Abstract
<p>The focus on the present study is on the point-source approximation of a seismic source. First, we compare the synthetic motions on the free surface resulting from different analytical evolutions of the seismic source (the Gabor signal (G), the Bouchon ramp (B), the Cotton and Campillo ramp (CC), the Yoffe function (Y) and the Liu and Archuleta function (LA)). Our numerical experiments indicate that the CC and the Y functions produce synthetics with larger oscillations and correspondingly they have a higher frequency content. Moreover, the CC and the Y functions tend to produce higher peaks in the ground velocity (roughly of a factor of two). We have also found that the falloff at high frequencies is quite different: it roughly follows ω<span><sup>−2</sup></span> in the case of G and LA functions, it decays more faster than ω<span><sup>−2</sup></span> for the B function, while it is slow than ω<span><sup>−1</sup></span> for both the CC and the Y solutions. Then we perform a comparison of seismic waves resulting from 3-D extended ruptures (both supershear and subshear) obeying to different governing laws against those from a single point-source having the same features. It is shown that the point-source models tend to overestimate the ground motions and that they completely miss the Mach fronts emerging from the supershear transition process. When we compare the extended fault solutions against a multiple point-sources model the agreement becomes more significant, although relevant discrepancies still persist. Our results confirm that, and more importantly quantify how, the point-source approximation is unable to adequately describe the radiation emitted during a real world earthquake, even in the most idealized case of planar fault with homogeneous properties and embedded in a homogeneous, perfectly elastic medium.</p>
Highlights
These fronts are completely missed in the case of the point-source, indicating that a single point-source approximation of a seismic source is unable to account for the radiation emitted by a supershear earthquake, the geometry, the seismic moment and the total slip of the event are the same
In this paper we have considered the propagation of seismic waves due to a point-source embedded in a perfectly elastic, homogeneous and isotropic medium
To extended fault models, such as 2-D or 3-D rupture problems, the present model physically assumes that all the dissipated energy and the seismic wave excitation come from a single point, in which is concentrated all the energy available for the simulated earthquake event
Summary
We mention here the so-called stochastic method [Hanks 1979, McGuire and Hanks 1980, Hanks and McGuire 1981, Boore 2003, Boore 2009], which are used to simulate the mean ground motion for a given earthquake at a specific station This method is still based upon a point-source approximation and it basically assumes that the source spectra is described by a single corner-frequency model [e.g., Brune 1970]. It is important to emphasize that this spectral decay in not the unique; Boore ([2003]; see his Table 2 and references cited therein) reports a significant number of source shapes used in literature It emerges that there is no a universally accepted, theoretical or empirical reason to a priori select one specific formulation of the point-source time evolution; in this light the quantitative results presented in this paper can provide some general guidance. It should be emphasized that the visual comparison between synthetic data from point-source models and recorded signals of given earthquake, routinely presented in many papers, is not a fully satisfactory validation of the method employed and does not answer the questions above
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