A new moment-tensor decomposition for seismic events in anisotropic media

Abstract

S U M M A R YInvestigating the mechanisms of small seismic sources usually consists of three steps: determining the moment tensor of the source; decomposing the moment tensor into parameters that can be interpreted in terms of physical mechanisms and displaying those parameters. This paper concerns the second and third steps. Two existing methods-the Riedesel-Jordan and Hudson-Pearce-Rogers parameters and displays-are reviewed, compared and contrasted, and advantages and disadvantages of the two methods are discussed. One disadvantage is that neither method takes into consideration the effect of anisotropy on the interpretation. In microseisms, anisotropy can be important. A new procedure based on the biaxial decomposition of the potency tensor is introduced which explicitly allows for anisotropy and interprets the moment tensor in terms of an isotropic pressure change and a displacement discontinuity on a fault. It is shown that this interpretation is always possible for any moment tensor whatever the anisotropy. To compare the pressure change with the displacement discontinuity, it is useful to be able to determine the volume change from the pressure source in any medium. This depends on the embedded bulk modulus, which differs from the normal bulk modulus. The embedded modulus in isotropic media is well known and the equivalent anisotropic result is derived in this paper. Interpreting a seismic source in terms of the volume change due to a pressure change and a displacement discontinuity on a fault allows a simple 3-D graphical glyph to be used to display the interpretation.

Moment tensor decompositions revisited

“…8b) suggested by Chapman and Leaney (2012) which resembles the CLVD-ISO diamond source-type plot ( Fig. 1) but adapted to a spherical metric.…”

“…This is somewhat inconvenient because some of the decomposed parts of the moment tensors are not defined in the source-type space and thus cannot exist independently as individual types of source. This also applies to the approach of Chapman and Leaney (2012), who proposed the ISO, DC and CLVD decomposition using the Euclidean norm and the CLVD with the major dipole oriented along the N axis. As a consequence, relative scale factor C CLVD * can never attain the value of ±1 for any moment tensor but only ±1/4.…”

“…(27) to produce the scalar seismic moment consistent with the standard definition for the pure DC source. According to Chapman and Leaney (2012), the base tensors are defined as: …”

“…This has recently motivated several authors to revisit the existing decompositions (Chapman and Leaney 2012;Zhu and Ben-Zion 2013) and sourcetype plots (Chapman and Leaney 2012;Tape and Tape 2012a, b) and to develop their modifications. In this paper, I summarize the physical conditions imposed on the moment tensor decompositions and present new equivalent formulas for the most common moment tensor decompositions.…”

Robust and Fast Probabilistic Source Parameter Estimation from Near‐Field Displacement Waveforms Using Pattern Recognition

“…As in Käufl et al (2014), we parametrize the space of moment tensors using a geometric parametrization suggested by Chapman and Leaney (2012) and Tape and Tape (2012) and additionally restrict ourselves to double-couple sources. The latter choice is mainly motivated by the consideration that a double couple is potentially easier to interpret than a full moment tensor source in the context of an early warning application.…”