Bayesian source inversion of microseismic events

doi:10.17863/CAM.15958

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Bayesian source inversion of microseismic events

Dissertation•DOI•

Bayesian source inversion of microseismic events

05 Jan 2016-

TL;DR: In this paper, the authors used the UK Natural Environment Research Council CASE studentship (NE/I018263/1) in partnership with Schlumberger Gould Research to conduct a case study.

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Abstract: Acknowledgements: This work was undertaken through a UK Natural Environment Research Council CASE studentship (NE/I018263/1) in partnership with Schlumberger Gould Research.

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Journal Article•DOI•

Strike‐slip faulting during the 2014 Bárðarbunga‐Holuhraun dike intrusion, central Iceland

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Thorbjörg Ágústsdóttir¹, Jennifer Woods¹, Tim Greenfield¹, Robert G. Green¹, Robert S. White¹, Robert S. White², Tom Winder¹, Bryndís Brandsdóttir², Sveinbjörn Steinthórsson², Heidi Soosalu - Show less +6 more•Institutions (2)

University of Cambridge¹, University of Iceland²

28 Feb 2016-Geophysical Research Letters

TL;DR: In this article, a 13-day period magma propagated laterally from the subglacial Barðarbunga volcano in the northern rift zone, Iceland, creating > 30,000 earthquakes at 5-7 km depth along a 48 km path before erupting on 29 August 2014.

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Abstract: Over a 13?day period magma propagated laterally from the subglacial Barðarbunga volcano in the northern rift zone, Iceland. It created >?30,000 earthquakes at 5–7?km depth along a 48?km path before erupting on 29 August 2014. The seismicity, which tracked the dike propagation, advanced in short bursts at 0.3–4.7?km/h separated by pauses of up to 81?h. During each surge forward, seismicity behind the dike tip dropped. Moment tensor solutions from the leading edge show exclusively left-lateral strike-slip faulting subparallel to the advancing dike tip, releasing accumulated strain deficit in the brittle layer of the rift zone. Behind the leading edge, both left- and right-lateral strike-slip earthquakes are observed. The lack of non-double-couple earthquakes implies that the dike opening was aseismic.

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123 citations

Cites methods from "Bayesian source inversion of micros..."

...Lower hemisphere fault plane solutions and inversions of the full moment tensor were constructed using a Bayesian moment tensor solution program MTINV [Pugh, 2015]....
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Journal Article•

Source type plot for inversion of the moment tensor

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J. A. H. dson, R. G. P. arce, R. M. R. gers

10 Dec 1989-Journal of Geophysical Research

57 citations

Journal Article•DOI•

種々の震源の深さに依る走時曲線;種々の震源の深さに依る走時曲線;On the Travel Time of Earthquake Waves sent from the Focus of various Deptys

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K. Wadati, K. Sagisaka, K. Masuda

01 Jan 1932-Journal of the Meteorological Society of Japan

41 citations

Journal Article•DOI•

Building icelandic igneous crust by repeated melt injections

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Tim Greenfield¹, Robert S. White¹•Institutions (1)

University of Cambridge¹

01 Nov 2015-Journal of Geophysical Research

TL;DR: In this paper, the authors use template waveforms from each swarm to detect and locate earthquakes with an automated cross-correlation technique and find that during melt intrusion high strain rates are produced in conjunction with high pore fluid pressures from the melt or exsolved carbon dioxide.

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Abstract: Observations of microseismicity provide a powerful tool for mapping the movement of melt in the crust. Here we record remarkable sequences of earthquakes 20 km below the surface in the normally ductile crust in the vicinity of Askja Volcano, in northeast Iceland. The earthquakes occur in swarms consisting of identical waveforms repeating as frequently as every 8 s for up to 3 h. We use template waveforms from each swarm to detect and locate earthquakes with an automated cross-correlation technique. Events are located in the lower crust and are inferred to be the result of melt being injected into the crust. During melt intrusion high strain rates are produced in conjunction with high pore fluid pressures from the melt or exsolved carbon dioxide. These cause brittle failure on high-angle fault planes located at the tips of sills. Moment tensor solutions show that most of the earthquakes are opening cracks accompanied by volumetric increases. This is consistent with the failure causing the earthquakes by melt injection opening new tensile cracks. Analysis of the magnitude distribution of earthquakes within a swarm reveals a complicated relationship between the imposed strain rates and the fluids that cause brittle failure. The magnitude of the earthquakes is controlled by the distance fluids can migrate along a fault, whereas the frequency of the events is controlled by the strain rate. Faults at the tips of sills act to focus melt transport between sills and so must be an important method of transporting melt through the lower crust.

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27 citations

Cites methods from "Bayesian source inversion of micros..."

...Moment tensors were derived by a Bayesian inversion of the polarities [Pugh, 2015] taking into account the probability of an incorrect polarity pick and a 1 km uncertainty in location....
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Journal Article•DOI•

MTfit: A Bayesian Approach to Seismic Moment Tensor Inversion

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David J. Pugh¹, Robert S. White¹•Institutions (1)

University of Cambridge¹

01 Jul 2018-Seismological Research Letters

TL;DR: The MTfit code was developed as part of a PhD project (Pugh 2015), funded under a Natural Environment Research Council (NERC) studentship at the University of Cambridge, as a CASE award with Schlumberger.

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Abstract: The MTfit code was developed as part of a PhD project (Pugh 2015), funded under a Natural Environment Research Council (NERC) studentship at the University of Cambridge, as a CASE award with Schlumberger. Seismometers were borrowed from the NERC SEIS-UK (loan 842).

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22 citations

References

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Journal Article•DOI•

A new look at the statistical model identification

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Hirotugu Akaike

01 Dec 1974-IEEE Transactions on Automatic Control

TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.

