The differential Kuster–Toksöz rock physics model for predicting S-wave velocity

Abstract

The Kuster–Toksoz (KT) model is a classical rock physics model concerning the influence of pore geometry on elastic wave velocities. However, this model is limited to a dilute concentration of pores, which means the porosity cannot be too high. In order to overcome this limitation, this paper transforms the KT model into a new differential Kuster–Toksoz (DKT) model. In other words, we propose a process in which porosity with certain geometries increases step by step from zero up to its final value. The simulation of the new model notably shows that it is superior to the classical KT model and the differential effective medium model since it takes multiple–porosity and higher porosity rocks into consideration. Furthermore, by combining the DKT model, the Gassmann equation and the Voigt–Reuss–Hill average equation, a S-wave velocity prediction procedure is proposed under the constraint of the P-wave velocity which is from the logging data. The new method is applied to both the measured data in laboratory and well data in logging. The results show that the predicted S-wave velocities match well with the measured ones, especially for data with high porosity. By comparing estimated S-wave velocity deduced from the new method and the KT model, the results demonstrate that the new method is effective for S-wave velocity prediction.