Integrated Interpretation

Paper 30

Earth Model Construction in Challenging Geologic Terrain: Designing Workflows and Algorithms That Makes Sense

de Kemp, E.A.[1] Jessell, M.W.[2], Aillères, L.[3], Schetselaar, E.M.[1], Hillier, M.[1], Lindsay, M.D [2], Brodaric, B. [1]

______1. Geological Survey of Canada (GSC), Ottawa, Canada 2. Centre for Exploration Technology (CET), University of Western Australia, Perth, Australia 3. School of Geosciences, Monash University, PO Box 28E, Victoria, 3800, Australia

ABSTRACT

Workflows are essential for establishing a successful community of practice. In the challenging domain of exploration for minerals in ancient orogenic belts there is currently a major gap in the 3D model development workflow. The essential exploration requirements for 3D modelling beyond the head frame in brownfields of mature mining camps or in greenfields of frontier regions must support rapid multi- realization calculation of geologically reasonable models. The current workflow supporting this task has been adapted from the hydrocarbon exploration industry and is not suited to handle the combined problem of data sparseness at depth and geologic complexity that is typical of the mineral exploration domain. Geological reasonableness is an essential quality of a model which resonates with the acquired knowledge of the geologist. Much of this knowledge however remains un-encoded in the constraining data such as the core geological relations, the full range of geologic observations and corresponding feature producing events as well as the character of controlling processes that sum up to produce the final configuration of a complex geologic model. The key to achieving geologically reasonable models is in designing a sensible workflow that complements what has been a more data driven approach with procedures that better capture all the knowledge we can derive from the terrain of interest. The high degree of uncertainty in these models will also require a workflow for better modelling of sparse data with a mixture of algorithms and approaches in a simulation environment that can produce a number of realizations based on natural ranges of observational data and possible geologic histories.

INTRODUCTION “Structural analysis yields, in common with geophysical methods, a physical characterization of the rock. However, it also yields, in common with geological methods a history of the rock. It has therefore, unlike geophysics, a considerable power of prediction which extends beyond the region surveyed.” K.L. Burns et al. 1969

Perhaps unique to the practice of earth science is the combined the map/model space our interpretation of rock unit distribution, application of spatial and historical reasoning used to solve what but also for the unit or class-relations and trends of those classes are often complex geological puzzles. These puzzles come to us to make geological sense. A geological map or a geological in the form observation sets that are both incomplete in giving model is a spatial extension of these class-relationships that at a us the whole geologic story, and in being spatially limited to a minimal respect known geologic history. Creation of these small subset of the volume of rock under investigation. Herein geologically reasonable models will happen only if the we attempt to forward the position for focusing this complex workflows used to create them and the algorithms that support effort into what are called workflows supported by algorithms the estimation of the model components makes sense. This designed for 3D geological modelling. summary is an attempt to set our sights on defining a workflow for modelling what can be considered complex geology (Figure The advancement of implicit modelling codes into the 3D 1), in sparse data terrain, and hopefully help focus the discussion geological modelling workflow has made a significant impact in on defining the core essentials of what is needed to better reducing model construction times by replacing much of the accomplish this challenging task. laborious digital hand carving in CAD type explicit modelling common to early approaches of 3D modelling. Unfortunately, GEOLOGICAL MODELLING WORKFLOWS we still need this level of user interactivity because implicit models are not always reflecting reasonable geologic Workflows are standardized processing and parameter selection configurations. Hence the need for insertion of ever more steps used to focus a complex task (Sternesky 2010). A interpreted control points to help move the model iteratively into workflow can be implemented in software or undertaken as something that makes sense geologically. The expectation by deliberate user driven tasks that can be returned iteratively our community of practice is for meaningful geologic map without having to always start at ground zero in a long process interpretation, or the equivalent in 3D or 4D geospatial model chain. Without a workflow we become quite unfocused and development. This expectation is to solve for and extend through increase risk of data corruption or loss, under or over estimating the features being modelled, and in the worst case achieve a

In “Proceedings of Exploration 17: Sixth Decennial International Conference on Mineral Exploration” edited by V. Tschirhart and M.D. Thomas, 2017, p. 419–439

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a) b)

c)

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Figure 1: Examples of difficult to model geologic scenarios using current 3D modelling workflows: a) Archean metamorphic terrain, poly- deformed paragneiss with folded intrusion, Teton Range, Wyoming. Courtesy of Marli Bryant Miller, Eugene, Oregon, [email protected] from http://marlimillerphoto.com/contact.html, b) Composite cross-section and deformation event sequence. Early cryptic tectonic event (S1/F1) of early recumbent folding causing stratigraphic repeats and overturning of beds, second generation tight refolding with axial plane fabric development, brittle extension and finally reverse faulting and rotation (de Kemp and Scott 2011; Scott, 2012), Northern British Columbia, c) Neo-Archean faulted dioritic intrusion network (purple) injected into felsic (yellow) to intermediate (green) volcanic sequence, Central Camp, Noranda, Québec.

Figure 2: Processing components and pathways of the current 3D modelling workflow.

Figure 3: Workflow concept for a combined data store for 1, 2, 3 and 4D objects, 2D (MapSim) and 3D GIS / GeoModelling system. (See Table 1 for component descriptions).

