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 1:10560 geologic maps of Laxfordian (Archean) age Lewisian rocks on a 26.8m 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~6.2 km s-1), mafic amphibolites (Vp— 6.75 km s-1), and intermediate composition schists (Vp—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 244m and a vertical correlation of about 133m (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° 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.