Estimating b-values and biases in small earthquake catalogues

2020 ◽  
Author(s):  
Gina-Maria Geffers ◽  
Ian Main ◽  
Mark Naylor
Keyword(s):  
Relative Proportion ◽  
Synthetic Data ◽  
Finite Size ◽  
B Value ◽  
Likelihood Method ◽  
Implicit Assumption ◽  
Earthquake Catalogues ◽  
Scale Free ◽  
Completeness Magnitude ◽  
Large Earthquakes

<p>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 – 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 – the completeness magnitude M<sub>c</sub>. 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.</p><p>We use the MGR distribution to describe the breakdown of scale-free behaviour at large magnitudes, introducing the roll-off parameter (θ) 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.</p>

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

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.

scholarly journals Bachatskiy induced earthquake on June 18, 2013, ML=6.1, I0=7 (Kuzbass)

2020 ◽  
Vol 2 (1) ◽  
pp. 48-61 ◽  
Author(s):  
Aleksandr Emanov ◽  
Aleksey Emanov ◽  
Aleksandr Fateev
Keyword(s):  
B Value ◽  
Mountain Area ◽  
Seismic Arrays ◽  
Seismic Activation ◽  
Background Seismicity ◽  
Single Process ◽  
Strip Mine ◽  
Large Earthquakes ◽  
Sayan Mountain ◽  
Natural Seismicity

The Bachatsky earthquake of 18 June 2013 and a seismic activation of the same name coal strip mine, started several years before the earthquake and still persists today, have been studied using temporal local seismic arrays in the area. It was found experimentally that the seismic process area is closely connected to open workings, and the earthquakes are extend-ed from the working bed to a depth of 4-5 km. Adjacent to the mine depression sedimentary rocks were activated. The technogenic seismic regime is continuous and not stationary: intervals of background seismicity with relatively weak and seldom events are disturbed by bursts of activity with a rise in the magnitude of stronger earthquakes and frequency of occurrence of weak events. The seismic activation may last for 1–3 months. During the last five years, four seismic activations have been recorded, three of which were generated by large earthquakes of 09.02.2012, ML4.3; 04.03.2013, ML3.9; 18.06.2013, ML6.1. The last one was completed by a series of perceptible earthquakes with local magnitude of 3.0–3.5. The focal mechanism of the Bachatsky earthquake is a thrust fault with one of the motion planes corresponding to the anthropogenic impact. The earthquake flow forms a single process in the space with the b-value of the Gutenberg-Richter relationship different from the natural seismicity. The studied induced seismicity does not correspond to the structural regularities of natural seismicity in the Altai-Sayan mountain area. The findings prove that the Bachatsky earthquake and associated activation can be considered as man-made events.

scholarly journals Seismic analysis using maximum likelihood of gutenberg-richter

2017 ◽  
Vol 1 (1) ◽  
pp. 34-40
Author(s):  
Arum Handini Primandari ◽  
Khusnul Khotimah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Seismic Analysis ◽  
B Value ◽  
Likelihood Method ◽  
Natural Phenomena ◽  
Earthquake Occurrence ◽  
Precise Prediction ◽  
Great Damage

An earthquake is one of catastrophe which often claim numerous lives and cause great damage to infrastructure. Multiple studies from various field have been conducted in order to make a precise prediction of earthquake occurrence, such as recognizing the natural phenomena symptoms leading to the shaking and ground rupture. However, up till now there is no definite method that can predict the time and place in which earthquake will occur. By assuming that the number of earthquake follow Gutenberg-Richter law, we work b-value derived using Maximum Likelihood Method to calculate the probability of earthquake happen in the next few years. The southern sea of D.I. Yogyakarta was divided into four areas to simplify the analysis. As the result, in the next five years the first and second area have high enough probability (>0.3) to undergo more than 6.0-magnitude earthquake.

scholarly journals Power-law distribution of degree–degree distance: A better representation of the scale-free property of complex networks