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Component Description Concepts/Linkages

A spatial and attribute geo-object data base capable of storing geometric objects representing Earth Data Store geological features. Controlling data objects and the resultant models derived from algorithms Knowledge Embedding and/or interpretations which are accessible through spatial and attribute query mechanisms (1, 2, 3, 4D). An organizing system which temporally orders and controls how geologic features are sequenced Geological Reasonableness, Geologic Event in the modelling process. Raw geo-objects are put in a geological context by encoding their Knowledge Embedding Manager relative binary temporal relationships. Also, geological knowledge is embedded from occurrence metrics or proxies from other similar geological scenarios. A mechanism to ask spatial, attribute and geological type questions. Geological Reasonableness Query Engine

A geo-object that has essentially a unique temporal occurrence in the geologic record for a given GEM, Implicit Modelling, Event Features region. Geological processes produce these features at specific events in the geological history. Spatial Agents

Geo-objects that form from injection, dilation and/or assimilation of pre-existing material. Sparse Regional Intrusive Features Includes Sills, dykes, domes, plutons and batholiths Modelleing, SURFE, Spatial Agents

Geo-object over printings and geometric transformations of pre-existing features. Folds, faults and Knowledge Embedding, Structural Features associated observation or derived sites with planar and linear fabrics properties. GEM, Spatial Agents

Geo-object volumes formed by accumulation. Marine or Aeolian sediments, lavas and sediment Knowledge Embedding, Depositional Features gravity flows. MapSim

The total sequence of temporal events that make up a rock record. Knowledge Embedding, Event History GEM

The earth processes responsible for creating event features. Geological Reasonableness, Event Processes Knowledge Embedding

Event Relationships Binary younger over older relative age relationships as observed from cross cutting, over-printing GEM, Knowledge or superposition geometries. Embedding

Simulation and A stochastic and/or deterministic spatial estimation calculator that can produce one or many MapSim, SURFE, Spatial Interpolation Engine model(s) or specific geo-feature realizations. For example a vector field of S2 on a cross-section or Agents, Sparse Regional a volumetric model of a batholith. Includes implicit calculators such as SURFE and/or plugins to Modelling Geomodeller, Leapfrog and SKUA. A 1,2 or 3D graphics environment which can represent various geo-feature data, with 3D glyphs Geological Reasonableness, Visualization Engine as well as derived individual or geo-model suites. This includes simulated 2D maps and cross- Sparse Regional Modelling sections (MapSim) and lithostratigraphic structural and property models. This could be accessible as an add-in tool in existing GIS.

An interactive environment for interpreting, editing and updating drill log classifications, map and Geological Reasonableness, Editor section information as well as model components. SPARSE, SURFE

Interface for bringing in source data and geological knowledge, as well as for output of models and 2D GIS, Drill Database, Input / Export their components in various standard forms. Observation Tables

Table 1: Geological Workflow Component Descriptions (presented in Figure 3) with the main concepts and linkages presented later in text

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result which is not useful for the intended audience. Ideally a complex scenarios would need to be accommodated such as good workflow can be used by different people to achieve the early cryptic structures that juxtapose regions of variable same result given the same input data and processing complexity and metamorphic overprinting events. For example, parameters. Workflows are a significant innovation achievement regional high strain zones and their associated fabric fields, of the oil and gas sector over the last twenty years (Perrin et al. superimposed folding and complex intrusive overprinting, low 2013) and are now becoming realized in the mining and mineral angle - parallel fault and horizon contacts, early possibly exploration communities. It is however early days for workflow diachronous events, and folded and intruded unconformities. development for modelling in regional sparse data domains, Also, importantly, lithology based modelling is needed when making it essential that more successful practices get shared, stratigraphic-geochronologic control is absent. tested and critiqued for a wide variety of geological settings. MODELLING REQUIREMENTS Several 3D geological modelling workflows are available from specific software applications (Geomodeller, Gocad/SKUA, Moving toward the goal of increasing geological reasonableness Leapfrog (GEO), Move3D, etc.) or different workflow paths in our models, we present a workflow concept (Figure 3) which within these packages (i.e. Targeting, Geophysical Inversion, is generally consistent with current practice but enhanced in five Structural – stratigraphic and property estimation workflows in key areas. These are: Mira Geosciences for Mining in Gocad/SKUA). For 3D geological model construction applications generally share a a) Integration of an observation and interpretation data store similar structure and are part of a much bigger data with 2D GIS and 3D modelling processes in a single infrastructure which may include 2D GIS and access to a 1D environment. This is now, to varying degrees, part of many data storage for litho-stratigraphic borehole and/or electric logs mine-oriented commercial packages. (Figure 2). The workflow domains can be described in general as data to model transformation environments. For hydrocarbon b) Encoding of deeper geological history to allow input of and lithospheric environments we perform a transform of 3D controlling geological events and temporal relationships typical (seismic) data to 3D models. A 2D (GIS) to 3D transform for of complex geologic environments. This was pioneered in greenfields and 1D (drill holes) to 3D for mining. In mineral Noddy (Jessell, 1981) but aspects of this are included in implicit exploration and mapping applications the raw data tends to go packages since they require fault and stratigraphic relationships through a preprocessing stage in a GIS environment in which to be defined. Recent work by Laurent et al. (2016) has extended sub-set selection, interpretation, classification and elevation this to other overprinting relationships. attribution can take place. This is not the case with hydrocarbon exploration workflows which start directly with 3D seismic and c) Association of features (specific spatial geological objects i.e. well log data. Functions for data conversion, input data fault, fabric, fold axis) and events to geologic environments and selection, a mechanism for associating subsets of the data to geological knowledge constraints. The use of geological faults, and stratigraphic horizon features are common to most plausibility as a constraint is in its infancy (Wellmann et al. workflows. Each workflow allows the user to set parameters 2014) and will remain a challenging area for research for some defining the model space, the model resolution, and output data time. structure. d) A wider range of simulation based algorithms to handle Most packages now have embedded implicit modelling surface sparse data (stochastic structural modelling, spatial agents, estimation methods which greatly automate the 3D construction SVM, etc.; Cherpeau et al. 2010, 2012; Jessell et al. 2014). process. Currently, 3D modelling is for the most part, a one way and a one-off process. Data flows from 2D GIS to the 3D e) Generation of multiple realization models in the form of 2D environment in a linear manner. Data can be interpreted in the maps and sections (MapSim) and 3D model suites accompanied GIS where there may be other supports from remote sensing for with uncertainty mappings. (Jessell et al. 2010; Wellmann et al. example, and a rich cartographic display with structural 2010; Lindsay et al. 2012; Caumon, 2014). symbology. Interpreted geologic features, derived from maps and/or sections, stratigraphic and structural contacts are exported GEOLOGICAL REASONABLENESS from 2D GIS and become the new constraints in 3D GIS. The Geological reasonableness is a qualitative property of judgement supporting data is often left behind in the 2D GIS geodatabase. indicating how geologically sensible a final model appears. All Once a 3D model has been created it is usually only done once, modellers have had the underwhelming experience of similarly with 2D geological map development, since it is such a incredulity at seeing their initial model results, which fit all the laborious and technical process. We propose to alter this data but make absolutely no geologic sense (Figure 4). This is paradigm through a workflow in which there is no fundamental understandable given the underutilization of the available distinction between 2D or 3D modelling, and in which the geological constraints in the current workflows. The geological observation and geological relationship data store is central to topology, namely the sum of all geologic relationships, and the workflow. geometric forms are important components of ‘geological reasonableness’. Being able to represent, encode and manage This workflow design process has already been initiated to deal geologic topology is critical to making reasonable geologic with, for example, mid-crustal nappes and multi-generational models. folding (Maxelon et al. 2009; Laurent et al. 2015). Other

