Test of rock physics models for prediction of seismic velocities in shallow unconsolidated sands: a well log data case

This paper tests the ability of various rock physics models to predict seismic velocities in shallow unconsolidated sands by comparing the estimates to P and S sonic logs collected in a shallow sand layer and ultrasonic laboratory data of an unconsolidated sand sample. The model fits are also evaluated with respect to the conventional model for unconsolidated sand. Our main approach is to use Hertz-Mindlin and Walton contact theories, assuming different weight fractions of smooth and rough contact behaviours, to predict the elastic properties of the high porosity point. Using either the Hertz-Mindlin or Walton theories with rough contact behaviour to define the high porosity endpoint gives an over-prediction of the velocities. The P-velocity is overpredicted by a factor of similar to 1.5 and the S-velocity by a factor of similar to 1.8 for highly porous gas-sand. The degree of misprediction decreases with increasing water saturation and porosity.Using the Hertz-Mindlin theory with smooth contact behaviour or weighted Walton models gives a better fit to the data, although the data are best described using the Walton smooth model. To predict the properties at the lower porosities, the choice of bounding model attached to the Walton Smooth model controls the degree of fit to the data, where the Reuss bound best captures the porosity variations of dry and wet sands in this case since they are caused by depositional differences. The empirical models based on lab experiments on unconsolidated sand also fit the velocity data measured by sonic logs in situ, which gives improved confidence in using lab-derived results.