We propose an objective threshold determination method for detecting outliers from the empirical distribution of cross-correlation coefficients among seismic waveforms. This method is aimed at detecting seismic signals from continuous waveform records. In our framework, detectability is automatically determined from Akaike’s Information Criterion (AIC). We applied the method of seismic signal detection to continuous records collected over 2 years. The results show that the maximum value of network cross-correlation coefficients sampled from each constant interval can be approximated by the theory of extreme value statistics, which provides a parametric probability density function of maxima. Using the function, outliers can be considered with a reasonable criterion.

Source time functions are essential observable quantities in seismology; they have been investigated via kinematic inversion analyses and compiled into databases. Given the numerous available results, some empirical laws on source time functions have been established, even though they are complicated and fluctuate along time series. Theoretically, stochastic differential equations, which include a random variable and white noise, are suitable for modeling such complicated phenomena. In this study, we model source time functions as the convolution of two stochastic processes (known as Bessel processes). We mathematically and numerically demonstrate that this convolution satisfies some of the empirical laws of source time functions, including non-negativity, finite duration, unimodality, a growth rate proportional to t³, ω⁻²-type spectra, and frequency distribution. We interpret this convolution and speculate that the stress drop rate and fault impedance follow the same Bessel process.