@article{HolschneiderTeramoBottarietal.2004,
  author    = {Holschneider, Matthias and Teramo, A. and Bottari, A. and Termini, D.},
  title     = {On the relevance of the spatial distribution of events for seismic hazard evaluation},
  issn      = {0921-030X},
  year      = {2004},
  abstract  = {Seismic hazard evaluation is proposed by a methodological approach that allows the study of the influence of different modelling assumptions relative to the spatial and temporal distribution of earthquakes on the maximum values of expected intensities. In particular, we show that the estimated hazard at a fixed point is very sensitive to the assumed spatial distribution of epicentres and their estimators. As we will see, the usual approach, based on uniformly distributing the epicentres inside each seismogenic zone is likely to be biased towards lower expected intensity values. This will be made more precise later. Recall that the term "bias" means, that the expectation of the estimated quantity ( taken as a random variable on the space of statistics) is different from the expectation of the quantity itself. Instead, our approach, based on an estimator that takes into account the observed clustering of events is essentially unbiased, as shown by a Monte-Carlo simulation, and is configured on a 11011-isotropic macroseismic attenuation model which is independently estimated for each zone},
  language  = {en}
}
@article{ZollerHolschneiderBenZion2004,
  author    = {Zoller, Gert and Holschneider, Matthias and Ben-Zion, Yehuda},
  title     = {Quasi-static and quasi-dynamic modeling of earthquake failure at intermediate scales},
  year      = {2004},
  abstract  = {We present a model for earthquake failure at intermediate scales (space: 100 m-100 km, time: 100 m/nu(shear},
  language  = {en}
}
@article{KuleshHolschneiderDialloetal.2005,
  author    = {Kulesh, Michail and Holschneider, Matthias and Diallo, Mamadou Sanou and Xie, Q. and Scherbaum, Frank},
  title     = {Modeling of wave dispersion using continuous wavelet transforms},
  issn      = {0033-4553},
  year      = {2005},
  abstract  = {In the estimate of dispersion with the help of wavelet analysis considerable emphasis has been put on the extraction of the group velocity using the modulus of the wavelet transform. In this paper we give an asymptotic expression of the full propagator in wavelet space that comprises the phase velocity as well. This operator establishes a relationship between the observed signals at two different stations during wave propagation in a dispersive and attenuating medium. Numerical and experimental examples are presented to show that the method accurately models seismic wave dispersion and attenuation},
  language  = {en}
}
@article{ChambodutPanetMandeaetal.2005,
  author    = {Chambodut, Aude and Panet, I. and Mandea, Mioara and Diament, M. and Holschneider, Matthias and Jamet, O.},
  title     = {Wavelet frames : an alternative to spherical harmonic representation of potential fields},
  issn      = {0956-540X},
  year      = {2005},
  abstract  = {Potential fields are classically represented on the sphere using spherical harmonics. However, this decomposition leads to numerical difficulties when data to be modelled are irregularly distributed or cover a regional zone. To overcome this drawback, we develop a new representation of the magnetic and the gravity fields based on wavelet frames. In this paper, we first describe how to build wavelet frames on the sphere. The chosen frames are based on the Poisson multipole wavelets, which are of special interest for geophysical modelling, since their scaling parameter is linked to the multipole depth (Holschneider et al.). The implementation of wavelet frames results from a discretization of the continuous wavelet transform in space and scale. We also build different frames using two kinds of spherical meshes and various scale sequences. We then validate the mathematical method through simple fits of scalar functions on the sphere, named 'scalar models'. Moreover, we propose magnetic and gravity models, referred to as 'vectorial models', taking into account geophysical constraints. We then discuss the representation of the Earth's magnetic and gravity fields from data regularly or irregularly distributed. Comparisons of the obtained wavelet models with the initial spherical harmonic models point out the advantages of wavelet modelling when the used magnetic or gravity data are sparsely distributed or cover just a very local zone},
  language  = {en}
}
@article{HolschneiderDialloKuleshetal.2005,
  author    = {Holschneider, Matthias and Diallo, Mamadou Sanou and Kulesh, Michail and Ohrnberger, Matthias and Luck, E. and Scherbaum, Frank},
  title     = {Characterization of dispersive surface waves using continuous wavelet transforms},
