SUMMARY We describe a parametrization of moment tensors that is suitable for use in algorithms for moment tensor inversion. The parameters are conceptually natural and can be easily visualized. The ingredients of the parametrization are present in the literature; we have consolidated them into a concise statement in a geometric setting. We treat several familiar moment tensor topics in the same geometric setting as well. These topics include moment tensor decompositions, crack‐plus‐double‐couple moment tensors, and the parameter ε that measures the difference between a deviatoric moment tensor and a double couple. The geometric approach clarifies concepts that are sometimes obscured by calculations.

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