Agnès Helmstetter

Seismicity rate immediately before and after main shock rupture from high-frequency waveforms in Japan

[1] We analyze seismicity rate immediately before and after 82 main shocks with the magnitudes ranging from 3 to 5 using waveforms recorded by the Hi-net borehole array in Japan. By scrutinizing high-frequency signals, we detect � 5 times as many aftershocks in the first 200 s as in the Japan Meteorological Agency catalogue. After correcting for the changing completeness level immediately after the main shock, the aftershock rate shows a crossover from a slower decay with an Omori’s law exponent p = 0.58 ± 0.08 between 20 and 900 s after the main shock to a faster decay with p = 0.92 ± 0.04 after 900 s. The foreshock seismicity rate follows an inverse Omori’s law with p = 0.73 ± 0.08 from several tens of days up to several hundred seconds before the main shock. The seismicity rate in the 200 s immediately before the main shock appears steady with p = 0.35 ± 0.50. These observations can be explained by the epidemic-type aftershock sequence (ETAS) model, and the rate-and-state model for a heterogeneous stress field on the main shock rupture plane. Alternatively, nonseismic stress changes near the source region, such as episodic aseismic slip, or pore fluid pressure fluctuations, may be invoked to explain the observation of small p values immediately before and after the main shock.

Afterslip and aftershocks in the rate‐and‐state friction law

Istituto Nazionale di Geofisica e Vulcanologia, Italy (INGV); nCentre National de la Recherche Scientifique (CNRS); nExxonMobil Upstream Research Company

Relation between stress heterogeneity and aftershock rate in the rate-and-state model

[1]xa0We estimate the rate of aftershocks triggered by a heterogeneous stress change, using the rate-and-state model of Dieterich. We show that an exponential stress distribution Pτ(τ) ∼ exp(−τ/τ0) gives an Omori law decay of aftershocks with time ∼1/tp, with an exponent p = 1 − Aσn/τ0, where A is a parameter of the rate-and-state friction law and σn is the normal stress. Omori exponent p thus decreases if the stress “heterogeneity” τ0 decreases. We also invert the stress distribution Pτ(τ) from the seismicity rate R(t), assuming that the stress does not change with time. We apply this method to a synthetic stress map, using the (modified) scale invariant “k2” slip model (Herrero and Bernard). We generate synthetic aftershock catalogs from this stress change. The seismicity rate on the rupture area shows a huge increase at short times, even if the stress decreases on average. Aftershocks are clustered in the regions of low slip, but the spatial distribution is more diffuse than for a simple slip dislocation. Because the stress field is very heterogeneous, there are many patches of positive stress changes everywhere on the fault. This stochastic slip model gives a Gaussian stress distribution but nevertheless produces an aftershock rate which is very close to Omoris law, with an effective p ≤ 1, which increases slowly with time. We obtain a good estimation of the stress distribution for realistic catalogs when we constrain the shape of the distribution. However, there are probably other factors which also affect the temporal decay of aftershocks with time. In particular, heterogeneity of Aσn can also modify the parameters p and c of Omoris law. Finally, we show that stress shadows are very difficult to observe in a heterogeneous stress context.

Brittle creep, damage, and time to failure in rocks

We propose a numerical model based on static fatigue laws in order to model the time-dependent damage and deformation of rocks under creep. An empirical relation between time to failure and applied stress is used to simulate the behavior of each element of our finite element model. We review available data on creep experiments in order to study how the material properties and the loading conditions control the failure time. The main parameter that controls the failure time is the applied stress. Two commonly used models, an exponential tfexp (bs/s0) and a power law function tfsb0 fit the data as well. These time-to-failure laws are used at the scale of each element to simulate its damage as a function of its stress history. An element is damaged by decreasing its Youngs modulus to simulate the effect of increasing crack density at smaller scales. Elastic interactions between elements and heterogeneity of the mechanical properties lead to the emergence of a complex macroscopic behavior, which is richer than the elementary one. In particular, we observe primary and tertiary creep regimes associated respectively with a power law decay and increase of the rate of strain, damage event and energy release. Our model produces a power law distribution of damage event sizes, with an average size that increases with time as a power law until macroscopic failure. Damage localization emerges at the transition between primary and tertiary creep, when damage rate starts accelerating. The final state of the simulation shows highly damaged bands, similar to shear bands observed in laboratory experiments. The thickness and the orientation of these bands depend on the applied stress. This model thus reproduces many properties of rock creep, which were previously not modeled simultaneously.

