Service: Detect the most intensely networked locales
FIND where your exploration tenements display heightened structural complexity. A case study of Ontario's Kirkland Lake region gives a taste of what's possible with complexity maps.
The problem of incorrectly appraising prospects is a continual threat when undertaking any exploration campaign. 
But whenever attempts to unravel the full deformation history of a tenement creates more questions than answers, a way to salvage things may be to map the area's geological complexity.
This is possible because, fortunately, places where rocks have been put through the ore-mineralization wringer usually show signs of being relatively structurally complex. 
Complexity and fault connectivity
Faults, folds, shear zones and lithological contacts can help carry or occlude any metals-bearing fluids passing through a region on their way to more thermodynamically-friendly locales. 
Under the right conditions, an intricate network built from these kinds of geological structures not only hosts highways for high-volume fluid transport, but also supplies sites where physical and chemical conditions induce metal-ore precipitation. 
In a recent paper hinting that complexity may one day be a go-to measure for sniffing out ore mineralization, researchers at the China University of Geosciences, Jiangnan Zhao, Shougu Chen and Renguang Zuo, along with Netherlands' University of Twente researcher Emmanual John Carranza laid out the results of a study of geological complexity in a tin-ore district in southwestern China. 
The researchers said highly complex zones of rocks "likely experienced multiple processes that played critical roles in the formation of [ore] deposits", because such zones tended to have a high probability of having well-developed fault connectivity.
They said their findings suggested that the complexity of faults' spatial distribution could be used as a vector to ore.
Researchers have been looking at the idea that geological complexity — the spatial distribution of geological features such as folds, faults and lithological contacts — is associated with the occurrence of special ore-forming environments.   
Why do some rock volumes appear more complexly structured than others?
It's thought that the interaction between inelastic and elastic behavior in stressed rocks results in complex rock-failure effects and complex strain redistribution patterns. The result is that some locales become highly deformed, while others remain screened out and so appear relatively untouched. 
A scientific side-debate that arose about geological complexity involved whether the distribution of known ore deposits is best explained by complexity or complexity gradients   . Nevertheless, for explorers, the debate about complexity versus complexity gradients may be neither here nor here — because if you've measured one of these two properties, you can work backward to arrive at the other one.
Complexity is useful to explorers across a range of ore types. For instance:
- structurally-controlled gold in greenstone-granite areas such as those in the Yilgarn and in Canada   ,
- Mt Isa-style copper  ,
- porphyry copper, such as those in western USA , and
- other hydrothermal deposits  ,
are some of the mineralization styles encompassed in the geological complexity literature.
Ways to assess geological complexity have included, among others:
- fractal dimension       
- fuzzy logic 
- texture analysis  
Fathom Geophysics assesses complexity by using a mimicry filter. The approach as roughly analogous to judging how well a cuttlefish has camouflaged areas of its skin by mimicking the colors and patterns of the underlying sandy seabed. If the cuttlefish has skin areas that aren't camouflaged well, then those areas are where the animal's instinctive mimicry process performed worst. The cuttlefish is sitting on seabed that has a more complex pattern than it can reproduce.
The overall approach is:
- Perform predictive calculations to try to 'flatten' the data perfectly.
- Areas where the above step fails are attributed, by definition, as being more complex than areas where it succeeds.
- The resulting complexity map spatially quantifies throughout the exploration area the degree to which mimicry failed or succeeded. For the case study shown here, the yellow-, orange- and red-colored areas are where the mimicry performed worst, and hence are the areas demonstrating the greatest structural complexity.
Case study: Kirkland Lake region
For a taste of what's possible with complexity mapping, we've processed public-domain magnetic data available for the metallogenically well-endowed Kirkland Lake region of Ontario, Canada (Figure 1).
FIGURE 1: Reduced-to-the-pole (RTP) magnetic data for the case study area, the Kirkland Lake greenstone-granite region in Ontario, Canada. Deposit locations and names were defined using information from a Geological Survey of Canada database on orogenic gold deposits.
The case-study's map area includes the orogenic gold deposits of Kirkland Lake, Bidgood Kirkland, Upper Canada, McBean, Queenston, Victoria Creek, Omega, Upper Beaver, Beaverhouse Lake, Kerr Addison and Chesterville. (Orogenic gold is also known as structurally-controlled gold and as lode gold.) The area also contains a multitude of more-minor gold shows.
The region's geology (Figure 2) forms part of a greenstone-granite terrane in the Archean-aged Superior Province. Canada-based researchers Vladimir Ispolatov, Bruno Lafrance, Benoit Dube, Robert Creaser and Michael Hamilton presented field-based mapping work on the geological and structural setting of gold mineralization in the Kirkland Lake area in a 2008 paper. 
