Estimates of upper-crustal heterogeneity in the Baltic Shield from seismic scattering and borehole logs

TECTONOPHYSICS ELSEVIER

Tectonophysics 286 (1998) 171 - 183

Estimates of upper-crustal heterogeneity in the Baltic Shield from seismic scattering and borehole logs C.E.R. Line a, R.W. Hobbs b,*, D.B. Snyder b ~ Mobil North Sea Ltd., 3 Clement's Inn, London WC2A 2EB, UK h BIRPS, Bullard Laboratories, Madingl
Abstract Constraints on small-scale heterogeneity in the upper crust of the Baltic Shield were obtained from stochastic modelling of a variety of seismic data from the BABEL and Siljan Ring surveys. A non-linear least-squares inversion scheme was applied to wavefield fluctuations in seismic reflections to obtain statistical parameters of the medium through which the wave energy propagated. The reflections are from dolerite sills intruded at depths of 6-12 km into the Palaeoproterozoic upper crust of the central Baltic Shield. Analysis of the BABEL data set reveals that the upper crust is a weakly scattering stochastic medium, with velocities characterised by an exponential autocorrelation function with a correlation length of 150 4- 50 m and rms velocity perturbation of 1.5 4- 0.5%. Further inversions show that most of the scattering occurs within the upper few kilometres of the crust. Analysis of the Siljan seismic data set reveals heterogeneity with length scales of 210 4- 50 m and a velocity perturbation of about 1.0%. The autocovariance and power spectrum of the sonic log, and studies of frequency-dependent Q in VSP data, from the Gravberg-1 borehole, give consistent estimates of basement heterogeneity. The upper crust in this region is characterised by a correlation distance of 35 zt: 5 m and rms velocity perturbation of 4-6% in the uppermost 1-2 km of crust, associated with near-surface fracturing, and a correlation distance of 140 + 50m and rms velocity perturbation of 1.5 4-0.5% in the uppermost 6-8 km, associated with compositional heterogeneity. © 1998 Elsevier Science B.V. All rights reserved.

Keywords: correlation distance; heterogeneity; scattering; stochastic

1. Introduction Much research in recent years has been directed towards the study of wave propagation in layered and heterogeneous media, where the heterogeneities within the m e d i u m are randomly distributed and occur on a wide range of scales (Frankel and Clayton, 1986; Wu and Aki, 1988; Wu and Flattd, 1990). In the *Corresponding author. Fax: + 4 4 [email protected]

(1223) 360779; E-mail:

Earth's interior such variations occur at scales down to the grain size of rocks (Holliger et al., 1994). These heterogeneities may be due to spatial variations in composition, porosity and fracturing, and changing conditions in pore pressure, temperature and stress. A full deterministic description of such features, so numerous and varied, is neither possible nor particularly desirable; they can be more usefully represented by statistical models (Mandelbrot, 1983). The scattering of seismic energy from wavelength-scale heterogeneities in continental crust re-

0040-1951/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII $ 0 0 4 0 - 1 9 5 1 ( 9 7 ) 0 0 2 6 3 - 1

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C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

suits in perturbations in amplitude and phase in seismic arrivals. Wavelength-scale heterogeneity can produce significant seismic scattering and attenuation, and may be of importance in imaging the Earth's interior (Gibson and Levander, 1988; Holliger et al., 1994; Levander et al., 1994). The aim of this research is to investigate the effects of upper-crustal heterogeneity on seismic imaging of geological structures in the deeper crust. A variety of techniques, in most cases applied independently by each group of previous workers, were combined to provide a deeper understanding of the nature and origin of upper-crustal heterogeneity. Deterministic modelling of crustal features in unmigrated seismic data is subject to spatial averaging in the vertical direction over a distance of ,~/4 (where ,k is the dominant seismic wavelength) and in the horizontal direction over a distance of the order of the Fresnel zone (Berkhout, 1984). In migrated data the horizontal resolution limit is in theory reduced to ,k/2, but in practice is limited by the accuracy of the migration velocities used. Stochastic modelling, on the other hand, provides constraints on crustal heterogeneity of scales down to the order of the seismic wavelength and is independent of the assumptions of the velocity model used in migration. Such heterogeneity may be related to fracturing in the basement rocks, or to compositional variations. The data used are from the Svecofennian province of the Baltic Shield and includes: (I) normal-incidence seismic data from line 1 of the BABEL survey (BABEL Working Group, 1993), collected in the Bothnian Sea (Fig. 1); (2) normal-incidence data from line 5/7 of the Siljan seismic data set, collected in the area of the Siljan Ring impact structure (box labelled S in Fig. 1) in central Sweden (Juhlin and Pedersen, 1987); (3) vertical seismic profile (VSP) data; and (4) borehole sonic log data. The latter two from the Gravberg-t borehole, coincident with surface location 478 of Siljan line 5/7 (Juhlin, 1990a,b). Examples of normal-incidence stacked sections from the BABEL and Siljan surveys are shown in Fig. 2. They both feature bright crustal reflections, at TWTs of 2-4 s, ,that correspond to dolerite sills intruded into the predominantly silicic Palaeoproterozoic crust, 1.5-1.8 Ga in age. In the case of the BABEL data these sills crop out on the nearby Swedish mainland. In the case of the Siljan data the corre-

