Rupture Heterogeneity and Directivity Effects in Back‐Projection Analysis

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. Plain Language Summary With the deployment of continental scale seismic arrays, seismologists can quickly locate the high‐frequency seismic radiation sources and track the earthquake rupture propagation using a technique called back‐projection. It is a signal beamforming technique application in seismology, and similar applications can be found in fields such as radar, wireless communication, and radio astronomy. Recent studies have proposed multiple advancements in improving the back‐projection location. However, the physical interpretation of the amplitude of stacked high‐frequency source radiations, which is commonly referred to as beam power, is still challenging since the analysis is not based on a fo