The probability of a strong shock to nucleate inside a small area A that just experienced another strong event, should be lower than the probability predicted by the tapered Gutenberg-Richter (TGR) model. This is because a lot of elastic energy has already been released in the first strong shock, and it takes time to recover to the previous state. However, this fact is not taken into account in the TGR model. Due to this limitation, we propose the energy-varying TGR (TGRE) model. Here, we impose the corner seismic moment to be a space-time function depending on the amount of elastic energy E currently available in a small area A. More precisely, our energy-varying corner seismic moment Mc (E) increases with the square of the time elapsed since the last resetting event, which is supposed to have reset the elastic energy in the small area A to a minimum value.
In practice, the taper of TGRE is abruptly shifted to the left just after the occurrence of a strong shock, and then it slowly recovers to the long-term value with the energy-reloading process. We impose TGRE to verify an invariance condition: when considering large domains, where a single strong event cannot significantly affect the whole energy available, TGRE becomes the TGR. A sensitivity analysis also shows that the dependence of Mc (E) on its parameters is not substantial in the short-term, proving that their specific choice, as long as reasonable, cannot affect the results of any analysis involving TGRE.
To evaluate the reliability and applicability of the TGRE model, we applied it to the Landers sequence (USA) which started with the Mw7.3 mainshock that occurred on the 28th of June 1992. First, we found out that the seismic moment-frequency distribution (MFD) close to the fault system affected by the mainshock is statistically-significantly different from that of earthquakes off-faults, showing a lower corner magnitude. This result is entirely independent of modeling, and it underlines the need for an energy-varying MFD at short spatiotemporal scales. Then, we have shown that TGRE may explain well the difference in the MFDs for the Landers sequence, and that the results are stable for possible variations of its parameters. Notably, we obtained positive evidence in favour of the TGRE fit, with respect to TGR, for Landers data within one week, one month, six months and one year since the Mw7.3 mainshock (Fig. 1 shows the results for one week). Most of the times, the evidence is “substantial” and “strong” (terminology by Kass & Raftery, 1995).
The results suggest that TGRE can be profitably used in operational earthquake forecasting, as the model is simple and rooted in clearly stated assumptions. It requires some more or less explicit subjective choices. However, we think they are less subjective than ignoring the empirical evidence that shows that strong triggered earthquakes do not nucleate on a fault just ruptured by another strong event. Rather than focusing on the details of the model, which is obviously not the only one possible, we mainly aim to get across the message of including an energy dependency in MFD: We claim that self-organized criticality at large spatiotemporal scales changes in intermittent criticality at small space-time domains recently experiencing a significant release of energy.
This study has been recently published on BSSA:
As future work, we aim at evaluating the TGRE reliability and the comparison with alternative models through prospective tests