Jean-Robert Grasso

Poroelastic stressing and induced seismicity near the Lacq gas field, southwestern France

o Hundreds of shallow, small to moderate earthquakes have occurred near the Lacq deep gas field in southwestern France since 1969. These earthquakes are clearly separated from tectonic seismicity occurring in the Pyrenees, 25 km to the southwest. The induced seismicity began when the reservoir pressure had declined by • 30 MPa. Repeated levehng over the field shows localized subsidence reaching a maximum of 60 mm in 1989. Segall (1989) suggested that poroelastic stressing, associated with volumetric contraction of the reservoir rocks, is responsible for induced seismicity associated with fluid extraction. To test this model, we compare the observed subsidence and hypocentral distributions with the predicted displacement and stress fields. We find that the relationship between average reservoir pressure drop and subsidence is remarkably linear, lending support to the linear poroelastic model. Displacements and stresses are computed based on a priori knowledge of the reservoir geometry, materiM properties, and reservoir pressure changes. The computed vertical displacements are found to be in excellent agreement with the subsidence observed from leveling. Stress perturbations accompanying gas extraction, computed using the same parameters, are found to be • 0.2 MPa or less. Changes in Coulomb failure stress are computed assuming that shp occurs on optimally oriented planes. The predicted failure zones correlate very well with the spatial distribution of earthquakes if the perturbing stresses are small in comparison to the ambient regional deviatoric stresses and if the minimum regional compresslye stress axis is vertical. Accurate determination of focal mechanisms of the induced events would allow a more rigorous test of the poroelastic model and could lead to important inferences about the crustal stress state.

Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws

[1]xa0The inverse Omori law for foreshocks discovered in the 1970s states that the rate of earthquakes prior to a mainshock increases on average as a power law ∝ 1/(tc − t)p′ of the time to the mainshock occurring at tc. Here, we show that this law results from the direct Omori law for aftershocks describing the power law decay ∼ 1/(t − tc)p of seismicity after an earthquake, provided that any earthquake can trigger its suit of aftershocks. In this picture, the seismic activity at any time is the sum of the spontaneous tectonic loading and of the activity triggered by all preceding events weighted by their corresponding Omori law. The inverse Omori law then emerges as the expected (in a statistical sense) trajectory of seismicity, conditioned on the fact that it leads to the burst of seismic activity accompanying the mainshock. In particular, we predict and verify by numerical simulations on the epidemic-type aftershock sequence (ETAS) model that p′ is always smaller than or equal to p and a function of p, of the b-value of the Gutenberg–Richter law (GR), and of a parameter quantifying the number of direct aftershocks as a function of the magnitude of the mainshock. The often documented apparent decrease of the b-value of the GR law at the approach to the mainshock results straightforwardly from the conditioning of the path of seismic activity culminating at the mainshock. However, we predict that the GR law is not modified simply by a change of b-value but that a more accurate statement is that the GR law gets an additive (or deviatoric) power law contribution with exponent smaller than b and with an amplitude growing as a power law of the time to the mainshock. In the space domain, we predict that the phenomenon of aftershock diffusion must have its mirror process reflected into an inward migration of foreshocks toward the mainshock. In this model, foreshock sequences are special aftershock sequences, which are modified by the condition to end up in a burst of seismicity associated with the mainshock. Foreshocks are not just statistical creatures but are genuine forerunners of large shocks as shown by the large prediction gains obtained using several of their qualifiers.

From diffuse to localised damage through elastic interaction

Local damage processes that have been reported for ductile and brittle macroscopic behaviours are shown here to provide a possible link between these two contrasting behaviours. Using a local progressive damage law within a linear tensorial elastic interaction model, we reproduce experimentally observed macroscopic non-linear behaviours that continuously range from ductility with diffuse damage to brittleness with localised damage. The model exhibits power law distributions of damage events in space and size domains. The diffuse-localised and induced ductile-brittle transition appear to be controlled by the internal friction angle which influences the local interaction geometry.

