Revised Accelerated Moment Release Under Test: Fourteen Worldwide Real Case Studies in 2014–2018 and Simulations

Abstract

Periods of accelerated seismicity have been observed during the preparation process of many large earthquakes. This accelerating seismicity can be detected by the Accelerated Moment Release (AMR) method and its recent Revised version (R-AMR) when the two techniques are applied to earthquake catalogues. The main aim of this study is to investigate the seismicity preceding large mainshocks and possibly increase our comprehension of the underlying physics. In particular, we applied both the AMR and R-AMR to the seismicity preceding 14 large worldwide shallow earthquakes, i.e. with focal depth less than 40 km, with magnitude M > 6 for Mediterranean area, and M ≥ 6.4 in the rest of the world, occurred from 2014 to 2018. Twelve case studies were analysed in the framework of SwArm For Earthquake study project funded by ESA, comprising the period 2014–2016; two additional cases were also considered to confirm the goodness of the methodology outside the period of the project catalogues. In total, R-AMR shows better performances than AMR, in 11 cases out of 14. In particular, in four out of 14 cases (i.e. 28.6%), the R-AMR method shows that acceleration exists due to an evident clustering in time–space on the faults, thus guiding the convergence of the fit; in seven cases (i.e. 50%) the R-AMR discloses acceleration, although no clustering around the fault is present; the remaining three cases (i.e. 21.4%) show no emerging acceleration from background. Finally, when R-AMR is compared with simulations, we verify that in most of the cases the acceleration is real and not casual.

Appendices

Appendix 1: Detailed Comparison of the Two Methods: The Case Studies

1.1 Chile 2014 Earthquake

Figure 11 shows the similar behaviour of the cumulative strain analysed by R-AMR and AMR. This similarity is essentially due to the accelerating character of the seismicity close, both in space and time, to the mainshock occurrence. The most relevant difference is the R-AMR smoothing effect due to distance in the linear part at the beginning of the curve of large (far) M6+ events (skyblue stars), which were cut by distance threshold in AMR instead. In the latter case, the acceleration is the characteristic of the seismicity close to the fault and that is the reason why both methods were successful in “predicting” correctly the time-to-failure of the mainshock (within a few days), as well as for the estimated magnitude (see in particular M(B) = 8.1 and 8.0), in close agreement with the actual M8.2. It is interesting to notice the resemblance of the maximum distance R_max (Fig. 2, left) reached by the AMR with respect to the inner radius R₀ in the R-AMR algorithm (Fig. 2, right): in fact, this distance characterizes the region with the no attenuation $\left( {\gamma = 0} \right)$ in both schemes.

Fig. 11

Chile 2014 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods. Notice the number of M6+ events, in particular those close to the mainshock occurrence (vertical dashed line)

1.2 Japan 2016 Earthquake

Differently from the other Japan earthquake occurred in 2015, for this event both methods produced their outcomes. A quick comparison between the behaviour of the two curves shows that R-AMR was able to put in evidence the accelerating seismicity of the region better than AMR, even if C-factor for both algorithms indicates its presence. However, starting from September 2015, several large events (M6+) preceded the considered mainshock producing the two sequences of aftershocks clearly visible in Fig. 12, left and right. Just few days before the impending mainshock, a series of events happened close to the fault, probably contributing to trigger the large earthquake under inspection. As consequence of this preceding activation, the R-AMR was able to reduce the difference between the “predicted” and actual time of failure (around 110 days late for AMR, while only 29 days for R-AMR).

Fig. 12

Japan 2016 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods. The oval marks some large events (several months before) and a sequence preceding the mainshock

1.3 Gibraltar and Ecuador 2016 Earthquakes

In these two cases, AMR did not give any results, making impossible a comparison to the R-AMR counterpart (Fig. 13).

Fig. 13

Plots of R-AMR behaviour for the Gibraltar 2016 and Ecuador 2016 case studies. No comparison to AMR method is possible since this latter did not return outcomes

Nevertheless in both cases, different for tectonic settings and mainshock magnitudes, a close and quite large event preceded by a few hours the mainshock and this drove the fit towards a “good” result (measured by the C-factor and R²) in terms of acceleration and “predicted” time (C ≅ 0.29 and almost three days for Gibraltar; C ≅ 0.44 and just 1 h for Ecuador). However, we notice that actually the goodness of the two fits is questionable if we consider the few data (due to an extension of R₀ = 10 km): this may have biased the outcomes, making not possible a reasonable computation, as for example for the predicted magnitudes M(A) and M(B).