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Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

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47,133 citations

"Bayesian source inversion of micros..." refers methods or result in this paper

...This approach is consistent with the Akaike and Bayesian information criteria (Akaike, 1974; Schwarz, 1978), but the resulting value corresponds directly to the posterior model probability, so can also be used as a test of the hypothesis that an event is non-double-couple....
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...These posterior model probabilities provide a useful estimate of the model type, consistent with but more easily understood than the other approaches for estimating model type, such as the Akaike information criterion (Akaike, 1974) and the Bayesian information criterion (Schwarz, 1978)....
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...Unlike the Akaike and Bayesian information criteria (Akaike, 1974; Schwarz, 1978), the resulting value corresponds directly to the posterior model probability, so can also be used as a test of the hypothesis that an event is non-doublecouple....
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...This estimate is more intuitive than those provided by the Akaike and Bayesian information criteria (Akaike, 1974; Schwarz, 1978), since the resulting value corresponds directly to the posterior model probability, so can also be used as a test of the hypothesis that an event is non-double-couple....
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...vii viii Nomenclature Akaike Information Criterion (AIC)....
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Estimating the dimension of a model

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Gideon Schwarz

01 Jan 2005

TL;DR: In this paper, the problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion.

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Abstract: The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.

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36,760 citations

"Bayesian source inversion of micros..." refers methods or result in this paper

...This approach is consistent with the Akaike and Bayesian information criteria (Akaike, 1974; Schwarz, 1978), but the resulting value corresponds directly to the posterior model probability, so can also be used as a test of the hypothesis that an event is non-double-couple....
[...]
...These posterior model probabilities provide a useful estimate of the model type, consistent with but more easily understood than the other approaches for estimating model type, such as the Akaike information criterion (Akaike, 1974) and the Bayesian information criterion (Schwarz, 1978)....
[...]
...Introduced by Schwarz (1978), this provides a com- parison betweenmodels of different parameter sizes, based on themaximum likelihood and the number of observations....
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...Unlike the Akaike and Bayesian information criteria (Akaike, 1974; Schwarz, 1978), the resulting value corresponds directly to the posterior model probability, so can also be used as a test of the hypothesis that an event is non-doublecouple....
[...]
...This estimate is more intuitive than those provided by the Akaike and Bayesian information criteria (Akaike, 1974; Schwarz, 1978), since the resulting value corresponds directly to the posterior model probability, so can also be used as a test of the hypothesis that an event is non-double-couple....
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Journal Article•DOI•

Equation of state calculations by fast computing machines

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N. Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, Edward Teller - Show less +1 more

01 Jun 1953-Journal of Chemical Physics

TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.

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Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.

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35,161 citations

"Bayesian source inversion of micros..." refers background in this paper

...Monte Carlo random sampling (Metropolis et al., 1953; Hastings, 1970) is the most basic approach, but can easily be parallelised....
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Journal Article•DOI•

Monte Carlo Sampling Methods Using Markov Chains and Their Applications

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W. K. Hastings¹•Institutions (1)

University of Toronto¹

01 Apr 1970-Biometrika

TL;DR: A generalization of the sampling method introduced by Metropolis et al. as mentioned in this paper is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates.

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Abstract: SUMMARY A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed. For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. That is, in order to evaluate the integral J = X) p(x)dx = Ev(f), where p(x) is a probability density function, instead of obtaining independent samples XI, ..., Xv from p(x) and using the estimate J, = Zf(xi)/N, we instead obtain the sample from a distribution with density q(x) and use the estimate J2 = Y{f(xj)p(x1)}/{q(xj)N}. This may be advantageous if it is easier to sample from q(x) thanp(x), but it is a difficult method to use in a large number of dimensions, since the values of the weights w(xi) = p(x1)/q(xj) for reasonable values of N may all be extremely small, or a few may be extremely large. In estimating the probability of an event A, however, these difficulties may not be as serious since the only values of w(x) which are important are those for which x -A. Since the methods proposed by Trotter & Tukey (1956) for the estimation of conditional expectations require the use of importance sampling, the same difficulties may be encountered in their use. (iii) Use a simulation technique; that is, if it is difficult to sample directly from p(x) or if p(x) is unknown, sample from some distribution q(y) and obtain the sample x values as some function of the corresponding y values. If we want samples from the conditional dis

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14,965 citations

"Bayesian source inversion of micros..." refers background in this paper

...Monte Carlo random sampling (Metropolis et al., 1953; Hastings, 1970) is the most basic approach, but can easily be parallelised....
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Journal Article•DOI•

Preliminary reference earth model

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Adam M. Dziewonski¹, Don L. Anderson²•Institutions (2)

Harvard University¹, California Institute of Technology²

01 Jun 1981-Physics of the Earth and Planetary Interiors

TL;DR: In this paper, a large data set consisting of about 1000 normal mode periods, 500 summary travel time observations, 100 normal mode Q values, mass and moment of inertia have been inverted to obtain the radial distribution of elastic properties, Q values and density in the Earth's interior.

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9,266 citations

"Bayesian source inversion of micros..." refers background or methods in this paper

...On a global scale there are simple one-dimensional models, such as the preliminary Earth model (Dziewonski and Anderson, 1981), and more complex three dimensional models (e.g. Ritsema et al., 1999; Kustowski et al., 2008) and on smaller scales, there are many regional tomographic models (e.g.…...
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...On a global scale there are simple one-dimensional models, such as the preliminary Earth model (Dziewonski and Anderson, 1981), and more complex three dimensional models (e....
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...25, which is a Poisson’s ratio consistent with rock up to depths of the deepest subduction zone earthquakes (Christensen, 1996; Dziewonski and Anderson, 1981)....
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