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Figure 4: Comparison of synthetic geological 3D models of refolded isoclinal horizons, all using the same data; a) In-put data is uniaxial, with many adjacent opposing top directions as indicated by the equal-area Schmidt plot, b) Manually developed SPARSE explicit control model solution characterized by composite F1 – F2 plunge, c) Gocad/SKUA implicit model, d) SURFE implicit general radial basis function model.

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a)

b)

c)

Figure 5: Geometric and geologic topology: a) Eigenhoefer 9 geometric element adjacency rules for quantifying binary geometric relations. This scheme can be applied to R1+n. The relation ‘inclusion’ would be indicated with an integer value of 261. D3 folding produces FP3 (fold axial plane 3rd generation) event, intrusive contact with older paragneiss (Orange-igneous protruding into blue paragneiss part of Circle), bottom circle indicates fold and fabric overprint of the igneous gneiss contact (blue line in circle). b) Geologic topology can be indicated with symbology for single event features (rounded squares) in binary relation (Circles with 2 internal event elements) to younger event features of all types, depositional, erosional, structural and intrusive events. F3 folding and associated foliation overprinting igneous unit (orange), c) F2 folding and associated S2 foliations overprinting brittle normal fault - N.

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Achieving geological reasonableness is indeed one of the most continuity of horizons or fault networks, strike and dip ranges of difficult aspects of 3D geological modelling, familiar to anyone features, fold style parameters, unit volume ratios, facing vector who has had the task of building more complex models. This is ranges, percentages of overturning, etc. (Ramsay 1967; Lisle and perhaps an as yet un-quantified authenticity attribute embedded Toimil 2007). We need a workflow which can encode these in our models which speaks intuitively to most geologists. This metrics, to both constrain and asses how different the sum of all reasonableness factor is more than just assessing if the model or geologic geometries and relationships is in a given model, from its components are geometrically consistent with all the various what is expected geologically (Wellmann et al. 2013). Finally, data sets. It is a component of a global conceptual uncertainty. there are physical constraints in all natural systems which Given our existing tools for uncertainty characterization control the final geologic configuration expressed in a model. (Wellman et al. 2010, 2011) we may still have the possibility of Using geophysical rock property constraints to assess geological having a high degree of certainty in a model but things just look compatibility with geophysical observations is a broad area of wrong geologically or the model infers a false process such as modelling research which is contributing to the notion of thrusting instead of normal faulting. How do we judge if a given geological reasonability. Presumably the geologic model would model realization is geologically reasonable? To do this we need be more reasonable if embedded rock property distributions to at a minimum have a mechanism to encode geological were at a minimal consistent with the geophysical data and the relationships, which fortunately has had considerable conceptual population parameters of similar geological situations (Jessell groundwork and coding from Burns (1969, 1975, 1976, 1978) 2001; Jessell et al. 2010). On the far horizon geologically and an early 3D forward 3D modelling implementation from reasonable models will need to be consistent with expected Jessell (1981) and a recent extension by Thiele et al. (2016). thermal-mechanical processes (Hobbs et al. 2007). These Spatial adjacency relations between objects can be physically coupled 3D and 4D models using geometrically mathematically encoded using geometric topology methods. For constrained data would be able to develop reasonable geologic example, one method used in GIS processing for binary object configurations consistent with specified ranges of heat flow, relationships uses Eigenhoefer rules (Figure 5a; Eigenhofer and model rheologies and deformation phases throughout the Franzosa 1991, Eigenhofer et al. 1993, Zlatanova, 2000), which geologic event history. One could envision separate workflows can be reduced to a core subset for geological features for lower, middle and upper crustal situations in which chevron (GeoFeatures) in geologic domains (Schetselaar and de Kemp, folds do not get produced at the lower crust and recumbent 2006; Wang et al. 2016). The Eigenhoefer relations are solely sheath folds tend not to occur in the front ranges of the upper geometric, however we are, in addition, concerned with the crust. The challenge is to make a geological reasonableness geologic content of those relations. For example there could be a property that is useful in describing how close a model is from stratigraphic sequence that has been injected with a set of what is expected from the knowledge base of the geological synchronous intrusive sills. Each binary sill-layer relationship system that would essentially combine all of these properties. would yield the same Eigenhoefer number (inclusion number = Such a schema for encoding the combined geometric and 261) but remain undifferentiated within an event history for the geologic topology, or geological reasonableness, would need to geologic sequence. Symbolizing the geologic events and event be encoded into the core of a 3D modelling platform and relations (Figures 5b, c) is useful for compiling and interpreting essentially be the basis of what we refer to as the Geologic geological observations and in developing a standard encoding Event Manager (GEM). that later geoprocessing could tap into for map and model simulation. KNOWLEDGE EMBEDDING - GEOLOGIC

