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velocity of sound through liquids is very much slower than that through
solids, so the detectors pick up the first arrival of a signal that has passed
down the wall of the borehole. The device measures the time of arrival at
the 1st and 2nd (or first and third, depending on which spacing is being
used) and the difference is recorded as the transit time. If the sonde is sym-
metrical in the borehole, the passages through mud to each detector will be
equal, and the recorded transit time is the true transit time over‘the distance
separating the detectors (1 or 3 ft: 0.30 or 0.91 m). The newer, compensated
type is so designed that the average of an upward and a downward signal is
correct even if the sonde is not symmetrical with the borehole.
The geometry of the wall of the borehole is important, and if it is irregular
due to washouts (see the Caliper log) the results may be erratic with the
travel times too long. A signal not received at a detector (due perhaps to
attenuation) leads to wild fluctuations in the trace on the log. This is called
cycle skipping, and such sections must be ignored.
Together with the transit time is recorded the integrated transit time,
each pip on this track indicating an increase of one millisecond in the total
travel time (except opposite cycle skipping). Interval velocities can there-
fore be computed by counting the pips between the limits of interest. Hence
the sonic log can be used to help seismic interpretation not only by identi-
fying lithologies with velocities, but also by the generation of synthetic
seismograms for the identification of reflectors.
The Sonic log, as we saw in Chapter 3, can also be used to estimate poros-
ity. This is a complex matter that still has no good theoretical basis. Work
by Wyllie and his co-workers (Wyllie et al., 1956, 1958) led to the so-called
time average formula :

f= (At-Atmati-i,)/(Atfluid -At,a~). (6.11)
The transit time through solids (Atmatrix; i.e., at zero porosity) is about
52-55 ps/ft in quartz, 45-50 ps/ft in carbonates, and about 190 ps/ft
in liquids, so the porosity can be estimated once the transit time, At, has
been measured. This time-average formula has two weaknesses, long re-
cognized. First, it is a linear equation in porosity and transit time, although
there is a great deal of empirical evidence suggesting that the true relationship
is not linear. Secondly, correction factors are needed for all but small poros-
ities. It seems therefore that these correction factors are required because
the time average formula is not correct.
Chapman (1981, p. 223) assumed that the sonic path lies in solids only,
by virtue of the fact that the transit time in liquids is about four times that
in solids, and that porosity affects the length of this path (a sort of tortuosity
in solids). He suggested the formula (abbreviating the suffix):
f= 1 - (~t,,/~t)~ 1 - (~t,,/nt)”. (6.12)
.=
This is a non-linear equation that gives satisfactory results in several areas