  issn      = {0956-540X},
  year      = {2005},
  abstract  = {In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain},
  language  = {en}
}
@article{ZollerHolschneiderBenZion2005,
  author    = {Zoller, Gert and Holschneider, Matthias and Ben-Zion, Yehuda},
  title     = {The role of heterogeneities as a tuning parameter of earthquake dynamics},
  issn      = {0033-4553},
  year      = {2005},
  abstract  = {We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity ("quasidynamic model''). The model produces a "brittle- ductile'' transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: ( 1) high stress drop barriers in near- vertical directions and ( 2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations},
  language  = {en}
}
@article{DialloKuleshHolschneideretal.2005,
  author    = {Diallo, Mamadou Sanou and Kulesh, Michail and Holschneider, Matthias and Scherbaum, Frank},
  title     = {Instantaneous polarization attributes in the time-frequency domain and wavefield separation},
  issn      = {0016-8025},
  year      = {2005},
  abstract  = {We introduce a method of wavefield separation from multicomponent data sets based on the use of the continuous wavelet transform. Our method is a further generalization of the approach proposed by Morozov and Smithson, in that by using the continuous wavelet transform, we can achieve a better separation of wave types by designing the filter in the time-frequency domain. Furthermore, using the instantaneous polarization attributes defined in the wavelet domain, we show how to construct filters tailored to separate different wave types (elliptically or linearly polarized), followed by an inverse wavelet transform to obtain the desired wave type in the time domain. Using synthetic and experimental data, we show how the present method can be used for wavefield separation},
  language  = {en}
}
@article{NarteauShebalinHolschneider2005,
  author    = {Narteau, C. and Shebalin, P. and Holschneider, Matthias},
  title     = {Onset of power law aftershock decay rates in southern California},
  issn      = {0094-8276},
  year      = {2005},
  abstract  = {Aftershocks rates seem to follow a power law decay, but the question of the aftershock frequency immediately after an earthquake remains open. We estimate an average aftershock decay rate within one day in southern California by stacking in time different sequences triggered by main shocks ranging in magnitude from 2.5 to 4.5. Then we estimate the time delay before the onset of the power law aftershock decay rate. For the last 20 years, we observe that this time delay suddenly increase after large earthquakes, and slowly decreases at a constant rate during periods of low seismicity. In a band-limited power law model such variations can be explained by different patterns of stress distribution at different stages of the seismic cycle. We conclude that, on regional length scales, the brittle upper crust exhibits a collective behavior reflecting to some extent the proximity of a threshold of fracturing},
  language  = {en}
}
@article{KuleshDialloHolschneider2005,
  author    = {Kulesh, Michail A. and Diallo, Mamadou Sanou and Holschneider, Matthias},
  title     = {Wavelet analysis of ellipticity, dispersion, and dissipation properties of Rayleigh waves},
  issn      = {1063-7710},
  year      = {2005},
  abstract  = {This paper is devoted to the digital processing of multicomponent seismograms using wavelet analysis. The goal of this processing is to identify Rayleigh surface elastic waves and determine their properties. A new method for calculating the ellipticity parameters of a wave in the form of a time-frequency spectrum is proposed, which offers wide possibilities for filtering seismic signals in order to suppress or extract the Rayleigh components. A model of dispersion and dissipation of elliptic waves written in terms of wavelet spectra of complex (two-component) signals is also proposed. The model is used to formulate a nonlinear minimization problem that allows for a high-accuracy calculation of the group and phase velocities and the attenuation factor for a propagating elliptic Rayleigh wave. All methods considered in the paper are illustrated with the use of test signals. (c) 2005 Pleiades Publishing, Inc},
  language  = {en}
}
@article{ZollerHainzlHolschneideretal.2005,
  author    = {Zoller, Gert and Hainzl, Sebastian and Holschneider, Matthias and Ben-Zion, Yehuda},
  title     = {Aftershocks resulting from creeping sections in a heterogeneous fault},
  issn      = {0094-8276},
  year      = {2005},
  abstract  = {We show that realistic aftershock sequences with space-time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law},
  language  = {en}
}