Testing self‐organized criticality by induced seismicity

We examine the hypothesis proposed in recent years by several authors that the crust is in a self-organized critical (SOC) state. This hypothesis has been suggested on the basis of the observation of power law distributions, such as the Gutenberg-Richter law for earthquakes and the fault length distribution, and of the fractal geometry of sets of earthquake epicenters and of fault patterns. These self-similar properties are shared by simplified models of the crust exhibiting a spontaneous organization toward a critical point characterized by similar scale-invariant properties. The term “critical” is here used in the sense of phase transitions such as the Curie point in magnetism. The usefulness of a hypothesis is measured by its predictive and explanatory power outside the range of observations that have helped defined it. We thus explore how the SOC concept can help in understanding the observed earthquake clustering on relatively narrow fault domains and the phenomenon of induced seismicity. We review the major reported cases of induced seismicity in various parts of the world and find that both pore pressure changes (±Δp) and mass transfers (±Δm) leading to incremental deviatoric stresses of <1 MPa are sufficient to trigger seismic instabilities in the uppermost crust with magnitude ranging up to 7.0 in otherwise historically aseismic areas. Once triggered, stress variations of at least 1 order of magnitude less but still larger than the ∼0.01 MPa tidal stress are enough to sustain seismic activity. We argue that these observations are in accord with the SOC hypothesis as they show that a significant fraction of the crust is not far from instability and can thus be made unstable by minute perturbations. This property is shared by simplified models of SOC. Not all perturbations, however, trigger seismic activity; this is also compatible with the SOC hypothesis which embodies naturally the existence of large heterogeneities in the stress field. The induced seismicity is found to obey generally the Gutenberg-Richter law up to a magnitude cutoff which correlates well with the width of the local seismogenic bed, ranging in size from that of mine pillars for mining-induced seismicity to the thickness of brittle sedimentary beds in the vicinity of dams or depleted hydrocarbon reservoirs. In conclusion, the properties of induced seismicity and their rationalization in terms of the SOC concept provide further evidence that potential seismic hazards extend over a much larger area than that where earthquakes are frequent.

A constant influx model for dike propagation: Implications for magma reservoir dynamics

[1]xa0Most observations of seismicity rate during dike propagation on basaltic volcanoes show (1) rate stationarity despite possible variations of the dike tip velocity, (2) frequent lack of clear and monotonic hypocenter migration following dike propagation, and (3) event occurrences located backward with respect to the dike tip position. On these bases, the origin of the seismicity contemporary to dike intrusion within basaltic volcanoes cannot be solely related to the crack tip propagation. Seismicity rather appears to be the response of the edifice itself to the volumetric deformation induced by the magma intruding the solid matrix. The volume change induced into the volcano edifice over time by the intruding magma is equal to the magma flux injected into the dike from the reservoir. The consequence of this is that the stationary seismicity rate observed during the intrusion is a proxy for the magma flux withdrawn from the reservoir. We consider a two-phase dike propagation model, including a first vertical propagation followed by a lateral migration along a lithological discontinuity. We explore (1) under which geophysical conditions the vertical dike is fed at constant flow rate of magma and (2) dike propagation patterns. Implications entailed by constant volumetric flux on the Piton de la Fournaise volcano case study suggest a minimum size for the magma reservoir of about 1 km3 and a maximum value for the initial magma reservoir overpressure of about 2.2 MPa. Considering similar magma inflow rates during vertical and lateral dike propagation phases, we reproduce independent estimates of propagation velocities, rise times, and injected volumes when applying the model to the August 2003 Piton de la Fournaise eruption.

Interactions between earthquakes and volcano activity

[1]xa0Using the 1973–2005 worldwide catalogues for M ≥ 4.8 seismicity and VEI ≥ 0 volcano eruptions, we find a significant, when tested against catalogue randomizations, increase of eruption onsets on the earthquake day. This result emerges from stacking time series of daily eruption rates relatively to earthquake time, t0, over the whole seismicity catalogue. It is stronger for earthquake-volcano pairs for which the volcano is within ten rupture size from the epicenter. These results show that M ≥ 4.8 − VEI ≥ 0 earthquake-volcano pairs are as important for interaction processes as the M ≥ 7 and VEI ≥ 2–5 pairs previously reported to interact. The clustering in time for earthquake-eruption pairs is not bounded to t0. It remains above the background noise 6–10 days before and after t0, and follows a power law distribution. These patterns, which are similar to the direct and inverse Omoris laws observed for tectonic earthquakes, are the first evidence for the volcano eruptions to be contemporary of a stochastic brittle damage in the earth crust. The clustering we observe in time and space (i) rejects the earthquake triggering as the single process that drive earthquake-volcano interactions; (ii) supports a regional tectonic coupling in the earth crust damage.

Long term friction: From stick‐slip to stable sliding

[1]xa0We have devised an original laboratory experiment where we investigate the frictional behaviour of a single crystal salt slider over a large number of deformation cycles. Because of its physical properties, salt, an analogue for natural faults, allows for frictional processes plastic deformation and pressure solution creep to operate on the same timescale. During the same experiment, we observe a continuous change of the frictional behaviour of the slider under constant conditions of stiffness, temperature and loading velocity. The stick-slip regime is progressively vanishing, eventually reaching the stable sliding regime. Concomitantly, the contact interface, observed under the microscope, develops a striated morphology with contact asperities increase in length and width, arguing for an increase in the critical slip distance dc. Complementary experiments including velocity jumps show that the frictional parameters of the rate and state friction law, a and b, progressively vanish with accumulated slip. The ultimate stage of friction is therefore rate and state independent under our experimental conditions.