lation of the reflectors to dolerite sills is confirmed by geophysical logs and geological cores from the Gravberg-I borehole and from amplitude-versus-offset studies (Juhlin, 1990a,b). A stochastic inverse modelling scheme was applied to the seismic reflections from the sills in order to obtain estimates of statistical parameters describing the heterogeneity of the overlying crust. The scheme is based on the theory of wave propagation through random media (WPRM), a scalar wave-scattering theory based on the parabolic wave approximation (Flatt6 and Wu, 1988).

2. Theoretical background In stochastic modelling, crustal velocities of the Earth are represented as the superposition of a background deterministic component and a random stochastic component. The stochastic component, representing the smaller-scale fluctuations in slowness is assumed to be zero-mean, and is represented by its spatial autocovariance function (ACF). ACFs are commonly Gaussian, exponential or Von Karman in form (Frankel and Clayton, 1986; see also Goff and Jordan, 1988). The form of the ACF represents the scale dependence, or 'roughness' of the heterogeneous medium. The Hurst number is related to the degree of clustering. The power spectral density (PSD) is the Fourier transform of the ACE The dominant size of heterogeneity is given by a correlation distance, a, and the degree of heterogeneity is given by the rms fractional velocity perturbation ~. The theory of wave propagation through random media (WPRM), originally developed by Chernov (1960), describes weak wavefield fluctuations and attenuation in plane waves arising from acoustic scattering in heterogeneous media. Whilst it has already been applied to the analysis of teleseismic data by Aki (1973), Capon (1974), Capon and Berteussen (1974), Berteussen et al. (1975, 1977), Powell and Meltzer (1984) and Wu and Flatt6 (1990), we apply it to controlled-source data. The theory is used to derive phase and amplitude covariance functions for a generalised heterogeneous medium (Wu and Aki, 1988, pp. 178-185) and is subject to the Rytov approximation, which is valid for smoothly varying fluctuations in slowness. It is also subject to the parabolic wave approximation which states that scattering is predominantly small-angle (Wu and

C.E.R. Line et al./Tectonophysics 286 ~1998) 171-183

173

26°E 66°N

55°N

5°E

--~] Archean and Svecofennian (>~1.8Ga)

~

Post Svecofennian (< 1.8 Ga)

FFF~ Upper Proterozoic and Phanerozoic cover ii_.l._l,_iJ ~ Caledonides Fig. I. A portion of the Baltic Shield and its major geologic domains (adapted from Gaal and Gorbatchev, 1987); also shown are the locations of BABEL lines 1, 6 and 7. The rectangle on line I indicates the part of the data studied here. The area of the Siljan Ring is outlined in the box labelled S.

