A Normalized Distance Test for co‐determining the completeness magnitude and b‐value of earthquake catalogs

The Gutenberg-Richter (GR) b-value represents the relative proportion of small to large earthquakes in a scale-free population. For tectonic seismicity, this is often close to unity, but some studies have shown the b-value to be elevated (>1) in both volcanic and induced seismicity. However, many of these studies have used relatively small datasets &#8211; in sample size and magnitude range, easily introducing biases. This leads to incomplete catalogues above the threshold above which all events are assumed to be recorded &#8211; the completeness magnitude Mc. At high magnitudes, the scale-free behaviour must break down because natural tectonic and volcano-tectonic processes are incapable of an infinite release of energy, which is difficult to estimate accurately. In particular, it can be challenging to distinguish between regions of unlimited scale-free behaviour and physical roll-off at larger magnitudes. The latter model is often referred to as the modified Gutenberg-Richter (MGR) distribution.We use the MGR distribution to describe the breakdown of scale-free behaviour at large magnitudes, introducing the roll-off parameter (&#952;) to the incremental distribution. Applying a maximum likelihood method to estimate the b-value could violate the implicit assumption that the underlying model is GR. If this is the case, the methods used will return a biased b-value rather than indicate that the method used is inappropriate for the underlying model. Using synthetic data and testing it on various earthquake catalogues, we show that when we have little data and low bandwidth, it is statistically challenging to test whether the sample is representative of the scale-free GR behaviour or whether it is controlled primarily by the finite size roll-off seen in MGR.

Download Full-text

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

Frontiers in Earth Science ◽

10.3389/feart.2021.663385 ◽

2021 ◽

Vol 9 ◽

Author(s):

Pınar Büyükakpınar ◽

Simone Cesca ◽

Sebastian Hainzl ◽

Mohammadreza Jamalreyhani ◽

Sebastian Heimann ◽

...

Keyword(s):

Water Level ◽

Pore Pressure ◽

Monitoring Network ◽

B Value ◽

Seismogenic Zone ◽

Seismicity Rate ◽

Pressure Diffusion ◽

Completeness Magnitude ◽

Water Level Variations ◽

Spatio Temporal

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 Mw 5.5 and Mw 5.1 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.

Download Full-text

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

Seismological Research Letters ◽

10.1785/0220210017 ◽

2021 ◽

Author(s):

Matteo Taroni ◽

Jiancang Zhuang ◽

Warner Marzocchi

Keyword(s):

Spatial Variability ◽

Bayes Factor ◽

Likelihood Estimation ◽

B Value ◽

Earthquake Forecasting ◽

Earthquake Catalog ◽

High Definition ◽

Novel Approach ◽

Completeness Magnitude

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.

Download Full-text

Inadvertent changes in magnitude reported in earthquake catalogs: Their evaluation through b-value estimates

Bulletin of the Seismological Society of America ◽

10.1785/bssa0850061858 ◽

1995 ◽

Vol 85 (6) ◽

pp. 1858-1866

Author(s):

F. Ramón Zúñiga ◽

Max Wyss

Keyword(s):

Simple Procedure ◽

B Value ◽

Reporting Rate ◽

Magnitude Scale ◽

Earthquake Catalog ◽

Data Set ◽

Earthquake Catalogs ◽

Fitting Method ◽

Seismicity Rates ◽

Frequency Magnitude

Abstract A simple procedure is presented for analyzing magnitudes and seismicity rates reported in earthquake catalogs in order to discriminate between inadvertently introduced changes in magnitude and real seismicity changes. We assume that the rate and the frequency-magnitude relation of the independent background seismicity do not change with time. Observed differences in the frequency-magnitude relation (a and b values) between data from two periods are modeled as due to a transformation of the magnitude scale. The transformation equation is found by a least-squares-fitting process based on the seismicity data for earthquakes large enough to be reported completely and by comparing the linear relation of one period to the other. For smaller events, an additional factor accounting for increased (decreased) detection is allowed. This fitting technique is tested on a data set from Parkfield for which two types of magnitudes, amplitude and duration, were computed for each earthquake. We found that the b-value fitting technique yielded virtually the same result as a linear regression assuming the same errors in the two magnitudes. The technique is also applied to interpret the nature of reporting rate changes in a local (Guerrero, Mexico) and a regional (Italy) earthquake catalog. In Guerrero, a magnitude change in 1991.37 can be modeled about equally well by Mnew = Mold + 0.5 or by Mnew = 1.02 Mold + 0.38, but residuals with the latter transformation are smaller. In Italy, a magnitude change in 1980.21 cannot be modeled satisfactorily by a simple magnitude shift but is well described by a compression of the magnitude scale given by Mnew = 0.67 Mold + 1.03. The proposed b-slope fitting method provides a means to interpret quantitatively, and in some cases correct for, artificial reporting rate changes in earthquake catalogs.

