Rocks containing more than one mineral

The analysis presented here has been limited for simplicity to the case of single mineral porous rocks. In fact the main parts of the analysis do not change in any significant way if the rock has multiple constituents. The well-known result of Brown and Korringa (1975) states that

K = K_dr + ^2/K_s-/K_+ /K_f   and  =_dr,   where K_s is the unjacketed bulk modulus of the composite solid frame, $K_\phi$ is the unjacketed pore modulus of the composite solid frame, $\alpha = 1 - K_{dr}/K_s$ is the appropriate Biot-Willis (1957) parameter for this situation. The remaining parameters have the same significance as in (Gassmann). The functional dependence of K_sat on the saturation S is clearly the same in both formulas. If we were trying to infer properties of the solid from these formulas, then of course (BK) would be more difficult to interpret. But for our present purposes, we are only trying to infer porosity, saturation values, and saturation state. For these physical parameters, the analysis goes through without change.