David Marsan

Multifractal Cascade Dynamics and Turbulent Intermittency

Turbulent intermittency plays a fundamental role in fields ranging from combustion physics and chemical engineering to meteorology. There is a rather general agreement that multifractals are being very successful at quantifying this intermittency. However, we argue that cascade processes are the appropriate and necessary physical models to achieve dynamical modeling of turbulent intermittency. We first review some recent developments and point out new directions which overcome either completely or partially the limitations of current cascade models which are static, discrete in scale, acausal, purely phenomenological and lacking in universal features. We review the debate about universality classes for multifractal processes. Using both turbulent velocity and temperature data, we show that the latter are very well fitted by the (strong) universality, and that the recent (weak, log-Poisson) alternative is untenable for both strong and weak events. Using a continuous, space-time anisotropic framework, we th...

Positive trend in the mean speed and deformation rate of Arctic sea ice, 1979–2007

Using buoy data from the International Arctic Buoy Program, we found that the sea ice mean speed has substantially increased over the last 29 years (+17% per decade for winter and +8.5% for summer). A strong seasonal dependence of the mean speed is also revealed, with a maximum in October and a minimum in April. The sea ice mean strain rate also increased significantly over the period (+51% per decade for winter and +52% for summer). We check that these increases in both sea ice mean speed and deformation rate are unlikely to be consequences of a stronger atmospheric forcing. Instead, they suggest that sea ice kinematics play a fundamental role in the albedo feedback loop and sea ice decline: increasing deformation means stronger fracturing, hence more lead opening, and therefore a decreasing albedo. This accelerates sea ice thinning in summer and delays refreezing in early winter, therefore decreasing the mechanical strength of the cover and allowing even more fracturing, larger drifting speed and deformation, and possibly a faster export of sea ice through the Fram Strait. The September minimum sea ice extent of 2007 might be a good illustration of this interplay between sea ice deformation and sea ice shrinking, as we found that for both winter 2007 and summer 2007 exceptionally large deformation rates affected the Arctic sea ice cover.

Extending Earthquakes' Reach Through Cascading

Earthquakes, whatever their size, can trigger other earthquakes. Mainshocks cause aftershocks to occur, which in turn activate their own local aftershock sequences, resulting in a cascade of triggering that extends the reach of the initial mainshock. A long-lasting difficulty is to determine which earthquakes are connected, either directly or indirectly. Here we show that this causal structure can be found probabilistically, with no a priori model nor parameterization. Large regional earthquakes are found to have a short direct influence in comparison to the overall aftershock sequence duration. Relative to these large mainshocks, small earthquakes collectively have a greater effect on triggering. Hence, cascade triggering is a key component in earthquake interactions.

Causal space‐time multifractal processes: Predictability and forecasting of rain fields

Building on earlier cascade models of rainfall, we propose a model of space-time rain fields based on scaling dynamics. These dynamics are indeed related to the space-time symmetries of the turbulent medium within which rainfall occurs : the underlying phenomenology corresponds to a cascade of structures with lifetimes depending only on the scale of the structures. In this paper we clarify two major issues : the scaling anisotropy between space and time, and the need to respect causality, i.e., a fundamental asymmetry between past and future. We detail how this arrow of time breaks the mirror symmetry with respect to the spatial hyperplane, and how it can be introduced in continuous multiplicative cascade models so as to remove the artificial temporal mirror symmetry of earlier models. We show that such a causal multifractal field can be understood as the result of an anomalous diffusion acting on the singularities of the field. Finally we will exploit and test these models through (1) a succinct analysis of rainfall data, (2) numerical simulations of the temporal decorrelation of two initially similar fields (accounting for the loss of predictability of the process), and (3) a forecasting method for multifractal rain fields.

A new estimation of the decay of aftershock density with distance to the mainshock

[1] We investigate how aftershocks are spatially distributed relative to the mainshock. Compared to previous studies, ours focuses on earthquakes causally related to the mainshock rather than on aftershocks of previous aftershocks. We show that this distinction can be made objectively but becomes uncertain at long time scales and large distances. Analyzing a regional earthquake data set, it is found that, at time t following a mainshock of magnitude m, the probability of finding an aftershock at distance r relative to the mainshock fault decays as r −g , where g is typically between 1.7 and 2.1 for 3 ≤ m <6 and is independent of m, for r less than 10 to 20 km and t less than 1 day. Uncertainties on this probability at larger r and t do not allow for a correct estimation of this spatial decay. We further show that a static stress model coupled with a rate‐and‐state friction model predicts a similar decay, with an exponent g = 2.2, in the same space and time intervals. This suggests that static stress changes could explain the repartition of aftershocks around the mainshock even at distances larger than 10 times the rupture length. Citation: Marsan, D., and O. Lengline (2010), A new estimation of the decay of aftershock density with distance to the mainshock, J. Geophys. Res., 115, B09302, doi:10.1029/2009JB007119.

Multiscaling nature of sonic velocities and lithology in the upper crystalline crust: evidence from the KTB Main Borehole

The observed scaling of sonic logs is generally described using a monofractal model (fractional Brownian motion with Hurst exponent typically between 0.1 and 0.2, or fractional Levy motion); even though such a description recognizes the existence of the self-similarity of the logs, it offers only a limited account of the actual symmetry, as it misses the displayed heterogeneous fractality. Intermittency of the velocity increments is here observed, and calls for the use of a multifractal description. We quantify such a multifractality in the case of the P-wave sonic log recorded at the KTB Main Borehole. We also show that the associated lithology, inferred from the gamma log, has a multifractal distribution as well, though characterized by a stronger intermittency. It can be expected that the multifractality of the sonic log is partially induced by the lithology, though the observed discrepancy in the degree of intermittency between the two logs indicates that the scaling symmetry of the seismic velocity is probably due to many different contributions. Such statistics for both sonic and gamma logs have important implications on our understanding of wave propagation and rock strength and permeability in the crystalline crust, as they show the crust to be more heterogeneous than is usually modeled.

