Modulus decomposition of compressional and shear velocities in sand bodies

The advent of borehole shear slowness measurements in sonically slow formations has lead to breakthroughs in the subsurface profiling of geological bodies. In sand bodies, compressional and shear velocities depend predictably on porosity, mineralogy, grain contacts, and fluid saturation. An interpretation is best performed by decomposing the velocities into moduli that are intrinsic measures of the rock frame and pore fluid compressibilities. Careful experiments on pure materials (i.e., pure quartz sandstones) demonstrate two simplifying constitutive relationships. First, the bulk and shear frame moduli are simple functions of the porosity. A comparison of the measured shear frame modulus to the prediction for the pure material distinguishes sand from shale. Second, the ratio of the bulk and shear frame moduli is a constant 0.9 independent of the porosity. The measured velocities are directly inverted to yield the bulk modulus of the pore fluid. The fluid saturation effects are so dramatic at high porosity that not only gas but oil may also be distinguished from water. The relationships are tested in several case studies where the results are encouraging. Finite-frequency effects may complicate the interpretation where filtrate invasion is significant. Attenuation provides further information because compressional absorption is particularly sensitive to gas saturation. A potential application of the modulus decomposition may be to quantify, in amplitude versus offset seismics proximal to the wellbore, the fractional change in shear frame modulus from the fractional change in pore fluid modulus.