Keynote Presentation: Moment Tensor Decomposition and Interpretation

2014 ◽  
Author(s):  
C. Chapman
Keyword(s):  
Moment Tensor ◽  
Tensor Decomposition ◽  
Keynote Presentation

Visualizing effects of anisotropy on seismic moments and their potency-tensor isotropic equivalent

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. C85-C97 ◽  
Author(s):  
Nepomuk Boitz ◽  
Anton Reshetnikov ◽  
Serge A. Shapiro
Keyword(s):  
Radiation Pattern ◽  
Elastic Anisotropy ◽  
Moment Tensor ◽  
Matrix Multiplication ◽  
Tensor Decomposition ◽  
P Wave ◽  
Propagation Path ◽  
Tectonic Deformation ◽  
Radiation Patterns ◽  
Rock Anisotropy

Radiation patterns of earthquakes contain important information on tectonic strain responsible for seismic events. However, elastic anisotropy may significantly impact these patterns. We systematically investigate and visualize the effect of anisotropy on the radiation patterns of microseismic events. For visualization, we use a vertical-transverse-isotropic (VTI) medium. We distinguish between two different effects: the anisotropy in the source and the anisotropy on the propagation path. Source anisotropy mathematically comes from the matrix multiplication of the anisotropic stiffness tensor with the source strain expressed by the potency tensor. We analyze this effect using the corresponding radiation pattern and the moment tensor decomposition. Propagation anisotropy mathematically comes from the deviation between the polarization and the propagation direction of a quasi P-wave in an anisotropic medium. We investigate both effects separately by either assuming the source to be anisotropic and the propagation to be isotropic or vice versa. We find that both effects have a significant impact on the radiation pattern of a pure-slip source. Finally, we develop an alternative visualization of source mechanisms by plotting beach balls proportional to their potency tensors. For this, we multiply the potency tensor with an isotropic elasticity tensor having the equivalent shear modulus [Formula: see text] and [Formula: see text]. In this way, we visualize the tectonic deformation in the source, independently of the rock anisotropy.

A Student’s Guide to and Review of Moment Tensors

1989 ◽  
Vol 60 (2) ◽  
pp. 37-57 ◽  
Author(s):  
M. L. Jost ◽  
R. B. Herrmann
Keyword(s):  
Point Source ◽  
Moment Tensor ◽  
Tensor Decomposition ◽  
Seismic Source ◽  
Order Moment ◽  
Review Of Literature ◽  
Moment Tensors ◽  
Numerical Examples ◽  
Testing Algorithms ◽  
The Moment

Abstract A review of a moment tensor for describing a general seismic point source is presented to show a second order moment tensor can be related to simpler seismic source descriptions such as centers of expansion and double couples. A review of literature is followed by detailed algebraic expansions of the moment tensor into isotropic and deviatoric components. Specific numerical examples are provided in the appendices for use in testing algorithms for moment tensor decomposition.

scholarly journals Generalized orthonormal moment tensor decomposition and its source-type diagram

2020 ◽  
Author(s):  
Ting-Chung Huang ◽  
Yih-Min Wu
Keyword(s):  
Seismic Moment ◽  
Decomposition Method ◽  
Moment Tensor ◽  
Tensor Decomposition ◽  
New Method ◽  
Seismic Moment Tensor ◽  
Linear Vector ◽  
Source Type ◽  
Sign Problem ◽  
Double Couple

Abstract Moment tensor decomposition is a method for deriving the isotropic (ISO), double-couple (DC), and compensated linear vector dipole (CLVD) components from a seismic moment tensor. Currently, there are two families of methods, namely, standard moment tensor decomposition and Euclidean moment tensor decomposition. Although both methods can usually provide workable solutions, there are some minor inconsistencies between the two methods: an equality inconsistency that occurs in standard moment tensor decomposition and the pure CLVD unity and flip basis inconsistency encountered in Euclidean moment tensor decomposition. Moreover, there is a sign problem when disentangling the CLVD component from a DC-dominated case. To address these minor inconsistencies, we propose a new moment tensor decomposition method inspired by both previous methods. The new method can not only avoid all these minor inconsistencies but also withstand deviations in ISO- or CLVD-dominated cases when using source-type diagrams.

scholarly journals Seismic radiation analyses in anisotropic media based on general dislocation source model

2021 ◽  
Vol 18 (2) ◽  
pp. 231-240
Author(s):  
Yi Yao ◽  
Yibo Wang
Keyword(s):  
Focal Mechanism ◽  
Moment Tensor ◽  
Source Region ◽  
Slope Angle ◽  
Tensor Decomposition ◽  
Anisotropic Media ◽  
Dislocation Model ◽  
Seismic Moment Tensor ◽  
Dislocation Source ◽  
The Moment

Abstract Anisotropy affects the focal mechanism and makes it complicated. A shear motion generates a pure double-couple (DC) source in isotropic media. While in anisotropic media, it will produce non-DC components, which contain isotropic (ISO) and compensated linear vector dipole (CLVD) components. Besides, coupled with the diversity of fault motion, the source may become extremely complicated. In this paper, the seismic moment tensor is obtained based on the dislocation model, and then a variety of analyses are performed with the moment tensor, including moment tensor decomposition, radiation pattern, radiated energy ratio and seismic propagation characteristics. Since the anisotropy of the medium also influences seismic wave propagation, a hypothesis is made that the source region is minimal and anisotropic, but the propagation path is isotropic. The research gives some interesting conclusions. It is found that the anisotropy mainly affects the focal mechanism under low slope angle while high slope angle has little effect on the polarity. In terms of the moment tensor decomposition, if only one of ISO or CLVD exists, it can be asserted that the source region is anisotropic because ISO components are accompanied by CLVD components in isotropy media. As for the DC component, the results indicate it is one of the most important factors for determining the ratio of radiant energy. This paper presents some valuable findings of the focal mechanism of the general dislocation source under anisotropy, which helps to recognise the source characteristics of the earthquake and build solid foundations for the subsequent inversion of the focal mechanism.

Language in mental retardation: Individual and syndromic differences, and neurogenetic variation 1Based on a keynote presentation at the Third European Conference on Psychological Theory and Research in Mental Retardation, Geneva, September 1st, 2000.

2001 ◽  
Vol 60 (3) ◽  
pp. 161-178 ◽  
Author(s):  
Jean A. Rondal
Keyword(s):  
Mental Retardation ◽  
Language Development ◽  
Oral Language ◽  
Psychological Theory ◽  
Genetic Syndromes ◽  
Explanatory Variables ◽  
Keynote Presentation ◽  
Genetic Origins ◽  
The Sixties ◽  
The Individual

Predominantly non-etiological conceptions have dominated the field of mental retardation (MR) since the discovery of the genetic etiology of Down syndrome (DS) in the sixties. However, contemporary approaches are becoming more etiologically oriented. Important differences across MR syndromes of genetic origin are being documented, particularly in the cognition and language domains, differences not explicable in terms of psychometric level, motivation, or other dimensions. This paper highlights the major difficulties observed in the oral language development of individuals with genetic syndromes of mental retardation. The extent of inter- and within-syndrome variability are evaluated. Possible brain underpinnings of the behavioural differences are envisaged. Cases of atypically favourable language development in MR individuals are also summarized and explanatory variables discussed. It is suggested that differences in brain architectures, originating in neurological development and having genetic origins, may largely explain the syndromic as well as the individual within-syndrome variability documented. Lastly, the major implications of the above points for current debates about modularity and developmental connectionism are spelt out.

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