An implementation of geologic topology assessment is presented EVENT MANAGER by (Thiele et al. 2016) for comparing models and model suites Much of geology involves the integration and upscaling of local with various graph representations (Figure 6), but is restricted to binary relationships (Figure 7) which help inform us about the the simple Eigenhoefer relationship equivalent to non- geological history. We envision a workflow which would overlapping adjacency. The method contributes significantly to manage all constraint data and resultant geometric features in a geological reasonableness assessment as adjacency networks geologically robust manner consistent with a complex and deep could be compared subjectively or quantitatively to what is geological history (Jessell 1981; Jessell et al. 2010, 2014; accepted as a reasonable topology network of an area or Aillières et al. 2014). This would be synchronized with a 2D alternatively new relations may be interesting for mineral GIS and a 3D modelling platform. Ideally there would be a exploration model analysis. single 2D and 3D seamless GIS environment, in which data management, interpretation, modelling and visualization occur Geological complexity is another aspect of geological in an iterative fashion, not the linear one-way, one-model reasonableness indicating the number and range of types of approach that currently exists (compare the flow paths of relationships (Pellerin et al. 2014). For example, the number of Figures 1 and 2). Ongoing standards research (Le et al. 2013) fault-horizon contacts, fault-fault or intrusion-fault relations and development of 3D modelling for urban infrastructure such occurring in various models. In addition, there is a wide range of as CityGML, which seems farther ahead in terms of GIS and 3D potential geometrics for characterizing geological features and modelling integration, can perhaps serve as a way forward for feature relations. Thickness constraints between horizons or total our domain. A CityGML integrated 3D geotechnical extension sequence volumes, aspect ratios of plutons, smoothness- model (to be somewhat confusing also referred roughness and surface contact angles, plunge ranges of folds,

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Figure 6: Network topology graphs with possible adjacency matrix encodings of various geologic scenarios, modified from Theile (2016) and Burns (1975). Scenarios; 1) simple conformable sequence, 2) unconformity over overturned and folded sequence, 3) irregular intrusion added, 4) late extensional fault cutting intrusion, unconformity and early folds. Graph nodes represent geological unit and fault block volumes only. Volume adjacency relations are represented as lines connecting graph nodes and coloured by geological type (conformable = yellow, unconformable = yellow dashed, intrusive = red and tectonic = black). Matrix cells are assigned integer values reflecting relative age and geologic contact type. Values determined from adjacency of row unit to column unit. For example if unit A is older then B, a value of 1 is assigned. If unit B is younger then unit A, according to a depositional contact observation, the cell value would be multiplied by -1. If no contact relations are observed between units the value is 0, until a derived relation can be established (derived values not calculated here). Keeping age polarity (+/-) intact, each cell value increases for each contact type (depositional conformable = 1, unconformable = 10, intrusive = 20 and tectonic = 30).

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to as 3D-GEM) already has an association to the GeoSciML class GeologicFeature and is sub-classes like GeologicUnit, GeologicStructure, and importantly GeologicEvent, and the feature type GeologicRelation which all exist in this standard (Tegtmeier et al. 2014).

The GEM would capture and encode all the possible geologic process based events, relatively instantaneous geological events that appear in the geological history, and their mutual relationships, that is the geologic topology, in a temporal data base, which acts as the rule set for subsequent modelling steps (Figure 8 and 9). In this knowledge system GeoFeatures reflect the process that created it, for example an intrusive contact is a GeoFeature which results from igneous emplacement and crystallization of magma. This intrusive GeoEvent will produce several geological relationships or GeoRelations that may or may not overprint other pre-existing GeoFeatures. For example four GeoRelations may exist from an intrusive cutting a pre- existing meta-sedimentary horizon, the two adjacent layers to the horizon, and the internal planar fracture set in the meta- sedimentary layers. Aside from the GeoFeature to GeoFeature relationships, each of these in turn may have one of eight possible temporal relation types. These provide a rich set of Figure 7: Example of mega-crenulation in fault zone with steep temporal constraints for controlling the ranges of possible F2 fold plunge (blue crayon) rotated into the fault plane. GeoFeature-GeoFeature geometries that the modelling Indicates late movement with S2 crenulation fabric overprint algorithms must respect in order to ensure the final model is at a and crenulation folding of earlier S1/S0 foliation. A binary minimal consistent with the GeoRelation data. relation between F2 and S1/SO GeoFeatures.

