Representation of seismic sources sustaining changes of elastic moduli

We discuss analytical results on seismic radiation during rapid episodes of inelastic brittle deformation that include changes of elastic moduli in the source volumes. The full source tensor rate is shown to be the sum of (i) a moment rate term associated with the product of the rate of transformational strain and current local tensor of elastic moduli and (ii) the rate of damage-related term given by the product of the time derivative of the elastic moduli and current local elastic strain. Order of magnitude estimates indicate that the damage source term can be larger than the moment term for small events and the region around rupture front. However, the moment term integrated over the entire rupture zone is likely to be considerably larger than the damage term for large crack-like ruptures. The formulation provides rigorous definitions that can be used to estimate different source terms and associated radiated seismic fields in numerical simulations, experiments and field studies that have information on changes of elastic moduli in brittle source regions. Using elastic moduli taken from reference earth models in the analysis of seismic moment can lead to overestimation of the moment and artificial spatial variations.