@article{BettenbuehlRusconiEngbertetal.2012, author = {Bettenb{\"u}hl, Mario and Rusconi, Marco and Engbert, Ralf and Holschneider, Matthias}, title = {Bayesian selection of Markov Models for symbol sequences application to microsaccadic eye movements}, series = {PLoS one}, volume = {7}, journal = {PLoS one}, number = {9}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0043388}, pages = {10}, year = {2012}, abstract = {Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.}, language = {en} } @article{HaynPanetDiamentetal.2012, author = {Hayn, Michael and Panet, I. and Diament, M. and Holschneider, Matthias and Mandea, Mioara and Davaille, A.}, title = {Wavelet-based directional analysis of the gravity field evidence for large-scale undulations}, series = {Geophysical journal international}, volume = {189}, journal = {Geophysical journal international}, number = {3}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1111/j.1365-246X.2012.05455.x}, pages = {1430 -- 1456}, year = {2012}, abstract = {In the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophysical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings.}, language = {en} } @article{HolschneiderNarteauShebalinetal.2012, author = {Holschneider, Matthias and Narteau, C. and Shebalin, P. and Peng, Z. and Schorlemmer, Danijel}, title = {Bayesian analysis of the modified Omori law}, series = {Journal of geophysical research : Solid earth}, volume = {117}, journal = {Journal of geophysical research : Solid earth}, number = {6089}, publisher = {American Geophysical Union}, address = {Washington}, issn = {2169-9313}, doi = {10.1029/2011JB009054}, pages = {12}, year = {2012}, abstract = {In order to examine variations in aftershock decay rate, we propose a Bayesian framework to estimate the {K, c, p}-values of the modified Omori law (MOL), lambda(t) = K(c + t)(-p). The Bayesian setting allows not only to produce a point estimator of these three parameters but also to assess their uncertainties and posterior dependencies with respect to the observed aftershock sequences. Using a new parametrization of the MOL, we identify the trade-off between the c and p-value estimates and discuss its dependence on the number of aftershocks. Then, we analyze the influence of the catalog completeness interval [t(start), t(stop)] on the various estimates. To test this Bayesian approach on natural aftershock sequences, we use two independent and non-overlapping aftershock catalogs of the same earthquakes in Japan. Taking into account the posterior uncertainties, we show that both the handpicked (short times) and the instrumental (long times) catalogs predict the same ranges of parameter values. We therefore conclude that the same MOL may be valid over short and long times.}, language = {en} } @article{KurtenbachEickerMayerGuerretal.2012, author = {Kurtenbach, E. and Eicker, A. and Mayer-Guerr, T. and Holschneider, Matthias and Hayn, M. and Fuhrmann, M. and Kusche, J.}, title = {Improved daily GRACE gravity field solutions using a Kalman smoother}, series = {Journal of geodynamics}, volume = {59}, journal = {Journal of geodynamics}, number = {3}, publisher = {Elsevier}, address = {Oxford}, issn = {0264-3707}, doi = {10.1016/j.jog.2012.02.006}, pages = {39 -- 48}, year = {2012}, abstract = {Different GRACE data analysis centers provide temporal variations of the Earth's gravity field as monthly, 10-daily or weekly solutions. These temporal mean fields cannot model the variations occurring during the respective time span. The aim of our approach is to extract as much temporal information as possible out of the given GRACE data. Therefore the temporal resolution shall be increased with the goal to derive daily snapshots. Yet, such an increase in temporal resolution is accompanied by a loss of redundancy and therefore in a reduced accuracy if the daily solutions are calculated individually. The approach presented here therefore introduces spatial and temporal correlations of the expected gravity field signal derived from geophysical models in addition to the daily observations, thus effectively constraining the spatial and temporal evolution of the GRACE solution. The GRACE data processing is then performed within the framework of a Kalman filter and smoother estimation procedure. The approach is at first investigated in a closed-loop simulation scenario and then applied to the original GRACE observations (level-1B data) to calculate daily solutions as part of the gravity field model ITG-Grace2010. Finally, the daily models are compared to vertical GPS station displacements and ocean bottom pressure observations. From these comparisons it can be concluded that particular in higher latitudes the daily solutions contain high-frequent temporal gravity field information and represent an improvement to existing geophysical models.}, language = {en} } @article{SchachtschneiderHolschneiderMandea2012, author = {Schachtschneider, R. and Holschneider, Matthias and Mandea, M.}, title = {Error distribution in regional modelling of the geomagnetic field}, series = {Geophysical journal international}, volume = {191}, journal = {Geophysical journal international}, number = {3}, publisher = {Wiley-Blackwell}, address = {Hoboken}, issn = {0956-540X}, doi = {10.1111/j.1365-246X.2012.05675.x}, pages = {1015 -- 1024}, year = {2012}, abstract = {In this study we analyse the error distribution in regional models of the geomagnetic field. Our main focus is to investigate the distribution of errors when combining two regional patches to obtain a global field from regional ones. To simulate errors in overlapping patches we choose two different data region shapes that resemble that scenario. First, we investigate the errors in elliptical regions and secondly we choose a region obtained from two overlapping circular spherical caps. We conduct a Monte-Carlo simulation using synthetic data to obtain the expected mean errors. For the elliptical regions the results are similar to the ones obtained for circular spherical caps: the maximum error at the boundary decreases towards the centre of the region. A new result emerges as errors at the boundary vary with azimuth, being largest in the major axis direction and minimal in the minor axis direction. Inside the region there is an error decay towards a minimum at the centre at a rate similar to the one in circular regions. In the case of two combined circular regions there is also an error decay from the boundary towards the centre. The minimum error occurs at the centre of the combined regions. The maximum error at the boundary occurs on the line containing the two cap centres, the minimum in the perpendicular direction where the two circular cap boundaries meet. The large errors at the boundary are eliminated by combining regional patches. We propose an algorithm for finding the boundary region that is applicable to irregularly shaped model regions.}, language = {en} } @article{ShebalinNarteauHolschneider2012, author = {Shebalin, Peter and Narteau, Clement and Holschneider, Matthias}, title = {From alarm-based to rate-based earthquake forecast models}, series = {Bulletin of the Seismological Society of America}, volume = {102}, journal = {Bulletin of the Seismological Society of America}, number = {1}, publisher = {Seismological Society of America}, address = {Albany}, issn = {0037-1106}, doi = {10.1785/0120110126}, pages = {64 -- 72}, year = {2012}, abstract = {We propose a conversion method from alarm-based to rate-based earthquake forecast models. A differential probability gain g(alarm)(ref) is the absolute value of the local slope of the Molchan trajectory that evaluates the performance of the alarm-based model with respect to the chosen reference model. We consider that this differential probability gain is constant over time. Its value at each point of the testing region depends only on the alarm function value. The rate-based model is the product of the event rate of the reference model at this point multiplied by the corresponding differential probability gain. Thus, we increase or decrease the initial rates of the reference model according to the additional amount of information contained in the alarm-based model. Here, we apply this method to the Early Aftershock STatistics (EAST) model, an alarm-based model in which early aftershocks are used to identify space-time regions with a higher level of stress and, consequently, a higher seismogenic potential. The resulting rate-based model shows similar performance to the original alarm-based model for all ranges of earthquake magnitude in both retrospective and prospective tests. This conversion method offers the opportunity to perform all the standard evaluation tests of the earthquake testing centers on alarm-based models. In addition, we infer that it can also be used to consecutively combine independent forecast models and, with small modifications, seismic hazard maps with short- and medium-term forecasts.}, 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} }