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Stress drop is a key factor in earthquake mechanics and engineering seismology. However, stress drop calculations based on fault slip can be significantly biased, particularly due to subjectively determined smoothing conditions in the traditional least-square slip inversion. In this study, we introduce a mechanically constrained Bayesian approach to simultaneously invert for fault slip and stress drop based on geodetic measurements. A Gaussian distribution for stress drop is implemented in the inversion as a prior. We have done several synthetic tests to evaluate the stability and reliability of the inversion approach, considering different fault discretization, fault geometries, utilized datasets, and variability of the slip direction, respectively. We finally apply the approach to the 2010 M8.8 Maule earthquake and invert for the coseismic slip and stress drop simultaneously. Two fault geometries from the literature are tested. Our results indicate that the derived slip models based on both fault geometries are similar, showing major slip north of the hypocenter and relatively weak slip in the south, as indicated in the slip models of other studies. The derived mean stress drop is 5-6 MPa, which is close to the stress drop of similar to 7 MPa that was independently determined according to force balance in this region Luttrell et al. (J Geophys Res, 2011). These findings indicate that stress drop values can be consistently extracted from geodetic data.

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.

Aseismic transient driving the swarm-like seismic sequence in the Pollino range, Southern Italy
(2015)

Tectonic earthquake swarms challenge our understanding of earthquake processes since it is difficult to link observations to the underlying physical mechanisms and to assess the hazard they pose. Transient forcing is thought to initiate and drive the spatio-temporal release of energy during swarms. The nature of the transient forcing may vary across sequences and range from aseismic creeping or transient slip to diffusion of pore pressure pulses to fluid redistribution and migration within the seismogenic crust. Distinguishing between such forcing mechanisms may be critical to reduce epistemic uncertainties in the assessment of hazard due to seismic swarms, because it can provide information on the frequency-magnitude distribution of the earthquakes (often deviating from the assumed Gutenberg-Richter relation) and on the expected source parameters influencing the ground motion (for example the stress drop). Here we study the ongoing Pollino range (Southern Italy) seismic swarm, a long-lasting seismic sequence with more than five thousand events recorded and located since October 2010. The two largest shocks (magnitude M-w = 4.2 and M-w = 5.1) are among the largest earthquakes ever recorded in an area which represents a seismic gap in the Italian historical earthquake catalogue. We investigate the geometrical, mechanical and statistical characteristics of the largest earthquakes and of the entire swarm. We calculate the focal mechanisms of the M-l > 3 events in the sequence and the transfer of Coulomb stress on nearby known faults and analyse the statistics of the earthquake catalogue. We find that only 25 per cent of the earthquakes in the sequence can be explained as aftershocks, and the remaining 75 per cent may be attributed to a transient forcing. The b-values change in time throughout the sequence, with low b-values correlated with the period of highest rate of activity and with the occurrence of the largest shock. In the light of recent studies on the palaeoseismic and historical activity in the Pollino area, we identify two scenarios consistent with the observations and our analysis: This and past seismic swarms may have been 'passive' features, with small fault patches failing on largely locked faults, or may have been accompanied by an 'active', largely aseismic, release of a large portion of the accumulated tectonic strain. Those scenarios have very different implications for the seismic hazard of the area.

In this study, we analyze acoustic emission (AE) data recorded at the Morsleben salt mine, Germany, to assess the catalog completeness, which plays an important role in any seismicity analysis. We introduce the new concept of a magnitude completeness interval consisting of a maximum magnitude of completeness (M-c(max)) in addition to the well-known minimum magnitude of completeness. This is required to describe the completeness of the catalog, both for the smallest events (for which the detection performance may be low) and for the largest ones (which may be missed because of sensors saturation). We suggest a method to compute the maximum magnitude of completeness and calculate it for a spatial grid based on (1) the prior estimation of saturation magnitude at each sensor, (2) the correction of the detection probability function at each sensor, including a drop in the detection performance when it saturates, and (3) the combination of detection probabilities of all sensors to obtain the network detection performance. The method is tested using about 130,000 AE events recorded in a period of five weeks, with sources confined within a small depth interval, and an example of the spatial distribution of M-c(max) is derived. The comparison between the spatial distribution of M-c(max) and of the maximum possible magnitude (M-max), which is here derived using a recently introduced Bayesian approach, indicates that M-max exceeds M-c(max) in some parts of the mine. This suggests that some large and important events may be missed in the catalog, which could lead to a bias in the hazard evaluation.