1.4 Nepal 2016 Earthquake

If we consider the acceleration measured by the C-factor, we see that, differently from AMR, R-AMR is able to return it well (Fig. 14). However, in both cases, we notice that the number of data included in the analyses are not many because the analyses restrict data within a smaller distance than the DbA’s radius, and this probably limits the included data for realistic outcomes (e.g. Mignan 2008).

Fig. 14

Nepal 2015 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods

Nevertheless, as evidenced by the same yellow cell colour in Table 4, we want to highlight that the inner radius R₀ is almost equal to the value of the theoretical fault length L: differently from the previous cases with a very small radius, this result may instead confirm the goodness of the hypothesis that the fault region without attenuation is delimited by the inner circle.

1.5 North Aegean Sea (Greece) 2014 Earthquake

Something different happened in this case study as shown in Fig. 15. Here, R-AMR returned a value of C ≅ 0.38 in comparison to C ≅ 0.46 of AMR, meaning that the linear model does not fit well data in both cases. However, this slight acceleration in data did not drive the fit towards a sound $t_{f}$ “prediction”, particularly in the R-AMR analysis. However, it is particularly noteworthy, in this case, the almost coincidence of the R₀ with the AMR maximum distance R_max (250 vs 230 km).

Fig. 15

North Aegean Sea 2014 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods

1.6 Chile 2015 Earthquake

In this case (Fig. 16), almost both algorithms are able to catch the acceleration, if we base our judgement on the C-factor. Nevertheless, the results are strongly influenced by the different distances explored by the two algorithms: AMR reaches a maximum search distance, R_max = 220 km, which is inside the inner circle R₀ = 310 km of the R-AMR, thus resulting in a subset of it. We recall that for this particular event, we had to cut in time the catalogue to avoid the preceding M8.2 case study.

Fig. 16

Chile 2015 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods

Although this difference results in a small dataset explored by AMR, we can still recognise an acceleration which drives this algorithm towards an anticipating time-to-failure. On the other hand, some distant seismicity, included by R-AMR, leads this latter model to a failure time which is otherwise distant in the future. In this case, motivated by the similar area with no attenuation, we argue that the AMR acceleration is more apparent than real because it should be present also in R-AMR data. Its absence may be due to the attenuation of those events that contribute to acceleration in AMR.

Another similarity we want to emphasise is that between the inner radius R₀ ≅ 310 km and the theoretical length L = 321 km, as evidenced by the same orange cell colour in Table 4. This result maybe confirms the goodness of the hypothesis that the fault region, without attenuation, is delimited by the inner circle: indeed, we get that these two values are most of the times similar within 40% and few times even less that 20% (see blue values in Table 4).

1.7 Sumatra 2016 Earthquake

For this event (Fig. 17) searching for the minimum C-factor, both methods reached almost the same maximum distance, which is much smaller than the DbA’s radius: ~ 640 km $\ll$ 2495 km. However, the inspected region is mainly in the sea, where it is difficult to have a detailed (complete) catalogue. Moreover, basing our judgement on the C-factor, we can conclude that only R-AMR succeeded in highlighting an acceleration otherwise hidden in data: indeed, the linear trend of the cumulative strain in AMR is evident. Since it appears here, we want to evidence an effect on data due to the attenuation factor, which is characteristic of R-AMR: both in the end and in the middle of the R-AMR strain, you can see data alignments. This happens when a certain number of even large events, close in time, are located far from the epicentre and are subject to the attenuation. This is one of the main features of the new formulation: it helps to discriminate far, although large, earthquakes, that therefore have limited effect on the source region of the impending mainshock.

