@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{DialloSchmitt2004,
  author    = {Diallo, Mamadou Sanou and Schmitt, D. R.},
  title     = {Noise reduction in interferometric fringe patterns with mean curvature diffusion},
  issn      = {1017-9909},
  year      = {2004},
  abstract  = {Dual beam electronic speckle interferometers provide raw data in the form of maps of wrapped relative phase or fringe patterns. Interpretation of such fringe patterns is complicated by aliased and random speckle noise. This noise can result in misidentification of the phase at a given point in the image. Automated determination of the loci of fringe extrema, useful for quantitative evaluation, are particularly affected. A nonlinear image filtering technique referred to as mean curvature diffusion is applied to overcome this difficulty. This technique essentially smooths the image without a substantial reduction in the magnitude of the underlying trends that here represent the fringes. Mean curvature diffusion uses calculations analogous to those for the diffusion of heat with the difference that the diffusion coefficient, reminiscent of thermal diffusivity, varies spatially within the Image with a value given by the reciprocal of the local surface gradient. At a given point in the image, the rate of surface diffusion depends only on the average value of the normal curvature in any two orthogonal directions and not on its magnitude; this allows the lower frequency underlying components of the image structure to be retained. The method is tested on both calculated and real speckle interferograms to highlight the effectiveness of this smoothing technique relative to more standard smoothing algorithms. (C) 2004 SPIE and IST},
  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{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{DialloKuleshHolschneideretal.2006,
  author    = {Diallo, Mamadou Sanou and Kulesh, Michail and Holschneider, Matthias and Kurennaya, Kristina and Scherbaum, Frank},
  title     = {Instantaneous polarization attributes based on an adaptive approximate covariance method},
  series = {Geophysics},
  volume    = {71},
  journal   = {Geophysics},
  number    = {5},
  publisher = {SEG},
  address   = {Tulsa},
  issn      = {0016-8033},
  doi       = {10.1190/1.2227522},
  pages     = {V99 -- V104},
  year      = {2006},
  abstract  = {We introduce a method for computing instantaneous-polarization attributes from multicomponent signals. This is an improvement on the standard covariance method (SCM) because it does not depend on the window size used to compute the standard covariance matrix. We overcome the window-size problem by deriving an approximate analytical formula for the cross-energy matrix in which we automatically and adaptively determine the time window. The proposed method uses polarization analysis as applied to multicomponent seismic by waveform separation and filtering.},
  language  = {en}
}
@article{DialloKuleshHolschneideretal.2006,
  author    = {Diallo, Mamadou Sanou and Kulesh, Michail and Holschneider, Matthias and Scherbaum, Frank and Adler, Frank},
  title     = {Characterization of polarization attributes of seismic waves using continuous wavelet transforms},
  issn      = {0016-8033},
  doi       = {10.1190/1.2194511},
  year      = {2006},
  abstract  = {Complex-trace analysis is the method of choice for analyzing polarized data. Because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics, it can be used to separate and characterize these waves. Traditional methods of complex-trace analysis only give the instantaneous attributes as a function of time or frequency. However. for transient wave types or seismic events that overlap in time, an estimate of the polarization parameters requires analysis of the time-frequency dependence of these attributes. We propose a method to map instantaneous polarization attributes of seismic signals in the wavelet domain and explicitly relate these attributes with the wavelet-transform coefficients of the analyzed signal. We compare our method with traditional complex-trace analysis using numerical examples. An advantage of our method is its possibility of performing the complete wave-mode separation/ filtering process in the wavelet domain and its ability to provide the frequency dependence of ellipticity, which contains important information on the subsurface structure. Furthermore, using 2-C synthetic and real seismic shot gathers, we show how to use the method to separate different wave types and identify zones of interfering wave modes},
  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}
}