, seismic quiescence was noted in the hypocentral area of the M7.3 earthquake about two years before the occurrence of this mainshock. The locations of the M7.3 and M7.4 earthquakes around the down-dip edge of the slip area of the 2011 M9.0 Tohoku earthquake suggests that the variations in seismic activity detected in this study mainly reflect stress increases due to the coseismic slip and postseismic deformation of this great earthquake. The present study suggests that the effect of viscoelastic relaxation is a dominant factor in the deeper section. Furthermore, the variations in seismicity may also reflect heterogeneous structures within the slab.

Fracture Electromagnetic Radiation Induced by a Seismic Active Zone (in the Vicinity of Eilat City, Southern Israel)

This paper deals with the quantitative analysis of measured fracture-induced electromagnetic radiation (FEMR) near the Dead Sea Transform using the Angel-M1 instrument, which enables the recording of FEMR signals in a 3D manner. The results showed both the possibility of estimating the sizes of micro-fractures that are the sources of radiation and assessing the direction of the fractures’ locations to the measuring device, as well as the range of magnitude (Mw) of the impending “events” (EQs) associated with the FEMR measurements. Moreover, the relation between the measured FEMR activity (the number of FEMR hits per unit of time) and the FEMR event magnitudes showed consistency with the Gutenberg–Richter relationship for the region. Such measurements could therefore constitute a preliminary ‘field reinforcement’ towards a valid EMR method for a real earthquake forecast, which would provide much earlier warnings than seismic methods. The observed FEMR measurements could only be used to assess the stress concentrations and micro-fracturing in the region since they related to the very initial nucleation phase of a “virtual” earthquake. Nonetheless, they provide the necessary feasibility test for a forecasting method since all of the lab-measured FEMR features were confirmed in the field.

Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada

Hydraulic fracturing (HF) can trigger induced seismicity, but documented occurrences tend to be localized compared with the regional extent of industry operations. Factors that determine intrinsic geological susceptibility of a given region to induced seismicity remain incompletely understood. To address this uncertainty, we have developed a stochastic modeling approach to enable statistical testing of hypotheses regarding the distribution of induced seismicity. For reference, we adopted a null hypothesis that HF-induced seismic events are randomly associated with HF wells. Realizations of synthetic induced-seismicity catalogs are generated based on the Gutenberg–Richter relationship for magnitudes and explicit assumed spatial relationship(s) between HF wells and other known features, such as mapped structural corridors. Uncertainties in observed event locations and magnitudes are also considered. Based on 1000 independent realizations for each test scenario, normalized correlation coefficients, Bayesian information criteria and other statistical measures are used to quantify the similarity of synthetic catalogs to the observed seismicity distribution. We applied this approach to induced seismicity associated with HF operations within the Montney Formation, in western Canada. Three hypotheses were tested, each showing a statistically significant improvement over the null hypothesis. A previous machine-learning-based model for Seismogenic Activation Potential (SAP) showed the highest correlation between observed and synthetically generated seismicity catalogs. Our method has been developed using cloud-based computing and is easily adapted to other regions and data types.

An Earthquake Early Warning Method Based on Bayesian Inference

Earthquake early warning (EEW) systems can give people warnings before damaging ground motions reach their site and can reduce earthquake-related losses. It has been shown that Bayesian reference can be used to estimate earthquake magnitude, location, and the distribution of peak ground motion using observed ground-motion amplitudes, predefined prior information, and appropriate attenuation relationships. In this article, we describe a Bayesian approach to earthquake early warning (EEW) systems for the estimation of magnitude (M) and peak ground-motion velocity (PGV) using the Gutenberg–Richter relation as a priori probability derived from statistical historical earthquake information from the Japanese KiK-net. Moreover, using the magnitude Mj = 4.5 and PGV = 0.4 cm/s as the warning threshold, an earthquake hazard discrimination model was established. Following this, the proposed approach was compared with the traditional fitting method to analyze the earthquake hazard discrimination using an Mj = 4.3 earthquake in the Mt. Fuji area and an Mj = 5.5 earthquake in the Ibaraki area of Japan as examples. The results are as follows: (1) The probabilistic algorithm founded on the predictive model of the magnitude from the average period (τc) and PGV from the displacement amplitude (Pd) from the initial 3 s of the P wave is able to provide a fast and accurate estimation of the final magnitude and location. (2) The Bayesian inference approach for the earthquake hazard discrimination model has a 2.94% miss rate and a 5.88% false alarm rate, which is lower than that of the traditional fitting method, thus increasing the accuracy and reliability of earthquake hazard estimation.