Location of Seismic Signals Associated with Microearthquakes and Rockfalls on the Séchilienne Landslide, French Alps

Abstract The Sechilienne rockslide, in the French Alps, has recently been instrumented with three seismic arrays. This network has recorded numerous rockfalls and local microearthquakes. Because the media is highly fractured, it is difficult to identify and pick first arrivals. Beam-forming methods were therefore used to locate these events. The method has been adapted to take into account the heterogeneity of seismic wave velocities. The location accuracy has been estimated to be about 50xa0m for epicenters by applying the method to calibration shots. Depth is less constrained due to uncertainties on the velocity model and due to the seismic network geometry. This method of location has then been applied to rockfalls and microearthquakes. Most rockfalls initiate in the most active part of the rockslide called Les Ruines; the others are located on a recent eroded area aside from Les Ruines. The network also allows the estimation of the rockfall trajectory and propagation speed. Finally, 55 microearthquakes have been located within two zones. Microearthquakes are located within the first 250xa0m below the surface. Most microearthquakes are located in Les Ruines, the most active part of the rockslide, where the velocity has increased from 0.5 m/yr in 1996 to 1.4 m/yr in 2008. These events are located close to three faults that delimit a mass of about 3.6 million m 3 . Other events are located close to the summital scarp, in a zone moving at a few centimeters per year. The western part of the rockslide, which moves more slowly, did not produce any event large enough to be detected simultaneously by all stations. This seismic monitoring suggests that only a very small fraction of the deformation is released through seismic events.

Monitoring of snow avalanches using a seismic array: Location, speed estimation, and relationships to meteorological variables

[1]xa0Monitoring snow avalanches is necessary in order to better understand their triggering mechanisms and ultimately improve forecast performance. Seismic monitoring has been developed by several groups over the last 20 years and holds great potential to detect, locate, and characterize snow avalanches. During the 2009–2010 winter, a seismic antenna was installed in the French Alps close to the village of Saint-Christophe-en-Oisans (1700 m above sea level). The array of seven sensors operated during 50 days in October and November 2009 under snow-free conditions and during 40 days in January and February 2010 in presence of snow. It recorded different types of seismic events including snow avalanches, rockfalls, shots, and regional and local microearthquakes. Eighty avalanche signals were visually identified. Using a beam-forming method, we were able to locate snow avalanches on slopes of various orientations in a radius of about 3 km and track their propagation. The location technique allowed for the estimation of avalanches front speed, which ranged between 12 and 32 m s−1. The method can also distinguish dry and wet snow avalanches. Durations of avalanches can be as long as 380 s because of the length of the slopes in the area. Seismic monitoring provides a catalog of avalanches with precise times, which can be used to analyze the impact of meteorological forcings on the avalanche triggering. Snowfall is found to be the dominant forcing of avalanche activity during this period, as revealed by the strongest correlation. For the period of study, our results suggest that the impact of precipitation on the snowpack instability lasts for about 6 days.

Characterization and comparison of landslide triggering in different tectonic and climatic settings

[1]xa0The spatial and temporal distributions of landslides in six catalogues are analyzed in order to better understand landslide triggering mechanisms. The six landslide catalogs are New Zealand, Yosemite (California), Grenoble (French Alps), Val dArly (French Alps), Australia, and Wollongong (New South Wales, Australia). Landslides are clustered in time for all catalogs. For New Zealand, Yosemite, Australia, and Wollongong, the frequency of landslides varies between 1 and 1000 events per day and is well fitted by a power law: there is no characteristic scale for daily rates. When the large rates of daily landslides are known to be rain or earthquake triggered, our results suggest the same triggering may hold for the small daily rates. Earthquakes are found to trigger landslides for the New Zealand, Yosemite, and Australia areas at distances as large as 20 times their fault lengths. There is no evidence of landslides triggered by earthquakes for the three other catalogs. Small M ≤ 4 earthquakes have little influence on landslide triggering, if any, for all catalogs. For New Zealand, Yosemite, Val dArly, Australia, and Wollongong, the number of landslides per month is significantly correlated with monthly rainfall. A correlation with temperature is found only for Grenoble and New Zealand. Landslide triggering (strong clustering in time and space) is more important in New Zealand than in Grenoble, probably because the forcing (seismicity and climate) is stronger in New Zealand than in the French Alps but possibly also because of a high sensitivity to landslides in New Zealand. We suggest that intensity of clustering in space and time can be used to assess the importance of landslide triggering and the processes responsible for triggering.

Basal icequakes recorded beneath an Alpine glacier (Glacier d'Argentière, Mont Blanc, France): Evidence for stick‐slip motion?