Aki, 1988, p. 6602). Since the theory is a scalar, rather than an elastic theory, density variations in the medium are not considered. Scalar wave theory is assumed to be adequate for small-angle scattering (Aki, 1973, p. 1342). 3. Method Wavefield fluctuations arising from scattering were estimated in the crustal reflections in the BA-

BEL and Siljan normal-incidence data sets. Field observations of the dolerite sills at outcrop on the Swedish mainland adjacent to the Bothnian Sea confirm that the sills show variations in mineralogy and relief that are slowly varying in the plane of intrusion (Line et al., 1997). Thus wavefield fluctuations in the sill reflections arising from features in the sills were assumed to be slowly varying, and estimated by least-squares fitting of a polynomial function to the observed wavefield variation. The

174

C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

(A) S 0

ol

x (km)

N 10

t

(B) S G-1 0

cO

x (km)

N 10

q~

v

v

~2 I--

I--

3 Fig. 2. A l0 km stack section of (A) BABEL line l, and (B) Sijan lines 5-7, showing subhorizontal crustal reflections from dolerite sills at 2-4 s two-way time (TWT). The sills were sampled in cores and interpreted from borehole logs of the Gravberg-I borehole (G-l). Section (B) as processed by Juhlin and Pedersen (1987).

lowest-order polynomial for which residual fluctuations are stationary and approximately Gaussian was used. Residual fluctuations in the reflections were attributed to small-angle scattering of the wave during its passage through the overburden. The data were subjected to bandpass-filtering to a narrow frequency band close to the dominant frequency, predictive deconvolution to remove waterbottom multiples, F/K filtering for apparent velocities of <6 km/s to remove steeply dipping noise, normal-moveout correction and stacking, and the travel time and peak amplitude of the first arrival were then picked for a particular event. Smoothly varying background functions were estimated in the phase and log(amplitude) variations and removed, and covariance functions were calculated from the residual fluctuations in phase and log(amplitude). A non-linear damped least-squares inversion was then carried out to determine the values of a and ~ that optimise the fit between WPRM predicted and observed covariance functions in phase and amplitude fluctuations. Stacking produces a filtering effect in trace-totrace perturbations, since rays that pass through different parts of the crust are being combined into the

stacked trace. In addition, the rays have travelled different distances through the crust and are thus subject to differing amounts of scattering. However, comparison of stacked shot-by-shot synthetics and plane-wave synthetics through heterogeneous media (Line, 1996) shows that trace-to-trace perturbations are not suppressed significantly if the stacking aperture (i.e. streamer length) is comparable to the Fresnel zone of the reflected energy (both are ~3 km in this case). Most importantly, stacking maximises the signal-to-noise of the primary reflections, which is crucial if this analysis is to be effective. Two models were considered for inversion. In each case seismic energy propagates from sources at the surface down to a reflector at depth zR and then reflects back to receivers at the surface. In the first case the entire portion of the crust overlying the reflector was assumed to be a single stochastic medium, for which the parameters a and ~ were determined. In the second case scattering was assumed to be occurring predominantly within some layer with upper and lower depth limits z~ and z2, respectively, and the parameters a, ~, zj and z2 were determined.

C.E.R. Line et al./Tectonophysics 286 (1998) 171 183

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LAG (m) Fig. 3. Wavefield perturbations for the reflection segment shown in Fig. 2A: (A) travel-time fluctuation relative to an estimated background variation; (B) log(amplitude) fluctuation relative to the estimated background variation; (C) autocorrelation functions of observed phase fluctuation (symbols) and modelled curves (lines); (D) autocorrelation functions of corresponding log(amplitude) fluctuations; (E) cross-correlation function of observed phase and log(amplitude) fluctuations (symbols) and modelled curves (lines). The modelled curves are as predicted by WPRM theory for an exponential medium with: (1) L fixed at 16 kin, with a = 107 m, ~ = 2.1% (solid line); and (2) position of the scattering layer allowed to vary, with best-fit values of =1 = 0.5 kin, =2 = 1.5 kin. a = 140 m. = 5.0% (dotted line). A noise level of 14% estimated for the data implies an uncertainty in travel time of 4-4 ms and in log(amplitude) of ±0.14 (shown by the vertical bars).

