PRACTICAL IMPORTANCE

At first glance there seems to be no need for extending conventional wave propagation measurements to include coupling effects, since just using an isotropic elastic assumption has served well for the purpose of exploration. Introducing more degrees of freedom would apparently be just a nuisance. However industry is now shifting its priorities to making more and more detailed studies of small effects that characterize temporal changes in rock properties. It is quite common to monitor producing areas with 3D surveys, where the geometry is kept the same over a large time period. Such measurements, in general, show only small changes in the amplitudes and velocities of seismic waves. These changes can be produced by a variety of causes: depletion of the reservoir, progression of a subsurface fire front, CO₂ flooding or hydro-fracturing for enhanced oil recovery. Measurements in such an environment, targeted to a certain formation, serve as a basis for accurately estimating rock properties and, more importantly, how these properties change. In this context of minute changes, we need to formulate a description of wave propagation that not only includes primary effects, such as anisotropic elasticity, but also takes secondary (coupled, not second order) effects into account. Enhanced oil recovery and monitoring could benefit from the unified description this paper offers.

Future data acquisition might include electromagnetic waves, as well as seismic waves. Existing purely elastic algorithms could be generalized to accommodate coupled waves.

The examples of quartz and PZT2 indicate that we can expect coupling effects in the range of a few percent of velocity change in naturally occurring rock types. I propose measurements in shale and other metamorhpic rocks containing hydro-carbons, to see how large a piezoelectric effect they show. Shales are produced by high pressure and high temperature metamorphosis, similar to the artificial manufacturing process of PZT2. Several rock types containing quartz in one form or another have been found to show piezoelectricity (Nitsan, 1977; Sobolev et al.,1984). However I could not find any literature that records effects in rocks relevant to hydro carbons.

Moreover the literature discribing the measurement of elastic constants in shale lacks many details that would clarify what kind of thermal, elastic or electric boundary conditions were applied. The measured constants might well include electrical stiffening effects, instead of being purely elastic, as previously assumed. The boundary conditions would have a significant effect if piezoelectricity were present.