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V. A. Cheverda, V.I. Kostin, “R-Pseudoinverses for Compact Operators in Hilbert Spaces: Existence and Stability,” Journal of Inverse and Ill-Posed Problems, Vol. 3, No. 2, 1995, pp. 131–148. doi:10.1515/jiip.1995.3.2.131

has been cited by the following article:

• TITLE: Reliability of Attenuation Properties Recovery for Viscoelastic Media

  AUTHORS: Ekaterina Efimova, Vladimir Cheverda

  KEYWORDS: Viscoelasticity; Seismic Attenuation; Inverse Theory; Wave Propagation; Singular Value Decomposition; Diffraction Patterns

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.3 No.1B1, July 12, 2013

  ABSTRACT: The inverse problem of seismology for media with attenuation is considered in this paper. Generalized Standard Linear Solid is used to describe viscoelastic media. In the numerical solution certain parameterizations can be coupled, it means that true heterogeneity of the only one of parameters can be restored only as a perturbation of another. This is why important to investigate reliability of parameters recovery. By using method based on diffraction patterns it is possible to see whether the parameters are coupled. Singular value decomposition was used to study the possibility of recovering the parameters in practice. It was investigated the possibility of reconstructing of the density, impedances and attenuation properties. Coupling appears on the attenuation properties and impedances separately corresponding to the P-wave and S-wave. It is also should be noted that coupling decreases with increasing frequency range and the condition number.