176

C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

4. Results

The analysis of one of the reflection segments in the BABEL data is shown in Fig. 3. In the first case the entire overburden is treated as a single stochastic medium. Correlation functions are shown for the observed fluctuations and the fitted model; although good agreement is obtained for the log(amplitude) fluctuations, poorer agreement is obtained for the phase fluctuations and the cross-correlation function. The poor fit is either a result of the simplicity of stochastic model, or because wavefield fluctuations arise in the reflection due to features in the sill. For six reflection segments analysed, a best fit between theoretical and observed functions was obtained for an exponential medium; average values of a and were estimated as 135 -+- 40 m and 1.5 4- 0.5%, respectively. The use of Gaussian media resulted in estimates of correlation distance that were 1.5-2 times greater. Inversions of the Siljan normal-incidence data yielded similar estimates for an exponential medium, with a slightly higher at 210 :t: 50 m and ~ slightly lower at 0,7 4- 0,2%. Fig. 3 also shows fitted correlation functions for a variable position of scattering layer (dotted line). For the BABEL data set an improved match was obtained (particularly for the phase covariance function) by using a thinner 1-2 km scattering layer in the near surface with rms velocity perturbations up to 6%. This indicates that scattering is predominantly occurring in a 1-2 km zone of relatively high heterogeneity in the uppermost crust. The Siljan data set, however, provided little resolution for the depth of scattering layer, probably due to the greater amount of noise in this land-acquired data set. For the collection of reflection segments analysed, exponential media provide better agreement between observations and theory than Gaussian media. Although determination of optimum values of Hurst number (Goff and Jordan, 1988) was also attempted, the data and method were found to provide poor resolution for this parameter. Sills at shallower levels in the crust in each data set proved to be too weak or discontinuous for the inversion to be effective. For most of the segments analysed, a values cluster around similar values (150 -4- 40 m), whilst there is a trade-off between L and ~ values, with both being relatively poorly constrained. The problem of poor

partitioning between L and ~ values in this method has been described previously by Berteussen et al. (1975) and Wu and Flatt6 (1990). Synthetic modelling of wave propagation through heterogeneous media (Line, 1996) shows that the parabolic wave approximation holds for ka > 1 (where k is seismic wavenumber). The data used in this research have been found to satisfy the Rytov and parabolic wave approximations. 5. Attenuation in VSP data

Seismic attenuation was estimated from VSP data, collected in the Gravberg borehole in four runs over different depth ranges (Juhlin, 1990b). Effective attenuation 1/Qeft arises from scattering and inelastic attenuation, Q~ and Q~, respectively, and is given by: 1/Qeff = 1 / Q a + I/Q~

(1)

Whilst Q~ is assumed to be frequency independent to first-order (Jannsen et al., 1985), Qs is generally frequency dependent in the range ka ~ 1 (e.g., Wu, 1982), with maximum attenuation (minimum Q) occurring for seismic wavelengths similar to the size of scatterers. The decay of amplitude A of a plane wave, frequency f, travelling a distance z with velocity v0, is given by:

A(z) = A(0) exp-_[_rrfzv(_~]

(2)

(Aki and Richards, 1980). A (frequency-independent) Q~, for a given frequency interval was estimated using the spectral ratio method (Jannsen et al., 1985; Hobbs, 1990; Scheirer and Hobbs, 1990; Juhlin, 1990b), i.e. from the slope of A21, the ratio of spectra at depths z2 and =L (from Eq. 2):

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Amplitude spectra were calculated from a 150-ms window of the P-wave arrival. The velocity v0 was estimated from the P-wave travel times for each VSP data set. Fig. 4 shows a summary of P-wave velocities and Q-values obtained for different depth ranges. The frequency dependence of Q was also investigated from the decay in amplitude of each frequency

C.E.R. Line et al./Tectonophysics 286 (1998) 171 183

177

(A) P-wave Velocity

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component with depth (the spectral decay method). Fig. 5 shows the frequency dependence of Q calculated for two depth windows. 1/ Qet~'is a maximum at frequencies of 180 Hz and 45 Hz for the depth windows 300-1200 m and 4000-5600 m, respectively. The wavelengths corresponding to these frequencies infer a size of scatterer that is 4 3 0 m in the upper portions and 4140 m in the deeper portions of the borehole. However, since the data are fairly noisy and the estimation of intrinsic and scattering Q is highly problematic, these methods are relatively error-prone compared to the other methods presented in this paper. The rapidly increasing velocity and high attenuation of the uppermost 1.5 km of crust, and also variation of shear-wave anisotropy and Poisson's ratio with depth (Juhlin, 1990b) are attributed to heavy

fracturing in this zone. Below a depth of 1.5 km these fractures are largely closed due to the increase in lithostatic pressure. 6. Stochastic analysis of borehole data

