Rupture Heterogeneity and Directivity Effects in Back‐Projection Analysis

Abstract

The back projection method is a tremendously powerful technique for investigating the time dependent earthquake source, but its physical interpretation is elusive. We investigate how earthquake rupture heterogeneity and directivity can affect back‐projection results (imaged location and beam power) using synthetic earthquake models. Rather than attempting to model the dynamics of any specific real earthquake, we use idealized kinematic rupture models, with constant or varying rupture velocity, peak slip rate, and fault‐local strike orientation along unilateral or bilateral rupturing faults, and perform back‐projection with the resultant synthetic seismograms. Our experiments show back‐projection can track only heterogeneous rupture processes; homogeneous rupture is not resolved in our synthetic experiments. The amplitude of beam power does not necessarily correlate with the amplitude of any specific rupture parameter (e.g., slip rate or rupture velocity) at the back‐projected location. Rather, it depends on the spatial heterogeneity around the back‐projected rupture front, and is affected by the rupture directivity. A shorter characteristic wavelength of the source heterogeneity or rupture directivity toward the array results in strong beam power in higher frequency. We derive an equation based on Doppler theory to relate the wavelength of heterogeneity with synthetic seismogram frequency. This theoretical relation can explain the frequency‐ and array‐dependent back‐projection results not only in our synthetic experiments but also to analyze the 2019 M7.6 bilaterally rupturing New Ireland earthquake. Our study provides a novel perspective to physically interpret back‐projection results and to retrieve information about earthquake rupture characteristics.

Numerical simulations of seismo-acoustic nuisance patterns from an induced M1.8 earthquake in the Helsinki, southern Finland, metropolitan area

“…The near-perfect consistency of the polarities, and the good agreement of the P -to-S wave ratio between data and synthetics are governed by the source moment tensor properties that have been obtained from first motion polarity data (Hillers et al, 2020). The few visible inconsistencies between data and synthetics such as the S-wave properties at the N channel of the HEL1, PK01, KUN, and MKK stations suggest a small degree of structural heterogeneity, which is compatible with wave propagation phenomena inferred with array analysis techniques (Taylor et al, 2021;Li et al, 2022).…”

Back-projection results for the Mw7.5, 28 September 2018 Palu earthquake-tsunami

“…The basic principle of the back-projection method relies on the coherence of signals generated by the dense seismic arrays utilised to image the source characteristics [18,19,20]. A recent study working on the effects of rupture heterogeneity and directivity on back-projection imaging results has found that the image results are affected by the source frequency distribution and the array configuration [21]. This is complementary to previous studies (e.g.…”

The 2021 Mw 7.3 Madoi, China Earthquake: Transient Supershear Ruptures on a Presumed Immature Strike‐Slip Fault

“…It is not clear whether such rupture deceleration is controlled by a self‐evolving mechanism (featuring a dynamically self‐chosen rupture path) (Kame & Yamashita, 1999), or is caused by the encountering of a preexisting fault barrier (Xu & Ben‐Zion, 2013). In any case, the activated splay faults (Figure 12b), the pronounced aftershock activity (Figure 12a), and the complementary relation between local slip minimum and local off‐fault deformation maximum at ∼50 km (at W3 and E2 in Figure 12b) from the mainshock epicenter (He et al., 2022; Jin & Fialko, 2021; C. Li et al., 2023; Yuan et al., 2022) imply the involvement of some strengthening mechanism near the ends of the main fault, which can support the prediction of Xu and Ben‐Zion (2013) for sudden rupture deceleration.…”

“…The red stars, green squares, and cyan diamonds show the rupture speeds of the eastern fault and the western fault from the backprojection studies in this study, Q. Li et al (2022), and X. .…”