Pressure dependence of seismic Q – a microcrack‐based petrophysical model

The pressure dependence of the quality factor of acoustic waves is an extensively explored rock physical problem. To reasonably interpret laboratory measurements, a petrophysical model is required which provides the physical explanation of the nonlinear pressure dependence of the seismic quality factor. In this paper we highlight important features of seismic wave attenuation and propagation under varying pressure which contribute to creating a petrophysical model. The model is starting from the idea that microcracks are opened and closed under varying pressure. Within the confines of the model, differential equations are set up describing the relationship between microcrack density and confining pressure as well as between quality factor and microcrack density. Combining these equations, a three‐parameter expression is derived which has clear physical meaning. We found that the pressure dependence of the quality factor can be well described by a three‐parameter exponential equation in the form Q = Q 0 + Δ Q 0( 1 − exp  ( − λ σ ) )which gives also the physical meaning of pressure versus quality factor connection. The physical explanation of each parameter is clarified in the paper, i.e.Q 0is the quality factor at zero pressure,Δ Q 0is the possible range of quality factor and λ is a new petrophysical parameter (the logarithmic stress sensitivity). The model was applied on measurement data sets adopted from the literature. The material parameters of the model were determined by using linearized inversion method and the laboratory measurements were compared to the theoretical data. The theoretical data matched accurately with measured data proving that the petrophysical model applies well in practice.