Rupture directivity from energy envelope deconvolution: theory and application to 69 Ridgecrest M 3.5–5.5 earthquakes

Earthquake rupture directivity impacts ground motions and provides important insights on fault zone properties and earthquake physics. However, measuring directivity of small earthquakes is challenging due to their compact rupture sizes and complex path and site effects at high frequencies. Here, we develop a new approach that deconvolves energy envelopes of the S-coda waves to remove path and site effects and robustly resolve azimuthal variations in apparent source-time functions. Our method benefits from the coherence of energy envelopes for high-frequency seismic data, which provides more stable directivity results than regular deconvolution methods. We validate our method using synthetic tests and a well-documented moderate-sized event. We apply the algorithm to determine rupture directivities of 69 magnitude 3.5--5.5 earthquakes during the 2019 Ridgecrest earthquake sequence. The rupture directivities suggest an orthogonal interlocking fault system consistent with aftershock locations. Additionally, the rupture directivity pattern appears to correlate with spatial heterogeneity in earthquake stress drops. Our energy envelope deconvolution method enables directivity measurements at lower magnitudes than traditional approaches and has potential for constraining small earthquake rupture dynamics.