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Rupture directivity, implying a predominant earthquake rupture propagation direction, is typically inferred upon the identification of 2D azimuthal patterns of seismic observations for weak to large earthquakes using surface-monitoring networks. However, the recent increase of 3D monitoring networks deployed in the shallow subsurface and underground laboratories toward the monitoring of microseismicity allows to extend the directivity analysis to 3D modeling, beyond the usual range of magnitudes. The high-quality full waveforms recorded for the largest, decimeter-scale acoustic emission (AE) events during a meter-scale hydraulic fracturing experiment in granites at similar to 410 m depth allow us to resolve the apparent durations observed at each AE sensor to analyze 3D-directivity effects. Unilateral and (asymmetric) bilateral ruptures are then characterized by the introduction of a parameter kappa, representing the angle between the directivity vector and the station vector. While the cloud of AE activity indicates the planes of the hydrofractures, the resolved directivity vectors show off-plane orientations, indicating that rupture planes of microfractures on a scale of centimeters have different geometries. Our results reveal a general alignment of the rupture directivity with the orientation of the minimum horizontal stress, implying that not only the slip direction but also the fracture growth produced by the fluid injections is controlled by the local stress conditions.
Earthquakes occurring close to hydrocarbon fields under production are often under critical view of being induced or triggered. However, clear and testable rules to discriminate the different events have rarely been developed and tested. The unresolved scientific problem may lead to lengthy public disputes with unpredictable impact on the local acceptance of the exploitation and field operations. We propose a quantitative approach to discriminate induced, triggered, and natural earthquakes, which is based on testable input parameters. Maxima of occurrence probabilities are compared for the cases under question, and a single probability of being triggered or induced is reported. The uncertainties of earthquake location and other input parameters are considered in terms of the integration over probability density functions. The probability that events have been human triggered/induced is derived from the modeling of Coulomb stress changes and a rate and state-dependent seismicity model. In our case a 3-D boundary element method has been adapted for the nuclei of strain approach to estimate the stress changes outside the reservoir, which are related to pore pressure changes in the field formation. The predicted rate of natural earthquakes is either derived from the background seismicity or, in case of rare events, from an estimate of the tectonic stress rate. Instrumentally derived seismological information on the event location, source mechanism, and the size of the rupture plane is of advantage for the method. If the rupture plane has been estimated, the discrimination between induced or only triggered events is theoretically possible if probability functions are convolved with a rupture fault filter. We apply the approach to three recent main shock events: (1) the M-w 4.3 Ekofisk 2001, North Sea, earthquake close to the Ekofisk oil field; (2) the M-w 4.4 Rotenburg 2004, Northern Germany, earthquake in the vicinity of the Sohlingen gas field; and (3) the M-w 6.1 Emilia 2012, Northern Italy, earthquake in the vicinity of a hydrocarbon reservoir. The three test cases cover the complete range of possible causes: clearly human induced, not even human triggered, and a third case in between both extremes.