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3 C h a p t e r Onshore mainland LGC study
138 | P a g e Location
W ell
#
Well orient
ation N distribution R2
D-value Slope Cv Clustering FD (fault per metre) Assynt
Terrane 1 E-W 22 power-law 0.98 0.87 1.03 random 0.001
2 E-W 29 power-law 0.87 1.04 1.01 random 0.002
3 E-W 28 power-law 0.96 1.18 0.88 anti-clustered 0.002
4 E-W 20 power-law 0.94 0.50 0.95 anti-clustered 0.001
5 E-W 26 exponential 0.99 26.81 0.87 anti-clustered 0.001
6 E-W 17 power-law 0.92 1.15 1.05 random 0.001
7 E-W 25 exponential 0.96 28.42 0.81 anti-clustered 0.002
8 E-W 18 power-law 0.99 0.92 1.11 clustered 0.001
9 E-W 15 exponential 0.97 12.60 1.14 clustered 0.001
11 E-W 16 power-law 0.94 1.07 0.77 anti-clustered 0.001
12 E-W 18 power-law 0.98 2.19 0.61 anti-clustered 0.001
14 E-W 21 exponential 0.98 23.86 0.74 anti-clustered 0.001
19 N-S 40 power-law 0.99 1.19 0.89 anti-clustered 0.002
20 N-S 40 power-law 0.95 0.84 0.79 anti-clustered 0.002
21 N-S 43 exponential 0.98 46.17 1.02 random 0.002
22 N-S 34 exponential 0.98 33.13 0.95 anti-clustered 0.001
23 N-S 27 power-law 0.99 1.53 0.9 anti-clustered 0.001
24 N-S 28 power-law 0.96 0.90 1.06 random 0.001
25 N-S 16 power-law 0.97 0.78 0.89 anti-clustered 0.002
31 NW-SE 32 power-law 0.94 1.67 0.73 anti-clustered 0.002
32 NW-SE 37 exponential 0.98 40.48 0.96 anti-clustered 0.002
33 NW-SE 29 power-law 0.97 1.05 1.53 clustered 0.001
34 NW-SE 30 power-law 0.94 0.39 0.99 anti-clustered 0.002
38 NW-SE 26 exponential 0.95 31.94 0.94 anti-clustered 0.002
39 NW-SE 25 power-law 0.92 0.89 0.75 anti-clustered 0.002
45 NE-SW 23 power-law 0.96 1.13 1.09 random 0.001
46 NE-SW 27 power-law 0.98 0.85 1.22 clustered 0.001
47 NE-SW 21 power-law 0.94 0.65 1.5 clustered 0.001
Rhiconich
Terrane 15 E-W 17 power-law 0.98 0.53 1.18 clustered 0.001
16 E-W 17 power-law 0.99 1.23 1.01 random 0.002
26 N-S 15 power-law 0.95 0.49 1.39 clustered 0.001
27 N-S 13 exponential 0.96 51.04 0.42 anti-clustered 0.001
28 N-S 19 power-law 0.97 0.99 0.77 anti-clustered 0.001
29 N-S 22 power-law 0.94 1.32 1.11 clustered 0.001
40 NW-SE 21 power-law 0.95 1.02 1 random 0.001
41 NW-SE 31 power-law 0.98 1.34 1.03 random 0.002
42 NW-SE 11 power-law 0.95 1.14 0.74 anti-clustered 0.001
Table 3.3: Spatial attributes of faults from pseudo-wells created in the low resolution mainland LGC DEM study.
3 C h a p t e r Onshore mainland LGC study
139 | P a g e 3.2.4.2 –D-value
Those fault spacing distributions that exhibit power-law distributions have associated D-values (slope of the trend line). From the Assynt Terrane full resolution data set, the power-law distributions have D-values between 0.38 and 1.56, with E-W trending pseudo-wells showing the largest variations in D-value (Table 3.1). Over half of the power-law distributions from the Assynt Terrane exhibit D-values that are >1. The low resolution dataset from the Assynt Terrane shows a similarly wide variation in D-values for the power-law distributions (0.39 to 2.12, Table 3.3).
D-values from the Rhiconich Terrane power-law distributions vary between 0.35 and 1.09 (Table 3.1) with the low resolution dataset D-values varying between 0.49 and 1.34 (Table 3.3). The majority (84%) of spacing distributions from the Rhiconich Terrane high resolution dataset have D-values that are <1 (Table 3.1). This is in comparison to the low resolution spacing distributions where their associated D-values are commonly
>1, (67%, Table 3.3).
The Canisp Shear Zone power-law distributions exhibit D-values between 0.51 and 1.9 with N-S and NE-SW trending pseudo-wells exhibiting the highest D-values (Table 3.1). D-values for the Laxford Front power-law pseudo-well samples vary between 0.9 and 4.23 with NW-SE trending pseudo-wells exhibiting the largest values. The majority (80%) of D-values for power-law distributions in the Laxford Front area are >1 (in the Canisp Shear Zone only 50% of D-values are >1).
3.2.4.3 – Coefficient of variation (CV)
The coefficient of variation (CV) has been calculated for every pseudo-well sample in the regional mainland LGC study to gain an insight into the clustering relationships of the interpreted faults. Power-law distributions from the Assynt Terrane (high resolution) have CV values between 0.63 and 1.69 (Table 3.1), with the low resolution Assynt Terrane power-law distributions exhibiting CV values between 0.61 and 1.53 (Table 3.3). Exponential distributions in the Assynt terrane have CV values between 0.72 and 1 (high resolution) and 0.77 and 1.11 (low resolution), with the majority (>75%) of CV values <1 (Tables 3.2 & 3.3, respectively).