FIGURE 2: Interpreted geology in the Kirkland Lake region (Source: Ontario Geological Survey, 1:100,000 scale, Map Number P3425. Please refer to an original version of the map for lithological unit names and information).
After we mapped the region's structures (Figure 3) to get a feel for structural relationships contained in the magnetic data, we mapped the region's complexity at three different levels of relative detail: the small scale, the medium scale, and the broad scale.
FIGURE 3: Structures extracted from the Kirkland Lake region RTP magnetic data using Fathom Geophysics' computer-vision routines. Structures shown are those with wavelengths of between 0.8 kilometer and 2.4 kilometers.
Figure 4, Figure 5 and Figure 6 show the complexity mapping results for the analysis done at each scale. Results of a different method for mapping Kirkland Lake region's broad-scale complexity can be seen in a recently published scientific paper. (See reference .)
FIGURE 4: 'Fine scale' complexity map arrived at for the Kirkland Lake region RTP magnetic data using Fathom Geophysics' computer-vision routines.
FIGURE 5: 'Moderately coarse' complexity map arrived at for the Kirkland Lake region RTP magnetic data using Fathom Geophysics' computer-vision routines.
FIGURE 6: 'Very coarse' complexity map arrived at for the Kirkland Lake region RTP magnetic data using Fathom Geophysics' computer-vision routines.
We found the region's broad-scale complexity map particularly interesting. A relatively brief manual inspection showed that sinous arcs of heightened complexity (running roughtly east-west) seem cross-cut by straight high-complexity corridors that strike roughly north-northwest (Figure 7).
FIGURE 7: Manually-placed pale-white stripes highlighting broad trends observed in the 'very coarse' complexity map arrived at for the Kirkland Lake region RTP magnetic data using Fathom Geophysics' computer-vision routines. The sinuous east-west features run parallel to the regional fabric of the greenstone-granite lithologies. The corridors that strike roughly north-northwest have a cross-cutting relationship to the regional fabric.
Figure 8 illustrates the sorts of further analysis possible with a complexity map. We've taken our broad-scale complexity map and superimposed our structural analysis results over the top. These structures appear as black lines. At the same time, we've defined the areas containing the greatest broad-scale complexity by applying a threshold value. These areas are contained inside the white loops.
FIGURE 8: Black lines are structures extracted from the Kirkland Lake region RTP magnetic data, shown in vectorized form. The interiors of the white, rounded loops are where the 'very coarse' complexity is defined (using a thresholding procedure) as being relatively heightened. Underlying all of the lines is the 'very coarse' complexity map arrived at for the Kirkland Lake region RTP magnetic data using Fathom Geophysics' computer-vision routines.
Figure 9 shows the same black lines and white loops, but this time the base map is the Kirkland Lake region RTP magnetic data.
FIGURE 9: Black lines are structures extracted from the Kirkland Lake region RTP magnetic data, shown in vectorized form. The interiors of the white, rounded loops are where the 'very coarse' complexity is defined (using a thresholding procedure) as being relatively heightened. Underlying all of the lines is the RTP magnetic data for the Kirkland Lake region.
Not so unusual after all?
As far as we can tell, in the economic geology literature for the Kirkland Lake region, there's little to no mention of gold mineralization control by greenstone belt-crossing structures.
Rather, the region seems regarded as notorious for hosting deposits that appear controlled largely by the location of major belt-parallel structures.
For instance, in their 2008 field-based research paper, Ispolatov and his colleagues said of the region's orogenic gold deposits: "Mineralization is hosted by a first-order structure, the Larder Lake-Cadillac deformation zone, rather than by second- and/or third-order structures. Mineralized zones are commonly associated with gentle bends along the Larder Lake-Cadillac deformation zone."
"The observed localization of syndeformational, 'orogenic' gold mineralization in a first-order deformation zone is generally atypical," they said.
"In most economically significant gold camps associated with regional deformation zones, the largest deposits are hosted by subsidiary, second- or third-order faults and shear zones."
University of Ottawa and Geological Survey of Canada researchers Anne Pescheler, Keith Benn and Walter Roest in 2006 suggested that mineralizing fluids may have traveled along the deformation zone itself, from either greater depths or from the east. 
However, the gold story in the Kirkland Lake region may have additional, as-yet undocumented chapters.
Looking at the complexity maps we've produced, we reckon the research community — and gold explorers — should consider looking for groundtruthed evidence about whether the roughly north-northwest-striking features we've noted significantly control gold-deposit distribution.