Each geological history can be encoded from the geological observation data and once computed, the map or model can be examined to determine how well the geological relations and history are respected, contributing to improving the overall geologic reasonableness of the model. A simple binary encoding of single event feature to event feature age relations and a dependency legend graph is suggested for this process with an algebra originally developed by Kerry Burns (See Burns 1975 for details) and extended by Thiele et al. (2016). A similar and somewhat simpler encoding was used for stratigraphic and structural knowledge embedding in a 3D workflow (Figure 10) for modelling hydrocarbon reservoirs (Perrin, 2005; Perrin et al. 2013). The Burns method could be implemented as an event schema table in the GEM and the used for selection of algorithms, geometry control and later cross-checking of geologically encoded maps, sections and models. This encoded geologic history can still be expressed with a classical form of legends but also in line graph form (Figure 11) which has advantages when comparing histories. Importantly, with the implementation of a deeper geologic history encoding through GEM it will become possible to better order and call as needed, Figure 8: Extension of Burns (1975) temporal binary relations specific algorithms that deal with complex geology such as fold of geologic features with examples (Thiele et al. 2016). interference patterns (Laurent et al. 2014, 2015, 2016), intrusive networks and more knowledge constrained sparse data situations (de Kemp and Jessell, 2013).

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a) b)

c)

Figure 9: Burns (1975) application of geologic event algebra on complex geology using map units: a) alphabetic encoding of map unit events, b) adjacency age relations of units, c) raw unordered event matrix (top left), ordered event matrix filled in top right triangle (top right), final stacked and ordered matrix (bottom left), final event adjacency graph from oldest (unit L) to youngest (G).

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Figure 10: Example of Geological Event Schema for hydrocarbon applications. Arrow indicates the direction to younger fault feature, hence a branching geometry, which is opposite to the encoding of (Burns, 1975). Arrows in the Burns method point to the older feature. Graphs of fault to fault relations and horizon surface adjacency relationships (o = conformable, x = unconformable) from L unconformable basal contact through to topography T (from Perrin et al. 2005 and 2013).

a) b) Figure 11: Two methods representation methods of a geologic event history: a) Classic legend representation of individual event features annotated on maps and sections, from oldest at bottom to youngest at the top, b) A dependency legend graph encoding consistent geologic history from event relationships derived from analysis of the event history matrix, adapted from Burns (1975) and Harrap (2001).

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SPARSE REGIONAL MODELLING constraints for 3D modelling. Much of this data is off contact or in-equality constraint data which can be used directly in the Estimation of geologic trends is an essential component of implicit codes (Courrioux et al. 2006; Hillier et al. 2014), as well bedrock mapping. In 3D geological modelling, sub-surface trend as increasingly more constraints from the deformation history estimation can be challenging at the regional scale. Firstly this is (Laurent et al. 2014, 2015, 2016; Grose et al. 2015). However, due to sparseness of data which may not be adequate to directly regional data sets are spatially biased and clustered from non- support variogram analysis and modelling necessary for 3D uniform sampling at the surface of the earth. This sample bias, geostatistical estimation (Deutsch and Journel, 1998; Journel when using a purely data driven implicit approach will often and Kyriakidis, 2004). Secondly, geologic features are rarely produce geologically unreasonable depth solutions. In practice sampled at depth or at the frequency required to adequately this is mitigated through inserting knowledge constraints in the represent regional geofeature variations (i.e. McInerney et al. form of interpreted points and form lines along cross-sections 2005; de Kemp et al. 2016). Where supporting continuous data and/or combining results from explicit tools like SPARSE in a sets exist, such as seismic, electromagnetic, potential fields and hybrid manner, as input into the implicit calculation (ie. Collon derivatives thereof, anisotropy and gradient directions can be et al. 2016; Montsion et al. 2017). used to support trend estimation of geologic interfaces (Guillen et al. 2008). However in regional scales these are usually only partial directional supports derived from the 2D horizontal or vertical plane distribution of geophysical properties resulting in partial directional component estimations. This can be partially dealt with through unconstrained or constrained inversion and extraction of gradient samples from the solution distribution, but often presents an overly simplified model due to smoothing criteria of the global objective function (Linde et al. 2015). Deriving dip estimations from the geophysical data such as is done with WORMS (Austin and Blenkinsop, 2008) has been helpful for large regional scale features but needs to be interpreted carefully. Targeted forward modelling or inversion of the potential field can also be used at key boundaries where signal strength and enough property contrast exist to derive an estimation of dip (i.e. Percival and Tschirhart, 2017). By far the best, and until recently the most underused, estimation of local and regional spatial continuity are field based or high resolution Figure 12: Down dip traces (orange curves) estimated from DEM derived structural observations (Fernandez et al. 2009; constant depth dip observations (yellow tablets) using spatial Cracknell et al. 2013). When combined with eigen analysis these agents. Red ball is the search agent. Small blue dots are observations essentially serve as a proxy for the 3D variogram simulated Bézier grip frames calculated with a random noise principal component directions (Woodcock, 1977; Hillier et al. component. 2013). The planar and linear features such as bedding, gneissosity, igneous layering, and mineral aggregate, and stretching lineations, plunge of folds and various planar fabric intersections often reflect bulk rock mineral and compositional anisotropy that can directly reflect the gross trajectory of regional scale unit boundaries (Holdsworth, 1990). This is important data when dealing with poly-deformed terrain were non-stationarity is the norm. Implicit codes can now deal directly with these gradient constraints by bringing these into the workflow to control the trajectory and topology of the scalar field, through dual point co-kriging (Lajaunie et al. 1997; Chiles et al. 2004; Calcagno et al. 2008), implicit Discrete Smooth Interpolation in Structural Lab plug-in Gocad (Caumon et al. 2007, 2009, 2013), and with Radial Basis Functions in Leapfrog (Cowan et al. 2004) and SURFE (Hillier et al. 2015). Also, other estimators such as Structural Field Interpolator (SFI) for 3D visualization of structural form lines (Hillier et al. 2013), and manual spline editing tools with 3D symbolization from SPARSE (de Kemp and Sprague 2003; Sprague and de Kemp 2005; de Kemp, Schetselaar and Sprague, 2006) can be added as Figure 13: Spatial agent demonstrating 90 degree clockwise intermediary inputs into the implicit code calculations. quaternion rotation of bedding observation from point A proximal to data to point B at distal location. Rotation respects What is hopeful is that there is a wealth of geometric field geologic topology (top direction). This function could be observations that have been collected by geological surveys over incorporated into a 3D form trace algorithm. the last half century that can provide regional structural

