Gardner's relations and AVO inversion

Seismic reflection data contain information about the nature and the composition of a medium (its lithology, fluid content, porosity and so on). The lithological and fluid properties of a medium cannot be inferred from P-wave data alone: information on the S-wave response is also required. Although S-wave data are rarely directly acquired, S-wave information can be extracted from the P-wave amplitude-variation-with-offset (AVO). One consequence of this is a spurious correlation between estimated P-wave and S-wave properties; another is that S-wave related estimates are very sensitive to noise (Cambois 2000). AVO inversion is commonly applied as a means of retrieving P-wave and S-wave properties from seismic data. The use of a constraint, such as a Gardner-type relation, is highly recommended because, by reducing the number of parameters, it stabilizes the inversion. But the constraint introduces biases into the estimated parameters. As our ultimate aim is quantitative (rather than only qualitative) characterization of fluidfilled reservoirs, we studied the quantitative effects of using a Gardner constraint on AVO inversion. This paper shows results from synthetic models based on log data from four (one per AVO class) North Sea wells. A real data example from the North Sea illustrates the application of these results.