One of the main assumptions of WPRM theory is that heterogeneity of the medium concerned is dominated by variations in seismic velocity (or elastic parameters) rather than density. The stochastic properties of the sonic log from the Gravberg borehole were used to obtain further constraints of crustal heterogeneity in velocity. The stochastic properties of sonic logs have been previously analysed for boreholes penetrating crystalline basement rocks by Wu (1982), Leary (1991), Levander et al. (1994), Wu et al. (1994), Kneib (1995) and Holliger (1996), and

C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

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freq (Hz) Fig. 5. 1/Q values as a function of frequency, calculated for the depth range 300-1200 m (circles) and the depth range 4000-5600 m (stars). The arrows indicate the frequencies at which 1/Q is maximum.

also for boreholes in sedimentary rocks (Walden and Hosken, 1985). Fig. 6A shows sonic (P-wave) velocities derived from the Gravberg sonic log, after editing for spurious values due to cycle skipping (the error in calculated travel time arising from picking a different peak in the ultra-sonic waveform) and zones of non-stationary high-amplitude noise corresponding to borehole washout. The ACF of these velocities, after the removal of a background, linear velocity function, is shown in Fig. 6B. A non-linear damped least-squares inversion was carried out to obtain the best-fit ACF for a Von Karman medium; this is shown by the dashed curve. The corresponding PSD is shown in Fig. 6C.

The sonic log shows numerous low-velocity zones and high variability in the uppermost 1.2 km and a relatively uniform velocity between 1.2 and 4.0 kin. The small-scale variability in the lowermost portions is attributed to deteriorating borehole conditions below a depth of 4.0 krn (Juhlin, 1990b). Inversion of the ACF over the entire length of the log yielded a correlation distance of 38 m. Random noise in the data was estimated from the difference between zerolag and first non-zero-lag values of the ACF (Holliger, 1996). This analysis shows that rms random noise constitutes 40% of the total rms fluctuation in the log, The theoretical PSD of a Von Karman medium is flat up to a 'corner wavenumber' K~ = l/a,

Fig. 6. (A) The Gravberg sonic log, edited to remove outliers. The log is more variable in the uppermost 1.2 km of crust due to increased fracturing; below a depth of 4.0 km variability arises from the deteriorating condition of the borehole wall (Juhlin, 1990b). (B) Autocovariance function of P-wave velocities from the sonic log (solid line), after the removal of a linear background velocity function of v(z) = 5.5 + 0.10z km/s. The best-fit Von Karman ACF, obtained using the given parameters, is also shown (dashed line). (C) PSD for the sonic log P-wave velocities. Given values of a and v are deduced from the comer wavenumber and higher wavenumber slope. Noise and rms velocity perturbation dv are deduced from a Wiener inversion of the PSD. The arrows show wavenumbers corresponding toa=133manda=38m.

C.E.R. Line et al./Tectonophysics 286 (1998) 171 183

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C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

where a is the correlation distance previously defined. Above this wavenumber the spectrum shows a power-law dependence with an exponent equal to - ( 2 v + 1), where v is the Hurst number (Goff and Jordan, 1988). Above the signal bandwidth (frequencies K > K0) the spectrum is noise dominated and once again flat. The high-wavenumber power-law exponent of the observed PSD (Fig. 6C) was estimated by linear regression on a log-log plot, and shows a 1/K dependence or 'flicker noise' (Holliger, 1996). The corner wavenumber was estimated as the wavenumber at which the curve fell to 3 dB below its low-wavenumbet value and gives a correlation distance a = 133 m. Random noise was estimated using a Wiener inversion (Press et al., 1992, pp. 417-420) of the PSD. In this method the noise spectrum is assumed to be white, and is estimated outside the signal bandwidth (K > K0). The total noise fluctuation is then extrapolated over all wavenumbers and subtracted from the total fluctuation to give rms velocity perturbation. The noise estimated agrees extremely well with the previously obtained estimate from the ACF (an rms of ~95 m/s, or 40% of the total fluctuation); likewise, the residual fluctuation arising from velocity perturbations in the bedrock (~205 m/s). This is equivalent to 3.6% of the background velocity. Within the depth interval 0-1.2 km, rms velocity perturbation is 325 m/s, or 5.9 4- 2.0%; for the depth interval 1.2-3.9 kin, rms velocity perturbation is 116 m/s, or 1.9 ± 0.5%. These values from the sonic log are higher than those obtained from seismic data (3-6% in the uppermost 2 km, 1.5 ± 0.5% in the uppermost 8 km) since the scale range of heterogeneity that can be resolved by seismic methods is limited by the seismic wavelength. Assuming that the bedrock contains heterogeneity at both scales, i.e. both estimates of a are 'real', a break in the PSD slope should be observed at a wavenumber of 0.026 m -l (corresponding to a = 38 m) but is difficult to distinguish due to the high variability of the spectrum in that region (Fig. 6C). Thus the value of a estimated from the PSD was a = 133 m. Conversely, the ACF is best constrained at small lags. Thus the ACF inversion (Fig. 6B) yielded an estimate of a = 38 m. The sonic log is the result of a convolution between slowness variations in the bedrock and the