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Figure 14: Example of unconstrained triangulated surface construction using spatial agents. Note growth of surface occurs with simple geological rules, namely parts of surface cannot self intersect, must maintain consistent polarity, and avoid certain tear faults. These surfaces can be made to move toward data constraints exactly or with tolerance.

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SPATIAL AGENTS mapping and visualizing complex relationships within vector fields such as fabric intersections, fold trains, An area of current research for surface modelling in sparse vergence relationships and multiply folded and faulted regional domains is the use of spatial agents for enhancing stratigraphic boundaries. knowledge embedded estimation, projections and extension functions (Torrens, 2010; de kemp and Jessell, 2013). • Simple rules sets drive the agent interaction rather Applications of Spatial Agent Based Modelling (SABM) in the then solving for a single large global matrix. Agent geosciences have been largely confined to problems which approach has good optimization potential, it can involve time series, such as land use change due to climate, benefit from faster CPUs and could potentially be urbanization and hazards (Torrens, 2010). We have developed a easier to parallelize. Important when combining 3D simple demonstration set that produces solutions for sparse data, vector and multi-scalar properties from structural at ground level (Z = 0) to simulate ground traverse acquisition, fields (i.e. Burns, 1988; Hillier et al. 2013), for on-contact and structural data for fabric and form line geophysics and geology. estimation (Figure 12). Also, spatial agents can represent and handle planar and linear structure data as well as polarity control Currently these are implemented in NetLogo (see Spatial Agents of observations and estimations (Figure 13). We have also been links) which is a 2D and 3D agent based programming able to develop spatial agent triangulated meshing which can be environment. We envision these could possibly be used for controlled to grow from single point sources such as observation delineation of map units (in 2D and 3D) but also for internal sites, respect simple local rules to maintain local and over all property anisotropy estimation. surface polarity as well as topologic rules to accept or reject meshing solutions (Figure 14).

Although yet to be completely demonstrated, some characteristics of the SABM approach may be provide us with another tool for complex geological modelling. For example, some interesting qualities of agents;

• Can explore all the model space and all the data regardless of how irregular the space is and how varied or complex the data is. The approach can make many or no solutions, simple or complex depending on the model design. Generally traditional methods use more regular partitioned spaces, fixed coordinate systems and one or two geologic parameters.

• More suitable to natural multi-scalar complex systems in which agents can preserve contributions from all data. This is important as classical techniques generally produce global means when data is sparse and generalize dense data clusters to a local mean which is often geologically meaningless. Important in combining geology-structure-geophysics.

Figure 15: Synthetic example of encoding observations of • Rich variety of Rules, Missions (Beliefs) and geologic features (rounded squares) and feature binary behaviors can be applied while interacting with and relationships (circles) for MapSim a 2D map and section interrogating data thus supporting the interpretive simulation development. Yellow and blue are supracrustal units, process for the domain expert. orange is an intrusive, N indicates a normal fault. Small circles on map are field observation stations with site numbers. • Many algorithms including classic ones can still be applied (Kriging, DSI - Discrete Smooth Interpolation, RBF - Radial Basis Functions, IDW - Inverse distance MAP SIMULATION - MAPSIM Weighted, SVM - Support Vector Machine, etc. ) at 3D Graphics technologies for hardware (graphics cards, gpu local or regional scales depending on the architectures, displays) and software (animation, rendering, requirements. Can build-on and compliment rather scientific programing) are rapidly evolving to enhance many then replace existing systems. application domains, including 3D geological modelling. These advances, especially in implicit codes which are incrementally • Produces group – swarm behavior that emerges from adding to the list of constraint types used for geological simple agents interaction-communication. They can modelling, have increased automation and performance of estimate complex geometric features or trigger other model calculations. The one limitation however, is that standard spatial behaviors (discontinuities), topologic changes workflows using explicit, implicit or hybrid approaches still tend or spawn new agent driven events. Important when to produce only one model from the data. This impacts

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adversely on the ability to perform uncertainty analysis and a) model exploration activities that are required to interpret the more challenging terrains. To tackle this, we envision a multi- dimensional simulation environment, with the 2D component termed MapSim (see Figures 3 and 15), which supports uncertainty analysis and produces map and model suites rather than one-off products.

