We have developed statistical models of upper and middle crustal seismic
velocity heterogeneity based on geologic maps and petrophysical data
from the Lewisian gneiss complex, Scotland. The level of heterogeneity
we have measured is relevant to seismic exploration of the crystalline
crust using conventional reflection and refraction techniques. We
digitized two 1:10 560 geologic maps of Laxfordian (Archean) age
Lewisian rocks on a 26.8 m grid. Both maps are believed to be representative
of the upper and middle crust in north-western Scotland, and both
are believed to provide cross-sectional views of parts of the crust.
The digital maps were characterized by the statistics of their lithologic
populations and by their 2-D spatial autocorrelation functions. Different
lithologies were assigned seismic velocities appropriate for the
mid-crust using petrophysical data. Three lithologies are dominant:
silicic gneisses (Vp approximately 6.2 km s-1), mafic amphibolites
(Vp approximately 6.75 km s-1), and intermediate composition schists
(Vp approximately 6.5 km s-1). Both maps have self-affine spatial
fabrics.
The first map covers the core of a syncline. Its autocorrelation function
defines a medium with a fractal dimension of 2.78, a horizontal characteristic
length of about 244 m and a vertical correlation of about 133 m (aspect
ratio is 2:1). It has an essentially trimodal velocity (lithology)
population consisting of 37 per cent silicic gneiss, 43 per cent
mafic amphibolites, and 20 per cent schists. This map is representative
of 30-40 per cent of Laxfordian rocks. The second map is a plan view
which can be rotated 90-degrees about an axis perpendicular to strike
to give a cross-section. This map is characterized by a fractal dimension
of 2.55, with a horizontal correlation length of about 111 m and
a vertical correlation of about 38 m (aspect ratio 3:1). It has a
nearly bimodal population consisting of 77 per cent silicic gneisses
and 22 per cent mafic amphibolites. It is representative of 60-70
per cent of Laxfordian rocks.
Lastly we examine the seismic response of an upper to middle crust
based on our statistical models using acoustic and elastic 2-D finite-difference
synthetic seismograms. Short-offset shot records demonstrate that
a Lewisian upper crust produces scattered waves which significantly
disrupt signals reflecting from deeper levels. Measurements of transmission
scattering Q, and coda decay rates confirm that seismic scattering
in Lewisian-type crust is strong. The migrated CMP response of a
Lewisian crustal model shows the characteristic 'salt and pepper''
pattern often observed in the upper crust, and described, incorrectly,
as 'transparent'. We suggest that 'translucent' is a more appropriate
descriptor.