An Advanced Frequency Domain Methodology for Resolving Finite Source Attributes of Small to Moderate Earthquakes: Beyond Corner Frequency Analysis

Resolving the finite-source attributes of small to moderate earthquakes is essential for advancing our understanding of fault properties and earthquake physics. Time-domain approaches for source characterization are often unstable due to challenges in deconvolving path effects using co-located smaller earthquakes as empirical Green’s functions, as these methods are highly sensitive to seismic arrivals and noise levels. Frequency-domain analysis provides a more stable alternative by discarding phase information. However, the conventional approaches typically constrain only the rupture dimension and directivity using the corner frequency of apparent source spectra, assuming circular or linear rupture models, respectively. In this study, we present an advanced frequency-domain analysis by employing an elliptical rupture model and introducing a Bayesian inversion framework that fits the full apparent source spectra to estimate rupture length, width, propagation velocity, and directivity ratio. This approach fully leverages the observed spectra and widely deployed dense seismic arrays to constrain the rupture process beyond corner frequency analysis. Applied to several earthquakes with magnitudes ranging from 2 to 6, our method produces results consistent with seismic second moments and finite-fault inversion techniques. Unlike traditional methods, our framework estimates more accurate dynamic parameters such as stress drop, apparent stress, rupture energy, and critical slip distance without relying on circular rupture assumption. The method is easily automatable, enabling the development of an extensive earthquake catalog that includes dynamic and kinematic parameters for small to moderate events, thereby supporting statistical analyses of fault properties and deepening our understanding of earthquake source mechanisms.

Figure 1.  The finite-source attributes inversion for the Mw 2.3 event in 2016 Oklahoma. (a) The 2-D posterior joint probability density resulting from the Bayesian inversion. (b) The parameters of the ellipse rupture model. a and b are the semi-major and semi-minor axes of the ellipse rupture model, respectively.  defines the rupture directivity.  represents the rupture velocity, controlling the rupture front propagation.  denotes the directivity ratio, which controls the rupture's initial position. (c-d) The observed and predicted apparent source spectra, respectively. The estimated parameters of the rupture model are a = 85 ± 5 m,  b = 46 ± 5 m,  θ = 80 ± 1 °, v_r = 2.19 ± 0.02 km/s, and e = 0.18 ± 0.01, which are consistent with previous studies (Fan et al., 2018).