Revisiting Snoke’s (1987) Spectral Expressions: Coefficient Correction and Its Implications for Dynamic Insights

Minkyung Son 

Source parameters such as seismic moment, corner frequency, stress drop, radiated
energy, and apparent stress are often derived from the Brune (1970) source spectrum.
Building on this, Andrews (1986) formulated analytical relations that link those
parameters to spectral integrals of squared velocity and displacement, and Snoke
(1987) introduced an approximation that enables their practical estimation from limited-
band data. However, subsequent studies have adopted inconsistent numerical
coefficients in Snoke’s expression for the low-frequency spectral level. Our rederivation
confirms that the correct coefficient is 2, rather than 4^(1/4), and shows that the
discrepancy arises from a computational oversight in the original formulation. We
further clarify how Snoke’s integral approximation extends to radiated energy and
apparent stress, highlighting the linkage between inferred source parameters, dynamic
rupture process, and energy balance. This re-examination would support consistent
use of spectral formulations in earthquake source parameter estimation and
underscore the need for caution when estimating and interpreting source parameters,
especially secondary quantities.