A significant amount of development would be required to implement a MapSim environment, however much of the essential components are in place, including; wide range of 2D spatial class separation algorithms from machine learning (Support Vector Machine, Self Organized Maps, Voroni Partitioning etc.) that can calculate primitive skeletal and/or polygonal sets, as well as a rich class of graphic transformation functions (i.e. wire frame to parametric) that can be used to embed shape parameters (i.e. from Lisle and Toimil, 2007, Hudleston and Treagus 2010) and which could support scale changes. Importantly there is now implicit code available to calculate 3D solutions from observational data, including off- surface unit occurrences from ground traverses (Courrioux et al. 2006), which could be accessed from more common 2D GIS environments such as ArcGIS. Extracting feature traces could be achieved by intersecting surface realizations calculated from implicit or other 3D estimation codes with map/section planes or a DEM. This could be done in a stochastic manner (see an example see Cherpeau et al. 2010, 2012) through Monte Carlo sampling of the various shape distributions from local or similar proxy data sets. A 2D map, in plan view or as a cross section, b) can be thought of as an instance of a 3D model (Figure 16). In the case of 3D modelling, a 3D map is a specific representation of the model which hopefully gives some geoscientific meaning to the user.

Since most of our applications are dealing with under constrained geological models it is clear that more than a single model, and hence more than one map representation, is needed. The 2D MapSim component needs to be directly connected to full GIS functionality, but there is no reason that all visualization components (i.e. boreholes, 2D maps and sections, 3D models and 4D geologic history models) should not be c) connected to a data store and associated GIS. Historically the 2D GIS and 3D geological modelling worlds have been separated by a tedious export-import process which is inefficient, and often causes data corruption through topology reduction and property content losses. Importantly, information exported from GIS and subsequently used in 3D modelling is not data, it is manually interpreted or modelled information, in effect with this process we model on top of a model. With a seamless integrated 2D and 3D visualization and modelling environment we mitigate this practice, with data remaining robust while being able to directly examine models/maps derived from interpreted or calculated realizations. All operations, projections, queries, re- Figure 16: Example of targeted visualization of the Sullivan classifications, ordering etc. would all be directly interacting time horizon (red surface) from the regional model of the Purcell with a data store that hosts corporate, multi-project geospatial Anticlinorium, Southeastern British Columbia: a) GIS map view information including 1, 2, 3 and 4D geologic observational indicating Sullivan horizon as (red structural contours) on hill events, the event relations and derived feature maps, property shaded DEM with interpreted bedrock geology, mineralization distributions, and model suites. sites and structural observations (for details see de Kemp and Schetselaar, 2015), b) combined 2D east-west cross-section from Gocad/SKUA transecting 3D structural and stratigraphic model, c) fully rendered 3D volume. = de Kemp, E.A., et al. Earth Model Construction in Challenging Geologic Terrain 435