Fig. 17

Sumatra 2016 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods. For the R-AMR, evidenced by the ovals, the result of attenuation on a certain number of events far from the epicenter of the impending mainshock: they tend to align

1.8 Taiwan 2016 Earthquake

As in the previous case study (Sumatra 2016), the C-factor value (0.57 vs 0.91) is satisfactory for R-AMR method when compared to the AMR result (Fig. 18). However, it is evident the different datasets between them (their maximum distances are not so different if compared to the DbA’s radius). Even in this case study, the C-factor of the R-AMR evidences the acceleration in seismicity, but the small number of data points reflects in a value of ${\text{R}}^{ 2}_{\text{adj}} \approx 0. 9 1$, which is not as good as we would expect to unequivocally assess that seismicity accelerated. Nonetheless, please consider that half of the earthquakes are very close to (or even on) the fault (red points). This is one of those cases when, as stated by De Santis et al. (2015a), the method always returns a predicted time-to-failure $t_{f} ,$ thus leading to a false positive or a false negative prediction.

Fig. 18

Taiwan 2016 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods

1.9 Negative Cases: Kasos-Crete 2015, Lefkada 2015 and Japan 2015

In this work, we considered as negative cases those for which either $C > 0.6$ (i.e. the linear behaviour prevailed) or $R_{adj}^{2} < 0.9,$ that is the quality of the fit was not good enough. Figure 19 shows the corresponding results. The Kasos-Crete 2015 event falls in the first case, since the two fitting models are almost equivalent. Although even for Lefkada 2015 the C-factor indicates that the two models are equivalent, it differs from the previous one because large deviation from the linear behaviour is due to two large events (M6+) which happened several months before the mainshock, thus altering the trend of the proceeding seismicity on the fault region. The last case, Japan 2015, was the only one without result: the imposed thresholds for the acceptance of the fit $\left( {C< {1; R_{adj}^{2} } > 0.9} \right)$ were exceeded, so no outcome was produced. The black oval evidences the presence of a significant intermediate earthquake  and its aftershocks that change the normal trend of the curve.  

Fig. 19

Summary plot of the three unsuccessful case studies out of 14 (for convenience we show only R-AMR method): the first two show no acceleration (C ${ \lesssim }$ 1) for both AMR and R-AMR (Kasos-Crete 2015 and Lefkada 2015); for Japan 2015, the fit thresholds $\varvec{C}<{1;\varvec{ R}_{{\varvec{adj}}}^{2} } >0.9$ were exceeded, so no outcome was produced. The stars mark the M6+ events

1.10 Kodiak (Alaska) 2018 Earthquake

As in other previous case studies (e.g. Nepal 2015), the C-factor value is satisfactory for R-AMR method when compared to the AMR result (0.44 vs 0.73; Fig. 20). Both methods found the best solution almost in the same area (with slightly the same number of events), but the acceleration is better evidenced by the R-AMR method: indeed, the large M6+ event indicated by the star contributes less to the acceleration than in AMR (being it part of the background), whereas the closer event (red dot) certainly drives the dynamics leading to a better indication of failure.

Fig. 20

Kodiak (Alaska) 2018 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods

1.11 Nikol’skoye (Russia) 2017 Earthquake

Figure 21 shows the similar behaviour of the cumulative strain analysed by R-AMR and AMR. This similarity is likely due to resemblance of the maximum distance R_max reached by the AMR with respect to the inner radius R₀ in the R-AMR algorithm: in fact, this distance almost encloses the region with no attenuation $\left( {\gamma = 0} \right)$ in both schemes, and this is evidenced by the high percentage of events (about 90%) inside the inner radius R₀. Therefore, in this case, the R-AMR damping effect due to distance of the many large M6+ events (skyblue stars) is ineffective. This also may explain why both methods were successful in “predicting” correctly M(A) and M(B), the estimated magnitude (see, in particular, M(A) = 7.8 and 7.7, for AMR and R-AMR, respectively), in agreement with the actual M7.7.

Fig. 21

Nikol’skoye (Russia) 2017 earthquake. Comparison between the optimum solutions for AMR (left) and R-AMR (right) methods

Appendix 2: Mc of the USGS Catalogues

See Figs. 22, 23, 24, 25, 26, 27, 28, 29, 30, 31 and 32.

Fig. 22

Chile 2014. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 23

Japan 2016. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 24

Gibraltar 2016. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 25

Nepal 2015. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 26

North Aegean Sea 2014. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 27

Chile 2015. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 28

Sumatra 2016. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 29

Taiwan 2015. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 30

Kasos-Crete 2015. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 31

Lefkada 2015. Computation of completeness magnitude Mc from the USGS catalogue

Fig. 32

Japan 2015. Computation of completeness magnitude Mc from the USGS catalogue