The systematic dependence of the main parameters of the SBM, the local stress drop, and the barrier interval, , as inferred by Aki and Papageorgiou has been confirmed. The local stress drop is a relatively stable parameter over a wide magnitude range: ~161 bar, 114 bar, and 180 bar for interplate, extensional, and intraplate earthquakes, respectively (Halldorsson and Papageorgiou, 2005). Furthermore, the barrier interval increases with magnitude in a self-similar manner (see Fig 2). where R j is the random size of subevent j and t j its random rupture onset. The far-field seismic spectrum that is radiated from subevent j as it breaks is . . . . . . . . and the expectation is defined as VARIATIONS OF THE SPECIFIC BARRIER MODEL IN TERMS OF DIFFERENT DISTRIBUTIONS OF SUBEVENT SIZES AND RUPTURE TIMES Benedikt Halldorsson and Apostolos S. Papageorgiou Affiliation: Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY, 14260-4300, U.S.A. (B.H.). Department of Civil Engineering, University of Patras, Patras, Greece (A.S.P.). Email: bh25@buffalo.edu (B.H.), papaga@upatras.gr (A.S.P) Abstract The Specific Barrier Model (SBM), introduced and developed by Papageorgiou and Aki (1983a; 1983b; 1985) and recently calibrated by Halldorsson and Papageorgiou (2005), provides a complete, yet parsimonious, self-consistent description of the kinematic and geometric faulting process of an earthquake. The SBM is an idealized case of a complex seismic source in 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 composed of an aggregate of subevents of equal diameter, the “barrier interval”. Based on the work of Joyner and Boore (1986) and Papageorgiou (1988) the spatial extent of the subevents of the SBM was allowed to vary according to various prescribed probability density functions for subevent sizes, and closed form expressions of the corresponding aggregate far-field source spectra were derived. The sensitivity of the spectra to different assumptions regarding subevent rupture times was also quantified, and is shown to only affect the intermediate spectral slope. The high-frequency spectral asymptotes corresponding to different size-distributions do not differ dramatically from the far-field spectrum of the SBM, for a constant local stress drop. Furthermore, the relative difference is 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 be the most effective way to capture the essential characteristics of a more complex 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. Introduction Relationships of strong ground motion attenuation are important for estimating the seismic hazard at a site. For regions where strong motion data is abundant, such as California, empirical relationships have been developed and successfully used in seismic hazard analyses. However, for regions where recorded ground motion data are scarce, such as Eastern North America, it becomes imperative to use physical models to represent the ground motion generation and propagation. Of the physical earthquake models available in the literature, the SBM provides the most complete, yet parsimonious, self-consistent description of the earthquake faulting processes that are responsible for the generation of the high frequencies of ground motions, and at the same time provides a clear and unambiguous way of how to distribute the seismic moment on the fault plane. The latter requirement is necessary for synthesizing near-fault (i.e. in the vicinity of an extended source / fault) ground motions. Thus, the SBM applies both in the "near-fault" as well as in the "far-field" region, allowing for consistent ground motion simulations over the entire frequency range and for all distances of engineering interest. Furthermore, the model has been shown to capture effectively the essential characteristics of more complex seismic sources (Halldorsson, 2004). The Specific Barrier Model According to the specific barrier model the seismic fault may be visualized as an aggregate of circular subevents of equal diameter, …. filling up a rectangular fault of length L and width W, as shown schematically in Fig 1a. As the rupture front sweeps the fault plane with "sweeping velocity" V, a stress drop, (referred to as the "local stress drop") takes place in each subevent starting from its center and spreading radially with constant "spreading velocity”, . The radiation of elastic waves emitted from each crack as it breaks is based on a physical description of source processes using kinematic dislocation theory (Sato and Hirasawa, 1973), and it’s far- field source spectral shape is approximated by an omega-square spectrum. The modified far-field source spectrum of the SBM is: where N is the number of subevents, T is the source duration, is the source displacement spectrum of a single subevent, and is a high- frequency source complexity factor, accounting for the observed deviation of self-similar source scaling of earthquakes in interplate and extensional tectonic regimes (see Fig. 1b). (a) (b) Figure 1 – (a) In the SBM, the fault surface is visualized as composed of an aggregate of “subevents”. (b) Modified far-field source acceleration spectra of the SBM for interplate (solid), extensional (dash-dot) and intraplate (dashed) earthquakes. Figure 2 – (a) The systematic dependence of the barrier interval with magnitude for interplate earthquakes. The solid line shows the self-similar least-squares relation to barrier interval estimates from Aki and Papageorgiou (see their 1983a,b and 1988 papers), and Beresnev and Atkinson (2001). Far-field Spectrum of a Complex Source General Formulation The earthquake event is viewed as composed of N smaller earthquakes (subevents). The expected squared modulus of far-field seismic energy is (Joyner and Boore, 1986) where f X (x) is the probability density function (PDF) of the random variable X. Through the following simplifying assumptions of inter-independence of the subevent properties, the expectation in Eq. (2) can be written as follows (Joyner and Boore, 1986): The assumptions are: The subevents rupture independently of each other; R j is independent of t j ; Rupture times of different subevents follow the same probability distribution; Sizes of subevents are independent from each other; Subevent sizes follow the same probability distribution; Far-field seismic spectra from subevents follow the same functional form. Examples of the contribution of the two terms on the right hand side of Eq. (4) to the aggregate spectrum is shown in Fig. 3a and b. The specific barrier model, as a specific case of a complex seismic source, is a gross idealization of the kinematic and geometric faulting process of an earthquake. For example, the simplifying assumption of equal-size subevents may not hold, and a subevent population with variable sizes may be more appropriate and result in a more realistic description of the radiated seismic energy from the source. In this study we investigate the effects of the above, in addition to variable distributions of rupture onsets, on the radiated far-field spectra and compare with that of the specific barrier model. (4) (3) (2) (1) Annual Meeting 2005, Lake Tahoe, Nevada April 27 - 29, 2005