Didier Sornette (born 25 June 1957 in Paris) is a French researcher studying subjects including complex systems and risk management. He is Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich (ETH Zurich) and is also a professor of the Swiss Finance Institute, He was previously a Professor of Geophysics at UCLA, Los Angeles California (1996–2006) and a Research Professor at the French National Centre for Scientific Research (1981–2006).
Theory of earthquakes and fault networks
With his long-time collaborator Dr. Guy Ouillon, Sornette has been leading a research group on the "Physics of earthquakes" over the last 25 years. The group is active in the modelling of earthquakes, landslides, and other natural hazards, combining concepts and tools from statistical physics, statistics, tectonics, seismology and more. First located at the Laboratory of Condensed Matter Physics (University of Nice, France), then at the Earth and Space Department (UCLA, USA), the group is now at ETH-Zurich (Switzerland) since March 2006.
Earthquake prediction and forecasting
Earthquake prediction The group has tackled the problem of earthquake and rupture prediction since the mid-90s within the broader physical concept of critical phenomena.Sornette, D. (1999), Towards a truly multidisciplinary approach to earthquake prediction, in Nature debate April 1999, Is the reliable prediction of individual earthquakes a realistic scientific goal? Considering rupture as a second-order phase transition, this predicts that, approaching rupture, the spatial correlation length of stress and damage increases.Sornette, D., Vanneste, C. and Knopoff, L., (1992) "Statistical model of earthquake foreshocks", Phys. Rev. A 45, 8351–8357 (1992) This in turn leads to a power-law acceleration of moment and strain release, up to the macroscopic failure time of the sample (i.e. a large earthquake in nature). This prediction has been checked on various natural and industrial/laboratory data, over a wide spectrum of different scales (laboratory samples, mines, California earthquakes catalog), and under different loading conditions of the system (constant stress rate, constant strain rate). The most puzzling observation is that the critical power-law rate acceleration is decorated by log-periodic oscillations, suggesting a universal ratio close to 2.2. The existence of such oscillations stems from interactions between seismogenic structures (see below for the case of faults and fractures), but also offers a better constraint to identify areas within which a large event may occur. The concept of critical piezo-electricity in polycrystals Sornette, D., Lagier, M., Roux, S. and Hansen A., Critical piezoelectricity in percolation", J. Phys. France, 50, 2201–2216 (1989)Gaillard-Groleas, G., Lagier, M., and Sornette, D., Critical behaviour in piezoelectric ceramics", Phys.Rev.Lett.64, 1577 (1990)Lacour, O., Lagier, M., and Sornette, D., Effect of dynamical fluid compressibility and permeability on porous piezoelectric ceramics", J.Acoust.Soc.Am. 96 (6), 3548–3557 (1994) has been applied to the Earth's crust.Sornette, A. and Sornette, D., "Earthquake rupture as a critical point : Consequences for telluric precursors", Tectonophysics 179, 327–334 (1990)
Earthquake forecasting
Earthquake forecasting differs from prediction in the sense that no alarm is issued, but a time-dependent probability of earthquake occurrence is estimated. Sornette's group has contributed significantly to the theoretical development and study of the properties of the now standard Epidemic Type Aftershock Sequence (ETAS) model. In a nutshell, this model states that each event triggers its own direct aftershocks, which themselves trigger their own aftershocks, and so on... The consequence is that events cannot be labeled anymore as foreshocks, mainshocks or aftershocks, as they can be all of that at the same time (with different levels of probability). In this model, the probability for an event to trigger another one primarily depends on their separating space and time distances, as well as on the magnitude of the triggering event, so that seismicity is then governed by a set of seven parameters. Sornette's group is currently pushing the model to its limits by allowing space and time variations of its parameters. Despite the fact that this new model reaches better forecasting scores than any other competing model, it is not sufficient to achieve systematic reliable predictions. The main reason is that this model predicts future seismicity rates quite accurately, but fails to put constraints on the magnitudes (which are assumed to be distributed according to the Gutenberg-Richter law, and to be independent of each other). Some other seismic or non-seismic precursors are thus required in order to further improve those forecasts. According to the ETAS model, the rate of triggered activity around a given event behaves isotropically. This over-simplified assumption has recently relaxed by coupling the statistics of ETAS to genuine mechanical information. This is done by modelling the stress perturbation due to a given event on its surroundings, and correlating it with the space-time rate of subsequent activity as a function of transferred stress amplitude and sign. This suggests that triggering of aftershocks stems from a combination of dynamic (seismic waves) and elasto-static processes. Another unambiguous interesting result of this work is that the Earth crust in Southern California has quite a short memory of past stress fluctuations lasting only about 3 to 4 months. This may put more constraint on the time window within which one may look for both seismic and non-seismic precursors.
