Conclusions

Our modeling results indicate that Vernik and Nur were correct when they interpreted their core-sample traveltime measurements for Bakken Shale as representing vertical phase velocities. Although their $45^\circ$ qP measurement may have suffered some error because of the strong anisotropy, our modeling predicts the magnitude of that error should be several times smaller than the normal measurement errors.

We expect that the Bakken Shale example investigated here represents about the most anisotropic geological specimen likely to be encountered in the laboratory. If this is true then the traveltimes measured in similar laboratory core-sample experiments should also represent vertical phase velocities, assuming the critical ratio of core-sample height to transducer width is no greater than it was in their experiment (i.e., $\leq 3$). If the core-sample height to transducer width is larger it becomes more likely that some indeterminate quantity representing neither vertical phase nor vertical group velocity is being sampled; in case of doubt equations (7) and (8) can be used to estimate whether there might be a problem for the $45^\circ$ measurements in a particular experimental configuration.

Our modeling indicates that as an additional safeguard first breaks should be picked instead of first peaks whenever possible. This can be important in cases like the $45^\circ$ qP measurement in our example that are close to being detectably delayed due to side-slipping of the wavefront. In any case, note that it is highly unlikely a core-sample experiment could accidentally measure vertical group velocities; our numerical modeling suggests the core-sample height to transducer width ratio needs to be on the order of 20 (preferably even larger) to be reasonably sure of sampling vertical group velocities.

While it is comforting to know that core-sample traveltime measurements sample phase velocity, this still does not mean we are assured of finding accurate values for all the various anisotropy parameters we might wish to know. At least some sorts of errors are avoidable, and should be avoided. If we want to measure Thomsen's anisotropy parameter $\delta$we should clearly state whether we are using equation (4) or (5); the choice of equation makes a difference (unless the anisotropy is very weak). We find equation (5) to be the more useful. Unless we have reason to discount some of our measurements we should try to reconcile and use all available information; the more independent measurements we can use the more confidence we can have in the results. In particular, the $45^\circ$ SV measurement is often the single most important piece of data for constraining C₁₃.

Some errors may be unavoidable, unfortunately. For this reason it is important to have at least a rough idea of the reliability of the measured traveltimes and to use those input errors to determine what the corresponding output errors in the calculated anisotropy parameters may be. If the standard deviations in the measured traveltimes are too great the values of C₁₃ and $\delta$ derived from them may be effectively meaningless. For this reason when publishing elastic constants we should state what measurements we used to calculate the tabulated constants and what magnitude of error we expect in them. Similarly, when interpreting elastic constants published by someone else we must be wary if this information is not provided (Seriff and Sriram, 1991).