On worrying trends in statistical physics approaches to seismicity

This discussion is motivated by my casual observation over the recent years of many papers by physicists applying "new'' techniques to supposedly discover some new universal and hitherto supposedly unknown structure in earthquakes. Many if not most in my opinion are nothing but reformulation of known statistical laws, as I now argue with concrete examples. This opinion has been defended by other  knowledgeable statistician specialists of seismicity, the most vocal being perhaps Dr. Y.Y. Kagan at UCLA.

Many papers purport to characterize the space-time organization of seismicity in different regions of the world. Recent claims of universal laws for the distribution of waiting times and seismic rates between earthquakes have derived from the analyses of space-time windows. The flurry of interest from physicists comes from their fascination with the self-similar properties exhibited by seismicity (Gutenberg-Richter power law of earthquake seismic moments, Omori decay law of aftershock rates, fractal and multifractal space-time organization of earthquakes and faults) together with the development of novel concepts and techniques that may provide new insights.

But, and this is my main criticism based on several detailed examples discussed below that many of the new approaches and results do not stand scrutiny. IT IS THE JOB OF THE AUTHORS TO TEST on synthetic catalogs generated by benchmark models using the well-known laws in statistical seismology if their new methods provide just a new formulation of known patterns or if they give new insight. In summary, papers submitted which not do what I describe should be rejected.

To put the problem in perspective, I draw from several past claims on which I have personally worked to debunk the claims. Here is a non-exhaustive list with four detailed examples. Note that none of the papers claiming new regularities or results for earthquakes perform tests on synthetic catalogs generated by good benchmark models which just incorporate the know laws of seismology. They all lack from this perspective.

FIRST EXAMPLE

- Mega et al. used the "diffusion entropy" (DE) method to argue for a power-law distribution of time intervals between a large earthquake (the mainshock of a seismic sequence or cluster) and the next one.

M. S. Mega, P. Allegrini, P. Grigolini, V. Latora, L. Palatella, A. Rapisarda and S. Vinciguerra, Power law time distributions of large earthquakes, Phys. Rev. Lett., 90, 18850, 2003.

My paper with Helmstetter below shows that all the "new" discoveries reported by Mega et al. (including the supposedly new scaling) can be explained solely by Omori's law for intra-cluster times, without correlation between clusters.

A. Helmstetter and D. Sornette, Comment on "Power-Law Time Distribution of Large Earthquakes", Phys. Rev. Lett. 92, 129801 (2004). (Reply is Phys. Rev. Lett. Lett. 92, 129802 (2004))
(external pagehttp://arXiv.org/abs/physics/0307134)

SECOND EXAMPLE

- Claim of new universal laws in the distribution of recurrence times between
successive earthquakes in a given seismic region

[1] Bak, P., K. Christensen, L. Danon and T. Scanlon,
Unified scaling for earthquakes, Phys. Rev. Lett. 88, 178501, 2002.

[2] Corral A., Local distributions and rate fluctuations in a unified scaling
law for earthquakes - art. no. 035102. Physical Review E. 6803(3 Part 2), 5102, 2003.

My papers below with A. Saichev demonstrate that these supposedly new universal distributions of recurrence time derive from the known quantitative laws of seismicity:

(i) Gutenberg-Richter law, (ii) Omori's law, (iii) the fact that aftershocks also trigger their aftershocks, (iv) the fact that the distribution of distances between mainshocks and aftershocks has a power law tail, (v) the fertility law (the fact that earthquakes of magnitude M trigger of the order of 10^{a*M} aftershocks with a<=1), (vi) the fractal distribution of faults which are concentration centers for earthquakes.

[*] A. Saichev and D. Sornette,Theory of Earthquake Recurrence Times, 
J. Geophys. Res., 112, B04313, doi:10.1029/2006JB004536 (2007)
(external pagehttp://arxiv.org/abs/physics/0606001

[**] A. Saichev and D. Sornette "Universal'' Distribution of Inter-Earthquake Times Explained, Phys. Rev. Letts. 97, 078501 (2006)
(external pagehttp://arxiv.org/abs/physics/0604018)

THIRD EXAMPLE

- Davidsen and Paczuski claim to have found evidence contradicting thetheory of aftershock zone scaling (AZS) in favor of scale-free statistics.

J. Davidsen and M. Paczuski, Phys. Rev. Lett. 94, 048501 (2005).

In the comment below, we present three elements showing that Davidsen and Paczuski's results are insensitive to the existence of physical length scales associated with aftershock zones or main-shock rupture lengths, so that their claim is unsubstantiated.

M. Werner and D. Sornette, Comment on "Analysis of the Spatial Distribution Between Successive Earthquakes'' by Davidsen and Paczuski, Physical Review Letters, in press (2007)
(http://arxiv.org/abs/physics/0608161)

FOURTH EXAMPLE

- A growing number of papers endorse the present fashion on networks and "small-world networks" in particular and apply/adapt metrics of networks to earthquakes, proposing that the network approach allows them to reveal new patterns and new laws in earthquake physics. See for instance the 4 papers below.

Abe, S. and N. Suzuki, Scale-free network of earthquakes, Europhys. Lett., 65 (4), 581-586, 2004.

Baiesi, M. and M. Paczuski, Scale-free networks of earthquakes and aftershocks, Phys. Rev. E, 69, 066106, 2004.

Baiesi, M. and M. Paczuski, Complex networks of earthquakes and aftershocks, preprint at
external pagehttp://arxiv.org/abs/physics/0408018.

Baiesi, M., Scaling and precursor motifs in earthquake networks,
preprint at external pagehttp://arxiv.org/abs/cond-mat/0406198.

The major weakness of the approach in terms of networks of earthquakes is that it just conveys wishful thinking about the use of networks to better understand and model earthquakes. The authors have introduced different ways to construct "earthquake networks" and they document that the obtained networks present properties similar to other "small-world" networks. While one could say that this is useful because it provides some quantitative metrics to quantify the spatio-temporal complexity of earthquakes, the problem is that there are other previously well-established quantitative laws to describe it and the authors in their work have not attempted to check if the new network metrics provide new insights or are just reformulation of known quantitative laws (as the three above examples show it is often the case). The known laws are: (i) Gutenberg-Richter law, (ii) Omori's law, (iii) the fact that aftershocks also trigger their aftershocks, (iv) the fact that the distribution of distances between mainshocks and aftershocks has a power law tail, (v) the fertility law (the fact that earthquakes of magnitude M trigger of the order of 10^{a*M} aftershocks with a<=1), (vi) the fractal distribution of faults which are concentration centers for earthquakes. Using these facts, can we explain the observations of Abe and Suzuki, of Baiesi and Paczuski? If yes, this shows that the network approach to earthquakes is just a reformulation of known statistical properties of earthquakes. If no, this is interesting. But the authors have not even started to address this most important question.

In this vein, my own knowledge of seismicity makes me conjecture that many if not all of the properties documented by these authors can be derived from a simple statistical model of seismicity using the above laws (1-vi).

GENERAL RECOMMENDATION:

The authors should make links with the literature on statistical seismology which deals with these questions. It is their task to show that the new metrics that they propose give results that cannot be explained by the standard laws in statistical seismology. For this, there are well-defined benchmark models that incorporate these laws, that generate synthetic catalogs on which the new metrics can be tested.

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