@article{WangHainzlZoeller2014,
  author    = {Wang, Lifeng and Hainzl, Sebastian and Z{\"o}ller, Gert},
  title     = {Assessment of stress coupling among the inter-, co- and post-seismic phases related to the 2004 M6 Parkfield earthquake},
  series = {Geophysical journal international},
  volume    = {197},
  journal   = {Geophysical journal international},
  number    = {3},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggu102},
  pages     = {1858 -- 1868},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@misc{WangZoellerHainzl2014,
  author    = {Wang, Lifeng and Z{\"o}ller, Gert and Hainzl, Sebastian},
  title     = {Joint determination of slip and stress drop in a Bayesian inversion approach:},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {888},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43551},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-435511},
  pages     = {375 -- 388},
  year      = {2014},
  abstract  = {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.},
  language  = {en}
}
@article{WangZoellerHainzl2015,
  author    = {Wang, Lifeng and Z{\"o}ller, Gert and Hainzl, Sebastian},
  title     = {Joint Determination of Slip and Stress Drop in a Bayesian Inversion Approach: A Case Study for the 2010 M8.8 Maule Earthquake},
  series = {Pure and applied geophysics},
  volume    = {172},
  journal   = {Pure and applied geophysics},
  number    = {2},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0033-4553},
  doi       = {10.1007/s00024-014-0868-x},
  pages     = {375 -- 388},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@article{WangHainzlZoelleretal.2012,
  author    = {Wang, Lifeng and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias},
  title     = {Stress- and aftershock-constrained joint inversions for coseismic and postseismic slip applied to the 2004 M6.0 Parkfield earthquake},
  series = {Journal of geophysical research : Solid earth},
  volume    = {117},
  journal   = {Journal of geophysical research : Solid earth},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2011JB009017},
  pages     = {18},
  year      = {2012},
  abstract  = {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.},
  language  = {en}
}