"Viscoelastic finite difference modeling", J. O. Blanch and J. O. A. Robertsson and W. W. Symes Department of Computational and Applied Mathematics, Rice University TR 93-04, 1993 Abstract: Real earth media disperse and attenuate propagating waves. This anelastic behavior can be well described by a viscoelastic model. We have developed a finite difference simulator to model wave propagation in visco elastic media. The finite difference method was chosen in favor of other methods for several reasons. Finite difference codes are more portable than, for instance, pseudo spectral codes. Moreover, finite difference schemes provide a convenient environment to define complicated boundaries. The finite difference method for viscoelastic wave propagation has been thoroughly investigated with convergence tests, dispersion and stability analyses. Two 2-D examples illustrate the difference between viscoelastic and elastic wave propagation. "Viscoelastic finite difference modeling II" J. O. Blanch and J. O. A. Robertsson and W. W. Symes Department of Computational and Applied Mathematics, Rice University TR 93-16, 1993 Abstract: Real earth media disperse and attenuate propagating mechanical waves. This anelastic behavior can be described well by a viscoelastic model. We have developed a finite difference simulator to model wave propagation in visco elastic media. The finite difference method was chosen in favor of other methods for several reasons. Finite difference codes are more portable than pseudo spectral codes for instance. Moreover, finite difference schemes provide a convenient environment in which to define complicated boundaries. Several finite difference schemes for viscoelastic wave propagation are thoroughly investigated with convergence tests, dispersion and stability analyses. We illustrate our method and the importance of accurately modeling anelastic media through 2-D and 3-D examples from shallow marine environments. "Modeling of a constant Q: Methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique" J. O. Blanch and J. O. A. Robertsson and W. W. Symes Geophysics, 1995 vol 60. pp. 176-184 Also: CAAM TR 94-14 Abstract: Linear anelastic phenomena in wave propagation problems can be well modeled thrugh a viscoelastic mechanical model consisting of standard linear solids. In this paper we present a method for modeling of constant Q as a function of frequency based on an explicit closed formula for calculation of the parameter field. Several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant Q approximation. The proposed method enables substantial savings in computations and memory requirements. Experiments show that the new method also yields higher accuracy in the modeling of Q than, e.g., the Pade' approximant method. "Stability anlysis of finite-difference schemes for the viscoelastic wave equation" J. O. Blanch and W. W. Symes Department of Computational and Applied Mathematics, Rice University TR 94-35, 1999 Abstract: It is difficult to predict stability properties of a finite differene scheme. The stability can be investigated through the roots of the Z-transformed and Fourier transformed difference scheme (modal equation). It is possible to derive the modal equation with parameterized coefficients, to simultaneously investigate several schemes for the viscoelastic wave equation. Several conditionally stable schemes were found, where the most efficient is a staggered scheme with a stability condition closely resembling that of an elastic scheme.
Back to Joakim Blanch's Home Page
Back to the Rice Inversion Project Home Page
Back to CAAM Home Page
joakimb@caam.rice.edu