Ultrasonic velocity‐porosity relationships for sandstone analogs made from fused glass beads

Using fused glass beads, we have constructed a suite of clean sandstone analogs, with porosities ranging from about 1 to 43 percent, to test the applicability of various composite medium theories that model elastic properties. We measured P‐ and S‐wave velocities in dry and saturated cases for our synthetic sandstones and compared the observations to theoretical predictions of the Hashin‐Shtrikman bounds, a differential effective medium approach, and a self‐consistent theory known as the coherent potential approximation. The self‐consistent theory fits the observed velocities in these sandstone analogs because it allows both grains and pores to remain connected over a wide range of porosities. This behavior occurs because this theory treats grains and pores symmetrically without requiring a single background (host) material, and it also allows the composite medium to become disconnected at a finite porosity. In contrast, the differential effective medium theory and the Hashin‐Shtrikman upper bound overest...