Identification and characterization of growing large-scale en-echelon fractures in a salt mine
(2014)

The spatiotemporal seismicity of acoustic emission (AE) events recorded in the Morsleben salt mine is investigated. Almost a year after backfilling of the cavities from 2003, microevents are distributed with distinctive stripe shapes above cavities at different depth levels. The physical forces driving the creation of these stripes are still unknown. This study aims to find the active stripes and track fracture developments over time by combining two different temporal and spatial clustering techniques into a single methodological approach. Anomalous seismicity parameters values like sharp b-value changes for two active stripes are good indicators to explain possible stress accumulation at the stripe tips. We identify the formation of two new seismicity stripes and show that the AE activities in active clusters are migrated mostly unidirectional to eastward and upward. This indicates that the growth of underlying macrofractures is controlled by the gradient of extensional stress. Studying size distribution characteristic in terms of frequency-magnitude distribution and b-value in active phase and phase with constant seismicity rate show that deviations from the Gutenberg-Richter power law can be explained by the inclusion of different activity phases: (1) the inactive period before the formation of macrofractures, which is characterized by a deficit of larger events (higher b-values) and (2) the period of fracture growth characterized by the occurrence of larger events (smaller b-values).

Earthquake catalogs are probably the most informative data source about spatiotemporal seismicity evolution. The catalog quality in one of the most active seismogenic zones in the world, Japan, is excellent, although changes in quality arising, for example, from an evolving network are clearly present. Here, we seek the best estimate for the largest expected earthquake in a given future time interval from a combination of historic and instrumental earthquake catalogs. We extend the technique introduced by Zoller et al. (2013) to estimate the maximum magnitude in a time window of length T-f for earthquake catalogs with varying level of completeness. In particular, we consider the case in which two types of catalogs are available: a historic catalog and an instrumental catalog. This leads to competing interests with respect to the estimation of the two parameters from the Gutenberg-Richter law, the b-value and the event rate lambda above a given lower-magnitude threshold (the a-value). The b-value is estimated most precisely from the frequently occurring small earthquakes; however, the tendency of small events to cluster in aftershocks, swarms, etc. violates the assumption of a Poisson process that is used for the estimation of lambda. We suggest addressing conflict by estimating b solely from instrumental seismicity and using large magnitude events from historic catalogs for the earthquake rate estimation. Applying the method to Japan, there is a probability of about 20% that the maximum expected magnitude during any future time interval of length T-f = 30 years is m >= 9.0. Studies of different subregions in Japan indicates high probabilities for M 8 earthquakes along the Tohoku arc and relatively low probabilities in the Tokai, Tonankai, and Nankai region. Finally, for scenarios related to long-time horizons and high-confidence levels, the maximum expected magnitude will be around 10.

Due to large uncertainties and non-uniqueness in fault slip inversion, the investigation of stress coupling based on the direct comparison of independent slip inversions, for example, between the coseismic slip distribution and the interseismic slip deficit, may lead to ambiguous conclusions. In this study, we therefore adopt the stress-constrained joint inversion in the Bayesian approach of Wang et al., and implement the physical hypothesis of stress coupling as a prior. We test the hypothesis that interseismic locking is coupled with the coseismic rupture, and the early post-seismic deformation is a stress relaxation process in response to the coseismic stress perturbation. We characterize the role of stress coupling in the seismic cycle by evaluating the efficiency of the model to explain the available data. Taking the 2004 M6 Parkfield earthquake as a study case, we find that the stress coupling hypothesis is in agreement with the data. The coseismic rupture zone is found to be strongly locked during the interseismic phase and the post-seismic slip zone is indicated to be weakly creeping. The post-seismic deformation plays an important role to rebuild stress in the coseismic rupture zone. Based on our results for the stress accumulation during both inter- and post-seismic phase in the coseismic rupture zone, together with the coseismic stress drop, we estimate a recurrence time of M6 earthquake in Parkfield around 23-41 yr, suggesting that the duration of 38 yr between the two recent M6 events in Parkfield is not a surprise.