Our complexity mapping suggests that complexity corridors striking roughly north-northwest may have something to do with mineralization wherever they cross-cut the major greenstone-belt-parallel structures, such as the Larder Lake-Cadillac deformation zone (also known as the Kirkland-Cadillac deformation zone) and its splays (Figure 10 and Figure 11).
FIGURE 10: Monochrome version of the RTP magnetic data map of the Kirkland Lake region. Image has been supplied as a baseline reference for comparisons with the next image.
FIGURE 11: Manually-placed stripes highlighting broad trends observed in the 'very coarse' complexity map (see Figure 7 to see how placements were done). Shown in pale blue are the sinuous east-west features that run parallel to the regional fabric of the greenstone-granite lithologies. Shown in pale yellow are the corridors that strike roughly north-northwest and that have a cross-cutting relationship to the regional fabric. The interiors of the white, rounded loops are where the 'very coarse' complexity is defined (using a thresholding procedure) as being relatively heightened. Underlying everything is the monochrome version of the RTP magnetic data map of the Kirkland Lake region.
The structures responsible for producing the noticeable north-northwest-striking corridors in the broad-scale complexity map may have carried large volumes of metals-bearing fluids, directing them to locales favorable for inducing gold ore precipitation.
For instance, if the gold-bearing fluids were at least partly sourced from magmatic fluids expelled from the crystallization of felsic batholiths seen in the south of the case-study region, and if the fluids were migrating towards the north-northwest, then the highly sheared rocks in the Larder Lake-Cadillac deformation zone may have contained the first significant impermeable barriers to those migrating fluids.*
This in turn may have provided the fluids with opportunities to undergo the physico-chemical processes requisite for dropping out their gold content, such as deceleration, traveling along contorted paths, cooling, and reacting with any appropriate nearby lithologies.**
If something akin to this scenario turned out to be true, then the Kirkland Lake region's deposits would bear a closer-than-currently-claimed resemblance to more typical orogenic gold deposits, such as those in the greenstone-granite terranes of the Yilgarn in Western Australia and others elsewhere.***
The gold deposits of the Kirkland Lake region, arguably, would therefore look a little less like the black sheep of the orogenic gold family.
References and notes
 For example, see general discussion on targeting in: (a) E.D. Attanasi (1981) "Exploration decisions and firms in the mineral industries", Energy Economics, April Issue, 105-112. (b) J.W. Harbaugh (1984) "Quantitative estimation of petroleum prospect outcome probabilities: An overview of procedures", Marine and Petroleum Geology, Volume 1, November, 298-312. (c) J.B. Ramsey (1980) "The economics of oil exploration: A probability-of-ruin approach", Energy Economics, January Issue, 14-30.
 See, for example, discussion and cited work in: J. Zhao, S. Chen, R. Zuo, E.J.M. Carranza (December 2011) "Mapping complexity of spatial distribution of faults using fractal and multifractal models: Vectoring towards exploration targets", Computers and Geosciences, 37, 1958-1966.
 See, for example: R.H. Sibson (2004) "Controls on maximum fluid overpressure defining conditions for mesozonal mineralisation", Journal of Structural Geology, 26, 1127-1136. Sibson said the requirement for "near-lithostatic values of fluid-pressure ot offset the overburden pressure [of hundreds of megapascals] and create void-space in [mesozonal] environments has long been recognized. ... The restricted circumstances under which this may occur has direct implications for exploration in the mesozonal environment."
 See, for example, discussion and cited work in: S. Micklethwaite, H.A. Sheldon and T. Baker (2010) "Active fault and shear processes and their implications for mineral deposit formation and discovery", Journal of Structural Geology, 32, 151-165. They said: "Geological structure has a first-order spatial relationship with hydrothermal ore deposits."
 F.P. Bierlein, F.C. Murphy, R.F. Weinberg and T. Lees (2006) "Distribution of orogenic gold deposits in relation to fault zones and gravity gradients: Targeting tools applied to the Eastern Goldfields, Yilgarn Craton, Western Australia", Mineralium Deposita, 41, 107-126. They said: "Clearly, gold deposit location is controlled by the interaction of numerous factors that were active across many scales."
 See, for example, discussion and cited work in: P.F. Hodkiewicz, R.F. Weinberg, S.J. Gardoll and D.I. Groves (2005) "Complexity gradients in the Yilgarn Craton: Fundamental controls on crustal-scale fluid flow and the formation of world-class orogenic-gold deposits", Australian Journal of Earth Sciences, 52, 831-841.
 A. Ford and T.C. McCuaig (2010) "The effect of map scale on geological complexity for computer-aided exploration targeting", Ore Geology Reviews, 38, 156-167.
 A. Ford and T.G. Blenkinsop (2008) "Evaluating geological complexity and complexity gradients as controls on copper mineralisation, Mt Isa Inlier", Australian Journal of Earth Sciences, 55, 13-23.
