DigiFract A software and data model implementation for flexible ...

Computers & Geosciences 54 (2013) 326–336

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DigiFract: A software and data model implementation for flexible acquisition and processing of fracture data from outcrops N.J. Hardebol a,n, G. Bertotti a,b a b

Delft University of Technology Department of Geotechnology, Stevinweg 1, 2628 CN Delft NL, The Netherlands VU University Amsterdam, Dept. Tectonic and Structural Geology, De Boelelaan 1085, 1081HV Amsterdam, NL, The Netherlands

a r t i c l e i n f o

a b s t r a c t

Article history: Received 25 January 2012 Received in revised form 29 October 2012 Accepted 30 October 2012 Available online 8 November 2012

This paper presents the development and use of our new DigiFract software designed for acquiring fracture data from outcrops more efficiently and more completely than done with other methods. Fracture surveys often aim at measuring spatial information (such as spacing) directly in the field. Instead, DigiFract focuses on collecting geometries and attributes and derives spatial information through subsequent analyses. Our primary development goal was to support field acquisition in a systematic digital format and optimized for a varied range of (spatial) analyses. DigiFract is developed using the programming interface of the Quantum Geographic Information System (GIS) with versatile functionality for spatial raster and vector data handling. Among other features, this includes spatial referencing of outcrop photos, and tools for digitizing geometries and assigning attribute information through a graphical user interface. While a GIS typically operates in map-view, DigiFract collects features on a surface of arbitrary orientation in 3D space. This surface is overlain with an outcrop photo and serves as reference frame for digitizing geologic features. Data is managed through a data model and stored in shapefiles or in a spatial database system. Fracture attributes, such as spacing or length, is intrinsic information of the digitized geometry and becomes explicit through follow-up data processing. Orientation statistics, scan-line or scan-window analyses can be performed from the graphical user interface or can be obtained through flexible Python scripts that directly access the fractdatamodel and analysisLib core modules of DigiFract. This workflow has been applied in various studies and enabled a faster collection of larger and more accurate fracture datasets. The studies delivered a better characterization of fractured reservoirs analogues in terms of fracture orientation and intensity distributions. Furthermore, the data organisation and analyses provided more independent constraints on the bed-confined or through-going nature of fractures relative to the stratigraphic layering. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Geologic field acquisition Natural fracture description Customizing GIS Data model and spatial analyses

1. Introduction This study presents a workflow and software that aims at the digital acquisition and characterization of natural fracture networks in the field. Field surveys typically aim at quantifying fracture densities, length and orientations distributions (e.g., Eyal et al., 2001; Underwood et al., 2003) for which the scan-line method is a commonly adopted survey technique (e.g., La Pointe and Hudson, 1985; Priest, 2004). Such characterization of natural fracture networks is important for the description of rock strength and slope stability in geo-engineering (e.g., Sturzenegger et al., 2007) and for the description of surface analogues of buried fractured aquifers in hydrogeology (e.g., Surrette et al., 2008)

n

Corresponding author. Tel.: þ31 15 27 82707; fax: þ31 15 27 81189. E-mail address: [email protected] (N.J. Hardebol).

0098-3004/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cageo.2012.10.021

and hydrocarbon reservoirs in petroleum geology (Nelson, 1987; Odling et al., 1999). Field surveys for quantitative data collection face various challenges that involve resolution, length-scale and spatial dimension issues and acquisition bias when collecting quantitative data from outcrops (Baecher, 1983; Manda and Mabee, 2010; Priest, 2004). A common method to quantify the density of natural fracture networks is through a physical scan-line, a 1D sampling technique with the inherent limitation to characterize the distribution of fractures in 3D (e.g., Manda and Mabee, 2010). The observational quality of field surveys can be improved with optical remote sensing technology (LiDAR or photogrammetry; e.g., Enge et al., 2007) that can describe the outcrop exposure surface by precise 3D point clouds or textured surface representations with photo overlay. Regardless of the outcrop surface representation, the geometries of geologic features that intersect with the outcrop surface need to be traced. With the advance of high resolution 3D

