A simple way to model the pressure dependency of rock velocity

• A multicomponent differential effective medium model for velocity is developed.
• Variation of stiff and compliant porosity with pressure is used as input parameters.
• Constant stiff and compliant pore aspect ratios are used to model the pressure dependent velocity.

Modeling the pressure dependency of rock velocity is important for interpreting and comparing the seismic and earthquake data from different depths. This study develops a multicomponent differential effective medium model for the elastic properties of porous rocks with two types of pores in the grain background without mixing order. The developed model is applied to modeling the pressure dependent elastic velocity of porous rocks by incorporating the variation of stiff and compliant porosity as a function of pressure. The pressure dependent stiff and compliant porosity were inverted from the measured total porosity under pressure using a dual porosity model, and the unknown constant stiff and compliant pore aspect ratios were inverted by best fitting the modeled velocity to the measured data. Application of the approach to a low porosity granite and a medium porosity sandstone sample showed that the pressure dependency of rock velocity can be satisfactorily modeled by the developed model using the pressure dependent stiff and compliant porosity and carefully estimated stiff and compliant pore aspect ratio values.