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## Stress-glut representation by orthogonal moment-tensor fields

Thomas H. Jordan, & Alan Juarez

Published August 15, 2018, SCEC Contribution #8748, 2018 SCEC Annual Meeting Poster #281

Seismic radiation from indigenous sources of arbitrary complexity can be represented by 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 density into a set of orthogonal tensor fields of increasing degree, up to six in number, ordered by their first nonzero polynomial moments. The 0th-degree field is the projection of the stress-glut density onto its 0th polynomial moment, which defines the seismic moment tensor, Aki seismic moment M0, and centroid-moment tensor (CMT) point source. Our representation theorem generalizes the point-source approximation to a sum of multipoles that features the CMT monopole as its leading term. The 1st-degree field contributes a dipole, the 2nd-degree field contributes a quadrupole, and so on. We define the total scalar moment MT to be the integral of the scalar moment density, and we use the representation theorem to partition this total moment into a sum of moments for each degree. These moments are based on energy averaging, rather than the linear averaging that yields the Aki moment. If the faulting is simple enough, MT = M0 and the higher-degree terms will be small; however, when the faulting is more complex, MT > M0 and radiation from the higher-degree fields becomes sensible, especially at higher frequencies. We decompose various fault-rupture models to illustrate how the higher-degree terms characterize the source complexities, and we compute synthetic seismograms to characterize the radiation. Application to simple planar faulting shows that out-of-plane variations in slip-vector orientation reduce M0/MT more than in-plane variations of similar magnitude. We decompose stress-glut realizations from the Graves & Pitarka (2016) rupture simulator. Typical values of M0/MT are 0.8-0.9, consistent with analytical results. The higher-degree fields of the GP-16 sources typically produce substantial radiation up to degree 4; only the isotropic term is zero. We describe new inverse problems posed by the representation theorem, and we speculate on methods for their solution. Source models for the 2016 Kaikoura earthquake (Mw 7.8) indicate that the higher-degree radiation fields were large enough (M0/MT = 0.7) that it may possible to invert global datasets for at least some of the higher-degree multipoles.

Key Words
Source theory, earthquakes, seismic moment, stress glut, source mechanism

Citation
Jordan, T. H., & Juarez, A. (2018, 08). Stress-glut representation by orthogonal moment-tensor fields. Poster Presentation at 2018 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)