system response of the logging tool (Holliger, 1996). In the above analyses the log was not deconvolved tbr system response, since this was unknown. Whilst such a deconvolution would have little effect on the estimation of the correlation distance a or rms velocity perturbation ~, it would decrease the estimation of Hurst number v slightly. This does not however explain why the Hurst number v determined from the ACF (~0.3) is higher than that obtained from the PSD C'-0). Synthetic models show that a sigilificant degree of white noise in a self-affine system can lead to an under-estimation of Hurst number from the PSD (Line, 1996). A Hurst number between 0 and 0.3 seems likely.

7. Discussion The self-affine nature of the upper crust implies that heterogeneity is present at a wide range of scales. The degree of heterogeneity sampled by a physical experiment will therefore have some dependence on the resolution window of the data. For example, the rms velocity perturbation estimated from borehole sonic logs is greater than that estimated from coincident seismic data; seismic data can only resolve heterogeneity down to the order of the seismic wavelength, whilst the spatial resolution of sonic logs is less than 1 m. Similarly, an inversion will not resolve correlation distances that lie outside the resolution window of the data used. Thus, the 40-m scale fracturing was not resolved by the surface seismic methods (of frequencies 15-45 Hz). The different data sets also sample the crystalline basement in different orientations. Transverse covariance functions in surface seismic data are linked mainly to horizontal correlation distances, although the theory also assumes that the heterogeneities are approximately isotropic. The characteristic scales of the sonic logs relate to heterogeneity in the vertical direction, e.g. vertical spacing of fractures. Both the scattering and attenuation analyses of the VSP data implicitly assume an isotropic, heterogeneous medium. Comparison of the larger characteristic scale of the sonic log (133 m) and the correlation distances obtained from the surface seismic data suggest that compositional heterogeneity in the granitoid basement of the Siljan Ring is approximately isotronic.

C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

The likely origins of fracturing in the area include natural weathering, de-glaciation, tectonic movements, the impact event and intrusion of dolerites and granites (Juhlin, 1990b). The Gravberg borehole is located in the mega-block zone of the impact structure, which is characterised by major block faulting of the basement. Fracture zones horizontally spaced at ~250-m intervals persist down to a depth of 6000 m. Many of these coincide with boundaries of doleritic and granitic intrusions. Others are visible in the normal-incidence data as features dipping at low angles to the south (Juhlin, 1990a). The sense of dip of these features is consistent with postimpact normal faulting towards the centre of the impact structure (Juhlin and Pedersen, 1987). Thus the larger fault zones in the uppermost 6 km of crust appear to be related to the impact and magma intrusion events. Fractures associated with tectonic faulting or post-impact faulting are expected to show some degree of clustering and alignment, either perpendicular to the direction of minimum stress (Crampin et al.. 1984), or parallel to active faults (Crampin et al., 1990). Velocity anisotropy studies (Juhlin, 1990b) suggest that in the Siljan Ring only ~10c~ of cracks are aligned, i.e. most are of random orientation. Furthermore, heterogeneity of the basement seems to be associated with Hurst numbers in the range 0-0.5. In analyses of scattering in seismic data presented here, the upper crust has been modelled as an exponential medium; this corresponds to a Hurst number of 0.5. Hurst numbers of 0.5 or less arise

