Variations of the specific barrier model-part I: effect of subevent size distributions

The specific barrier model (SBM), introduced and developed by Papageorgiou and Aki (1983a; 1983b; 1985) and recently re-calibrated by Halldorsson and Papageorgiou (2005) for earthquakes of different tectonic regions, is a particular case of a composite seismic source model according to which the seismic moment is distributed in a deterministic manner on the fault plane on the basis of moment and area constraints. Namely, it assumes that a rectangular fault surface is filled with an aggregate of non-overlapping subevents modeled as circular cracks of equal diameter, the 'barrier interval', on which a 'local stress drop' takes place. In the present work, we relax the basic assumption regarding subevent size of the SBM. Subevents, still modeled as circular cracks, are allowed to vary in size according to various prescribed probability density functions controlling the frequency of occurrence of subevent sizes. Closed form expressions of the 'far-field' spectra of the composite source are derived using an approach proposed by Joyner and Boore (1986). The seismic energy radiated by individual subevents arrives at a site in a time window the duration of which is related to the duration of rupture and the source-site geometry. The effect of the distribution of 'arrival times' on the spectral amplitudes of the composite source is investigated in a companion paper, referred to as Part II. The type of subevent size distribution and its allowed size range directly affects the number of subevents required to satisfy the moment constraint. A larger number of subevents leads to increased 'complexity' of the earthquake which generally results in relatively higher source acceleration spectral levels at high-frequencies. The level of the plateau of the high-frequency acceleration spectral amplitudes, corresponding to different size-distributions, does not differ significantly from that of the far-field spectrum of the SBM, for a constant local stress drop. Furthermore, the differences observed in the spectral amplitudes of the SBM and its variants are likely to be less than the expected uncertainty associated with local stress drop values determined from strong-motion data. Thus, despite its simplifying assumptions, the SBM appears to provide the most simple, yet effective, description that captures the essential characteristics of a composite seismic source. This is especially advantageous for consistent strong-motion modeling in the 'near-fault', as well as in the 'far-field' region for earthquake engineering applications.