 E.-J. Holden, J.C. Wong, P. Kovesi, D. Wedge, M. Dentith and L. Bagas (in press) "Identifying structural complexity in aeromagnetic data: An image analysis approach to greenfields gold exploration", Ore Geology Reviews.
 J.R. Austin and T.G. Blenkinsop (2009) "Local to regional scale structural controls on mineralisation and the importance of a major lineament in the eastern Mount Isa Inlier, Australia: Review and analysis with autocorrelation and weights of evidence", Ore Geology Reviews, 35, 298-316.
 T.G. Hildenbrand, B. Berger, R.C. Jachens and S. Ludington (2000) "Regional crustal structures and their relationship to the distribution of ore deposits in the western United States, based on magnetic and gravity data", Economic Geology, 95, 1583-1603.
 See for example: J.J. Walsh and J. Watterson (1993) "Fractal analysis of fracture patterns using the standard box-counting technique: Valid and invalid methodologies", Journal of Structural Geology, 15, 12, 1509-1512.
 See for example: P.A. Cowie, D. Sornette and C. Vanneste (1995) "Multifractal scaling properties of a growing fault population", Geophysical Journal International, 122, 457-469.
 See for example: C.H. Scholz (1997) "Scaling properties of faults and their populations", International Journal of Rock Mechanics and Mining Sciences, 34, 3-4, Paper Number 273.
 See for example: R. Perez-Lopez, C. Paredes and A. Munoz-Martin (2005) "Relationship between the fractal dimension anisotropy of the spatial faults distribution and the paleostress fields on a Variscan granitic massif (Central Spain): The F-parameter", Journal of Structural Geology, 27, 663-677.
 See for example: E.J.M. Carranza (2009) "Controls on mineral deposit occurrence inferred from analysis of their spatial pattern and spatial association with geological features", Ore Geology Reviews, 35, 383-400.
 See for example: P. Gumiel, D.J. Sanderson, M. Arias, S. Roberts and A. Martin-Izard (2010) "Analysis of the fractal clustering of ore deposits in the Spanish Iberian pyrite belt", Ore Geology Reviews, 38, 307-318.
 C.M. Knox-Robinson (2000) "Vectorial fuzzy logic: A novel technique for enhanced mineral prospectivity mapping, with reference to the orogenic gold mineralization potential of the Kalgoorlie Terrane, Western Australia", Australian Journal of Earth Sciences, 47, 929-941.
 See for example: G.R.J. Cooper and D.R. Cowan (2005) "The use of textural analysis to locate features in geophysical data", Computers and Geosciences, 31, 882-890.
 See for example: E.-J. Holden, M. Dentith and P. Kovesi (2008) "Towards the automated analysis of regional aeromagnetic data to identify regions prospective for gold deposits", Computers and Geosciences, 34, 1505-1513.
 V. Ispolatov, B. Lafrance, B. Dube, R. Creaser and M. Hamilton (2008) "Geologic and structural setting of gold mineralization in the Kirkland Lake - Larder Lake Gold Belt, Ontario", Economic Geology, 103, 1309-1340. They said the fluids responsible for Kirkland Lake deposit's mineralization had different original compositions than mineralizing fluids knocking around elsewhere in the Larder Lake-Cadillac deformation zone and its splays. They said: "Therefore, we interpret the Kirkland Lake gold deposit to represent a separate hydrothermal system, which is not part of the regional 'orogenic' hydrothermal system associated with the Larder Lake-Cadillac deformation zone."
 A.P. Pescheler, K. Benn and W.R. Roest (2006) "Gold-bearing fault zones related to Late Archean orogenic folding of upper and middle crust in the Abitibi granite-greenstone belt, Ontario", Precambrian Research, 151, 143-159.
* Also, if the chemistry of fluids varied laterally according to which part of the southern batholith complex they came from, it may help explain one of the findings of Isopolatov and others (2008), namely that the chemistry of the Kirkland Lake deposit suggested its mineralization arose from a hydrothermal system that was separate from the system (or systems) responsible for orogenic gold deposits farther east along the Larder Lake-Cadillac deformation zone.
** Lithologies such as mafic and ultramafic units.
*** For instance, the overall geological relationships and architecture just mentioned, along with several geological features described in Isopolatov and others (2008), seem reminiscent of the general situation in northern Finland's Central Lapland Greenstone Belt, as described by: M.-L. Airo and S. Mertanen (2008) "Magnetic signatures related to orogenic gold mineralization, Central Lapland Greenstone Belt, Finland", Journal of Applied Geophysics, 64, 14-24.