2020 ◽  
Vol 117 (26) ◽  
pp. 14812-14818 ◽  
Author(s):  
Bin Zhou ◽  
Xiangyi Meng ◽  
H. Eugene Stanley
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Power Law ◽  
Real World ◽  
Preferential Attachment ◽  
Statistical Tests ◽  
Finite Size ◽  
Distance Distribution ◽  
Scale Free ◽  
Degree Distance

Whether real-world complex networks are scale free or not has long been controversial. Recently, in Broido and Clauset [A. D. Broido, A. Clauset,Nat. Commun.10, 1017 (2019)], it was claimed that the degree distributions of real-world networks are rarely power law under statistical tests. Here, we attempt to address this issue by defining a fundamental property possessed by each link, the degree–degree distance, the distribution of which also shows signs of being power law by our empirical study. Surprisingly, although full-range statistical tests show that degree distributions are not often power law in real-world networks, we find that in more than half of the cases the degree–degree distance distributions can still be described by power laws. To explain these findings, we introduce a bidirectional preferential selection model where the link configuration is a randomly weighted, two-way selection process. The model does not always produce solid power-law distributions but predicts that the degree–degree distance distribution exhibits stronger power-law behavior than the degree distribution of a finite-size network, especially when the network is dense. We test the strength of our model and its predictive power by examining how real-world networks evolve into an overly dense stage and how the corresponding distributions change. We propose that being scale free is a property of a complex network that should be determined by its underlying mechanism (e.g., preferential attachment) rather than by apparent distribution statistics of finite size. We thus conclude that the degree–degree distance distribution better represents the scale-free property of a complex network.

EnKF estimation of the viscoelastic deformation and the viscosity

2020 ◽  
Author(s):  
Makiko Ohtani
Keyword(s):  
Data Assimilation ◽  
Crustal Deformation ◽  
Surface Deformation ◽  
Synthetic Data ◽  
Ground Surface ◽  
Inelastic Strain ◽  
Large Earthquake ◽  
Forward Model ◽  
Viscoelastic Deformation ◽  
Large Earthquakes

<p>Following large earthquakes, postseismic crustal deformations are often observed for more than years. They include the afterslip and the viscoelastic deformation of the crust and the upper mantle, activated by the coseismic stress change. The viscoelastic deformation gives the stress change on the neighboring faults, hence affects the seismic activity of the surrounding area, for a long period after the large earthquake. So, estimating the viscoelastic deformation after the large earthquakes is important.</p><p>In order to estimate the time evolution of the viscoelastic deformation after a large earthquake, we also need to know the viscoelastic structure around the area. Recently, the Ensemble Kalman filter method (EnKF), a sequential data assimilation method, starts to be used for the crustal deformation data to estimate the physical variables (van Dinther et al., 2019, Hirahara and Nishikiori, 2019). With data assimilation, we get a more provable estimation by combining the data and the time-forward model than only using the data. Hirahara and Nishikiori (2019) used synthetic data and showed that EnKF could effectively estimate the frictional parameters on the SSE (slow slip event) fault, addition to the slip velocity. In the present study, I applied EnKF to estimate the viscosity and the inelastic strain after a large earthquake, both the physical property and the variables.</p><p>First, I constructed the forward model simulating the evolution of the viscoelastic deformation, following the equivalent body force method (Barbot and Fialko, 2010; Barbot et al., 2017). This method is appropriate for applying EnKF, because the ground surface deformation rate is represented by the inelastic strain at the moment, and the history of the strain is not required. Then, we applied EnKF based on the forward model and executed some numerical experiments using a synthetic postseismic crustal deformation data.</p><p>In this presentation, I show the result of a simple setting. I assumed the medium to be two layers with a homogeneous viscoelastic region underlying an elastic region. The synthetic data is made by giving a slip on a fault at time <em>t</em> = 0 and simulating the time evolution of the ground surface deformation. For assimilation, I assumed that the slip on the fault and the stress distribution just after the large earthquake is known. Then we executed the assimilation every 30 days after the large earthquake. I found that I can get a good estimation of the viscosity after <em>t</em> > 150 days.</p>

