Rock Physics modeling of Unconsolidated Sands:  Accounting for Non-Uniform Contacts and
Heterogeneous Stress Fields in the Effective Media Approximation with applications to
Hydrocarbon Exploration

We show that by treating the contact stiffness as a variable, one can extend the effective
medium approximation used to obtain elastic stiffness of a random pack of spherical grains. 
More specifically, we suggest calibrating the effective media approximation based on
contact mechanics by incorporating non-uniform contact models. 

The simple extension of the theory provides a better fit to many laboratory and field
 experiments and can provide insight to the micromechanical bonds associated with
unconsolidated sediments. 

This approach is motivated by repeated observations of shear-wave measurements in
unconsolidated sands where observed shear-wave velocities are lower than predicted
by the Hertz-Mindlin contact theory. 

We present in detail the calibration process for well-log data from a North Sea well
penetrating a shallow gas discovery and a deepwater well in the Gulf of Mexico.
Finally, we demonstrate the benefit of using this model
for AVA analysis of shallow sand targets in exploration and reservoir studies