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This article was submitted to Solid Earth Geophysics, a section of the journal Frontiers in Earth Science

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Large earthquakes occurring worldwide have long been recognized to be non Poisson distributed, so involving some large scale correlation mechanism, which could be internal or external to the Earth. We have recently demonstrated this observation can be explained by the correlation of global seismicity with solar activity. We inferred such a clear correlation, highly statistically significant, analyzing the ISI-GEM catalog 1996–2016, as compared to the Solar and Heliospheric Observatory satellite data, reporting proton density and proton velocity in the same period. However, some questions could arise that the internal correlation of global seismicity could be mainly due to local earthquake clustering, which is a well-recognized process depending on physical mechanisms of local stress transfer. We then apply, to the ISI-GEM catalog, a simple and appropriate de-clustering procedure, meant to recognize and eliminate local clustering. As a result, we again obtain a non poissonian, internally correlated catalog, which shows the same, high level correlation with the proton density linked to solar activity. We can hence confirm that global seismicity contains a long-range correlation, not linked to local clustering processes, which is clearly linked to solar activity. Once we explain in some details the proposed mechanism for such correlation, we also give insight on how such mechanism could be used, in a near future, to help in earthquake forecasting.

Worldwide seismicity does not follow a Poisson distribution (e.g.,

However, the character and properties of the internal correlation observed in global seismicity have never been analyzed before: it is not clear, for instance, if it only depends from local clustering, which could only be due to the very trivial and well known physical mechanisms of stress redistribution (

In this paper, after recalling the main results of

Once demonstrated the robustness, against any possible bias due to other local stress interaction effects, of the correlation between global seismicity and solar activity, we discuss more the proposed physical mechanism for the triggering effect.

Finally, we discuss how the new evidence could be, in future, used to improve earthquake forecast.

By interpreting the internal correlation of global seismic catalogs, an important concern would be to investigate the role played by local, short-range clustering, which mainly depends from well recognized physical mechanisms of stress interaction (

So, in order to obtain a declustered catalog we used the ISC-GEM catalog (

We used two data sets both based on the ISC-GEM catalog (

The first data set, we applied such a de-clustering procedure, is relative to the shallow (depth < 60 km) M ≥ 8.00 events that occurred since 1905. There are 83 of them. We manually de-clustered it so to discard even events, located within the mentined distance, occurring to within 3 years from another one. We remained with 76 events. Both data sets are available as

The second data set is relative to the shallow (depth < 60 km) M ≥ 6.00 events that occurred since 1964. The choice of 1964 as lower bound is due to the fact that epicentral location quality dramatically increases starting from that date.

Once the new de-clustered catalog was obtained, we checked it for poissonianity. Then, we applied the algorithm devised by _{i}) = −log[SP(Δt_{i})]/Δt_{i}_{i}) is the Survival Probability Function at the Δt_{i} timing interval. If the data set where truly poissonian, SP(Δt) = exp (−μΔt) (where μ is the average value of Δt), so that λ should be constant over the entire Δt_{i} data set. This approach is even more powerful than that devised by

Poisson’s test according to

In _{i} of 20.000 s or less the non poissonianity is evident. In _{i} spans over more orders of magnitude with respect to Δd_{i}. This means that events are more clustered in time than in space, so that a kind of long range interaction, which is not destroyed by the local de-clustering, exists in the catalog. The obvious consequence of this finding is that a global process is affecting the seismicity.

^{6} pairs.

Once we stated the de-clustered seismic catalogs still are non poissonian, so evidencing a long range correlation among the worldwide earthquakes we want to specify its origin.

