The main borehole of the German Continental Deep Drilling Program
(KTB) extends over 9000 m into a crystalline upper crust consisting
primarily of interlayered gneiss and metabasite. We present a joint
analysis of the velocity and lithology logs in an effort to extract
the lithology component of the velocity log. Covariance analysis
of lithology log, approximated as a binary series, indicates that
it may originate from the superposition of two Brownian stochastic
processes (fractal dimension 1.5) with characteristic scales of similar
to 2800 m and similar to 150 m, respectively. Covariance analysis
of the velocity fluctuations provides evidence for the superposition
of four stochastic process with distinct characteristic scales. The
largest two scales are identical to those derived from the lithology,
confirming that these scales of:velocity heterogeneity are caused
by lithology variations. The third characteristic scale, similar
to 20 m, also a Brownian process, is probably related to fracturing
based on correlation with the resistivity log. The superposition
of these three Brownian processes closely mimics the commonly observed
1/k decay (fractal dimension 2.0) of the velocity power spectrum.
The smallest scale process (characteristic scale similar to 1.7 m)
requires a low fractal dimension, similar to 1.0, and accounts for
similar to 60% of the total rms velocity variation. A comparison
of successive logs from 6900-7140 m depth indicates that such variations
are not repeatable and thus probably do not represent true velocity
variations in the crust. The results of this study resolve disparity
between the differing published estimates of seismic heterogeneity
based on the KTB sonic logs, and bridge the gap between estimates
of crustal heterogeneity from geologic maps and borehole logs.