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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−2 in the case of G and LA functions, it decays more faster than ω−2 for the B function, while it is slow than ω−1 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.
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