A simple but powerful model for simulating elastic wave velocities in elastic silicate rocks

We describe a practical velocity model for elastic silicate rocks developed from the Kuster and Toksoz, differential effective medium and Gassmann theories. The model divides the total pore space into two parts, one associated with sand grains and the other associated with clays (including bound water). The difference in pore geometry makes the clay fraction more compliant with increasing porosity than the sand fraction. The model accurately simulates the combined effect of lithology, porosity, clay content, water saturation and fluid type on laboratory and logging P-and S-wave velocities. Velocity dispersion is modelled by considering the relaxed and unrelaxed extremes of fluid how. Of three possible schemes for predicting S-wave logs from other logs, prediction from the P-wave sonic and porosity logs is generally the most accurate; comparisons of blind test predictions and S-wave logs at two Norwegian North Sea wells demonstrate the accuracy and robustness of the method. The predictions were further improved once geological information was provided on the formations encountered in the well. Examples of application to the prediction of velocity dispersion and dry frame moduli, the detection of hydrocarbons from crossplotting the P-wave and S-wave sonic velocities, and sonic log editing confirm the flexibility, accuracy and reliability of the model. The model has proved invaluable in constructing accurate models of the seismic reflection response in the vicinity of wells.