On Seismological Stress-Drop Estimates for Earthquake Sources Simulated on Rate-and-State Faults

Seismologists estimate stress drops of small earthquakes based on specific theoretical source models. We explore the accuracy of the stress-drop estimates for several earthquake source models obtained in dynamic simulations on rate-and-state faults. We consider Madariaga-like symmetric circular sources as well as sources with directivity, elongated shapes, partial ruptures, and complex changes in the slip direction. The energy-based average stress drops computed directly on the fault for all simulated source models range from 1.5 to 5 MPa. We consider a range of focal depths and fault dips that results in 980 scenarios overall with respect to a surface network of 16 stations, where we produce synthetic waveforms assuming a known homogeneous velocity structure, and use them to obtain seismologically inferred stress drops. For the second-moment approach and spectral-fitting approach based on S waves and n = 2, the stress drops for most sources are reproduced well on average but with a significant scatter from nearly 0.01 to 100 MPa, representative of scatter for natural earthquakes, despite the actual stress-drop variation of 1.5–5 MPa. The scatter is smaller by a factor of 2 for the second-moment approach. The spectral-fitting approach based on P waves consistently underestimates the stress drops for noncircular sources. All approaches underestimate stress drops for ring-like sources, which leave part of the seismogenic patch unruptured. The spectral estimates are significantly affected by different averages of corner frequencies over the focal sphere for our sources versus typically assumed simple theoretical sources, as was already pointed out for some of the sources by Kaneko and Shearer (2015) and Lin and Lapusta (2018). For both second-moment and spectral methods, the scatter is amplified by partial coverage of the focal sphere by the assumed station geometry, which can also cause systematic depth-dependent artifacts.