Gassmann's equation and fluid‐saturation effects on seismic velocities

Gassmann's (1951) equations commonly are used to predict velocity changes resulting from different pore‐fluid saturations. However, the input parameters are often crudely estimated, and the resulting estimates of fluid effects can be unrealistic. In rocks, parameters such as porosity, density, and velocity are not independent, and values must be kept consistent and constrained. Otherwise, estimating fluid substitution can result in substantial errors. We recast the Gassmann's relations in terms of a porosity‐dependent normalized modulus Kn and the fluid sensitivity in terms of a simplified gain function G. General Voigt‐Reuss bounds and critical porosity limits constrain the equations and provide upper and lower bounds of the fluid‐saturation effect on bulk modulus. The “D” functions are simplified modulus‐porosity relations that are based on empirical porosity‐velocity trends. These functions are applicable to fluid‐substitution calculations and add important constraints on the results. More importantly, the simplified Gassmann's relations provide better physical insight into the significance of each parameter. The estimated moduli remain physical, the calculations are more stable, and the results are more realistic.