Generalized orthonormal moment tensor decomposition and its source-type diagram
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ORIGINAL ARTICLE
Generalized orthonormal moment tensor decomposition and its source-type diagram Ting-Chung Huang
· Yih-Min Wu
Received: 10 December 2019 / Accepted: 10 August 2020 © The Author(s) 2020
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
T.-C. Huang () · Y.-M. Wu Department of Geosciences, National Taiwan University, 1, Sec. 4, Roosevelt Road, 106, Taipei, Taiwan e-mail: [email protected] Y.-M. Wu e-mail: [email protected] Y.-M. Wu NTU Research Center for Future Earth, National Taiwan University, Taipei, 10617, Taiwan Y.-M. Wu Institute of Earth Sciences, Academia Sinica 128, Sec. 2, Academia Road, Nangang, Taipei, 11529, Taiwan Y.-M. Wu National Center for Research on Earthquake Engineering, National Applied Research Laboratories, No. 200, Section 3, Xinhai Rd, Taipei, 106, Taiwan
when disentangling the CLVD component from a DCdominated 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. Keywords Focal mechanism · Compensated linear vector dipole · Theoretical seismology Article highlights • We examine the inconsistencies among current moment tensor decomposition methods. • Based on insights from observations of these inconsistencies, we propose an overall consistent moment tensor decomposition method. • We discuss some interesting features of the proposed method and how to extend it to additional applications.
1 Introduction The seismic moment tensor, which describes the basic characteristics of an earthquake, constitutes one of the most crucial quantities derived from point-source approximations. The spectral decomposition theorem guarantees that the moment tensor must contain real eigenvalues. To associate a physical process with an earthquake, the three-eigenvalue tuple
J Seismol
is decomposed into three elementary components: the isotropic (ISO) component, the double-couple (DC) component, and the compensated linear vector dipole (CLVD) (Knopoff and Randall 1970) component. However, there is no universal method for decomposition. In recent years, some interest in revisiting the decomposition methods has arisen due to progress in observing non-DC microseismic events (Miller et al. 1998; Eaton and Forouhideh 2010; Chapman 2019). Moment ten
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