A global-optimization-based spectral decomposition method and its application to resolving source parameters of small earthquakes at Parkfield

Abstract:

The Spectral Decomposition (SD) and stacking method proposed by Shearer et al. (2006) has been widely used in different studies to simultaneously solve for stress drops under a series of assumptions. Shearer et al. (2006) (abbr. SH2006) assumed self-similarity, and required all magnitudes bins to have the same stress drop when solving for an empirical correction spectrum (ECS) to correct for individual event spectra; Chen and Abercrombie (2020) (abbr. CA2020) improved the method with no assumptions of stress drop scaling (different magnitude bins can have different stress drops), and perform grid search for a besting fitting stress drop for a reference magnitude bin to solve for the ECS. Synthetic tests in CA2020 show that the improved method recovers input stress drop with higher accuracy than SH2006. Application of the method from CA2020 to the Parkfield borehole network revealed systematic spatial and temporal variations in relationship with the 2004 M6 earthquake.

However, the grid search process in CA2020 is not computationally efficient, and if the corner frequency of the reference magnitude bin exceeds the resolution limit, systematic underestimation of stress drop can be observed. As an improvement, we introduce Differential Evolution method to solve for the stress drops in different magnitude bins together via Monte-Carlo method. Our tests show that the proposed method can reduce the total time by more than twice depending on cost function convergence speed. Further synthetic tests that consider realistic noise level and attenuation are needed to fully understand the performance of the new method.

After synthetic tests, we plan to apply the new methods to both the surface and borehole networks in the Parkfield segment to calculate stress drops for small earthquakes via spectral analysis. The new results will be used to investigate the resolution of small earthquake stress drop with different recording parameters, and the robustness of spatial and temporal variations of stress drops.