The classical model for moment tensors

A seismic moment tensor is a description of an earthquake source, but the description is indirect. The moment tensor describes seismic radiation rather than the actual physical process that initiates the radiation. A moment tensor 'model' then ties the physical process to the moment tensor. The model is not unique, and the physical process is therefore not unique. In the classical moment tensor model, an earthquake arises from slip along a planar fault, but with the slip not necessarily in the plane of the fault. The model specifies the resulting moment tensor in terms of the slip vector, the fault normal vector and the Lame elastic parameters, assuming isotropy. We review the classical model in the context of the fundamental lune. The lune is closely related to the space of moment tensors, and it provides a setting that is conceptually natural as well as pictorial. In addition to the classical model, we consider a crack plus double-couple model (CDC model) in which a moment tensor is regarded as the sum of a crack tensor and a double couple.