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textured surface representations (from LiDAR or photogrammetry), both (semi-)automatic tracing of discontinuities (Kudelski et al., 2011) and data collection from virtual outcrops (McCaffrey et al., 2010) have, in principle, become possible. However, our acquisition approach concedes with the understanding that many key observations and interpretation decisions still need to be made manually in the field with direct ‘hands-on’ access to the outcrop. These include not only observations such as the infill or displacement indicators of fractures; the tracing of geometries also require decisions, for instance that of fracture terminations, which are best made in the field. This paper presents the design and utility of DigiFract; a new software that was developed to acquire fracture data from outcrop surfaces more efficiently and more completely than done with traditional survey techniques. We designed a practical workflow and software to facilitate the acquisition of fracture field-data by digitizing geometries from georectified outcrop photos loaded into a GIS and by assigning attribute information such as fracture infill and orientation. This offers a flexible solution for digital data collection directly in the field. The DigiFract software has been used in various acquisition campaigns over the past few years during which a few hundred outcrop stations and many thousand fractures and bed surfaces have been collected. DigiFract was successfully used for field studies in the Tanqua-Karoo Basin (South Africa) (Bertotti et al., 2007), of the Tata anticline in Central Morocco comprising in folded siliciclastic succession, for fracture characterization of a thick succession of fluvial sands in Jordan (Strijker et al., 2012) and for the Latemar carbonate platform in the Dolomites of North Italy Boro et al., (2012). Among other objectives, these studies aimed at quantitative definition of fracture stratigraphy and mechanical units (Eyal et al., 2001; Bertotti et al., 2007). This paper will first outline the acquisition workflow and afterward describe the design and use of the software. The paper will close with a brief show case of the user interfaces for data entry in DigiFract and will give examples of flexible fracture data processing.

2. Design rationale 2.1. Digital field acquisition rationale The main basis for the design of a new workflow was recognizing the need for a more efficient and digital approach to systematic collection of fracture data from outcrops and for reducing acquisition bias. Natural fracture distributions in the field may be sampled by the commonly adopted scan-line method (La Pointe and Hudson, 1985; Priest, 2004). This method returns statistical parameters that typically serve as input for generating discrete fracture networks for reservoir modelling (Gringarten, 1996; Odling et al., 1999; Priest, 2004). Such a description of the fracture distribution is biased by the positioning of the physical scan-line in the outcrop (Terzaghi, 1965; Chesnaux et al., 2009; Manda and Mabee, 2010). Fracture spacing/densities measured along 1D scan-lines lack spatial information on fracture terminations and connectivity; information which can be captured from 2D outcrop surfaces. Fracture distributions are therefore better characterized when the shape and position of fracture intersection lines with semi-vertical outcrops and sub-horizontal pavements are mapped (e.g., Underwood et al., 2003; Ghosh and Mitra, 2009). These line traces capture the terminations of fractures relative to stratigraphic and mechanical boundaries (e.g., other fracture sets). Clearly, geologic features such as fractures and stratigraphic boundaries form 3D structures. Mapping structures on an individual 2D outcrop surface gives, although much better, still partial information on

Fig. 1. (a) Description of geologic features by geometries (Point, LineString, Polygon) based on the ‘Simple Feature’ OGC specifications (OGC, 2010a). The geometries and vertices are shown in a (u,v) coordinate system together with a feature index numbering. (b) Geometries of geologic features defined in ‘Well Known Text’ representation, a commonly used GIS format for the handling of geometries. A Point(1.4 5.2) geometry holds one vertex. A LineString and Polygon hold a set of vertices that are separated by a comma. The first and last vertex of a Polygon should be the same to close the geometry. (c) A set of spatial relationship functions, among which are intersects() and within() boolean functions that return (-) a True or False (i–iii) and the intersection() operation function (iv). The latter executes an operation that creates a new geometry, for instance aPoint as the intersection of two lines. (d) The 2.5D ‘digitizing surface’ (DigiSurface) definition in 3D space with the x-axis in E–W direction, the y-axis in N-S direction and an upward z-axis. The Digitizing surface itself holds an 2-D (u,v) coordinate system in which 2D Simple Feature geometries of geologic fracture and bedding line traces are defined.

spatial distribution and relationships. 3D spatial distributions can be constrained by combining geometric information from multiple outcrop surfaces with variant orientations.