Seismicity and deformation induced by magma accumulation at three basaltic volcanoes

We analyzed the evolution of volcano-tectonic (VT) seismicity and deformation at three basaltic volcanoes (Kilauea, Mauna Loa, Piton de la Fournaise) during phases of magma accumulation. We observed that the VT earthquake activity displays an accelerating evolution at the three studied volcanoes during the time of magma accumulation. At the same times, deformation rates recorded at the summit of Kilauea and Mauna Loa volcanoes were not accelerating but rather tend to decay. To interpret these observations, we propose a physical model describing the evolution of pressure produced by the accumulation of magma into a reservoir. This variation of pressure is then used to force a simple model of damage, where damage episodes are equivalent to earthquakes. This model leads to an exponential increase of the VT activity and to an exponential decay of the deformation rate during accumulation phases. Seismicity and deformation data are well fitted by such an exponential model. The time constant, deduced from the exponential increase of the seismicity, is in agreement with the time constant predicted by the model of magma accumulation. This VT activity can thus be a direct indication of the accumulation of magma at depth, and therefore can be seen as a long-term precursory phenomenon, at least for the three studied basaltic volcanoes. Unfortunately, it does not allow the prediction of the onset of future eruptions, as no diverging point (i.e., critical time) is present in the model.

Observation of diffusion processes in earthquake populations and implications for the predictability of seismicity systems

Scale invariance, either in space or in time, has been shown in many papers to characterize earthquake distributions. Unfortunately, little work has been dedicated to looking at the general space-time scaling invariance of seismicity systems, even though a better understanding of how the two domains (spatial and temporal) link together could help the development of the stochastic dynamical modeling of earthquake populations. In this paper we report the observation of diffusion processes of temporally correlated seismic activity for three different data sets: a mine (Creighton Mine, Canada), the Long Valley Caldera in eastern California, and a 7-year period of recorded seismic activity in southern California. The observed subdiffusion processes are indicative of the general space-time scaling of the system, taking the form of a slow power law growth R(t) similar to t(H) of the mean distance R(t) between the main event arid the temporally correlated afterevents occuring after a delay t. H is found on average to be small (0.1 for Creighton Mine, 0.22 for the Long Valley Caldera, and 0.22 for the southern California main events with magnitude greater than or equal to 1.5) but fluctuates significantly from one main event to the other: the diffusion is found to be intermittent (non-Gaussian) and multiscaling, and except for the Long Valley Caldera, a systematic correlation between the sizes of the main event and subsequent afterevents and the growth exponent H is observed. While classical viscous relaxation models (e.g., elastic listhosphere-plastic asthenosphere coupling, or fluid flow triggered by sudden changes in pore pressure) have been proposed to characterize this relaxation by homogeneous (i.e., nonintermittent) normal (H = 0.5) diffusion processes, the direct implication of the reported results is that seismicity systems, at spatial scales from meters to hundreds of kilometers and small (microearthquakes in a mine) to intermediate magnitudes, relax spatiotemporally in a nonelastic way, revealing the stochastic space-time scale-invariant nature of such systems. Since these diffusion processes correspond to a loss of information with time on the location of the main event, they can be used to investigate the limits of predictability, at all spatial scales, of seismicity systems in terms of the spatiotemporal clustering of temporally correlated earthquakes.

Impact of Aseismic Transients on the Estimation of Aftershock Productivity Parameters

Abstract The epidemic‐type aftershock sequence (ETAS) model has been shown to describe successfully the statistical seismicity properties, if earthquake triggering is related to tectonic forcing and earthquake‐induced stress changes. However, seismicity is locally often dominated by stress changes related to transient aseismic processes. To avoid erroneous parameter estimations leading to biased forecasts, it is important to account for those transients. We apply a recently developed iterative algorithm based on the ETAS model to identify the time‐dependent background and ETAS parameters simultaneously. We find that this procedure works well for synthetic data sets if catalog errors are appropriately considered. However, ignoring the time dependence leads to significantly biased parameter estimations. In particular, the α ‐value describing the magnitude dependence of the triggering kernel can be strongly underestimated if transients are ignored. Low α ‐values have been previously found for swarm activity, for which transient aseismic processes are expected to play a major role. These observed anomalously low α ‐values might thus indicate the importance of transient forcing, rather than being due to differences in the earthquake–earthquake trigger mechanism. To explore this, we apply the procedure systematically to earthquake clusters detected in southern California and to earthquake swarm activity in Vogtland/Western Bohemia. While low α ‐values are mostly shown to be a consequence of catalog errors and time‐dependent forcing but not related to different earthquake–earthquake interaction mechanisms, some significant low values are observed in high heat‐flow areas in California, confirming the existence of thermal control on earthquake triggering.

Monitoring Aseismic Forcing in Fault Zones Using Earthquake Time Series

The dynamics of earthquake occurrences is controlled both by fault in- teraction processes and by long-term, tectonic loading of the faults. In addition, tran- sient loading can be caused by aseismic deformation episodes, for example during crustal fluid migration or slow slip events. These forcing transients are best revealed by geodetic measurements. However, this type of instrumentation is not always avail- able, or is not always sensitive enough to detect significant anomalies. In such cases, one is better off exploiting the seismicity signature of these transients in order to char- acterize them. We here explore different ways to do so. Interearthquake time statistics are found to be prone to damping out fluctuations in forcing rate. A more accurate method is developed by comparing the data with a triggering model that accounts for earthquake interactions. The changes in fault loading rates are then well recovered, both in duration and in intensity.