We then apply the de-clustering method previously described to this catalog. Such a de-clustered catalog has only 3,241 events, instead of 6,612 of the original one analyzed by

We used the conceptual

In ^{−3} for the proton density. We want to stress that such a best fitting threshold is only slightly larger than the best one used for the original (non de-clustered) catalog in ^{−3} is another, almost equivalent, best fitting value also for the original catalog. We see that total fraction of failures amounts to 10% for the de-clustered catalog (it is 5.5% for the original catalog), so indicating the correlation is highly significant. In the next chapter, we will discuss anyway in more detail the results obtained, with different threshold values, for the original and the de-clustered catalog.

Modified Molchan diagrams (

We have then demonstrated that also cutting from the catalog the local clustering, a long-range internal correlation remains, which is still significantly correlated with proton density due to solar activity.

Although the non poissonian character of worldwide earthquake catalogs was a well recognized effect since more than half a century, we demonstrate here, for the first time in a clear way, that internal correlation among worldwide earthquakes is dominated by a long range clustering effect. Such effect is well distinct from local clustering, which is due to local stress interaction among the faults.

Once such long range effect has been identified, we have shown that correlation between solar activity and earthquakes still holds even for de-clustered data sets, after removing the local clustering effects. This means that the long range internal correlation of the worldwide catalog, which has not a simple physical explanation, is certainly linked with proton density modulated by solar activity. We could also speculate if the short range clustering, which is generally interpreted in terms of local stress interaction, would also be affected by proton density. In principle, there would be no reason to neglect interaction with solar activity at all scales. In fact, the correlation inferred by

However, besides we were able, by using an appropriate de-clustering technique, to isolate and put in evidence the long range internal correlation of the worldwide earthquake catalog, we are anyway convinced (and the results obtained here, even more clear using the whole catalog, represent a further confirmation) that any statistical analysis to infer the properties of an earthquake sequence should avoid de-clustering procedures. As an example, it is quite obvious that the generation mechanism in case of multiple events is still poorly understood. For instance in Italy, in 2016, we had 3 M > 6 events spaced apart few tenths of kilometers. The first occurred on August 24th, the second on October 26th and the third on October 30th. The latter being also the largest. Does it means that stress transfer induced the three events in sequence or does it imply that a larger slow process, such as that envisaged by

The main reason however we are against declustering is that it certainly adds a high degree of subjectivity. There is in fact no commonly accepted method: declustering therefore would make any statistical finding about the catalog weaker.

We proceed now to discuss how our results correlate with the well known main cycles of solar activity. Some researchers had previously claimed the existence of some correlation between earthquake occurrence and the main period of solar activity, lasting 11 years (e.g.,

^{−3}, which appears to be a closely best fitting value for all the catalogs (the value of 15.5 counts cm^{−3} used by Marchitelli et al. for the original catalog gives an almost equivalent total prediction failure: 0.054 instead of 0.055). The total prediction failures for the original catalog are 0.05 for both the total catalog and the first half; whereas it is 0.17 for the second part, in the period of considerably lower solar activity. For the de-clustered catalog, the total prediction failure is 0.10 for the total catalog, 0.07 for the first half and 0.23 for the second half. These results confirm the observation that, in periods of lower solar activity, the correlation between proton density and global earthquakes is lower.

Once the correlation between solar activity (proton density) and worldwide seismicity is assessed, as we demonstrate, beyond any reasonable doubt, what remains is to describe the mechanism producing such a correlation.

Once the most appropriate mechanism will be precisely assessed for the solar-earthquake interactions, is could likely represent a powerful element to help in earthquake forecast. Actually, a large number of methods devoted to earthquake forecast have been implemented: an extensive review can be found, for example, in

Publicly available datasets were analyzed in this study. This data can be found here:

PH elaborated statistical programs and analyses; VM worked the original idea; GN and CT wrote the core of the paper; all authors participated to the data analysis and interpretation, and contributed to write the final version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We gratefully acknowledge Paolo Plescia and Alexey Lyubushin, who reviewed the paper and greatly helped to improve it. This work has been partially supported by the project OT4CLIMA, funded by the Italian Ministry of Education, University and Research (

The Supplementary Material for this article can be found online at: