A simple derivation of the effective stress coefficient for seismic velocities in porous rocks

The effect of confining stress and pore pressure on seismic velocities is important for such geophysical applications as overpressure prediction from seismic data (Eaton, 1975; Dutta, 2002; Huffman, 2002; Sayers et al., 2002) and, more recently, for hydrocarbon production monitoring using time-lapse seismic measurements (Tura and Lumley, 1999; Landr⊘, 2001). The dependence of seismic velocity on pressure has been confirmed for a variety of rocks by laboratory measurements of elastic wave velocities in samples with varying pressure in pore fluids (see, e.g., Wyllie et al., 1958; Todd and Simmons, 1972; Eberhart-Phillips et al., 1989; Prasad and Manghnani, 1997). In general, for a rock subjected to a given confining stress σc, higher pore pressures P correspond to lower compressional and shear velocities. Confining stress has a similar effect (but with opposite sign) on seismic velocities.