A High-Resolution Earthquake Catalog for the 2004 Mw 6 Parkfield Earthquake Sequence Using a Matched Filter Technique

Abstract We present the high-resolution Parkfield matched filter relocated earthquake (PKD-MR) catalog for the 2004 Mw 6 Parkfield earthquake sequence in central California. We use high-quality seismic data recorded by the borehole High Resolution Seismic Network combined with matched filter detection and relocations from cross-correlation derived differential travel times. We determine the magnitudes of newly detected events by computing the amplitude ratio between the detections and templates using a principal component fit. The relocated catalog spans from 6 November 2003 to 28 March 2005 and contains 13,914 earthquakes, which is about three times the number of events listed in the Northern California Seismic Network catalog. Our results on the seismicity rate changes before the 2004 mainshock do not show clear precursory signals, although we find an increase in the seismic activity in the creeping section of the San Andreas fault (SAF) (about ∼30 km northwest of the mainshock epicenter) in the weeks prior to the mainshock. We also observe a decrease in the b-value parameter in the Gutenberg–Richter relationship in the creeping section in the weeks prior to the mainshock. Our results suggest stress is increasingly released seismically in the creeping section, accompanied by a decreasing aseismic creeping rate before the mainshock occurrence. However, b-value and seismicity rates remain stable in the Parkfield section where the 2004 mainshock ruptured. This updated catalog can be used to study the evolution of aftershocks and their relations to afterslip following the 2004 Parkfield mainshock, seismicity before the mainshock, and how external stresses interact with the Parkfield section of the SAF and the 2004 sequence.

Revealing the spatiotemporal complexity of the magnitude distribution and b-value during an earthquake sequence

The Magnitude–Frequency-Distribution (MFD) of earthquakes is typically modeled with the (tapered) Gutenberg–Richter relation. The main parameter of this relation, the b-value, controls the relative rate of small and large earthquakes. Resolving spatiotemporal variations of the b-value is critical to understanding the earthquake occurrence process and improving earthquake forecasting. However, this variation is not well understood. Here we present remarkable MFD variability during the complex 2016/17 central Italy sequence using a high-resolution earthquake catalog. Isolating seismically active volumes (‘clusters’) reveals that the MFD differed in nearby clusters, varied or remained constant in time depending on the cluster, and increased in b-value in the cluster where the largest earthquake eventually occurred. These findings suggest that the fault system’s heterogeneity and complexity influence the MFD. Our findings raise the question “b-value of what?”: interpreting and using MFD variability needs a spatiotemporal scale that is physically meaningful, like the one proposed here.

Analysis of seismic strain release related to the tidal stress preceding the 2008 Wenchuan earthquake

