A geometric comparison of source-type plots for moment tensors

Abstract

We describe a general geometric framework for thinking about source-type plots for moment tensors. We consider two fundamental examples, one where the source-type plot is on the unit sphere, and one where it is on the unit cube. The plot on the sphere is preferable to the plot on the cube: it is simpler, it embodies a more natural assumption about eigenvalue probabilities and it is more consistent with the conventional Euclidian definition of scalar seismic moment. We describe the source-type plots of Hudson, Pearce and Rogers in our geometric context, and we find that they are equivalent to a plot on the cube. We therefore suggest the plot on the sphere as an alternative.