Multifractal stress activated (MSA) model of rupture and earthquakes
Ouillon and Sornette have developed a pure statistical physics model of earthquake interaction and triggering, aiming at giving more flesh to the purely empirical ETAS linear model. The basic assumption of this "Multifractal stress activated" modelOuillon, G. and D. Sornette, Magnitude-Dependent Omori Law: Empirical Study and Theory, J. Geophys. Res., 110, B04306, doi:10.1029/2004JB003311 (2005)Sornette, D. and G. Ouillon, Multifractal scaling of thermally activated rupture processes, Phys. Rev. Lett., 94, 038501, DOI: 10.1103/PhysRevLett.94.038501 (2005) is that, at any place and time, the local failure rate depends exponentially on the applied stress. The second key ingredient is to recognize that, In the Earth crust, the local stress field is the sum of the large scale, far-field stress due to plate motion, plus all stress fluctuations due to past earthquakes. As elastic stresses add up, the exponentiation thus makes this model nonlinear. Solving it analytically allowed them to predict that each event triggers some aftershocks with a rate decaying in time according to the Omori law, i.e. as 1/tp, but with a special twist that had not been recognized heretofore. The unique prediction of the MSA model is that the exponent p is not constant (close to 1) but increases linearly with the magnitude of the mainshock. Statistical analyses of various catalogs (California, Japan, Taiwan, Harvard CMT) have been carried out to test this prediction, which confirmed it using different statistical techniques (stacks to improve signal to noise ratio, specifically devised wavelets for a multiscale analysis, extreme magnitude distributions, etc.).Ouillon, G., D. Sornette, and E. Ribeiro, Multifractal Omori law for earthquake triggering: new tests on the California, Japan and worldwide catalogues", Geophys. J. Int., 178, 215–243 (2009)Tsai, C.-Y., Ouillon, G., and D. Sornette, New empirical tests of the Multifractal Omori law for Taiwan, Bull. Seismol. Soc. Am., 102, 5, DOI:10.1785/0120110237 (2011) This result thus shows that small events may trigger a smaller number of aftershocks than large ones, but that their cumulative effect may be more long-lasting in the Earth crust. A new technique has also recently introduced, called the barycentric fixed mass method, to improve considerably the estimation of multifractal structures of spatio-temporal seismicity expected from the MSA model.Kamer, Y., G. Ouillon and D. Sornette, The Barycentric Fixed Mass Method for Multifractal Analysis, Physical Review E 88, 022922 (2013)
Faulting, jointing and damage
A significant part of the activity of Sornette's group has also been devoted to the statistical physics modelling as well as properties of fractures and faults at different scales. Those features are important as they may control various transport properties of the crust as well as represent the loci of earthquake nucleation.
Statistical physics models of fractures and faults
Sornette and Sornette (1989)Sornette, A. and D. Sornette, Self-organized criticality and earthquakes", Europhys.Lett. 9 (no.3), 197–202 (1989) suggested to view earthquakes and global plate tectonics as self-organized critical phenomena. As fault networks are clearly self-organized critical systems in the sense that earthquakes occur on faults, and faults grow because of earthquakes,Sornette, A., Ph. Davy and D. Sornette, "Growth of fractal fault patterns", Phys. Rev. Lett. 65, 2266–2269 (1990)Sornette, D., Self-organized criticality in plate tectonics, in the proceedings of the NATO ASI "Spontaneous formation of space-time structures and criticality", Geilo, Norway 2–12 April 1991, edited by T. Riste and D. Sherrington, Dordrecht, Boston, Kluwer Academic Press (1991), volume 349, pp. 57–106Sornette, D. and J. Virieux, "A theory linking large time tectonics and short time deformations of the lithosphere", Nature 357, 401–403 (1992) resulting in hierarchical properties, the study of their statistics should also bring information about the seismic process itself.Sornette, D. and Ph. Davy, "Fault growth model and the universal fault length distribution", Geophys. Res. Lett. 18, 1079–1081 (1991) Davy,