transformations. Not a simple task to embed in a workflow. DISCUSSION Existing event to event transformation tools already exist for modelling simple geologic scenarios for example the UVT Geological models need to represent the entire suite of transform (Mallet, 2008; Dutranois et al. 2010) used in SKUA®. geological events that have affected the model space. The The UVT transform effectively maps simple pre-faulted observation record of these cumulative events, if properly depositional geometries to a horizontal Cartesian grid through collected and managed, will be able to support the spatial and stratigraphic correlations across fault blocks. A more advanced temporal mapping of the region. Each event may have a unique system would need a more elaborate GEM employing geologic and possibly significant contribution to the internal geometry of event logic and event algebra similar to that already developed the model, so it is essential that the workflow support the (i.e. Burns, 1975). It would also need to employ yet to be characterization and temporal ordering of all the geological developed physically coupled and possibly simulation based events, not just the last few (See Table 1 & Figure 3). For algorithms (Cherpeau et al. 2010, 2012) which are consistent example, an early deformation resulting in a regional with deformation pathways for given material rheologies (Hobbs décollement may have resulted in regional scale overturning of a et al. 2007), in deeper crustal terrains for non-coaxial stratigraphic succession. Early tectonic events such as this tend heterogeneous deformation (Passchier 1987) and fluid flow for to be cryptic features due to later superimposed deformation and volcanic and intrusive emplacement (Nelson et al. 2011; Putnam intrusive events. Their geometries becoming hidden in the et al. 2015; Rivalta et al. 2015, Kruger and Kisters 2016). Many cumulative complex patterns that are produced from protracted of these as yet underdeveloped estimators for more complex geologic histories. irregular geometries will need to be developed. Preliminary use of spatial agents with some geologic behaviour controls may One of the main shortcomings of current 3D geologic modelling prove useful as a way forward but there may be a wide range of workflows are the limited number of supported geological other graphics approaches to reproduce multi-scaler patterned events and the possible features they produce. This is generally objects (Wang et al. 2017, Boiangiu et al. 2016) from computer limited to modelling of late high angle brittle fault networks and graphics simulators. If these can be constrained to the a sedimentary stratigraphic pile. Geologic relations are encoded observational metrics, or proxies thereof, we can expect to see in the binary fault-fault branching network and a temporal more progress with the more challenging geological features sequence of conformable or unconformable horizons. Folding such as intrusions and poly-phase deformation histories. events are not specifically encoded in the workflow but will be represented provided there is adequate data sampling and/or interpretation supports such as from cross sections. Intrusive CONCLUSIONS models, such as salt domes, are difficult to do and limited to A sensible workflow designed to support the 3D modelling more manual explicit, or hybrid implicit approaches (Collon et community working in geologically complex settings is urgently al. 2016). Complex geological environments, i.e. mid-crustal needed. This workflow needs a simulation based approach environments from most shield and convergent orogenic which can produce model suites, that fit all the data not just a terrains, require a workflow with the ability to go deeper into the narrow sub-set thereof. The workflow should be as seamless as geological history and embed the full range of relative and possible between GIS and modelling functions for 2D and 3D absolute historical constraints that are available in the integration, visualization and interpretation. observation set. We will need to know how to model geology in a much better way, in these metamorphic settings, where there is More complex geologic event histories need to be managed and most of the potential for mineral wealth. For example, encoded through some form of GEM. Encoding of these algorithms that are great for modelling smoother mid-crustal histories and the data representing them can be tackled through a features may not be appropriate to model thin skinned low grade geological relationship data base which uses geological algebra foreland chevron folding (Hobbs et al. 2007). similar to that initiated by Burns (1975) and extended by Thiele et al. (2016). Spatial estimation algorithms (i.e. implicit codes) Structural data is critical in separating and ordering the need to be integrated with this process so that results can be geological history. Most 3D workflows have no facility to have consistent with geologic event histories, and therefore more as input these fabric relations that can influence not only geologically reasonable. anisotropy estimation (i.e. Eigen analysis; Woodcock, 1977) but also relative age relations critical for controlling model Deeper ore bodies have greater potential to be discovered in topology. For example, a large iron formation boulder in a basal brown and green fields regions through more consistent conglomerate may have an internal foliation distinct from the integration of geological and geophysical data. Rock property host matrix and other clasts, thus indicating pre-existing and historical survey information needs to be easily accessible to depositional event but also an earlier deformation not affecting support integrated inversion and forward modelling codes. the conglomerate and younger units. Public geoscience organizations can play a big role to increase efficiencies in this area. Regional 3D modelling of more complex terrains means dealing with these sorts of multiple geologic events that produce New methods will be needed to support the combined complex cumulative effects through geologic time. The events knowledge and data driven approach for 3D interpretation in the need to be modelled in sequence starting with the most recent regional complex geology domain. Spatial Agent based systems and working backwards respecting binary event to event offer an example of a way forward to deal with sparse data overprinting relationships and a range of geometric regions. However, many new algorithms and new approaches

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for extension, migration and projection will be needed in areas where we may have little hard constraints at depth, but more Calcagno P, J.P. Chilès, G. Courrioux, and A. Guillen 2008, abundant geological experience and knowledge to work with. Geological modelling from field data and geological knowledge: part I. Modelling method coupling 3D potential-field ACKNOWLEDGEMENTS interpolation and geological rules: Physics of the Earth and Planetary Interiors, 171 (1), 147–157. Our contributions in advancing the 3D geological modelling workflow for complex regional environments would not have Caumon, G., 2014, Thoughts on geological uncertainty possible without the active support over the last two decades assessment in integrated reservoir modeling: 2nd EAGE from many 3D software developers and vendors who provided Integrated Reservoir Modelling Conference - Uncertainty access to tools and data sets for the purpose of evaluation, Management: Are we Doing it Right?, Dubai, United Arab training and specific modelling exercises. We greatly appreciate Emirates, 16 – 19 November 2014. all their contributions, especially BRGM and Intrepid (Geomodeller), Leapfrog (GEO), Midland Valley (3D Move), Caumon, G., G. Gray, C. Antoine and M.O. Titeux, 2013, Dynamic Graphics (EarthVision) and ESRI (ArcScene and Three-dimensional implicit stratigraphic model building from CityView). Academic software for this current project was remote sensing data on tetrahedral meshes: theory and generously provided through Research for Integrative Numerical application to a regional model of La Popa basin, NE Mexico: Geology (RING), Paradigm® and Mira Geoscience Ltd. ESS IEEE Transactions on Geoscience and Remote Sensing, 51(3), Contribution number / Numéro de contribution du SST: 1613–1621. 20170123. Caumon, G., P. Collon-Drouaillet, L. Carlier, C. de Veslud, S. REFERENCES Viseur and J. Sausse, 2009, Surface-based 3D modelling of Aillères, L., T. Carmichael, E.A. de Kemp L. Grose, V. Kolin, geological structures: Mathematical Geoscience, 41, 927–945. G. Lautent, M. Lindsay and C. Yu Chui, 2014, 20 Years of 3D structural modelling. Where are we at? Where next?: 3D Interest Caumon, G, C. Antoine and A.L. Tertois, 2007, Building 3D Group Meeting at the Centre for Exploration Targeting, UWA. geological surfaces from field data using implicit surfaces: Proceedings of the 27th Gocad Meeting. Austin, J.R. and T.G. Blenkinsop, 2008, The Cloncurry Lineament: Geophysical and geological evidence for a deep Cherpeau, N., G. Caumon, and B. Lévy, 2010, Stochastic crustal structure in the Eastern Succession of the Mount Isa simulations of fault networks in 3-D structural modelling: Inlier: Precambrian Research, 163, 50–68. Comptes Rendus Geosciences, 342, 687−694.

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