Abstract. Tidal stresses could load or unload focal media and trigger small to moderate earthquakes in and around the focal region before a large or great earthquake. Based on the preliminary reference Earth model, we calculated the time series of tidal Coulomb failure stress (TCFS) acting on the focal fault plane of the Wenchuan earthquake. For earthquakes (2.5≤ML≤4.0) that occurred in and around the focal region from January 1990 to April 2008, we calculated the time rate of TCFS, ΔTCFS, at the occurrence time of each earthquake. These earthquakes were divided into two categories on the basis of the signs of ΔTCFS: one is positive earthquakes (PEQs) occurring at times of ΔTCFS &gt; 0 and the other negative earthquakes (NEQs) occurring at times of ΔTCFS &lt; 0. First, we obtained cumulative seismic strain release (CSSR) curves of NEQs and PEQs and found that the two curves nearly overlapped prior to September 2004 and then began to separate increasingly with time. We used a parameter Rp, the proportion of seismic strain release of PEQs, to investigate the effect of TCFS on earthquake occurrence and found that Rp was significantly higher than 0.5 about 6 months before the Wenchuan event at a 99 % confidence level, indicating a significant correlation between earthquake occurrence and increasing TCFS. Furthermore, we calculated the slope k (time rate) of the CSSR curve vs. time for PEQs and NEQs separately. It was observed in the pre-event period that the seismic strain release accelerated when TCFS increased but decelerated when TCFS decreased. The difference in the time rate of seismic strain release between PEQs and NEQs was quantified using Rk, the ratio of k for PEQs to that for NEQs. We discovered stable Rk values (around 1.0) until they began to rise rapidly with time in early 2005, reaching their highest value of 2.7 just before the Wenchuan event. Rk could reveal the promoting and inhibiting effects of tidal stress on seismic strain release. When kp increases alone or kn decreases alone, Rk will increase. Thus, an increase in Rk corresponds to a promoting effect during times of increasing TCFS and an inhibiting one during that of decreasing TCFS. Both effects were observed in the focal region prior to the Wenchuan mainshock. The b value in the Gutenberg–Richter relationship decreases as the tectonic stress in the crust increases. We also calculated the temporal evolution of the b value in the study region. It was observed that after 2.5 years of increasing tectonic stress, the focal region became unstable, and the tidal stress began to take effect. The effects of the tidal stress were gradually enhanced as the tectonic stress increased further. The increase in the tidal Coulomb failure stress may have aided the occurrence of earthquakes, whereas the decrease had the opposite effect. This observation may shed light on the seismogenic processes that led to the Wenchuan earthquake and its precursors.

Seismic microzoning of the Delhi metropolitan area, India— I: Seismicity modeling

AbstractSeismic activity parameters ( and values in a Gutenbdataer–Richter relationship, maximum magnitude , and predominant focal depths ) have been estimated for a grid of square cells of size 0.1° in latitudes and longitudes covering a large region bound by 24°−33°N and 72°−82°E to define input seismicity for microzoning of the Delhi metropolitan area. For this purpose, seven area types of seismic sources are first identified from a detailed seismotectonic evaluation of the region. Two of these sources form part of the Northwestern Himalaya and the remaining five encompass the intraplate area including and surrounding the National Capital Region. The seismic activity parameters are then estimated for each source zone by compiling a comprehensive catalog of 4483 past earthquakes with magnitudes of 2.0 or more covering the 1720–2020 period. All the grid cells in each source are initially assigned the same values of parameters , , and as those for the source zone; whereas parameter has been redefined for each grid cell using the cumulative occurrence rate of earthquakes above the minimum magnitude of completeness for the source zone. To account for possible uncertainties in past earthquake locations, values of the activity parameters thus assigned to all the grid cells in the region are spatially smoothed using an elliptical Gaussian kernel with a major axis along the predominant strike direction for the source zone of each grid cell. The grid cells across the source zone boundaries are also included in the smoothing process to normalize the effects of any subjectivity introduced in defining the source zone boundaries. Our estimations of seismic activity parameters thus obtained can be considered in the development of a robust and physically realistic seismicity model for practical engineering applications, which was made possible by our use of a sufficiently long duration of the earthquake catalog along with complete reporting of data up to magnitudes very close to the expected maximum magnitude in each source zone. We have also estimated the seismic activity parameters for the Hindu Kush subduction zone, which is then idealized by a point source.

