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Electronic Resource

Correlations of earthquake focal mechanisms (1992)

Kagan, Y. Y.

Oxford, UK : Blackwell Publishing Ltd

Geophysical journal international 110 (1992), S. 0

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ISSN: 1365-246X

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences

Notes: We performed a statistical analysis of the Harvard catalogue of seismic moment tensor solutions. We investigated the distribution of hypocentres on focal spheres of earthquakes. The hypocentres are concentrated along fault planes; the hypocentre distribution does not significantly differ for earthquakes in different depth ranges. To study the rotation of focal mechanisms, we have solved an inverse problem of 3-D rotation of double-couple earthquake sources, i.e., for each pair of focal mechanisms we find all four 3-D rotations which rotate one mechanism into another. The stochastic disorientation of focal mechanisms is well approximated by the rotational Cauchy distribution which has previously been identified through theoretical arguments and simulations as the result of stress perturbations caused by random defects in the medium. The Cauchy distribution is characterized by one parameter, K; K= 0 means no rotations, and K 〉 0.5 corresponds to approximatel random rotation. For earthquake focal mechanisms the value of K is between 0.05 and 0.1 in a fault zone, and it increases with distance between pairs of events. In directions other than a fault plane, K reaches the value 0.5; the Cauchy distribution is then close to completely random rotations. Although K increases slowly with depth, in general, disorientations of focal mechanisms in various depth ranges display the same dependence. Therefore, we can conclude that deep earthquakes are controlled by the same stress interaction regime as shallow events. The results of these measurements made us question the suitability of some terms and models that are commonly used in the theory of an earthquake source. For example, we argued that tectonic earthquakes rupture rock material which has large-scale defects (or faults), comparable in size with tectonic blocks in which they originate. Properties of the rocks should be significantly different from those of regular materials where the size of defects is typically much smaller than the scale of interest. These properties should strongly depend on the geometry (location and orientation) of major defects.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-246X.1992.tb00876.x

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2

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Seismic moment distribution (1991)

Kagan, Y. Y.

Oxford, UK : Blackwell Publishing Ltd

Geophysical journal international 106 (1991), S. 0

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ISSN: 1365-246X

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences

Notes: We review possible errors in determining the size of earthquakes. We propose that the size distribution can be effectively defined only for earthquake sequences, not for ‘individual’ earthquakes. As a result of the error analysis, we question the validity of many reported correlations between the b-value and spatio-temporal characteristics of tectonics and seismicity. The study of the distribution of earthquake seismic moment largely avoids the influence of these errors and biases, and is therefore superior to the standard analysis of the magnitude-frequency law. The gamma distribution is applied to describe the distribution of seismic moments of earthquake sequences. This distribution which generalizes the well-known Gutenberg-Richter (G-R) relation, is characterized by two parameters. We use the maximum likelihood method to determine the parameters of the gamma distribution for worldwide earthquakes in different depth ranges. The empirical distribution is derived from the moment-tensor catalogue compiled by the Harvard group. The β-value for scalar seismic moment of earthquake sequences (an analogue of the b-value in the G-R magnitude-frequency law) is close to 1/2 for all earthquakes, the value predicted by a critical branching model of seismicity. This result which will be improved as more seismic moment data become available, provides input for modelling of seismicity based on percolation or on self-organized criticality models. If β equals 1/2, then using the critical branching model we find that most small earthquakes in available catalogues are dependent shocks, i.e., aftershocks. Even among earthquakes of intermediate magnitudes, the number of dependent events may exceed that of independent events.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-246X.1991.tb04606.x

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3

Electronic Resource

Likelihood analysis of earthquake catalogues (1991)

Kagan, Y. Y.