Migration of seismic data from inhomogeneous media

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 751-767 ◽  
Author(s):  
Les Hatton ◽  
Ken Larner ◽  
Bruce S. Gibson
Keyword(s):  
Theoretical Approach ◽  
Synthetic Data ◽  
Velocity Model ◽  
Implicit Assumption ◽  
Geologic Structure ◽  
Structural Shape ◽  
Depth Migration ◽  
Position Errors ◽  
Time Migration ◽  
Imaging Results

Because conventional time‐migration algorithms are founded on the implicit assumption of locally lateral homogeneity, they leave events mispositioned when overburden velocity varies laterally. The ray‐theoretical depth migration procedure of Hubral often can provide adequate first‐order corrections for such position errors. Complex geologic structure, however, can so severely distort wavefronts that resulting time‐migrated sections may be barely interpretable and thus not readily correctable. A more accurate, wave‐theoretical approach to depth migration then becomes essential to image the subsurface properly. This approach, which transforms an unmigrated time section directly into migrated depth, more completely honors the wave equation for a medium in which variations in interval velocity and details of structural shape govern wave propagation. Where geologic structure is complicated, however, we usually lack an accurate velocity model. It is important, therefore, to understand the sensitivity of depth migration to velocity errors and, in particular, to assess whether it is justified to go to the added effort of doing depth migration. We show a synthetic data example in which the wave‐theoretical approach to depth migration properly images deep reflections that are poorly resolved and left distorted by either time migration or ray‐theoretical depth migration. These imaging results are, moreover, surprisingly insensitive to errors introduced into the velocity model. Application to one field data example demonstrates the superior treatment of amplitude and waveform by wave‐theoretical depth migration. In a second data example, deep reflections are so influenced by anomalous overburden structure that the only valid alternative to performing wave‐theoretical depth migration is simply to convert the unmigrated data to depth. When the overburden is laterally variable, conventional time migration of unstacked data can be as destructive to steeply dipping reflections as is CDP stacking prior to migration. A schematic example illustrates that when migration of unstacked data is judged necessary, it should normally be performed as a depth migration.

scholarly journals Scale-free tails in colombian financial indexes: a primer

ODEON ◽  
2016 ◽  
pp. 233 ◽  
Author(s):  
Carlos León
Keyword(s):  
Financial Markets ◽  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Stock Market Index ◽  
Scale Free ◽  
Market Index ◽  
Power Law Exponent

<p>A maximum likelihood method for estimating the power-law exponent verifies that the positive and negative tails of the Colombian stock market index (IGBC) and the Colombian peso exchange rate (TRM) approximate a scale-free distribution, whereas none of the heavy tails of a local sovereign securities index (IDXTES) are a plausible case for such distribution. Results also (i) support critiques regarding the flaws of ordinary least squares estimation methods for scale-free distributions; (ii) question the validity of Zipf’s law; (iii) suggest that IGBC and TRM display the scale-free nature documented as a stylized fact of financial returns, and that they may be following a gradually truncated Lévy flight; and (iv) suggest that local financial markets are self-organizing systems.</p>

scholarly journals A Spatial Biosurveillance Synthetic Data Generator in R

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Drew Levin ◽  
Patrick Finley
Keyword(s):  
Power Law ◽  
Real World ◽  
Degree Distribution ◽  
Transportation Network ◽  
Synthetic Data ◽  
Data Sets ◽  
Real World Data ◽  
Data Set ◽  
Scale Free ◽  
Data Generator

