Report 7 Viscoelastic Waveform Inversion as a Tool for AVO Studies

AVO studies have enjoyed a mixed success rate in predicting the existence of hydrocarbons in sediments. Sometimes AVO predictions are accurate, but other times they can be quite wrong. It seems likely that the success rate might increase if more sophisticated AVO methods could be employed such as full wave inversion. In fact elastic wave equation inversion has been applied to seismic data with some notable success. Two examples are the reconstruction of P-velocities in the Friendswood data (Zhou, 1993) and McElroy (Zhou and Schuster, 1995). There the P-velocity tomograms compared very well with the sonic log velocities to a resolution of about 2-3m. However the S-wave were affected by viscoelastic attenuation, so that the Swave inversion failed to achieve the desired high resolution or accuracy (Zhou and Schuster, 1995). In this report we assess the feasibility of using viscoelastic waveform inversion to accurately predict the Poisson ratio of subsurface lithology. Towards this goal, Viscoelastic waveform inversion is applied to both synthetic data and a crosswell field data set from the McElroy field, Texas. Previous elastic waveform inversion tomograms gave S-velocity profiles which did not correlate well with the S-sonic logs. Our new results show that the S-velocity profiles derived by the viscoelastic inversion method correlate well with the measured S-sonic logs. The S-velocity tomogram and Poisson ratio tomogram show a much higher resolution for the layered structures than the elastic results, and thus provide more useful information for reservoir characterization. 173 174REPORT 7. VISCOELASTIC WAVEFORM INVERSION AS A TOOL FOR AVO STUDIES INTRODUCTION Zhou and Schuster (1995) applied the elastic wave equation traveltime and waveform inversion method (WTW) to the McElroy field data set. They found that the resulting P-velocity waveform tomogram was much more resolved than P-velocity traveltime tomogram, and the reconstructed P-velocity profiles correlated quite well with the sonic logs. However there was only a weak correlation between the S-sonic logs and the S-velocity profiles between the depths of 2900 ft and 3000 ft, with the amplitudes of the S-velocity variations generally much smaller than those in the Ssonic logs. Zhou and Schuster (1995) conjectured that these discrepancies were due to errors in estimating the S-wave radiation patterns, as well as in neglecting attenuation in the inversion algorithm. Wang (1995) applied the viscoelastic wave equation waveform inversion method to synthetic crosswell viscoelastic data. But there was a mistake in programming the code for adjoint operator. Here the corrected viscoelastic waveform inversion method is applied to both synthetic data and the McElroy field data set. The inverted velocity tomograms for the synthetic data show that the viscoelastic WTW method correctly reconstructs the Pand Svelocity images. Furthermore, the inverted S-velocity profiles from the field data match the S-sonic logs better than the previous elastic WTW S-velocity profiles. The S-velocity tomogram and the Poisson ratio tomogram show a much higher resolution for the layered structures than the elastic WTW tomograms, and thus provide more useful information for reservoir characterization. THEORY In this section the viscoelastic WTW algorithm is presented. The goal is to reconstruct the Pand S-velocity models which minimize the following misfit function: