An energy-dependent earthquake moment-frequency distribution

Abstract

The magnitude-frequency distribution (MFD) of many earthquake catalogs is well described by the Gutenberg-Richter (GR) law, or its tapered version (TGR). This distribution is usually extrapolated to any subsets of the space-time window covered by the catalog. However, some empirical observations and logical thoughts may raise doubts about the validity of this extrapolation. For example, according to the elastic rebound theory, we may assert that the probability of a strong shock to nucleate within a short time-interval in a small area $\mathcal{A}$ just ruptured by another strong event, should be lower than that expected by GR (or TGR): a lot of energy has already been released, and it takes time to recover to the previous state. Here we put forward a space-time modification of the TGR, named TGRE (energy-dependent TGR), where the corner seismic moment becomes a time-varying energy function depending on: i) the conceivable strongest shock that may nucleate in $\mathcal{A}$; ii) the time elapsed since the last strong earthquake resetting the elastic energy in $\mathcal{A}$ to a residual value; iii) the rate of the energy recovering, linked to the recurrence time of the fault(s) involved. The model also verifies an invariance condition: for large space-time windows the occurrence of a strong shock doesn't affect significantly the whole elastic energy available, i.e., the TGRE becomes the TGR. The model is simple and rooted in clearly stated assumptions. To evaluate its reliability and applicability, we apply it to the Landers sequence in 1992. As expected by TGRE, we find that the MFD close to the fault system interested by the mainshock (Mw7.3) differs from that of earthquakes off-fault, showing a lower corner magnitude. We speculate that TGRE may be profitably used in operational earthquake forecasting, and explains the empirical observation that strongest aftershocks nucleate always outside the mainshock fault.