Summary

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.

References

Aki
K.
Chouet
L.B.
,
1975
.
Origin of coda waves: source attenuation and scattering effects
,
J. geophys. Res.
 ,
80
,
3322
3342
.
Aki
K.
Richards
P.G.
,
1980
.
Quantitative Seismology
 ,
Vols 1 and II
.
W. H. Freeman
.
San Francisco
.
Bamford
D.
,
1979
.
Seismic constraints on the deep geology of the Caledonides of northern Britain
, in
The Caledonides of the British Isles
 , pp.
93
96
, eds
Harris
AL.
Holland
C.H.
Leake
B.E.
,
Geol. Soc. of Lond. Spec. Publ.
8
.
Bamford
D.
Nunn
K.
Prodehl
C.
Jacob
B.
,
1977
.
LISPB-IV. Crustal structure of Northern Britain
,
Geophys. J. R. astr. Soc.
 ,
54
,
43
60
.
Barr
D.
Holdsworth
R.E.
Roberts
A.M.
,
1986
.
Caledonian ductile thrusting in a Precambrian metamorphis complex: the Moine of northwestern Scotland
,
Geol Soc. Am. Bull.
 ,
97
,
754
764
.
Brewer
J.A.
Matthews
D.H.
Warner
M.R.
Hall
J.
Smythe
D.K.
Whittington
R.J.
,
1983
.
BIRPS deep seismic reflection studies of British Caledonides—the WINCH profile
,
Nature
 ,
305
,
206
210
.
Brodie
K.H.
Rutter
E.H.
,
1987
.
Deep crustal extensional faulting in the Ivrea zone of northern Italy
,
Tectonophysics
 ,
140
,
193
212
.
Carbonell
R.
Smithson
S.B.
,
1991
.
Large-scale anisotropy within the crust in the Basin and Range province
,
Geology
 ,
19
,
698
701
.
Coward
M.P.
,
1984
.
Major shear zones in the Precambrian crust; examples from NW Scotland and southern Africa and their significance
, in
Precambrian Tectonics Illustrated
 , pp.
207
235
, ed.
Kroner
A.
Greiling
S.R.
,
Schweizerbart
,
Stuttgart
.
Emmerich
H.
,
1992
.
P-SV wave propagation in a medium with local heterogeneities: a hybrid formulation and its application
,
Geophys. J. Int.
 ,
109
,
54
64
.
Frankel
A.
Clayton
R.W.
,
1986
.
Finite difference simulations of seismic scattering: implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity
,
J. geophys. Res.
 ,
91
,
6465
6489
.
Gibson
B.S.
Levander
A.R.
,
1988
.
Lower crustal reflectivity patterns in wide-angle seismic recordings
,
Geophys. Res. Lett.
 ,
15
,
617
620
.
Gibson
B.S.
Levander
A.R.
,
1990
.
Apparent layering in common-midpoint stacked images of two-dimension ally heterogeneous target zones
,
Geophysics
 ,
55
,
1466
1477
.
Goff
J.A.
Jordan
T.H.
,
1988
.
Stochastic modeling of seafloor morphology: Inversion of sea beam data for second order statistics
,
J. geophys. Res.
 ,
93
,
13589
13608
.
Goff
J.A.
Holliger
K.
Levander
A.
,
1994
.
Modal fields: A new method for characterization of random seismic velocity heterogeneity
,
Geophys. Res. Lett
 ,
21
,
493
496
.
Goodwin
W.B.
Mccarthy
J.
,
1990
.
Composition of the lower crust in west central Arizona from three-component seismic data
,
J. geophys. Res.
 ,
95
, 20
097
20
109
.
Hall
J.
Al-Haddad
F.M.
,
1979
.
Variation of effective seismic velocities of mineral with pressure and its use in velocity prediction
,
Geophys. J. R. astr. Soc.
 ,
57
,
118
.
Hall
J.
Simmons
G.
,
1979
.
Seismic velocities of Lewisian metamorphic rocks at pressures to 8 kbar: relationship to layering in North Britain
.
Geophys. J. R. astr. Soc.
 ,
58
,
337
.
Higdon
R.L.
,
1991
.
Absorbing boundary conditions for elastic waves
,
Geophysics
 ,
56
,
231
241
.
Hobbs
R.W.
,
1990
.
Effective O determination using frequency methods on BIRPS data
.
Tectonophysics
 ,
173
,
25
30
.
Holbrook
W.S.
Mooney
W.D.
Christensen
N.I.
,
1992
.
the seismic velocity structure of the deep continental crust
, in
Continental Lower Crust
 , pp.
1
43
, eds
Fountain
DM.
Arculus
R.
Kay
R.W.
,
Elsevier
,
Amsterdam
.
Holliger
K.