While basal icequakes associated with glacier motion have been detected under Antarctica for several decades, there remains very little evidence of stick-slip motion for Alpine glaciers. Here we analyzed 2357 basal icequakes that were recorded at Glacier d’Argenti`ere (Mont-Blanc Massif) between February and November of 2012, and that are likely to be associated with basal sliding. These events have been classified into 18 multiplets, based on their waveforms. The strong similarity of the waveforms within each multiplet suggests an isolated repeating source. Despite this similarity, the peak amplitude within each multiplet varies gradually in time, by up to a factor of 18. The distribution of these events in time is relatively complex. For long time scales we observe progressive variations in the amplitudes of events within each multiplet. For intermediate time scales (hours), the events occur regularly in time, with typical return times of several minutes up to several hours. For short time scales (from 0.01 to 100 s), the largest multiplet shows clus- tering in time, with a power-law distribution of the interevent times. The location of these events and their focal mechanisms are not well constrained, because most of these events were detected by a single seismometer. Nevertheless, the locations can be estimated with an accuracy of a few tens of meters using a polarization analysis. The estimated average depth of the basal events is 179 m, which is in good agreement with the estimated glacier thickness. The relative changes in distance between the source and the sensor can be measured accurately by correlating separately the P-wave and S-wave parts of the seismograms of each event with the template waveforms, which are obtained by averaging the signals within each multiplet. We observed small variations in the times between the P-wave and the S-wave of up to 0.6 ms over 50 days. These variations cannot be explained by displacement of the sensor with respect to the glacier, but might be due to small changes in the seismic wave velocities with time. Finally, we found using numerical simulations that the observed signals are better explained by a horizontal shear fault with slip parallel to the glacier flow, than by a tensile fault. These results suggest that the basal events are associated with stick-slip motion of the glacier over rough bedrock. The rupture length and the slip are difficult to estimate. Nonetheless, the rupture length is likely to be of the order of meters, and the total seismic slip accumulated over one day might be as large as the glacier motion during the most active bursts.

Adaptively smoothed seismicity earthquake forecasts for Italy

We present a model for estimation of the probabilities of future earthquakes of magnitudes m ≥ 4.95 in Italy. This model is a modified version of that proposed for California, USA, by Helmstetter et al. [2007] and Werner et al. [2010a], and it approximates seismicity using a spatially heterogeneous, temporally homogeneous Poisson point process. The temporal, spatial and magnitude dimensions are entirely decoupled. Magnitudes are independently and identically distributed according to a tapered Gutenberg-Richter magnitude distribution. We have estimated the spatial distribution of future seismicity by smoothing the locations of past earthquakes listed in two Italian catalogs: a short instrumental catalog, and a longer instrumental and historic catalog. The bandwidth of the adaptive spatial kernel is estimated by optimizing the predictive power of the kernel estimate of the spatial earthquake density in retrospective forecasts. When available and reliable, we used small earthquakes of m ≥ 2.95 to reveal active fault structures and 29 probable future epicenters. By calibrating the model with these two catalogs of different durations to create two forecasts, we intend to quantify the loss (or gain) of predictability incurred when only a short, but recent, data record is available. Both forecasts were scaled to five and ten years, and have been submitted to the Italian prospective forecasting experiment of the global Collaboratory for the Study of Earthquake Predictability (CSEP). An earlier forecast from the model was submitted by Helmstetter et al. [2007] to the Regional Earthquake Likelihood Model (RELM) experiment in California, and with more than half of the five-year experimental period over, the forecast has performed better than the others.

Adaptive Spatiotemporal Smoothing of Seismicity for Long‐Term Earthquake Forecasts in California

We present new methods for time‐independent earthquake forecasting that employ space–time kernels to smooth seismicity. The major advantage of the methods is that they do not require prior declustering of the catalog, circumventing the relatively subjective choice of a declustering algorithm. Past earthquakes are smoothed in space and time using adaptive Gaussian kernels. The bandwidths in space and time associated with each event are a decreasing function of the seismicity rate at the time and location of each earthquake. This yields a better resolution in space–time volumes of intense seismicity and a smoother density in volumes of sparse seismicity. The long‐term rate in each spatial cell is then defined as the median value of the temporal history of the smoothed seismicity rate in this cell. To calibrate the model, the earthquake catalog is divided into two parts: the early part (the learning catalog) is used to estimate the model, and the latter one (the target catalog) is used to compute the likelihood of the model’s forecast. We optimize the model’s parameters by maximizing the likelihood of the target catalog. To estimate the kernel bandwidths in space and time, we compared two approaches: a coupled near‐neighbor method and an iterative method based on a pilot density. We applied these methods to Californian seismicity and compared the resulting forecasts with our previous method based on spatially smoothing a declustered catalog (Werner etxa0al. , 2011). All models use small M ≥2 earthquakes to forecast the rate of larger earthquakes and use the same learning catalog. Our new preferred model slightly outperforms our previous forecast, providing a probability gain per earthquake of about 5 relative to a spatially uniform forecast.