181

from fracturing with a clustering less than or equal to that of a random distribution. The smaller-scale fractures in the uppermost 1-2 km thus appear to be non-clustered and non-aligned. This may suggest that they are related to regional uplift associated with glacial erosion and de-glaciation and natural weathering, rather than tectonics or post-impact faulting. 8. Conclusions Stochastic analyses of surface seismic reflection data, VSP data and borehole logs have provided consistent constraints on upper-crustal heterogeneity. The combination of the different data has provided insight into the nature of the heterogeneity observed. The results of the various analyses are given in Table I and displayed in Fig. 7. Values of Hurst number v could only be derived from the sonic logs and thus cannot be compared between the different methods. Compositional heterogeneity in the uppermost l0 km of crust in the central Svecofennian province is best modelled as an exponential medium with a correlation distance of 150 ± 50 m and rms velocity perturbation of 1.0-2.0%. These correlation distances are estimated subject to the limits in resolution of the data and method in each case. A lower limit is imposed by the spatial sampling and an upper limit is imposed by the aperture of data and by the background velocity function removed. Estimates of a are useful insofar as they are the dominant scattering lengths observable in the data. They are interpreted to arise largely from

Table 1 Summary of results for the different data sets, with estimates of correlation distance a, rms velocity perturbation ~ and Hurst number v calculated tbr the depth intervals indicated, v could only be derived from the sonic logs Data sel BABE1, seismic

a (m)

e (%)

(L fixcd) tL varied)

135 + 40 150 ± 50

1.5 ± 0.5 4.3 :t::0.8

Siljan seismic

II, fixed)

210 + 50

0.7 + 0.2

Gravberg sonic

(ACF) (PSD)

38 =k 6 133 ± 30

5.9 := 2.0 1.9 ± 0.5

Gravberg VSP

(Q)

30 140 131 -k30 82 + 25 135 + 4 0

-

(WPRM)

3 . 6 ± 1.0 0.7 + 0.2 0.4±0.2

v

Depth mr. (km) 0 -8 0 2 0 -7

0.3 0

0 -12 1.2-3.9

-

0 1.2 4 6 0 1.2 0.8-2.4 2.1-3.9

-

182

C.E.R. Line et al./Tectonophysics 286 (1998) 171-183

(A) Correlation distance 250

200

t ....................................

150 4

• ......

!

5)

[]

-

(13

• BABEL nomal incidence

100• .......

[] <~ (b •

•

i

50 :::::::::::::::::::::

I

I

0.0

1.0

3.0

2.0

~

I

(B) R m s v e l o c i t y 6.0 @

i

4.0 5.0 6.0 DEPTH (km)

4~

4.0

i

I

~

7.0

I

~

8.O

I

9.0

10.0

perturbation • [] <~ •

50 2

Siljan normal incidence Gravberg Sonic Gravberg VSP (Q) Gravberg VSP (WPRM)

BABEL nomal incidence Siljan normal incidence Gravberg Sonic Gravberg VSP (WPRM)

3.o

I

2.0 i

[]

4>

-

•

4>

• •

. . . . . . . . . . .....

[]

•

E

0.0

1.0

2.0

3.0

4.0 5.0 6.0 DEPTH (km)

70

8.0

I

9.0

i

10.0

Fig. 7. Summary of results from the various data presented here: (A) values of correlation distance; (B) values of ~. Values of Hurst number v could only be derived from the sonic logs and thus cannot be compared between the different methods.

lithological variations within a predominantly silicic upper crust (e.g. intrusions of different composition), and from fracturing. Scattering and attenuation of seismic waves is dominantly in the uppermost 1-2 km of crust in the area of the Siljan Ring (or the uppermost 2-3 km of crust in the area of the Bothnian Bay), where a relatively high degree of fracturing (a mean fracture spacing of 435 m) gives rise to a much higher rms velocity perturbation of 3-6%. In general, the upper crust appears weakly scattering in the region of the central Svecofennian province, and this may be one reason why the BABEL and Siljan surveys have

been so successful in imaging features in the deeper crust.

Acknowledgements The authors would like to thank Chris Juhlin and others in the department of Geophysics of Uppsala University for the acquisition and processing of the Siljan normal-incidence data, and for supplying the VSP and borehole log data from the Gravberg- 1 borehole. Cambridge Earth Science Contribution number ESC 4976.

C.E.R. Line et al./Tectonophysies 286 (1998) 171-183

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