Magnitude-frequency Distribution Of Earthquakes Research Articles

Forecasting of Induced Seismicity Rates from Hydraulic Fracturing Activities Using Physics-Based Models for Probabilistic Seismic Hazard Analysis: A Case Study

One of the major challenges in seismic hazard analysis for induced seismicity is the forecasting of future seismicity rates, which are described by the Gutenberg–Richter parameters (a and b-values from the earthquake magnitude frequency distributions). In this study, we implement two methodologies in order to determine the Gutenberg–Richter parameters related to future induced seismicity: the Seismogenic Index and the Hydromechanical Nucleation model. We apply both methods in one recent case of induced seismicity: the Horn River Basin, Northeast B.C., Canada. We perform two tests to compare the predictions of both models with the observed seismicity. First, we compare the predicted number of earthquakes exceeding a certain magnitude per month with the observed number of earthquakes. In this test, both methods predict earthquake rates similar to the observed induced seismicity in the Horn River Basin. Second, we evaluate how appropriate are the predictions for specific magnitude ranges (given by forecasted Gutenberg–Richter parameters). In this case, both models make inaccurate predictions for specific magnitude ranges (annual magnitude frequency distributions), resulting in an under- or overestimation of the hazard but often with contradicting forecasts, despite using shared observations. The predictions under- and overestimate the hazard at different time points, due to the complexity in the evolution of the seismicity, and the assumption of constant b-values. As a result, these incorrect forecasts for future magnitude-frequency distributions lead to biased seismic hazard and ground motion predictions. More research effort is required in order to forecast more accurate Gutenberg–Richter parameters, particularly changes in the b-value, as observed in the Horn River Basin induced seismicity case.

A continuous-time HMM approach to modeling the magnitude-frequency distribution of earthquakes

ABSTRACTThe magnitude-frequency distribution (MFD) of earthquake is a fundamental statistic in seismology. The so-called b-value in the MFD is of particular interest in geophysics. A continuous time hidden Markov model (HMM) is proposed for characterizing the variability of b-values. The HMM-based approach to modeling the MFD has some appealing properties over the widely used sliding-window approach. Often, large variability appears in the estimation of b-value due to window size tuning, which may cause difficulties in interpretation of b-value heterogeneities. Continuous-time hidden Markov models (CT-HMMs) are widely applied in various fields. It bears some advantages over its discrete time counterpart in that it can characterize heterogeneities appearing in time series in a finer time scale, particularly for highly irregularly-spaced time series, such as earthquake occurrences. We demonstrate an expectation–maximization algorithm for the estimation of general exponential family CT-HMM. In parallel with discrete-time hidden Markov models, we develop a continuous time version of Viterbi algorithm to retrieve the overall optimal path of the latent Markov chain. The methods are applied to New Zealand deep earthquakes. Before the analysis, we first assess the completeness of catalogue events to assure the analysis is not biased by missing data. The estimation of b-value is stable over the selection of magnitude thresholds, which is ideal for the interpretation of b-value variability.

A Probabilistic Tsunami Hazard Study of the Auckland Region, Part I: Propagation Modelling and Tsunami Hazard Assessment at the Shoreline

Regional source tsunamis represent a potentially devastating threat to coastal communities in New Zealand, yet are infrequent events for which little historical information is available. It is therefore essential to develop robust methods for quantitatively estimating the hazards posed, so that effective mitigation measures can be implemented. We develop a probabilistic model for the tsunami hazard posed to the Auckland region of New Zealand from the Kermadec Trench and the southern New Hebrides Trench subduction zones. An innovative feature of our model is the systematic analysis of uncertainty regarding the magnitude-frequency distribution of earthquakes in the source regions. The methodology is first used to estimate the tsunami hazard at the coastline, and then used to produce a set of scenarios that can be applied to produce probabilistic maps of tsunami inundation for the study region; the production of these maps is described in part II. We find that the 2,500 year return period regional source tsunami hazard for the densely populated east coast of Auckland is dominated by events originating in the Kermadec Trench, while the equivalent hazard to the sparsely populated west coast is approximately equally due to events on the Kermadec Trench and the southern New Hebrides Trench.

Development of a volcanic hazard model for New Zealand

We commence development of a volcanic hazard model for New Zealand by applying the well- established methods of probabilistic seismic hazard analysis to volcanoes. As part of this work we use seismologically-based methods to develop eruption volume - frequency distributions for the Okataina and Taupo volcanoes of the central Taupo Volcanic Zone, New Zealand. Our procedure is to use the geologic and historical record of large eruptions (erupted magma volumes ≥ 0.01 cubic km for Taupo and ≥ 0.5 cubic km for Okataina) to construct eruption volume-frequency distributions for the two volcanoes. The two volcanoes show log-log distributions of decreasing frequency as a function of eruption volume, analogous to the shape of earthquake magnitude-frequency distributions constructed from seismicity catalogues. On the basis of these eruption volume-frequency distributions we estimate the maximum eruption volumes that Taupo and Okataina are capable of producing at probability levels of relevance to engineers and planners. We find that a maximum eruption volume of 0.1 cubic km is expected from Taupo with a 10% probability in 50 years, while Okataina may not produce a large eruption at this probability level. However, at the more conservative 2% probability in 50 years, both volcanoes are expected to produce large eruptions (0.5 cubic km for Okataina and 1 cubic km for Taupo). Our study therefore shows significant differences in eruption probabilities for volcanoes in the same physiographic region, and therefore highlights the importance of establishing unique eruption databases for all volcanoes in a hazard analysis.