Spatio-temporal analysis of East Asian seismic zones based on multifractal theory

Abstract In this article, the integrity of the seismic catalog obtained (1970–2014, M &gt; 2.8) was verified according to the Gutenberg–Richter relation, the appropriate minimum magnitude was determined, and the whole region was divided into five areas according to the geological structure background of the whole research object and the trend of the historical seismic zone. We applied multifractal analysis in each partition. The results showed that although in different geological backgrounds, before major earthquakes, the earthquake time series information dimension had different degrees of growth, and the parameter after the flame had different degrees of decline. To a certain extent, this reflected the seismic energy accumulation and release process. In addition, the variation of fractal parameters in scale-free regions of time series and spatial distribution series also indicated that these two kinds of sequences in different regions show the characteristics of a multifractal structure rather than a single and uniform fractal structure.

Statistical analysis of earthquake catalogs for seismic hazard studies around the Karliova Triple Junction (eastern Turkey)

A complete and comprehensive earthquake catalog is a substantial input to do probabilistic seismic hazard analysis. The Karliova triple junction (eastern Turkey) is characterized by an active seismicity mostly in the shallow crust. Origin times, earthquake locations, and magnitudes reported by the Kandilli Observatory and Earthquake Research Institute, Boğaziçi University (KOERI) and three international agencies (ISC, IRIS and EMSC) in the region bounded by latitudes 37.5° and 40.5° N and longitudes 37.5° and 42.5° E have been gathered in order to quantify the seismicity around the study area and calculate associated seismic parameters. The Magnitudes of completeness (Mc) and Gutenberg-Richter (GR) recurrence parameters (a- and b-values) have been estimated. The same Mc value of 2.7 has been obtained for all catalogs. After 2014, all earthquakes with magnitudes higher than 2.0 are reliably recorded. However, the b-value varied from 0.97 to 1.28. High b-value anomalies mostly for earthquakes with shallow depths (5–15 km) have been observed. A relatively lower b-values are found at depths <5 km. The most probable largest annual earthquakes are around Mw = 5.8. The seismic hazard parameters i.e. the maximum regional magnitude mmax, mean seismic activity rate λ, the slope of the frequency–magnitude Gutenberg–Richter relationship, and the β value (bln(10)) have been estimated. Using the Bayesian model for the earthquake occurrence in time and earthquake magnitude, which incorporates seismic information from historical and instrumental catalogs, the hazard parameters are presented in terms of the probability of exceedance for 1- 10- 50- and 100-year return periods with a b-value equal to 1.19 and mmax equal to 8.05. The highest probability of earthquakes, which may occur in an interval of 50 years is estimated as Mw = 7.0. The average recurrence interval of earthquakes with magnitudes 6.7 and 7.8 (the maximum observed magnitudes at KOERI catalog and instrumental earthquakes in the region, respectively) are ∼27 and ∼488 years.

Propagation of epistemic uncertainty in magnitude–frequency relations through PSHA using predictive distributions

The current practice of Probabilistic Seismic Hazard Analysis (PSHA) considers the inclusion of epistemic uncertainties involved in different parts of the analysis via the logic-tree approach. Given the complexity of modern PSHA models, numerous branches are needed, which in some cases leads to concerns regarding performance issues. We introduce the use of a magnitude exceedance rate which, following Bayesian conventions, we call predictive exceedance rate. This rate is the original Gutenberg–Richter relation after having included the effect of the epistemic uncertainty in parameter β. The predictive exceedance rate was first proposed by Campbell but to our best knowledge is seldom used in current PSHA. We show that the predictive exceedance rate is as accurate as the typical logic-tree approach but allows for much faster computations, a very useful property given the complexity of some modern PSHA models.

Bayesian estimation of b-value in Gutenberg–Richter relationship: a sample size reduction approach

Bayesian estimation of b-value in Gutenberg–Richter relationship: a sample size reduction approach

Contamination of Frequency–Magnitude Slope (b-Value) by Quarry Blasts: An Example for Italy

Abstract Artifacts often affect seismic catalogs. Among them, the presence of man-made contaminations such as quarry blasts and explosions is a well-known problem. Using a contaminated dataset reduces the statistical significance of results and can lead to erroneous conclusions, thus the removal of such nonnatural events should be the first step for a data analyst. Blasts misclassified as natural earthquakes, indeed, may artificially alter the seismicity rates and then the b-value of the Gutenberg and Richter relationship, an essential ingredient of several forecasting models. At present, datasets collect useful information beyond the parameters to locate the earthquakes in space and time, allowing the users to discriminate between natural and nonnatural events. However, selecting them from webservices queries is neither easy nor clear, and part of such supplementary but fundamental information can be lost during downloading. As a consequence, most of statistical seismologists ignore the presence in seismic catalog of explosions and quarry blasts and assume that they were not located by seismic networks or in case they were eliminated. We here show the example of the Italian Seismological Instrumental and Parametric Database. What happens when artificial seismicity is mixed with natural one?

