Assessing the scalar moment of moderate earthquake and the effect of lateral heterogeneity on normal modes—An example from the 2013/04/20 Lushan earthquake, Sichuan, China

•Significant difference exists for predicted M0 of a complex moderate earthquake.•The validity of predicted M0 can be effectively assessed by observed normal modes.•Normal modes of moderate earthquakes can assess upper mantle lateral heterogeneity.

Medium-frequency normal modes in the frequency range of 2.0–6.0 mHz excited by moderate earthquakes (6.0 < Mw < 7.0) are weak seismic signals and seldom concerned in academic study. We show that the validity of predicted M0 (scalar seismic moment) for a complex moderate earthquake can be effectively assessed by a systematic comparison of observed and synthetic medium-frequency spheroidal modes, and the effect of lateral heterogeneity on normal-mode amplitudes can also be well assessed in the comparison. For a complex moderate earthquake, the differences between predicted M0 derived from different inversion methods are significant, in some cases as large as factors of 1.56–3.18. In this study we focus on the Lushan earthquake, a moderate thrust event on 20 April 2013 in the Western Sichuan, China. Five reported M0 for the earthquake differ significantly from 0.4 × 1019 to 1.06 × 1019 N m, up to about 2.5 times difference. To assess the validity of reported M0, we compare observed with synthetic modes corresponding to five centroid moment tensor solutions at 17 stations, which located within epicental distances of 5–30° and distributed in a wide range of source-receiver azimuths. Synthetic modes corresponding to moment tensor solutions derived from long-period waveforms show good agreement to observations. However, synthetics corresponding to moment tensor solutions derived from body waves display significant deviations of amplitudes from observations. We show underestimate of M0 is the main cause for such a large deviation. Another important result obtained from the comparison is that lateral heterogeneity has very little effects on the amplitudes of spherical modes at frequencies below 6.0 mHz. This observational result is inconsistent with previous theoretical result of lateral structure perturbations to normal modes.