The b value spectrum and η value by the moment method

The earthquake size distribution is generally considered to obey the Gutenberg-Richter (GR) law. We have introduced the concept of the b value spectrum based on the moment method to investigate the deviation of the actual magnitude distribution of earthquakes from this law. This enables us to describe characteristic features of the magnitude frequency distribution of earthquakes. We found also a simple relation between the η value and the b value spectrum. Analysis using this scheme showed that the actual size distributions of earthquakes have large variations from case to case and sometimes deviate considerably from the widely assumed the GR formula.

A comparison of seismic and structural measurements of scaling exponents during tensile subcritical crack growth

The observed fractal nature of both fault length distributions and earthquake magnitude-frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity. In previous theoretical work, a positive correlation between the exponent D from the fracture length distribution, and the seismic or acoustic emission (AE) b-value has been inferred from a simple dislocation model of the seismic source. Here, we present the first experimental evidence for a correlation between D and b from a series of tensile fracture mechanics tests on crystalline rock, carried out in different environmental conditions, both air-dry and water-saturated, and at ambient temperature and pressure. The microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity, K I, and quantitative analyses of the resulting fracture patterns were carried out on the same specimens. It is found that AE b-values, ranging from 1.0 to 2.3, correlate negatively with the normalized stress intensity K I/ K IC , where K IC is the fracture toughness of the specimen. The microcrack length distribution exponent D, ranges from 1.0 to 1.7. Fluid presence has a first-order influence on both the AE and structure produced in these experiments. For experiments at low stress intensity or high fluid content, the activation of the stress corrosion mechanism for K I < K IC leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions, reflected in higher values of D and b. The exponent D is found to correlate positively with the AE b-value.

Deviation of magnitude frequency distribution of earthquakes from the Gutenberg-Richter law: detection of precursory anomalies prior to large earthquakes

We present a measure that represents the degree of deviation of the magnitude frequency distribution of earthquakes from the Gutenberg-Richter (GR) law. The magnitude frequency distribution of earthquakes has been considered to obey the GR law. Actual distributions, however, often deviate considerably from this law. Let n i , N, M 0 and b be the number of events with magnitude M i ∼ M i + ΔM, total number of earthquakes, lower limit of the magnitude and b value of the GR formula, respectively. Then the measure of deviation is given using Kullback-Leibler's mean information as C= ∑ i p(X i)ln[ p(X i) q(X i ] X i=M i−M 0 where p(X i) = n i N and q(X i) = b ln 10 exp (−b ln 10 X i) . Function q( X i ) denotes the GR distribution and thus this measure gives the degree of deviation of the magnitude distribution from the GR law. When the magnitude distribution of earthquakes fits the GR formula more closely, the ‘ C’ value becomes smaller and is zero if the distribution obeys the GR law exactly. Conversely, if the distribution deviates greatly from the GR law, the ‘ C’ index shows a large value. We have investigated the temporal variation of ‘ C’ values before and after large earthquakes and swarm earthquakes in Japan. Results show considerable variations of ‘ C’ values before and after large earthquakes. Prior to large earthquakes, ‘ C’ values become small, which indicates that magnitude distributions fit better to the GR law. The ‘ C’ indices show drastic change after mainshocks. During swarm earthquakes, the variation of ‘ C’ values is rather large, but ‘ C’ values are smaller than ordinary earthquakes. In some swarms the ‘ C’ indices reach a maximum at the time of the greatest activity. This measure is a useful tool with which to observe the characteristic properties of the seismic activity and may be used for detection of precursory phenomena of large earthquakes.

Analysis of the magnitude-frequency distribution for the 1983–1984 earthquake activity of Campi Flegrei, Italy

The magnitude-frequency distribution of earthquakes is one of the statistical relationships most frequently used to study the seismicity of a region. In this paper the Gutenberg-Richter frequency magnitude relationship is applied to the 1983–1984 earthquake sequence of Campi Flegrei, Italy, in order to estimate the space-time variation of the b-value, and its possible correlation with other geophysical parameters in the sequence. The investigated region has been divided into three areas on the basis of differences in seismic activity: (a) to the west of Pozzuoli, where seismicity occurred mostly as swarms; (b) to the east of Pozzuoli, where events mostly included single, high-energy earthquakes; and (c) in the western sector of the Gulf of Pozzuoli. Moreover, b-value estimates have been carried out according to different hypocentral depths of all seismic events in the sequence. The obtained results have shown strong depth variations of the b-value which might reflect important differences in failure conditions at different depths. Furthermore, a certain complexity in the shape of the obtained distribution functions n( M) has been pointed out. Temporal variations of b-value, computed both for the whole region and the different selected areas, seem to be meaningful because they do not depend on the number of shocks ΔN, the data overlap and the magnitude step ΔM. The rates of change of b-value Δb/ Δt, compared with the changing rates of seismic energy release ΔE/ Δt do not show a consistent correlation, hence the Δb/ Δt curve cannot be interpreted as a precursor to the other in any systematic way.

地震の規模別度数分布に関する新しい尺度

地震の規模別度数分布に関する新しい尺度

地震のマグニチュード別度数分布と余震面積と主震のマグニチュードとに関する宇津・関公式との関係

地震のマグニチュード別度数分布と余震面積と主震のマグニチュードとに関する宇津・関公式との関係