Physics for Geologists, Second edition

Some dangers of mathematical statistics 137
describes seismic P waves, probably because the wavelengths of seismic P
waves are very much longer than those of an acoustic borehole logging tool.
The P wave generated by an earthquake has a frequency of about one hertz
and a velocity of about 5 kms-I, so its wavelength is about 5 km. The P
wave generated in seismic exploration has a frequency of about 50 Hz and
a velocity of about 3 km s-l, so its wavelength is of the order of 60 m. The
acoustic log signal (20 kHz) has character over less than a metre and so its
wavelength is very much less than a metre - in fact, about 15 cm.
Any formula representing geological phenomena must be looked at care-
fully. At the end of Chapter 9 we looked at compaction curves, and came to
the conclusion that the common formula for the normal compaction trend
of mudstones with depth, as measured by the sonic or acoustic log,
could not possibly be right because as the dimensionless depth z/b becomes
very large, the shale transit time tends to zero, rather than to the transit time
when the porosity is zero. This we called the matrix transit time.
See Moroney (1956) for a painless but instructive introduction to statisti-
cal methods, even if he predated the pocket calculator days. See also Rosen
(1992: 178f.) for a good summary of the mathematical statistical techniques.
Copyright 2002 by Richard E. Chapman