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The above considerations are not unique to the characterization of natural fracture distributions. The survey technique we propose aligns well with the general pursuit for digital geological mapping (Clegg et al., 2006; Dey and Ghosh, 2008; McCaffrey et al., 2005). Technological advances and innovations in mobile Geographical Information hardware and software permitted geoscientists to undertake digital geological mapping (DGM), i.e., to capture geological field observations directly in a digital format (Schetselaar, 1995; Maerten et al., 2001; Brodaric, 2004; McCaffrey et al., 2005; Pavlis et al., 2010). Similar to these DGM approaches, the spatial distribution of fractures are best captured by digitizing the geometric relationships. Information such as fracture spacing result from subsequent data processing. Recognizing the cost of time spent in the field, digital acquisition should not only mean better quality but also higher efficiency. Enhanced field acquisition should help the collection of a sufficiently large datasets with a sufficiently high geometric precision in a time-efficient manner. We consider that, where possible, ‘hands-on’ acquisition of fracture geometries in the field provides the best guarantee of a clean dataset that separates data from noise. Also, ‘hands-on’ acquisition allows collecting additional information linked to each fracture (i.e., attributes) that cannot be registered when interpreting photos away from the outcrop. We chose for a relatively simple, low-cost and flexible acquisition set-up with a normal digital SLR camera and rugged tablet PC as hardware (see McCaffrey et al., 2005 and Clegg et al., 2006 for hardware evaluation). 2.2. Adopting geometric data management technology A Geographic Information System (GIS) is software designed for the handling of spatial raster and vector data. Its functionality that can help improve the acquisition and processing of geologic field data (e.g., Berry, 2000). A GIS includes tools for spatial referencing of outcrop photos, digitizing of geometries and for assigning attribute information. A GIS represents a geometry typically by a Point, LineString and Polygon on the Earth surface and lacks true three-dimensional description (e.g., McCaffrey et al., 2005) (Fig. 1a). Customization of a standard GIS is required (e.g., Pavlis et al., 2010; Schetselaar, 1995) to support geometric data collections at multiple length scales and not only in map view, but on surfaces of any orientation in 3D space. An aerial photo, for instance, in map view serves well for outlining location stations and primary

geologic features at a length scale of 101–103 m. Instead, the interpretation of individual outcrops may occur on an ‘arbitrary’ surface with the detection of individual features, like fractures, on length scales of 10  2–101 m. Our approach is to re-implement GIS functionality for digitizing geologic features on a planar surface of arbitrary orientation in 3D space (Fig. 1d). This planar surface forms an orthogonal projection of a potentially irregular outcrop surface and is referred to as the ‘digitizing surface’. Geologic data, like fractures or sedimentary layers, can be traced from an outcrop photo that is referenced to the ‘digitizing surface’. The digitized geometries are so called 2.5D and comply with Open GeoSpatial Consortium (OGC) standards (OGC, 2010a, 2010b). This has the advantage that a large arsenal of GIS tools can be adopted for the digitizing, storing and processing of geometries and that data can be easily exchanged with software like ArcGIS. Developing custom software from a GIS helps also to organize geologic data in a more ‘relational’ structure since it links geometric descriptions to attribute information in a database manner (Fig. 2). The use of a data model and a management system can improve the processing of data immensely. A data model describes the organisation of data such that the digital representation stays close to the field observations and is collected in a consistent manner. Digital abstraction of real world features is required to represent them as records in tables, or in programming terms, as data members of classes (Berry, 2000; Loudon, 2000; Gartner et al., 2001). The class or table definition provides data consistency and aid the development of a workflow and custom processing routines.

3. DigiFract software design The DigiFract framework (Fig. 3) for geologic field data acquisition and processing is designed on top of the Quantum GIS (QGIS; http://www.qgis.org) and consists of several modules. Beside the core modules for the application and user interface, the DigiFract software uses a flexible fractLib module with inoutput, fractdatamodel classes and analysis, orientation, and plotting libraries (Fig. 3). The framework combined facilitate the acquisition, management, and processing of fracture data. The functionality of the modules can be assessed both with Python scripting and with a user-friendly graphical interface that is implemented with the QGIS Application Programming Interface (API).

Fig. 2. Data storage concepts: (a) Hierarchical files in folders ‘data model’ (b) Relational data model with ‘containers’ specified within a Database Management System (DBMS) and accessed through SQL query requests.

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DigiFract Framework

DigiFract graphical user interface (GUI)

Python scripting

project management load&import

save&export

data acquisition specify & reference outcrop

digitize fractures, bedding etc..

data analysis scan-line processing

orientation statistics

scan-window processing

fractLib (python modules) in- output

analysisLib

fractdatamodel

import & export drivers for shp-files, sqlite and postgresql database

orientLib

plottingLib

scan-line and scan-window operators

OSGEO Spatial Libs with OGR and GDAL

numpy

scipy

shapely

pmagpy

Matplotlib

external libraries with open source license Fig. 3. DigiFract software architecture with the FractLib python module as kernel that contains the FracDataModel, both of which can be accessed through the graphical user interface and by scripting.