Estimation of fractal dimension and b-value of earthquakes in the Himalayan region

The Himalayan belt is known for seismic activities; however, activities across this belt are not uniform due to various factors, including stress regime, heterogeneity of subsurface material, and the manner by which the major tectonic Indian plate is colliding with the Eurasian plate. In this study, three sample regions spanning northwest to northeast Himalayas (Kashmir, Nepal, and northeast Himalayan regions) were selected, and their b-values and fractal dimensions from the investigation period of 1973–2015 were calculated. Subsequently, the b-value was calculated via the Gutenberg–Richter relation and maximum likelihood method, whereas the fractal dimension or D-value was calculated using the correlation integral technique. Upon subdividing the time duration into six equal interval subsets, a variation in b-value can be observed over the years. The period 1973–2015 was selected to ensure the sufficiency of data in each subset and an adequate number of subsets for comparisons. From the low b-values, possible high-stress regions and asperities can be inferred, and the variation in stress and heterogeneity of material can be observed from the northwest to northeast Himalayas. An increase in b-value was observed on moving from the northwest to northeast Himalayas during the period of investigation. From the D-value, the extent of the epicentre cluster was observed, revealing that the epicentres were far more clustered to a point in Nepal Himalayas than in the two other regions. The spatial distribution of epicentres was more or less in 1D (fractal dimension) in the northeast and northwest Himalayas, indicating their distribution along particular geological linear features, such as major faults. Hence, a comparative study of the three regions was achieved. On the basis of the b-value, the types of fault and tectonics can be predicted, and the frequency of earthquakes in these Himalayan regions can be better understood.

Seismicbvalue within the Montney play of northeastern British Columbia, Canada

Critical analysis of induced earthquake occurrences requires comprehensive data sets obtained by dense seismographic networks. In this study, using such data sets, I take a detailed investigation into induced seismicity that occurred in the Montney play of northeastern British Columbia, mostly caused by hydraulic fracturing. The frequency–magnitude distribution (FMD) of earthquakes in several temporal and spatial clusters show fundamental discrepancies between seismicity in the southern Montney play (2014–2018) and the northern area (2014–2016). In both regions, FMDs follow the linear Gutenberg–Richter (G–R) relationship for magnitudes up to 3.0. While in southern Montney, within the Fort St. John graben complex, the number of earthquakes at larger magnitudes falls off rapidly below the G–R line, within the northern area with a dominant compressional regime, the number of events increases above the G–R line. This systematic difference may have important implications with regard to seismic hazard assessments from induced seismicity in the two regions, although caution in the interpretation is warranted due to local variabilities. While for most clusters within the southern Montney area, the linear or truncated G–R relationship provide reliable seismicity rates for events below magnitude 4.0, the G–R relationship underestimates the seismicity rate for magnitudes above 3.0 in northern Montney. Using a well-located data set of earthquakes in southern Montney, one can observe generally that (1) seismic productivity correlates well with the injected volume during hydraulic fracturing and (2) there is a clear depth dependence for the G–R b value; clusters with deeper median depths show lower b values than those with shallower depths.

