STOCHASTIC CHARACTERIZATION AND SEISMIC RESPONSE OF UPPER AND MIDDLE CRUSTAL ROCKS BASED ON THE LEWISIAN GNEISS COMPLEX, SCOTLAND

We have developed statistical models of upper and middle crustal seism ic velocity heterogeneity based on geologic maps and petrophysical dat a from the Lewisian gneiss complex, Scotland. The level of heterogenei ty we have measured is relevant to seismic exploration of the crystall ine crust using conventional reflection and refraction techniques. We digitized two 1:10 560 geologic maps of Laxfordian (Archean) age Lewis ian rocks on a 26.8 m grid. Both maps are believed to be representativ e of the upper and middle crust in north-western Scotland, and both ar e 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. Diffe rent lithologies were assigned seismic velocities appropriate for the mid-crust using petrophysical data. Three lithologies are dominant: si licic gneisses (Vp approximately 6.2 km s-1), mafic amphibolites (Vp a pproximately 6.75 km s-1), and intermediate composition schists (Vp ap proximately 6.5 km s-1). Both maps have self-affine spatial fabrics. T he first map covers the core of a syncline. Its autocorrelation functi on defines a medium with a fractal dimension of 2.78, a horizontal cha racteristic 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 represe ntative of 30-40 per cent of Laxfordian rocks. The second map is a pla n 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 a n 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 scatter ed waves which significantly disrupt signals reflecting from deeper le vels. 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 characteri stic 'salt and pepper'' pattern often observed in the upper crust, and described, incorrectly, as 'transparent'. We suggest that 'translucen t' is a more appropriate descriptor.