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An Empirical Green’s Function Type Approach for Isolating Directivity Effects in Ground Motion Residuals: Examples from the 2022 Alum Rock and 2004 Parkfield Earthquakes

Grace A. Parker, Annemarie S. Baltay, & Evan T. Hirakawa

Submitted September 10, 2023, SCEC Contribution #13055, 2023 SCEC Annual Meeting Poster #186

We present a novel technique for partitioning ground motion model (GMM) residuals that mitigates tradeoffs between spatially varying source, path, and site effects, using the 2004 M6.0 Parkfield and 2022 M5.1 Alum Rock earthquakes as examples. These earthquakes both exhibited significant rupture directivity, which strongly influenced the spatial distribution of ground motion amplitude and frequency content. Typical ground motion modeling techniques treat earthquake-specific effects as single, frequency-dependent constants (i.e., event terms) meant to capture event-to-event variations in stress drop or moment release. This means that spatially varying source effects such as directivity or radiation patterns that are not well represented by a single constant are often mapped into the within-event residuals and attributed to path and site effects. Here we develop an empirical Green’s function (eGf)-type approach where we use ground motion residuals relative to an established GMM from smaller earthquakes co-located with the Parkfield and Alum Rock mainshocks. We estimate site terms from the eGf events, assuming because the earthquakes are co-located that they represent both repeatable path and site effects. We then subtract the eGf terms from the mainshock within-event residuals to isolate mainshock directivity effects. In this manner, we observe stronger and more consistent directivity effects than in simply modeling the observed mainshock ground motions alone. We find that directivity accounts for an order of magnitude variation in peak ground motions for the 2022 Alum Rock earthquake in both the forward and backwards directivity directions, and on average can explain 75% of the within-event variability. Fitting a directivity function to the adjusted residuals yields a best-fitting rupture velocity of about 2.4 km/s, consistent with conclusions based on kinematic rupture simulations. For the 2004 Parkfield earthquake, the adjusted residuals span about a factor of 3.5 in the forward and backward directivity directions. Directivity contributes 60% of the within-event variability for 2.0 s response spectra, the dominant directivity pulse period estimated by Spudich and Chiou (2013) for this earthquake. Our proposed method to quantify spatially varying source effects could allow for developing GMM-centered directivity models, and improves estimates of path and site effects by reducing the contribution of source effects to the within-event residuals.

Parker, G. A., Baltay, A. S., & Hirakawa, E. T. (2023, 09). An Empirical Green’s Function Type Approach for Isolating Directivity Effects in Ground Motion Residuals: Examples from the 2022 Alum Rock and 2004 Parkfield Earthquakes. Poster Presentation at 2023 SCEC Annual Meeting.

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