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S U M M A R YA modified Lax-Wendroff correction for wave propagation in attenuating and dispersive media described by Zener elements is presented. As opposed to the full correction, this new technique is explicit and offers large computational savings. The technique may be applied to a wide variety of hyperbolic problems. Here, the concept is illustrated for wave propagation in visco-acoustic media.

Attenuation and dispersion of the seismic pulse can strongly affect the outcome of amplitude versus offset (AVO) analysis. These anelastic aspects of wave propagation also influence the outcome of linear inversion for short scale fluctuations in elastic parameters, the model based analogue of AVO analysis. The viscoacoustic model provides a framework for illustration of these effects. An efficient time domain viscoacoustic finite difference scheme for synthesis of primaries only plane-wave (1-D model) and line source (2-D model) reflection records is the basis for linear inversion algorithms via iterative minimization of mean square error. This approach to inversion requires computation of the mean square error gradient. The gradient computation becomes feasible through the use of the adjoint state technique, together with a checkpointing scheme due to Griewank. Inversion of synthetic data in the plane-wave domain illustrates the sensitivity to attenuation of even qualitative aspects of inversion. Viscoacoustic 2-D inversion of a small part of the Mobil AVO data illustrates applicability to field data in the offset domain.

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