A theoretical study is made to investigate the excitation of short-period P- and S-waves, based on a stochastic fault model. The source model describes an earthquake as a finitely propagating unilateral rupture on a fault plane where fault heterogeneities (fault patches) are randomly distributed. The fundamental parameters are (1) average stress drop (2) fault dimension, (3) variance of stress drop, (4) patch corner frequency relevant to the fault patch sizes and (5) fault patch rupture directions. It is shown that the source effectively radiates short-period S-waves. This would reveal the reason why the strong ground motion of large earthquakes is mainly composed of S-waves. The short wavelength description of an earthquake is obtained by an energy-additive superposition of the stochastic fracturing of random fault patches. This gives rise to a seismic directivity effect peculiar to the incoherent short waves. This effect is studied in the frequency and time domains, especially for root-mean square and maximum accelerations. The excitation of strong motion accelerations is formulated by the stochastic part of earthquake faulting in terms of the variance of stress drop, fault dimension, and cut-off frequency, in addition to the short-period seismic directivity. © 1990.
