Analysis of Rock Properties for fining upward sandstone and sandstone-carbonate mixed systems in the Resistivity - Velocity domain.

P-wave velocity and electrical resistivity are standard measurements generally acquired when a well is drilled, and far more recently, also when seismic and controlled source electromagnetic (CSEM) surveys are performed jointly. Examining how these two geophysical measurements relate to each other is, therefore, important for reservoir characterization. We review bounds and several effective medium models for P- and S-wave velocities, and resistivity, and compare them with well log data for water-saturated unconsolidated sandstones and a mixed sandstone- carbonate system. Using these data allows us to focus in studying only the effect of porosity and lithology in velocity and resistivity. We also plot these data, bounds and estimates in the resistivity-velocity domain, creating two pair of "crossbounds", following Wempe (2000). Crossbounds are the result of combining the bounds of P-wave velocity and the bounds of normalized resistivity. The velocity Hashin- Shtrikman (HS) bounds can be modified to include the critical porosity. For resistivity, there are equivalent HS bounds, plus a modified upper bound defined by Wempe (2000). The inner crossbounds include: a lower and upper crossbounds. The lower crossbound is the HS bound for velocity versus the lower HS bound for resistivity. The upper crossbound is the upper HS bound for velocity versus the upper empirical bound for resistivity. The outer crossbounds are obtained by crossplotting the upper velocity bound and the lower resistivity bound; and the lower velocity bound and the upper resistivity bound. The data for a fining-upward sandstone tend to plot within the inner crossbounds in the normalized resistivity - velocity domain, suggesting that both elastic and electrical properties are changing in a similar manner, mostly due to the change in porosity and sorting. In the case of the mixed sandstone-carbonate system, we found that carbonate-rich sediments can be identified in the resistivity-velocity domain, since they are characterized by higher velocity and resistivity values. Another observation was that the inner crossbounds for S- wave velocity and resistivity are broader, therefore analyzing and modeling the data in the normalized resistivity-S- wave velocity space using specific models, such as Archie and the "soft sand" model, may be more useful than doing it in the normalized resistivity - P-wave velocity domain.