EXPANDED ABSTRACTS "Viscoelastic finite difference modeling" J. O. Blanch, J. O. A. Robertsson, W. W. Symes SEG 1993 expanded abstracts Summary: Dispersion and atteunation of waves propagating in real earth media can be described well by a viscoelastic model. We have developed a finite difference simulator to model wave propagation in viscoelastic 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. Several finite difference schemes for viscoelastic wave propagation are thoroughly investigated with dispersion and stabilty analyses. We found that small changes of finite difference schemes could make unstable schemes conditionally stable. The viscoelastic simulator does also provide good absorbing boundaries. An 2-D example is included which compares viscoelastic wave propagation to elastic wave propagation. "3-D viscoelastic modeling" Johan O. A. Robertsson, Joakim O. Blanch, Alan Levander, William W. Symes SEG 1993 expanded abstracts Summary: Real earth media disperse and attenuate propagating mechanical waves. We have developed 2-D and 3-D finite difference simulators to model wave propagation in viscoelastic media. Together with an algorithm to optimize for realistic dispersion and attenuation vs. frequency relations which we also have developed, we are able to simulate experiments from a realistsic perspective. We present a suite of 3-D simulations to illustrate our method. "Constant Q modeling: Preliminary results for a new algorithm" Joakim O. Blanch, Johan O. A. Robertsson, William W. Symes SEG 1994 expanded abstract Summary: Linear anelastic phenomena in wave propagation problems can be well modeled through 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 fields. The proposed method enables substantial savings in computations and memory requirements for viscoelastic wave simulation. Experiments show that the new method also yields higher accuracy in the modeling of Q than e.g., the Pade' approximant method "Linear Inversion in Layered Viscoacoustic Media Using a Time Domain Method" Joakim O. Blanch, William W. Symes SEG 1994 expanded abstract Summary: Real Earth media attenuate and disperse propagating waves. If these effects ar neglected, inversion can produce erroneous results. Viscoelasticity provides an appropriate and powerful tool to model these anelastic effects, so forms a plausible basis for inversion algorithms. The tau-p (intercept time-slowness) domain permits economical modeling and inversion of 3-D wave propagation in layered media. The adjoint state method leads to an efficient algorithm for linear least squares inversion of short wavelength model components. Numerical experiments show that accurate inversion requires conditioning of thedata by a time varying gain, hence also of the simulator output, to ``equalize'' the influence of earlier strong events and later attenuated events. "Efficient Iterative Viscoacoustic Linearized Inversion" Joakim O. Blanch, William W. Symes SEG 1995 expanded abstract (submitted) Summary: The adjoint state computation is essential for iterative inversion using full wave equation simulation. For dissipative systems like viscoacoustics however this computation appears to require storage of the entire time history of the forward reference field, or else its recomputation at every time step, both prohibitively expensive in a multidimensional setting. The computational complexity and storage requirements can both be reduced to a level only exceeding that of the foward computation by a logarithmic factor, through careful retention of a few intermediate time levels during the forward calculation. The feasibility of the resulting adjoint state computation is illustrated by linearized viscoacoustic 2D inversion of a small part of a field data set.
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