We study changes in effective stress (normal stress minus pore pressure) that occurred in the French Alps during the 2003-2004 Ubaye earthquake swarm. Two complementary data sets are used. First, a set of 974 relocated events allows us to finely characterize the shape of the seismogenic area and the spatial migration of seismicity during the crisis. Relocations are performed by a double-difference algorithm. We compute differences in travel times at stations both from absolute picking times and from cross-correlation delays of multiplets. The resulting catalog reveals a swarm alignment along a single planar structure striking N130 degrees E and dipping 80 degrees W. This relocated activity displays migration properties consistent with a triggering by a diffusive fluid overpressure front. This observation argues in favor of a deep-seated fluid circulation responsible for a significant part of the seismic activity in Ubaye. Second, we analyze time series of earthquake detections at a single seismological station located just above the swarm. This time series forms a dense chronicle of +16,000 events. We use it to estimate the history of effective stress changes during this sequence. For this purpose we model the rate of events by a stochastic epidemic-type aftershock sequence model with a nonstationary background seismic rate lambda(0)(t). This background rate is estimated in discrete time windows. Window lengths are determined optimally according to a new change-point method on the basis of the interevent times distribution. We propose that background events are triggered directly by a transient fluid circulation at depth. Then, using rate-and-state constitutive friction laws, we estimate changes in effective stress for the observed rate of background events. We assume that changes in effective stress occurred under constant shear stressing rate conditions. We finally obtain a maximum change in effective stress close to -8 MPa, which corresponds to a maximum fluid overpressure of about 8 MPa under constant normal stress conditions. This estimate is in good agreement with values obtained from numerical modeling of fluid flow at depth, or with direct measurements reported from fluid injection experiments.

We discuss to what extent a given earthquake catalog and the assumption of a doubly truncated Gutenberg-Richter distribution for the earthquake magnitudes allow for the calculation of confidence intervals for the maximum possible magnitude M. We show that, without further assumptions such as the existence of an upper bound of M, only very limited information may be obtained. In a frequentist formulation, for each confidence level alpha the confidence interval diverges with finite probability. In a Bayesian formulation, the posterior distribution of the upper magnitude is not normalizable. We conclude that the common approach to derive confidence intervals from the variance of a point estimator fails. Technically, this problem can be overcome by introducing an upper bound (M) over tilde for the maximum magnitude. Then the Bayesian posterior distribution can be normalized, and its variance decreases with the number of observed events. However, because the posterior depends significantly on the choice of the unknown value of (M) over tilde, the resulting confidence intervals are essentially meaningless. The use of an informative prior distribution accounting for pre-knowledge of M is also of little use, because the prior is only modified in the case of the occurrence of an extreme event. Our results suggest that the maximum possible magnitude M should be better replaced by M(T), the maximum expected magnitude in a given time interval T, for which the calculation of exact confidence intervals becomes straightforward. From a physical point of view, numerical models of the earthquake process adjusted to specific fault regions may be a powerful alternative to overcome the shortcomings of purely statistical inference.

Both aftershocks and geodetically measured postseismic displacements are important markers of the stress relaxation process following large earthquakes. Postseismic displacements can be related to creep-like relaxation in the vicinity of the coseismic rupture by means of inversion methods. However, the results of slip inversions are typically non-unique and subject to large uncertainties. Therefore, we explore the possibility to improve inversions by mechanical constraints. In particular, we take into account the physical understanding that postseismic deformation is stress-driven, and occurs in the coseismically stressed zone. We do joint inversions for coseismic and postseismic slip in a Bayesian framework in the case of the 2004 M6.0 Parkfield earthquake. We perform a number of inversions with different constraints, and calculate their statistical significance. According to information criteria, the best result is preferably related to a physically reasonable model constrained by the stress-condition (namely postseismic creep is driven by coseismic stress) and the condition that coseismic slip and large aftershocks are disjunct. This model explains 97% of the coseismic displacements and 91% of the postseismic displacements during day 1-5 following the Parkfield event, respectively. It indicates that the major postseismic deformation can be generally explained by a stress relaxation process for the Parkfield case. This result also indicates that the data to constrain the coseismic slip model could be enriched postseismically. For the 2004 Parkfield event, we additionally observe asymmetric relaxation process at the two sides of the fault, which can be explained by material contrast ratio across the fault of similar to 1.15 in seismic velocity.