Stress inversions from focal mechanisms require knowledge of which nodal plane is the fault. If such information is missing, and faults and auxiliary nodal planes are interchanged, the stress inversions can produce inaccurate results. It is shown that the linear inversion method developed by Michael is reasonably accurate when retrieving the principal stress directions even when the selection of fault planes in focal mechanisms is incorrect. However, the shape ratio is more sensitive to the proper choice of the fault and substituting the faults by auxiliary nodal planes introduces significant errors. This difficulty is removed by modifying Michael's method and inverting jointly for stress and for fault orientations. The fault orientations are determined by applying the fault instability constraint and the stress is calculated in iterations. As a by-product, overall friction on faults is determined. Numerical tests show that the new iterative stress inversion is fast and accurate and performs much better than the standard linear inversion. The method is exemplified on real data from central Crete and from the West-Bohemia swarm area of the Czech Republic. The joint iterative inversion identified correctly 36 of 38 faults in the central Crete data. In the West Bohemia data, the faults identified by the inversion were close to the principal fault planes delineated by foci clustering. The overall friction on faults was estimated to be 0.75 and 0.85 for the central Crete and West Bohemia data, respectively.

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.

Summary. Focal mechanisms of seismic sources in anisotropic media are more complicated than in isotropic media. Planar shear faulting produces pure double-coup