It is well known that sonic logs can be improved by using a petrophysical model to create a theoretical compressional and shear sonic. The measured sonic logs are only used as a guide. There are numerous techniques for doing this, although the most popular are the Xu, White and Keys model (Keys and Xu, Geophysics, 2002) and the Greenberg and Castangna method (Greenberg and Castangna, Geophysical Prospecting, 1992).
These methods and most others require that the subject well be analyzed accurately for porosity, water saturation, and major lithologic and/or mineral components. Using the petrophysical analysis the compressional and shear moduli are built up step by step. First the moduli of the rock mixture are computed, then porosity is added to the mixture and finally the fluids are added using the Gassmann equation (Gassmann, F., Vierteljahrschrift der Naturforschenden Gesellschaft, 1951). The last step is to use the final Gassmann bulk and shear moduli to compute the compressional sonic log and the shear modulus to compute the shear sonic log. Sonic logs containing any fluid mixture can then be computed once this rock framework is built (Batzle and Wang, Geophysics, 1992).
Past experience has shown us that measured sonic logs are subject to serious error due to borehole conditions and invasion. When the results of a petrophysical velocity model are used to compare wells to seismic or to build a rock strength model for pore pressure prediction or a well completion, the results are usually better than with the measured data alone.
The best procedures for building these valuable models have yet to be agreed upon by the industry because the technology is still new. One of the debates is about how to add porosity and what porosity to use. Many petrophysicists prefer to use total porosity and dry clay volume to build their model. Others, like this author, prefer to use effective porosity and wet shale volume. The reasons behind this choice are presented.
Petrophysical velocity modeling, to improve sonic logs and create better well ties to seismic sections, is important today for both AVO studies and seismic inversions. These petrophysical velocity models start with a petrophysical interpretation that describes the rock components. The interpretation provides the volumes of sand, shale, carbonate, etc. in the solid matrix, as well as the porosity of the rock and a description of the fluids filling the rock's pores. Using this description, compressional sonic velocity and shear sonic velocity are computed. Various methods can be used to make these calculations, but regardless of the method used great care must be taken to make sure that the volume definitions used in the petrophysical interpretation are the same as those used in the velocity model. This admonition is particularly important for the definitions of shale and porosity.
Numerous techniques for producing and presenting petrophysical interpretations have been published over the years.