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We have shown that unless the anisotropy is too strong, the transducers
are too narrow, or the core sample is too tall, core-sample first-break
measurements should measure the phase velocity. But what precisely do we mean
by ``too'' strong, narrow, or tall? It depends on the elastic properties
of the rock being measured. Of course if we knew the elastic
constants we wouldn't have to do the experiment in the first place!
Is there some warning sign to be found among the measurements in hand?
If the amplitude for the case is anomalously low compared
to the untroublesome and cases,
this could indicate the energy is missing the receiver and thus the
traveltime measurement should be regarded with suspicion.
Unfortunately amplitude variations
in such experiments can be caused in many ways, so this is not a reliable
indicator.

Another cross check is possible because some of the elastic constants
are overdetermined. In particular, (as we already saw) the key elastic
constant *C*_{13} can be found from either
the *q*P or *q*SV traveltime measurements;
assuming the velocity measurements at and can be trusted,
we can compare the values of *C*_{13} calculated from each of the
two measurements independently as a check.
There should not be a problem with both values of *C*_{13} erring in
the same direction due to side-slip effects.
Since the phase-velocity arrival time is the earliest possible,
a ``partial miss'' must always result in a delay, resulting in a
velocity measurement that is too low.
The effect of such a mismeasurement on the calculated value of *C*_{13}
depends on the wavetype;
a too-slow *q*P phase-velocity results in
finding a *C*_{13} (and ) that is too low,
while a too-slow *q*SV phase-velocity measurement results
in a *C*_{13} (and ) that is too high.

Probably the best way to estimate whether there might be
significant side-slip problems, though, is to use the (possibly inaccurate)
measured elastic constants to model the problem.
Analytically, the side-slip velocity is simply
.In the case of *q*P and *q*SV waves in
transverse isotropy the total side-slip at can be expressed directly in
terms of the core height *H* and the measured phase velocities:

| |
(7) |

where *V*_{X} is either *V*_{P} or *V*_{SV}, depending on which wavetype
the sideslip is being calculated for.
The corresponding equation for SH waves is quite simple:
| |
(8) |

Conveniently, these equations appear to be rather insensitive to the precise
value used for the phase velocity;
for our example could be varied by with only a
1mm resulting change in the calculated *q*P sideslip.
(The denominator does start to blow up if
, but hopefully this fact alone
would already have suggested there just *might* be a problem!)
If equations (7) or (8) indicate
the total sideslip is greater than about half the transducer width for
a given wavetype,
extra care should be taken when interpreting the corresponding
measurement as a phase velocity.

** Next:** Conclusions
** Up:** DISCUSSION
** Previous:** First break versus first
Stanford Exploration Project

12/18/1997