Power-law samples from the Rhiconich Terrane have CV values that vary between 0.87 and 2.2 for the high resolution datasets (Table 3.1). The low resolution power-law datasets for the Rhiconich Terrane area exhibit CV values between 0.42 and
3 C h a p t e r Onshore mainland LGC study
140 | P a g e 1.39 (Table 3.3). The majority of CV values (93%) for Rhiconich Terrane power-law distributions are >1. Exponential spacing distributions within the Rhiconich Terrane regional study exhibit CV values between 0.76 and 1.07 (high resolution, Table 3.2) and 1 (low resolution, Table 3.3). Most of the CV values (80%) from the Rhiconich Terrane exponential distributions have CV values around 1.
Canisp Shear Zone power-law samples have CV values that vary between 0.71 and 1.77, with many of the samples (47%) exhibiting clustered fault distributions (CV >1, Table 3.1). This is in contrast to the exponential samples for the Canisp Shear Zone which have CV values between 0.74 and 1.08, with the majority (88%) of samples exhibiting CV values <1 (Table 3.2).
3.2.4.4 – Fault density (FD)
Tables 3.1, 3.2 & 3.3 also contain information on the fault density for each pseudo-well in the high resolution and low resolution samples. In the high resolution dataset, the Assynt Terrane and Rhiconich Terrane pseudo-wells have an average fault density of 0.003 faults per metre (or 3 faults per kilometre). There is little apparent difference between the fault density values calculated for the power-law (Table 3.1) or the exponential (Table 3.2) spacing distributions in either terrane. The low resolution sample exhibits fault density values of only 0.001 faults per metre (or 1 fault per kilometre) for both the Assynt and Rhiconich Terranes (Table 3.3).
The Canisp Shear Zone exhibits average fault density values of 0.005 faults per metre, with one pseudo-well exhibiting a fault density value of 0.007 faults per metre (exponential distribution, Table 3.2). In the Laxford Front sample area the fault density values for both power-law and exponential distributions have an average of 0.003 faults per metre.
3.2.5 - Regional fault lineament connectivity
Fault connectivity in the mainland LGC has been analysed in 2-dimensions by interpreting all of the fault lineament intersections (nodes) from the high resolution datasets. This analysis illustrates how faults interact with each other, but does not consider fluid flow pathways between nodes. Therefore the resulting maps (Figure 3.12) only give an appreciation of the potential connectivity for the faults interpreted from the mainland LGC. It should also be noted that all of the faults interpreted from the
3 C h a p t e r Onshore mainland LGC study
141 | P a g e mainland LGC are assumed to be vertical and therefore the connectivity analysed in this study is also vertical.
The connectivity density maps show that when all of the fault lineaments are included (Figure 3.12a) the connectivity is higher within the Assynt Terrane, particularly south of Loch Glencoul (marked with a red star on the inset to Figure 3.12a). This pattern remains true when faults interpreted at 1:50,000 scale (Figure 3.12b) and 1:25,000 scale (Figure 3.12c) are analysed independently. Consistently the area surrounding the Canisp Shear Zone shows the highest connectivity density values. The 1:25,000 scale connectivity density map (Figure 3.12c) also shows an area of high density to the north of the LGC area in the Rhiconich Terrane. This area is associated with a major NW-SE trending normal fault (the Loch Inchard Fault).
3.2.5 – Regional fault lineament spatial analysis: Discussion
Population distribution plots from the mainland LGC exhibit both exponential and power-law spacing distributions (Figures 3.9 & 3.10). Power-law relationships are more common in the low resolution mainland LGC dataset, but the number of data points (less than 30 points) in each sample and the fact that they do not extend over more than one order of magnitude means that they represent a rather weak relationship and should be treated with caution. This is true for the majority of power-law distributions observed within the regional mainland LGC datasets.
The weak power-law spacing distributions may be a result of the sampling technique: because more than one prominent fault trend is being sampled by each pseudo-well, an exponential spacing distribution is more likely, as these are more commonly associated with fault sets that are distributed through a range of azimuths. At a regional scale, sampling one prominent fault orientation from the full fault network is difficult to do and therefore it is likely that exponential distributions will be more common.
3 C h a p t e
3 C h a p t e r Onshore mainland LGC study
143 | P a g e To test if the sampling process at the regional scale is responsible for the exponential and weak power-law spacing distributions, each fault azimuth group (N-S, NE-SW, E-W & NW-SE) has been sampled independently using perpendicular pseudo-wells (e.g. NW-SE trending pseudo-pseudo-wells sample NE-SW trending faults). To allow direct comparison with the results from a similar analysis from the Clair basement fault lineament maps, only the low resolution dataset has been used for the mainland LGC study. The population distribution plots from this study are shown in Figure 3.13.
The spacing distributions are consistently power-law for all pseudo-well azimuths when each fault azimuth group is sampled independently. It should be noted, however that these power-law relationships often contain less than 30 data points which means that they are not statistically robust. These weak power-law relationships suggest that the spatial relationships of faults within the regional mainland LGC dataset cannot be confidently used as an estimation of the spatial relationships of fault and fractures at different scales.
The majority (63%) of power-law pseudo-wells in the Assynt Terrane and the Laxford Front areas have CV values <1 (Table 3.1) which means that the faults exhibit anti-clustered (regularly spaced) or in some cases (when the CV value is close to 1) random spacing (Johnston et al., 1994). These anti-clustered fault spacing patterns are more commonly representative of exponential spacing relationships and do not reflect power-law datasets. Therefore it is likely that those pseudo-wells which have low CV values, and have been classed as power-law, instead, represent weakly defined exponential spacing distributions.
3 C h a p
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13: Populatio
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mainland LGC regional studdy. (a) E-W treending lineaments. (b) NW--SE trending liineaments. (c) N-S trendingg lineaments. (d) NE-SW treending lineam
144 | P a g ments.
g e