The effective medium

Last time, I wrote about the standard-issue composite display used in formation evaluation. The so-called Triple Combo is used to delineate each of the earth's porous media constituents in its own track. But it fails to deliver information about the whole rock, the net effect of all its parts. In contrast, an effective medium property, or bulk property, is one that represents the net effect of all constituents, an aggregate of all three. Examples of effective medium properties are:

  • –P-wave and S-wave velocity
  • –Bulk density
  • –Acoustic impedance and shear impedance

Effective properties are what seismic and other geophysical methods are sensitive to. As such, one of the goals of seismic rock physics is to establish site-specific relationships between the elements in the Triple Combo and seismic properties. Link constituents in 1D with effective measurements in 2D or 3D. 

Determining relationships between the Triple Combo and effective media properties is fraught with challenges. Earth materials are complex, have infinite compositional and textural variation, and are unpredictable even. Try modeling a DT log from gamma-ray, resistivity, and neutron and you will likely fail. Therefore, empirical methods are the only way to accurately characterize complex effective media. Another benefit and by-product of drilling and logging wells.

The Triple Combo doesn't inform how rocks, pores, and fluids affect seismic properties. Sonic (DT) and bulk density (RHOB), on the other hand, can be used to compute seismic properties exactly. They are just as important as the Triple Combo. Got a change from shale to sand? Or gas to brine? It's not an "effective" change if the impedance contrast is small or the layer too thin. Formation evaluation can be done by looking at individual elements, but geophysics sees the effective media as a whole. So to bridge the two, you need measurements that deliver the aggregate of all three.