ObjectiveTo develop a spatially accurate biosurveillance synthetic datagenerator for the testing, evaluation, and comparison of new outbreakdetection techniques.IntroductionDevelopment of new methods for the rapid detection of emergingdisease outbreaks is a research priority in the field of biosurveillance.Because real-world data are often proprietary in nature, scientists mustutilize synthetic data generation methods to evaluate new detectionmethodologies. Colizza et. al. have shown that epidemic spread isdependent on the airline transportation network [1], yet current datagenerators do not operate over network structures.Here we present a new spatial data generator that models thespread of contagion across a network of cities connected by airlineroutes. The generator is developed in the R programming languageand produces data compatible with the popular `surveillance’ softwarepackage.MethodsColizza et. al. demonstrate the power-law relationships betweencity population, air traffic, and degree distribution [1]. We generate atransportation network as a Chung-Lu random graph [2] that preservesthese scale-free relationships (Figure 1).First, given a power-law exponent and a desired number of cities,a probability mass function (PMF) is generated that mirrors theexpected degree distribution for the given power-law relationship.Values are then sampled from this PMF to generate an expecteddegree (number of connected cities) for each city in the network.Edges (airline connections) are added to the network probabilisticallyas described in [2]. Unconnected graph components are each joinedto the largest component using linear preferential attachment. Finally,city sizes are calculated based on an observed three-quarter power-law scaling relationship with the sampled degree distribution.Each city is represented as a customizable stochastic compartmentalSIR model. Transportation between cities is modeled similar to [2].An infection is initialized in a single random city and infection countsare recorded in each city for a fixed period of time. A consistentfraction of the modeled infection cases are recorded as daily clinicvisits. These counts are then added onto statically generated baselinedata for each city to produce a full synthetic data set. Alternatively,data sets can be generated using real-world networks, such as the onemaintained by the International Air Transport Association.ResultsDynamics such as the number of cities, degree distribution power-law exponent, traffic flow, and disease kinetics can be customized.In the presented example (Figure 2) the outbreak spreads over a 20city transportation network. Infection spreads rapidly once the morepopulated hub cities are infected. Cities that are multiple flights awayfrom the initially infected city are infected late in the process. Thegenerator is capable of creating data sets of arbitrary size, length, andconnectivity to better mirror a diverse set of observed network types.ConclusionsNew computational methods for outbreak detection andsurveillance must be compared to established approaches. Outbreakmitigation strategies require a realistic model of human transportationbehavior to best evaluate impact. These actions require test data thataccurately reflect the complexity of the real-world data they wouldbe applied to. The outbreak data generated here represents thecomplexity of modern transportation networks and are made to beeasily integrated with established software packages to allow for rapidtesting and deployment.Randomly generated scale-free transportation network with a power-lawdegree exponent ofλ=1.8. City and link sizes are scaled to reflect their weight.An example of observed daily outbreak-related clinic visits across a randomlygenerated network of 20 cities. Each city is colored by the number of flightsrequired to reach the city from the initial infection location. These generatedcounts are then added onto baseline data to create a synthetic data set forexperimentation.KeywordsSimulation; Network; Spatial; Synthetic; Data

scholarly journals The Spatio-temporal Analysis of b-value in the Banda Arc, Indonesia

2021 ◽  
Vol 873 (1) ◽  
pp. 012010
Author(s):  
Muhammad Bani Al-Rasyid ◽  
Mira Nailufar Rusman ◽  
Daniel Hamonangan ◽  
Pepen Supendi ◽  
Kartika Hajar Kirana
Keyword(s):  
Temporal Variation ◽  
Temporal Analysis ◽  
B Value ◽  
Spatial And Temporal Variation ◽  
Tectonic Structure ◽  
Time Period ◽  
Banda Arc ◽  
Spatio Temporal ◽  
The Impact ◽  
Large Earthquakes

Abstract Banda arc is a complex tectonic structure manifests by high seismicity due to the collision of a continent and an intra-oceanic island arc. Using the relocated earthquakes data from ISC-EHB and BMKG catalogues from the time period of 1960 to 2018, we have conducted a spatial and temporal variation of b-value using the Guttenberg-Richter formula in the area. Our results show that the spatial distribution of low b-values located in the south of Ambon Island and southeast of Buru Island. On the other hand, the temporal variation of b-value shows a decrease in the northern part of the Banda sea probably high potential to produce large earthquakes in the future. Therefore, further mitigation is needed to minimize the impact of earthquakes in the area.

Sign in / Sign up

Export Citation Format

Share Document