Oxford, UK : Blackwell Publishing Ltd

Geophysical journal international 106 (1991), S. 0

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ISSN: 1365-246X

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences

Notes: We apply several classes of stochastic multidimensional models to statistical analysis of earthquake catalogues using likelihood methods. We investigate the importance of including different earthquake parameters in the model: epicentral coordinates, hypocentral depth, time limits for interearthquake interaction, and especially spatial distribution of earthquakes as well as spatial aftershock patterns. Results of this study combined with other investigations, suggest that most distributions controlling earthquake interaction have a fractal or scale-invariant form. Developed models are used for statistical analysis of several earthquake catalogues to evaluate parameters of earthquake occurrence. These parameters are shown to be similar for shallow earthquakes of different magnitude ranges and seismogenic regions, confirming self-similarity of the earthquake process. Whereas intermediate earthquakes seem to emulate the pattern of shallow earthquake occurrence, albeit at a much smaller aftershock rate, deep earthquakes differ significantly in their properties. Predictability of standard shallow earthquake catalogues has been analysed; we present evidence that for the best available catalogues the predictability is close to 10 bits per earthquake. Several synthetic earthquake catalogues have been created and processed through the likelihood inversion scheme. The results from likelihood analysis of these catalogues confirm our approach.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-246X.1991.tb04607.x

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4

Electronic Resource

3-D rotation of double-couple earthquake sources (1991)

Kagan, Y. Y.

Oxford, UK : Blackwell Publishing Ltd

Geophysical journal international 106 (1991), S. 0

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ISSN: 1365-246X

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences

Notes: We discuss 3-D rotations by which one double-couple earthquake source can be rotated into another arbitrary double-couple. Due to the symmetry of double-couple sources, there are four such rotations. An algorithm is obtained in analytical form which is also available as a computer program solving the inverse problem of 3-D rotation of double-couple earthquake sources, i.e., for each pair of focal mechanisms or seismic moment tensor solutions the program finds all four rotations which rotate one mechanism into another. This algorithm may be used in a wide variety of studies of stress field causing earthquakes, investigations of the relationship between the focal mechanisms and the tectonic features of a seismogenic region, etc. The same inversion algorithm can be used to study the 3-D rotation of any symmetric second-rank tensor, such as the stress or strain tensor.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-246X.1991.tb06343.x

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5

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Random stress and earthquake statistics: spatial dependence (1990)

Kagan, Y. Y.

Oxford, UK : Blackwell Publishing Ltd

Geophysical journal international 102 (1990), S. 0

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ISSN: 1365-246X

Source: Blackwell Publishing Journal Backfiles 1879-2005

Topics: Geosciences

Notes: We calculate the 3-D stochastic rotations of focal mechanisms (disorientations) caused by stresses arising from the presence of many small, random, point defects that may surround the tip of an earthquake fault. These random stresses can be shown to be distributed according to a Cauchy distribution; as a consequence the next episode of fracture of a fault cannot be planar. The disorientation of focal mechanisms of these new rupture episodes is closely approximated by a rotational Cauchy distribution. As observed previously, the geometry of fault systems for natural earthquakes is consistent with these observations, since it too can be modelled by the Cauchy distribution. These observations indicate how the 3-D rupture process in rocks and other materials can be modelled. We also calculate distributions of disorientations caused by a uniformly random 3-D rotation of sources. These distributions are governed by symmetry properties of earthquake focal mechanisms. To take into account the source symmetry, we compare the Cauchy distribution which is due to influence of random stresses to the distributions caused by random rotations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1111/j.1365-246X.1990.tb04584.x

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6

Electronic Resource

Fractal dimension of brittle fracture (1991)

Kagan, Y. Y.

Springer

Journal of nonlinear science 1 (1991), S. 1-16

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ISSN: 1432-1467

Keywords: earthquake catalog statistics ; spatial distribution of hypocenters ; fractal dimension ; brittle fracture of rocks

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Summary Using a worldwide catalog of earthquakes we analyze the distribution of distances between pairs of earthquake hypocenters to determine the spatial fractal dimension δ of an earthquake fracture. As the time span of the catalog increases, δ asymptotically reaches the value 2.1–2.2 for shallow earthquakes. Approximately the same asymptotic value of dimension is obtained for a catalog of earthquakes with aftershocks removed. This value is compared with other known determinations of δ for brittle fractures. The fractal dimension declines to 1.8–1.9 for intermediate events (depth interval 71–280 km) and to about 1.5–1.6 for deeper events. Taking into account various possible errors and biases, we conclude that the fractal dimension of brittle shear fracture in rocks is 2.20 ± 0.05.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01209146

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