Mathematical review on source-type diagrams

Aso, Naofumi; Ohta, Kazuaki; Ide, Satoshi

doi:10.1186/s40623-016-0421-5

Cited by 15 publications

(16 citation statements)

References 49 publications

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“…Because none are perfect, we have only introduced one new parameterization, although many are possible, for example Aso et al . (). The new parameterization is based on the solid angles formed by the source‐type vector and the basic sources at the apexes of the permitted lune.…”

Section: Discussionmentioning

confidence: 97%

“…For brevity below, we refer to these as properties 1, 2 and 3. As in cartography, many projections are possible, and many different ISO, CLVD and DC source parameters have been suggested to interpret the eigen decomposition of the moment tensor (for instance, Aso et al 2016, have suggested 13 different parameterizations). A few are summarized here.…”

Section: O M E N T -T E N S O R D E C O M P O S I T I O N a N D P Amentioning

confidence: 99%

“…As with any projection or cartography problem, there are many different mappings or parameterizations possible, and all have advantages and disadvantages. Because none are perfect, we have only introduced one new parameterization, although many are possible, for example Aso et al (2016). The new parameterization is based on the solid angles formed by the source-type vector and the basic sources at the apexes of the permitted lune.…”

Section: O N C L U S I O N Smentioning

confidence: 99%

“…All the parameterizations suggested in the literature can be regarded as mappings of the source‐type vector, as has been emphasized by Tape and Tape () and Vavryc̆uk (). Many parameters have been suggested (Aso, Ohta and Ide have listed 13 different parameterizations). For visualization purposes, displaying the source types on the lune in a 3D plot is very satisfactory and straightforward.…”

Section: Introductionmentioning

confidence: 99%

“…They differ mainly in their normalizations or the scalar-moment factor. In the interests of brevity, we do not include the many others possible, for example Aso et al (2016). While the relative values of the parameters are useful for comparing different sources, the interpretation of their absolute values depends on the basic source types, their normalization and the definition of the moment magnitude.…”

Section: Introductionmentioning

confidence: 99%

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Yet another moment‐tensor parameterization

Chapman

2019

Geophysical Prospecting

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The source mechanism of a microseismic event, or any small earthquake, can be described by its moment tensor. The source type is described by a 3‐vector formed from the ordered, principal (eigen) values of the moment tensor and the source orientation from the normalized eigenvectors. The direction and magnitude of the principal‐value vector describe the source type and scalar moment, respectively. The source type can be described by the position of the principal‐value vector on the permitted lune of a unit sphere. As with any projection or cartography mapping, many parameterizations have been suggested to describe this position. Two dominate in the literature – the Riedesel–Jordan and Hudson–Pearce–Rogers parameters. All have advantages and disadvantages. In this paper, we review the most popular parameterizations, illustrating their similarities and the distortion they cause in the mapping between a uniform distribution of source types in the permitted lune and the parameter space. A new parameterization is suggested based on the solid angles formed by the principal‐value vector. This has the advantage of being simple to define geometrically in the principal‐value space (although the formulae are complicated), being naturally normalized and having a more uniform mapping than other parameterizations. However, we do not claim that this is the best or ideal parameterization, just a reasonable choice.

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Section: Discussionmentioning

confidence: 97%

Section: O M E N T -T E N S O R D E C O M P O S I T I O N a N D P Amentioning

confidence: 99%

Section: O N C L U S I O N Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Yet another moment‐tensor parameterization

Chapman

2019

Geophysical Prospecting

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Berkeley Seismic Moment Tensor Method, Uncertainty Analysis, and Study of Non-double-couple Seismic Events

Dreger

2018

Moment Tensor Solutions

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Exploratory Data Analysis of Earthquake Moment Tensor Catalog in Japan Using Non-linear Graph-Based Dimensionality Reduction

Kubo

Kimura

Shiomi

2023

Pure Appl. Geophys.

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The catalog of moment tensor solutions, which contains the information on spatial location, origin time and fault mechanism type of earthquakes, has been interpreted by researchers based on a wealth of past knowledge. However, the long-term routine analyses have led to the accumulation of a huge amount of data in the moment tensor catalog, and it is worth considering moving away from the artisanal approach. In this study, using dimensionality reduction of unsupervised machine learning, we performed exploratory data analysis of the moment tensor catalog in Japan to objectively obtain comprehensive images of seismic activity and to acquire knowledge on the spatial and temporal characteristics of the earthquake mechanism. Source parameters of the moment tensor catalog in Japan, spatial location (latitude, longitude, and focal depth) and source-mechanism diagram information were embedded in two-dimensional space via a non-linear graph-based dimensionality-reduction method, Uniform Manifold Approximation and Projection. On the embedding map, earthquakes in eastern and western Japan are distributed separately and are further embedded to reflect their characteristic fault mechanism and focal depth in each region. The similarity degree of the earthquakes can be obtained as the distance on the embedding map. This study demonstrates that the data visualization using dimensionality reduction is useful for intuitively and objectively understanding the regional characteristics of earthquake mechanisms. The embedding map can also be employed to visualize temporal changes in regional seismic activity and to perform a similarity search with a past event.

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Mathematical review on source-type diagrams

Cited by 15 publications

References 49 publications

Yet another moment‐tensor parameterization

Yet another moment‐tensor parameterization

Berkeley Seismic Moment Tensor Method, Uncertainty Analysis, and Study of Non-double-couple Seismic Events

Exploratory Data Analysis of Earthquake Moment Tensor Catalog in Japan Using Non-linear Graph-Based Dimensionality Reduction

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