Open Journal of Applied Sciences, 2013, 3, 84-88 doi:10.4236/ojapps.2013.31B1017 Published Online April 2013 (http://www.scirp.org/journal/ojapps) Reliability of Attenuation Properties Recovery for Viscoelastic Media Ekaterina Efimova, Vladimir Cheverda The laboratory “Numerical methods of inversion of geophysical wavefields”, A.A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS. Novosibirsk, Russia Email: EfimovaES@ipgg.sbras.ru Received 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 pos- sible to see whether the parameters are coupled. Singular value decomposition was used to study the possibility of re- covering 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 condi- tion number. Keywords: Viscoelasticity; Seismic Attenuation; Inverse Theory; Wave Propagation; Singular Value Decomposition; Diffraction Patterns 1. Introduction The main theme of the work is recovery of characteristics of viscoelastic media. For this purpose was considered numerical solution of two-dimensional inverse problem of seismology using the information recorded in the re- ceivers located on the surface of the Earth. It is known that a numerical model of viscoelastic media describes the geological structures, in particular hydrocarbon res- ervoirs. And the attenuation properties depend on the composition of the fluid. But there appears coupling of parameters of the me- dium in the numerical formulation of the problem that will be discussed in this article. Coupling of parameters means that the true heterogeneity of only one parameter would restore as a perturbation of other in the numerical solution. So if you use coupled parameters, your solution will be incorrect. Therefore, we need to find uncoupled set of parameters before developing and implementation of the algorithm. Determination the possibility of uncoupled reconstruc- tion of the parameters of a viscoelastic medium, such as density, elastic impedances and attenuation properties is the subject of this research. This problem was considered in other papers, in par- ticular, in [1], the problem was solved for the case of media with a velocity close to a constant value. There was also shown the inability simultaneous recovery of the velocity and attenuation properties in viscoelastic media without additional conditions [2]. 2. Numerical Description of Viscoelastic Media State equation provides the relationship between stresses and strains at the same time for ideal elastic media. But this is not true in viscoelastic media, which possess at- tenuation that caused by memory of the material. For such media stress state depends on all past states of strains and the state equation can be expressed with the use of the generalized Hooke's law. Media with attenua- tion mathematically can be described by the system of equations: / * / ( )/2 (,) ( , )/ (, ) . t kl ijkl u t div f t u u x t x G xt ij    d                              (1) 2.1. Generalized Standard Linear Solid Numerical resolution of such integral-differential system is very troublesome, so it is proposed to use Standard Copyright © 2013 SciRes. OJAppS