Inversion of Teleseismic Waveforms for Higher-Degree Moment Tensors of Complex Ruptures

Abstract:

A seismic source of arbitrary complexity can be represented as the sum of up to six orthogonal moment-tensor fields. In the point-source limit, the zeroth-degree (monopole) term is the centroid moment tensor (CMT), and each higher-degree term can be expressed as the product of a source-mechanism tensor orthogonal to the CMT, and to each other, and a multipole tensor (Jordan & Juarez, GJI, 2019; 2020). The higher-degree terms quantify the mechanism complexity of the source and the seismic radiation not represented by the CMT. If the source is complex, the total moment defined as the integral of the scalar moment density is larger than the Aki moment, and the higher-degree terms contribute more to the radiation. The estimation of higher-degree moment tensors does not require any knowledge of the geometrical support of the source (e.g., fault surfaces), and they provide integral constraints on space-time parametrizations of complex sources, such as finite fault inversions. We develop a sequential Bayesian method for estimating the higher-degree mechanisms and multipole tensors. The first step inverts for the CMT; the second for the dipole vector term plus a CMT correction; the third for the characteristic source dimensions and the quadrupole term plus lower-degree corrections. The data are phase-delay and amplitude-reduction times measured on multiple seismic phases of teleseismic waveforms with frequencies up to 10 mHz. We apply the methodology to the Mw 7.8 Kaikoura, New Zealand, earthquake of 2016, which is one of the most complex earthquakes ever recorded. It ruptured more than twenty crustal faults with different strikes, dips, and rakes, as well as the subduction megathrust beneath New Zealand. For the Kaikoura earthquake, we obtain dipole and quadrupole terms that are consistent with published finite-fault models. The results show that the 1^st-degree term is ~10% of the Aki moment, and the 2^nd-degree term is ~5%. Data residuals suggest that estimations of 3-rd and higher degree terms might be possible for the Kaikoura earthquake using higher-frequency observations and appropriate prior information of the parameter scaling relations.