Estimating of the b-Value Based on the Characteristic Earthquake Model

[Formula: see text]-value of the Gutenberg–Richter relation as an earthquake precursor depends on the tectonic setting features. This paper presents an alternative method to calculate [Formula: see text]-value in the presence of characteristic earthquakes. The proposed equation is based on the maximum likelihood method applied on the probability density function of the characteristic earthquake model. Data from real and simulated catalogs were used to evaluate the accuracy of the proposed model. For this purpose, 224 seismic event catalogs with various properties including catalogs’ sample size, the ratios of characteristic earthquakes number to catalog’s sample size [Formula: see text] and different magnitude of characteristic earthquakes were simulated. According to the estimated [Formula: see text]-values, the earthquake occurrence probability was calculated and discussed. The results indicate that the proposed method of estimation for [Formula: see text]-value has more adaptable consideration of the characteristic earthquake behavior.

The Unified Scaling Law for Earthquakes

This paper is a review of a long-continued research by many Russian and foreign scientists in the theory of self-organized criticality (SOC) in application to seismological data. We mean the Unified Scaling Law for Earthquakes (USLE). This law uses the spatial similarity of earthquake epicenters to derive a generalization of the classical Gutenberg–Richter relation. We discuss why this generalization is needed for practical problems that involve space–time parameters of seismicity, and we point out possible restrictions on practical applications. Several different methods are set forth for estimating the constants in USLE with examples of their practical use.

Aftershock Sequence and Statistics of the 2017 Mw 5.5 Pohang, South Korea, Earthquake: Implications of Fault Heterogeneity and Postseismic Relaxation

ABSTRACTThe sequence of foreshocks, mainshock, and aftershocks associated with a fault rupture is the result of interactions of complex fault systems, the tectonic stress field, and fluid movement. Analysis of shock sequences can aid our understanding of the spatial distribution and magnitude of these factors, as well as provide seismic hazard assessment. The 2017 Mw 5.5 Pohang earthquake sequence occurred following fluid-induced seismic activity at a nearby enhanced geothermal system site and is an example of reactivation of a critically stressed fault system in the Pohang basin, South Korea. We created an earthquake catalog based on unsupervised data mining and measuring the energy ratio between short- and long-window seismograms recorded by a temporary seismic network. The spatial distribution of approximately 4000 relocated aftershocks revealed four fault segments striking southwestward. We also determined that the three largest earthquakes (ML&amp;gt;4) were located at the boundary of two fault segments. We infer that locally concentrated stress at the junctions of the faults caused such large earthquakes and that their ruptures on multiple segments can explain the high proportion of non-double-couple components. The area affected by aftershocks continues to expand to the southwest and northeast by 0.5 and 1 km decade−1, respectively, which may result from postseismic deformation or sequentially transferred static coulomb stress. The b-values of the Gutenberg–Richter relationship temporarily increased for the first three days of the aftershock sequence, suggesting that the stress field was perturbed. The b-values were generally low (&amp;lt;1) and locally variable throughout the aftershock area, which may be due to the complex fault structures and material properties. Furthermore, the mapped p-values of the Omori law vary along strike, which may indicate anisotropic expansion speeds in the aftershock region.

Earthquakes Induced by Wastewater Injection, Part I: Model Development and Hindcasting

ABSTRACTIn the past decade, several parts of central United States, including Oklahoma, have experienced unprecedented seismicity rates, following an increase in the volumes of wastewater fluids that are being disposed underground. In this article, we present a semi-empirical model to hindcast the observed seismicity given the injection time history. Our proposed recurrence model is a modified version of the Gutenberg–Richter relation, building upon the seismogenic index model, which predicts a linear relationship between the number of induced events and the injected volume. Our methodology accounts for the effects of spatiotemporal pore-pressure diffusion, the stressing-rate dependency of the time lag between injection and seismicity rate changes, and the rapid cessation of seismicity upon unloading. We also introduced a novel multiscale regression, which enabled us to produce grid-independent results of increased spatial resolution. Although the model is generic to be applicable in any region and has essentially only two free parameters for spatial calibration, it matches the earthquake time history of Oklahoma well across various scales, for both increasing and decreasing injection rates. In the companion paper (Grigoratos, Rathje, et al., 2020), we employ the model to distinguish the disposal-induced seismicity from the expected tectonic seismicity and test its forecasting potential.