Levander
A.R.
,
1992
.
A stochastic view of lower crustal fabric based on evidence from the Ivrea Zone
,
Geophys. Res, Lett.
 ,
19
,
1153
1156
.
Holliger
K.
Levander
A.
,
1994
.
Structure and seismic response of extended continental crust: Stochastic analysis of the Strona-Ceneri and Ivrea zones
,
Italy, Geology
 ,
22
,
79
82
.
Holliger
K.
Carbonell
R.
Levander
A.R.
,
1992
.
Sensitivity of the lateral correlation function in deep seismic reflection data
,
Geophys. Res. Lett.
 ,
19
,
2263
2266
.
Holliger
K.
Levander
A.
Goff
J.A.
,
1993
.
Stochastic modeling of the reflective lower crust: petrophysical and geological evidence from the Ivrea Zone (northern Italy)
,
J. geophys- Res.
 ,
98
, 11
967
11980
.
Hurich
C.A.
Smithson
S.B.
,
1987
.
Compositional variation and origin of deep crustal reflections
,
Earth planet. Sci. Lett.
 ,
85
,
416
426
.
Levander
A. R.
,
1988
.
Fourth-order finite-difference P-SV seismograms
,
Geophysics
 ,
53
,
1425
1436
.
Levander
A.R.
Gibson
B.S.
,
1991
.
Wide-angle seismic reflections from two-dimensionally random target zones
,
J. geophys. Res.
 ,
96
,
10251
10
260
.
Levander
A.R.
Holliger
K.
,
1992
.
Small-scale heterogeneity and large-scale velocity structure of the continental crust
,
J. geophys. Res.
 ,
97
,
8797
8804
.
Levander
A.
Smith
S.K.
Hobbs
R.W.
England
R.W.
Snyder
D.B.
Holliger
K.
,
1994
.
the crust as a heterogeneous ‘optical’ medium
,
or ‘Crocodiles in the mist’, Tectonophysics
 ,
232
,
281
297
.
Luo
Y.
Schuster
G.
,
1991
.
Parsimonious staggered grid finite-differencing of the wave equation
,
Geophys. Res. Lett.
 ,
17
,
155
158
.
Mereu
R.F.
Ojo
S.B.
,
1981
.
the scattering of seismic waves through a crust and upper mantle with random lateral and vertical inhomogeneities
,
Phys. Earth planet. Inter
 ,
26
,
233
240
.
Mooney
W.D.
Brocher
T.M.
,
1987
.
Coincident seismic reflection and refraction measurements of the continental lithosphere: a global review
,
Rev. Geophys.
 ,
25
,
723
742
.
Powell
C.M.R.
,
1986
.
A wide-angle, multichannel seismic study of the continental lithosphere
,
PhD thesis
 ,
University of Cambridge
.
Scheirer
D.S.
Hobbs
R.W.
,
1990
.
Seismic attenuation in the continental crust SW of England
,
Geophys. J. Int.
 ,
103
,
553
540
.
Sills
J.D.
Rollinson
H.R.
,
1987
.
Metamorphic evolution of the mainland Lewisian complex
, in
Evolution of the Lewisian and Comparable Precambrian High Grade Terrains
 , pp.
81
92
, eds
Park
R.G.
Tarney
J.
,
Geol. Soc. of Lond. Spec. Publ.
8
.
Smith
P.J.
Bott
M.H.P.
,
1975
.
Structure of the crust beneath the Caledonian Foreland and Caledonian belt of the north Scottish shelf region
,
Geophys. J. R. astr. Soc.
 ,
40
,
187
205
.
Smithson
S.B.
Shive
P.N.
,
1977
.
Seismic velocity, reflections, and structure of the crystalline crust
, in
The Earth's Crust
 , Geophys. Monogr 20, pp.
254
270
,
American Geophysical Union
,
Washington, DC
.
Warner
M.
,
1990
.
Absolute reflection coefficients from deep seismic reflections
,
Tectonophysics
 ,
173
,
15
23
.
Watson
J.
,
1975
.
The Lewisian complex
, in
A Correlation of Precambrian Rocks in the British Isles
 , pp.
15
29
, eds
Harris
A.L.
Shackleton
R.M.
Watson
J.
Downie
C.
Harland
W.B.
Moorbath
S.
Geol. Soc. of Lond. Spec. Rep. 6.
Wever
T.
,
1990
.
Exposed continental crust seismic results to be tested
, in
Exposed Cross Sections of the Continental Crust
 , pp.
587
602
, eds
Salisbury
M.H.
Fountain
D.M.
,
Kluwer
,
Amsterdam
.
Wu
R.-S.
Aki
K.
,
1985
.
the fractal nature of inhomogeneities in the lithosphere evidenced from seismic wave scattering
,
Pageoph
 ,
123
,
805
818
.