The 2004 Mw 4.4 Rotenburg, Northern Germany, Earthquake and Its Possible Relationship with Gas Recovery

We study the 20 October 2004 M w 4.4 Rotenburg (Wumme)/Neuenkirchen earthquake, located in a previously aseismic region in the northern German sedimentary basin. We constrain the source parameter by using different techniques. A possible relationship between this event, the regional tectonic setting, and local gas recovery is investigated. Different waveform inversion and modeling approaches constrain the depth of the mainshock between 5 and 7 km. The source mechanism was oblique normal faulting on planes striking roughly north–south. An inversion for kinematic rupture parameters indicates a unilateral rupture propagation toward the north, consistent with the higher macroseismic intensities found toward the north in the region of Hamburg compared with those at a similar distance toward the south in the region of Hannover. Relocations of the mainshock and three of the largest aftershocks indicate that these events occurred within a few kilometers of three major gas fields and at depth close to gas production intervals. Comparison with seismicity triggered in the northern Netherlands by depletion of similar gas reservoirs in a similar tectonic environment suggests that the M w 4.4 Rotenburg event may be related to gas recovery. Online material: Focal mechanism and waveform fit.

The finite extension of fractal geometry and power law distribution of shallow earthquakes : a geomechanical effect

We study a dome structure (10×10×10 km3) at an intermediate scale between laboratory analyses and tectonic processes. Local gas extraction induced about 1000 events within the dome (1.0 ≤ M1 ≤ 4.2) recorded by a local network during 19 years (1974–1992). Two types of autosimilarity coefficients (b value and correlation dimension) are analyzed in three-dimensional (3-D) space. The hypocenter distribution shows a fractal pattern characterized by the noninteger value of the correlation dimension. Moreover the frequency-magnitude relation of the events obeys a power law. The existence of these two parameters shows that the spatial distribution of the earthquakes induced by the Lacq gas extraction is governed by a nonrandom behavior. We observe no temporal correlation between the temporal behavior of the b value (slope of frequency-magnitude relation) and D (correlation dimension). Three-dimensional fractal analysis of induced earthquakes allows us to define two distinct classes of events separated by a critical distance of 500 m. The first class (r > 500 m) shows a diffuse seismicity. This diffuse class of earthquakes (M1 500 m, D2 ≈ 1.3). The difference of one unit between the fractal dimension of the seismicity within the nests (D1) and the fractal dimension of the nests distribution (D2) suggests an influence of the geological dome structure on the spatial development of seismic nests. Moreover, a slope break above M1 = 3.0 (G-R relation) is observed on this second class (1.0 ≤ M1 ≤ 4.2). The slope break of both the b value and the fractal dimension at a common threshold (M1 ≈ 3.0 is equivalent to a 500-m fracture size) suggests a critical distance for the brittle behavior of the uppermost crust as proposed for tectonic earthquakes by Scholz (1991). Such a critical distance correlates in our study with the maximum thickness of local seismogenic layers (brittle calcareous layer versus ductile marly layer). On this basis we propose that (1) the finite extension of the earthquake power law is driven by the local setting and therefore is also a scale dependent process, (2) the geomechanical link between fractal behavior and fracture size, i.e., a physical mapping of the power law behavior, must also be found in the boundary values of the autosimilarity processes (slope breaks) rather than in the values of the power law exponents.

Recent deformation in the Turan and South Kazakh platforms, western central Asia, and its relation to Arabia-Asia and India-Asia collisions

In this study, we investigate the recent and active tectonics of the Turan and South Kazakh platforms in western central Asia. This area, which has been considered stable during the Tertiary, was struck in its eastern part (Gazli and Kyzyl-Kum) by three earthquakes of magnitude Ms ∼7.0 between 1976 and 1984. From structural observations we show that in the Kyzyl-Kum, Cenozoic deformation on structures oriented NW–SE is dominated by dextral strike-slip motion on a flower structure involving reactivated Late Paleozoic faults. This deformation is compatible with the stress pattern induced by the Pamir/Tien Shan collision zone. At the scale of the Turan-South Kazakh platform, comparison of repeated leveling measurements gives mean uplift rates of 5 mm yr−1 for most of the area south of the 44° latitude including the Kyzyl-Kum. These observations indicate that the Turan-South Kazakh platform has been actively deforming since recent times (Pleistocene) in response to the collision of both India and Arabia with Asia. Earthquake data also reveal that propagation of deformation from the Kopet Dagh and the Pamir/Tien Shan collision zones into the Turan-South Kazakh platform is accommodated aseismically except in the Kyzyl-Kum. This might reflect differences in the deformation style and nature of the upper crust in the Kyzyl-Kum and north of the Kopet Dagh respectively. We propose that the Gazli earthquakes highlight the northwestward continuation, within the Turan-South Kazakh platform and along reactivated older structures, of the deformation related to the Pamir indentation and to a lesser degree to the Arabia-Asia convergence.