The decomposition of moment tensors into isotropic (ISO), double-couple (DC) and compensated linear vector dipole (CLVD) components is a tool for classifying and physically interpreting seismic sources. Since an increasing quantity and quality of seismic data allow inverting for accurate moment tensors and interpreting details of the source process, an efficient and physically reasonable decomposition of moment and source tensors is necessary. In this paper, the most common moment tensor decompositions are revisited, new equivalent formulas of the decompositions are derived, suitable norms of the moment tensors are discussed and the properties of commonly used source-type plots are analysed. The Hudson skewed diamond plot is introduced in a much simpler way than originally proposed. It is shown that not only the Hudson plot but also the diamond CLVD-ISO plot and the Riedesel-Jordan plot conserve the uniform distribution probability of moment eigenvalues if the appropriate norm of moment tensors is applied. When analysing moment tensor uncertainties, no source-type plot is clearly preferable. Since the errors in the eigenvectors and eigenvalues of the moment tensors cannot be easily separated, the moment tensor uncertainties project into the source-type plots in a complicated way. As a consequence, the moment tensors with the same uncertainties project into clusters of a different size. In case of an anisotropic focal area, the complexity of moment tensors of earthquakes prevents their direct interpretation, and the decomposition of moment tensors must be substituted by that of the source tensors.Keywords Dynamics and mechanics of faulting . Earthquake source observations . Seismic anisotropy . Theoretical seismology
IntroductionThe moment tensor describes equivalent body forces acting at a seismic point source (Burridge and Knopoff 1964) and is a basic quantity evaluated for earthquakes on all scales from acoustic emissions to large devastating earthquakes. The most common type of the moment tensor is the double-couple (DC) source which represents the force equivalent of shear faulting on a planar fault in isotropic media. However, many studies reveal that seismic sources often display more general moment tensors with significant non-double-couple (non-DC) components ). An explosion is an obvious example of a non-DC source, but non-DC components can also be produced by the collapse of a cavity in mines (Rudajev and Šílený 1985;Šílený and Milev 2008), by shear faulting on a nonplanar (curved or irregular) fault (Sipkin 1986), by tensile faulting induced by fluid injection in geothermal or volcanic areas (Ross et al. 1996;Julian et al. 1997) when the slip vector is inclined from the fault and causes its opening (Vavryčuk 2001(Vavryčuk , 2011 Roessler et al. 2004Roessler et al. , 2007. Complications also arise if the source is situated at a material interface (Vavryčuk 2013).In order to identify which type of seismic source is physically represented by the retrieved moment tensor, Knopoff and Randall (1970...