S waves

What about S waves? For transversely isotropic (TI) media, there are two kinds of S waves, SH and qSV.

The SH wavefronts in TI media should be exactly elliptical, although the amount of elliptical anisotropy can be large. Other than this slight simplification (P-wave wavefronts aren't normally elliptical in TI media, but they probably aren't too weird in ordinary rocks either) measuring SH traveltimes should theoretically be very similar to the case for P waves already discussed. In practice, S-wave transducers are usually twice as large as P-wave transducers in any given experiment, so it is even more likely that a good first break corresponding to an accurate phase velocity will be measured. Figure  shows how this works in our numerical simulation of Vernik and Nur's experiment; although the ``sideways drift'' of the wavefront in the $45^\circ$SH case is nearly the same as for the $45^\circ$ qP case in Figure , the receiver transducer solidly encounters the all-important ``flat'' part of the wavefront instead of merely being grazed by it.

 

SHexam
Figure 6 Snapshots showing the behavior of SH waves in our $90^\circ$ (top) and $45^\circ$ (bottom) core-sample simulations. (The top plot shows the situation at 15.$\mu$s, the bottom at 17.5$\mu$s.) The SH wave in the $45^\circ$ case slips to the left about the same amount that the qP wave did in Figure , but the transducers are twice as wide so the wavefront hits the receiver anyway.

 

SVexam
Figure 7 Snapshots showing the behavior of qSV waves in our $90^\circ$ (top) and $45^\circ$ (bottom) core-sample simulations. (Both snapshots show the situation at 17.5$\mu$s.) It so happens that for this wavetype the $45^\circ$ phase direction and its associated group direction are nearly the same, so the wavefront in the $45^\circ$ case (lower plot) does not significantly crab sideways.

The case for qSV waves is trickier. In TI media these waves can be highly anisotropic and non-elliptical (for example see Figure ). On the minus side this means that ``esoteric'' anisotropic effects such as wavefront cusps could complicate picking the ``first break''. Cusps are always associated with precursive energy leading the main qSV arrival (theoretically anchoring it all the way back to the tail of the already-arrived qP wavefront). They are point-source, not plane-source phenomena, so in the worst case they might occur in experiments such as ours at the edges of the ``flat part'' of the wavefront. If qSV cusps prove to be problem in an experiment, it should be possible to lessen the confusion by making the transducers wider. On the plus side qSV wavefronts almost always have a near-symmetry about $45^\circ$, so the amount of ``side slip'' for $45^\circ$ cores should be small. Figure  demonstrates that the qSV waves in our numerical simulation are indeed the best-behaved of the lot. The sideways drift is only 3mm to the right, insignificant compared to the size of the S transducers. (Note the other two wavetypes drifted to the left.) Furthermore, the qSV wave was not preceded by a significant amount of precursive energy, so there should have been no special trouble picking the first break off the recorded signal.

It is somewhat ironic that qSV waves (normally thought of as the most complex of TI wavetypes) appear to be the most well-behaved here, while ``mild-mannered'' qP waves are the likeliest to be mismeasured.