The implications of anisotropy for seismic impedance inversion

Seismic inversion is an established technique for deriving acoustic impedance (AI) from seismic data using well log information as a low frequency constraint. However, within anisotropic strata e.g. shale, velocity logs measured in deviated wells will typically exhibit higher velocities than would have been recorded in vertical boreholes (Furre and Brevik 1998; Hornby et al. 1999). If this effect is not corrected for before building a low frequency impedance model for seismic inversion, impedance results will be biased around deviated well trajectories. Since this is quite a subtle effect, the unwary interpreter might assign geological meaning to inversion artefacts. In this paper we demonstrate a simple but effective method for correcting deviated well AI logs for anisotropic effects. We know that others have performed similar but more sophisticated corrections (e.g. Vernik 2001; Vernik and Fisher 2001), but are not aware of this pitfall with deviated wells being widely acknowledged. Further, we consider the implications of the revealed anisotropy for single and simultaneous angle-stack (elastic impedance (EI)) inversions and propose workflows for compensating for anisotropy. Seismic impedance inversion has become an integral part of the reservoir characterisation workflow, since interpretation and quantification of reservoir rock properties is made using AI layer data rather than seismic amplitudes which relate to AI contrasts (van Riel, 2000). Recently seismic AVO data have also been inverted, bringing additional constraints on reservoir properties, since knowledge of the elastic rock properties can improve lithological and/or fluid reservoir characterisation over the use of AI alone. Two main families of inversion methods have developed, which we will classify as deterministic and stochastic. In general, deterministic methods search for a single global optimum, with an objective function being the mismatch between seismic and synthetic data. By their nature, the resulting AI volume will have a high frequency spectrum determined and limited by the seismic data, and a low frequency spectrum derived from the well data. By contrast, the high frequency limit of AIs generated by stochastic methods is raised beyond the seismic spectrum using the high frequency content of well logs coupled with geostatistics. These AI results are therefore non-unique, making them suitable for statistical uncertainty analysis on many high-resolution models. Both deterministically- and stochastically-generated AIs are subsequently converted to models of reservoir properties (porosity, Vshale etc) via upscaled petro-elastic relationships. Final results include 3D models of reservoir properties and associated uncertainties that reflect uncertainties on seismic inversion results and petro-elastic relationships. To date, there has been relatively little consideration of the impact of anisotropy on impedance inversion, despite the increasingly widespread acceptance that sedimentary rocks, and in particular shales, are often quite strongly anisotropic (e.g., Thomsen, 1986). This is presumably due to the fact that until now most inversion work has been focused on zero/near-offset cubes with (near-) vertical wells in relatively calm structural environments, where the impact of anisotropy can largely be factored out in the wavelet calibration step. However, as the community begins to consider AVO and the inversion of far-offset substacks (e.g., Vernik 2001), it will become increasingly important to estimate and account for anisotropy at various stages of the processing. In this paper we first consider the discrepancies between real AI logs from adjacent vertical and deviated wells. We then describe a correction to the deviated logs assuming an anisotropic model dependent on the proportion of shale, and show the effect of this correction on the inversion results. Finally, we consider the implications of anisotropy for EI and simultaneous AVO inversion. Even though we have used the geostatistical inversion method (Haas and Dubrule 1994; Dubrule et al. 1998), all impedance inversion techniques benefit from accounting for anisotropy revealed by deviated well logs.