Download Full-text

Temporary seismic monitoring of the Sulmona area (Abruzzo, Italy): quality study of microearthquake locations

Natural Hazards and Earth System Sciences Discussions ◽

10.5194/nhessd-1-2353-2013 ◽

2013 ◽

Vol 1 (3) ◽

pp. 2353-2395

Author(s):

M. A. Romano ◽

R. de Nardis ◽

M. Garbin ◽

L. Peruzza ◽

E. Priolo ◽

...

Keyword(s):

Active Faults ◽

High Stress ◽

Velocity Model ◽

B Value ◽

Space Distribution ◽

Total Period ◽

Seismogenic Layer ◽

Time Space ◽

Duration Magnitude ◽

Completeness Magnitude

Abstract. Thanks to the installation of a temporary seismic network, a microseismicity study has been conducted in the Sulmona area (Abruzzo, Italy) with the aim of increasing the knowledge of seismogenic potential of existing active faults. In this work the first seven months (from 27 May to 31 December 2009) of recorded data have been analysed, over a total period of acquisition of about 30 months. Using a semi-automatic procedure, more than 800 local earthquakes has been detected, which highlight the background seismicity previously unknown. About 70% of these events have been relocated using a 1-D velocity model estimated specifically for the Sulmona area. Phase readings quality is checked and discussed, with respect to weighting schemes used by location algorithms, too. The integration of temporary network data with all the other data available in the region enable us to obtain a statistically more robust dataset of earthquake locations. Both the final hypocentral solutions and phase pickings are released as online Supplement. Local magnitude values of the newly detected events ranges between −1.5 and 3.7 and the completeness magnitude for the Sulmona area during the study period is about 1.1. Duration magnitude coefficients have been estimated as well, for comparison/integration purposes. Local Gutenberg–Richter relationship, estimated from the microseismic data, features low b value, possibly suggesting that the Sulmona area is currently undergoing high stress, in agreement with other recent studies. The time-space distribution of the seismic activity with respect to the known active faults, as well the seismogenic layer thickness, are preliminarily investigated.

Download Full-text

The Reliance of the Earthquake B-Value on Depth and Focal Mechanism

Iraqi Geological Journal ◽

10.46717/igj.54.1d.1ms-2021-04-21 ◽

2021 ◽

Vol 54 (1D) ◽

pp. 1-10

Author(s):

Emad Al-Heety

Keyword(s):

Moment Tensor ◽

Focal Depth ◽

Seismic Hazard Assessment ◽

B Value ◽

Strike Slip ◽

Focal Mechanisms ◽

Likelihood Method ◽

Centroid Moment Tensor ◽

B Values ◽

Completeness Magnitude

The earthquake size distribution (b-value) is a significant factor to recognize the seismic activity, seismotectonic, and seismic hazard assessment. In the current work, the connection of the b-constant value with the focal depth and mechanism was studied. The effect of the study scale (global, regional and local) on the dependence of b-value on the focal mechanisms was investigated. The database is quoted from the Global Centroid Moment Tensor catalog. The selected earthquakes are the shallow normal, reverse and strike-slip events. The completeness magnitude (Mc) is 5.3. The maximum likelihood method is utilized to compute the b-value. The obtained results show that the b-value is decreasing with depth to range 10-20 km, then increases to the depth of 40km. The turning point of b-value (increasing of b-value) locates at the depth of the transition brittle-ductile zone. Globally and regionally, low, moderate, and high b-values are associated with reverse, strike-slip, and normal focal mechanisms, respectively, while locally, the relation between b-values and focal mechanisms shows different association trends, such as low, moderate, and high b-values are associated with normal, strike-slip, and reverse focal mechanisms and so on.

Download Full-text

The Effect of Declustering on the Size Distribution of Mainshocks

Seismological Research Letters ◽

10.1785/0220200231 ◽

2021 ◽

Author(s):

Leila Mizrahi ◽

Shyam Nandan ◽

Stefan Wiemer

Keyword(s):

Seismic Hazard Assessment ◽

B Value ◽

Aftershock Sequence ◽

Earthquake Catalogs ◽

Magnitude Distribution ◽

Independent Events ◽

Potential Source ◽

Epidemic Type Aftershock Sequence ◽

Frequency Magnitude Distribution ◽

Frequency Magnitude

Abstract Declustering aims to divide earthquake catalogs into independent events (mainshocks), and dependent (clustered) events, and is an integral component of many seismicity studies, including seismic hazard assessment. We assess the effect of declustering on the frequency–magnitude distribution of mainshocks. In particular, we examine the dependence of the b-value of declustered catalogs on the choice of declustering approach and algorithm-specific parameters. Using the catalog of earthquakes in California since 1980, we show that the b-value decreases by up to 30% due to declustering with respect to the undeclustered catalog. The extent of the reduction is highly dependent on the declustering method and parameters applied. We then reproduce a similar effect by declustering synthetic earthquake catalogs with known b-value, which have been generated using an epidemic-type aftershock sequence model. Our analysis suggests that the observed decrease in b-value must, at least partially, arise from the application of the declustering algorithm on the catalog, rather than from differences in the nature of mainshocks versus fore- or aftershocks. We conclude that declustering should be considered as a potential source of bias in seismicity and hazard studies.

Download Full-text