Viscoelastic seismic parameters are expressions of underlying petrophysical properties. Theoretical and empirically derived petrophysical/seismic relations exist, but each is limited in the number and the range of values of the variables used. To provide a more comprehensive empirical model, we combined lab measurements from 18 published data sets and well log data for sandstone samples, and determined least-squares coefficients across them all. The dependent variables are the seismic parameters of bulk density (ρ), compressional and shear wave velocities (Vp and Vs), and compressional and shear wave quality factors (Qp and Qs). The independent variables are effective pressure, porosity, clay content, water saturation, permeability, and frequency. As the derived expressions are empirical correlations, no causal relations should be inferred.

Prediction of ρ is based on volumetric mixing of the constituents. For Vp and Vs predictions, separate sets of coefficients are fitted for three water saturation conditions: dry, partially saturated, and fully saturated. Predictions of Vp and Vs are fitted as functions of porosity, clay content, effective pressure, saturation, and frequency. Predictions of 100/Qp are fitted as a function of porosity, clay content, permeability, saturation, frequency, and pressure. Interactions between effective pressure, saturation, and frequency are included. Predictions of 100/Qs are obtained from Qs/Qp and 100/Qp.

The result is a composite model that is more comprehensive than previous models and that predicts seismic properties from the petrophysical properties. Empirically estimated values of ρ, Vp, Vs, 100/Qp, and 100/Qs for the composite data over all saturations predict the measurements with correlation coefficients (R2) that range from a low of 0.65 (for 100/Qs) to a high of 0.90 (for Vp). As the fitted relations have been derived from data with limited parameter ranges, extrapolation is not advised, and they are not intended to substitute for locally derived relations based on site-specific data. Nevertheless, the derived expressions produce representative values that will be useful when approximate, internally consistent predictions are sufficient. Potential future applications include building of seismic reservoir models from petrophysical data and analysis of the sensitivity of seismic data to changes in reservoir properties.

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