Representation of Complex Seismic Sources by Orthogonal Moment Tensor Fields

Date: 4/25/2019

Time: 10:45 AM

Room: Cascade I

Seismic radiation from indigenous sources can be represented by the excess of model stress over actual stress, a second-order tensor field that Backus named the stress glut. We prove a new representation theorem that exactly and uniquely decomposes any stress-glut (or strain-glut) density into a set of orthogonal tensor fields of increasing degree, up to six in number, ordered by their first nonzero polynomial moments. The zeroth-degree field is the projection of the stress-glut density onto its zeroth polynomial moment, which defines the seismic moment tensor, Aki seismic moment M₀, and centroid-moment tensor (CMT) point source. The higher-degree fields describe mechanism complexity—source variability that arises from the spacetime variations in the orientation of the stress glut. The representation theorem generalizes the point-source approximation to a sum of multipoles that features the CMT monopole as its leading term. The first-degree field contributes a dipole tensor with a mechanism orthogonal to the CMT, the second-degree field contributes a quadrupole tensor, and so on, up to six orthogonal fields in all. We define the total scalar moment M_T to be the integral of the scalar moment density, and we use the representation theorem to partition this total moment into a sum of fractional moments for each degree. If the faulting is simple enough, M₀ approximates M_T. When the faulting is more complex, however, M₀ < M_T; the higher-degree fields will contribute more to the radiation, and this contribution will increase with frequency. We decompose stress-glut realizations from the Graves & Pitarka (2016) rupture simulator; typical values of M₀/M_T are 0.82-0.92. We compute synthetic seismograms to illustrate the radiation patterns of the higher-degree fields and their frequency dependence. Decomposition of source models for the 2016 Kaikoura earthquake indicates that the radiation from the higher-degree fields was large enough (M₀/M_T = 0.67-0.82) that it should be possible to invert global datasets for the low-degree multipoles.

Presenting Author: Thomas H. Jordan

Authors