3.1. Software platform and library dependencies QGIS provides a tool-rich GIS user interface for handling and (geo)referencing digital backdrop images, for digitizing geometric features and for adding attribute information. QGIS furthermore offers a versatile platform for our DigiFract development through its API and comes with numerous additional open source libraries. The DigiFract framework makes use of the OGR/GDAL geospatial data translation library (http://www.gdal.org/) for the reading/writing of data in ArcGIS shapefiles and PostgreSQL PostgreSQL (2010) and SQLite (http://sqlite.org/) databases. Geometric operations in DigiFract rely strongly on the GEOS Geometry Engine (http://trac.osgeo.org/geos/) that is accessed through the Shapely Python library (http://trac.gispython.org/ lab/wiki/Shapely). In addition, Scipy/NumPy Python libraries are used for scientific computations (http://numpy.scipy.org/) and the Matplotlib plotting library (http://matplotlib.sourceforge.net/) for generating publication quality figures. Finally, DigiFract uses the pmagpy Python module (http://earthref.org/tools/pmagpy/) and Rstat library (http://www.r-project.org/) for orientation statistics. Thus, the DigiFract framework represents a flexible code that is based on the Cþþ, Qt and Python programming languages. C/Cþþ provides the back-bone of geometrical and numerical classes and operators and Qt supports the fast design of user friendly graphical user interfaces. Python is a dynamic programming language (Dubois et al., 1996; Lutz and Ascher, 1999) that supports objectoriented design for application development as well as a high-level flexible scripting environment (similar to MatLab).

Python modules give access to a wide range of numerical and geographical libraries that often rely on an efficient C/Cþþ implementation. Using Python as the outer shell of C/Cþþ based spatial and numerical libraries and Qt graphical user interface helped developing a robust, user-friendly and flexible software. 3.2. Data storage and handling A range of data formats can be considered for storage that, whether based on open or proprietary standards, fall within two broad categories of (1) file and (2) database storage (Fig. 2). An example of the first is the Shapefile (.shp) format that was developed and regulated by Esri (1998). The format is adopted in many GISs because of its open specification for vector data interoperability based on Point, LineString or Polygon ‘Simple Features’ data types (Fig. 1b) in compliance with OpenGISs Consortium ISO standards (OGC, 2010a). Alternative to the storage of files in different folders (Fig. 2b) is the storage of data by a Database Management System (DBMS) (Fig. 2b). A DBMS is a software system for managing data by cross-referencing a series of tables. The database system typically runs on a server with remote access, although a stand-alone configuration on field-PCs is also possible. A DBMS uses a data model that is implemented and accessed by transactional statements written in the common Structural Query Language (SQL). Database interaction with SQL includes insert, update and delete rules and functions that assures data consistency (e.g., Loudon, 2000; Gartner et al., 2001).

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Project

Fracture

DigiSurface outcropStation

strat_units

bed_surface

sampling_spot & props baselines projection_lines

Fig. 4. Fracture data model outlined in a Unified Modeling Language (UML) scheme, outlining the Feature relationships, Feature attributes and data types as implemented in the DigiFract software and in the data file and database storage.

V meter

I acquisition stages:

The DigiFract software supports both the reading from and writing of data to shapefiles and PostgreSQL DBMS (Refractions Research, 2008). The DBMS is spatially enabled with the PostGIS plug-in to support the OGC ‘Simple Feature’ SQL standards (OGC, 2010b). An intermediate (hybrid) data storage solution is offered by the public SQLite database-file format, which provides a relational data structure and SQL access functionality to a local file (Kreibich, 2010) and with the Spatialite extension with the implementation of OGC SQL. A SQLite database represents an interesting candidate for future storage of DigiFract data in the field, whereas PostgreSQL has the capacity of a powerful central repository.

a

U meter

b a

II b

3.3. Fracture data model 2m N

processing stage:

The fracture data model can be depicted as the structuring of geologic data in ‘containers’ (Fig. 2b) that are implemented as relational tables in the PostgreSQL DBMS and as Python classes within the DigiFract software. The data model enables the loading of fracture data into the DigiFract software from the DBMS or parsed from shapefiles into a cache data model based on the Python implementation. The data model is outlined by the scheme in Fig. 4. The OutcropStation class forms the centre of the relational data model (Fig. 4) and is linked to the DigiSurface class. An OutcropStation instance can hold one or more DigiSurface instances and contains attributes, such as date and time of acquisition, the name of the operator and outcrop-station and a general description field. Furthermore, an OutcropStation holds, beside the link to one or more DigiSurfaces, a relational link with a parent Project. The Project class manages administrative attributes such as project_leader, period of acquisition, project_map and ownership/permission rights. For the implementation in the DBMS this means an one-to-many relationship with a unique project_id index as primary key in the project table and a project_id reference index in OutcropStation table as foreign key (Fig. 4). Within the Python Project class this same relation is implemented with a list_of_outcrops instance. The DigiSurface class contains the description attributes of the ‘digitizing surface’, of which a planar surface description in 3D space is described by a basePoint and baseLine and dip direction and angle of the surface (Fig. 2d). In future, an irregular surface

III orientations

digital scan-line 2m

fract. spacing

fract. height

Fig. 5. Outline of our fracture data acquisition and processing workflow facilitated by our custom DigiFract software. The workflow 3-steps: by a ‘digitizer’ and an ‘observer’ at a selected outcrop: (I) Taking and uploading a photo (a) of the outcrop surface to tablet PC (b) and georeferencing the photo as backdrop image in DigiFract. (II) Digitizing of fractures by ‘digitizer’ at distance (a) under direction of an ‘observer’ at the outcrop (b) and adding attributes as measured by the ‘observer’. (III) Fracture analyses such as spacing calculation in the dataprocessing stage.

description from optical remote sensing technology (LiDAR or photogrammetry; e.g., Enge et al., 2007) can also be included. The DigiSurface class further contains a reference to an georectified backdrop image and a Polygon that defines a bounding geometry on the surface to specify a target area for digitizing and subsequent processing. The georectified photo of the outcrop is draped over this ‘digitizing surface’ from which geologic features can be digitized in a relative 2D coordinate system. The DigiSurface class holds references to all the features acquired on the ‘digitizing surface’. The Fracture, BedSurface and

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StratUnit tables in the relational database contain digisurface_id foreign_key references and in the Python implementation the DigiSurface class contains lists of these instances. The Fracture, BedSurface and StratUnit classes contain a geometry descripting of the 2D traces of the feature that is digitized on the ‘digitizing surface’. The classes contain each an appropriate set of attributes, which for Fractures include dip azimuth and angle (Ortner et al., 2002), infill and type (mode I opening fractures or mode II shear fractures; Schults and Fossen, 2008).

4. DigiFract software usage 4.1. The workflow The workflow that our DigiFract software facilitates is outlined in Fig. 5 and includes an acquisition and initial processing stage (Bertotti et al., 2007). The Graphical User Interface (GUI) with three central tab-windows (Fig. 6) can display the ‘Location Map’, ‘Digitizing Surface’ and ‘Processing Output’ canvasses (Fig. 6). Functionality to digitize geometries, georectify photos or handle orientation data is not unique to DigiFract. However, new is the customization of GIS functionality for use in the field and integration with structural geology functionality into one systematic workflow and software. For instance, fractures that are digitized with DigiFract, combine a geometry description with attribute information that can be directly analysed with spatial statistical routines and presented in orientation and intensity plots. Also, a conventional GIS supports no instant representation of features in both a conventional map projection and arbitrary semi-vertical digitizing surface. The combination of the ‘Location Map’ and ‘Digitizing Surface’ windows in DigiFract allows simultaneous access to multiple views of the dataset. Establishing a seamless workflow is the critical element that turns quantitative and digital geologic field acquisition from a cumbersome into a feasible procedure. 4.1.1. Field acquisition The field acquisition stage starts by taking an outcrop photo, loading this into the DigiFract software installed on a Table PC (Fig. 5I). The photo is georectified and used as backdrop for

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digitizing fractures and other geologic features. For practical reasons, the acquisition is best performed with an ‘observer’ at the outcrop and a ‘digitizer’ at distance. The ‘digitizer’ operates the Table PC and digitizes features while exchanging with the ‘observer’ who has ‘hands-on’ access to the outcrop and determines the precise trace of fractures and bedding on the outcrop surface, measures orientations and provides attribute information such as opening, infill and displacement indicators where present. The interplay between a ‘digitizer’ and ‘observer’ provides both the detail and overview to assure the right balance in accuracy and efficiency of data collection and for making better collective decisions on the nature of the acquired features. Experience shows that such decisions can only be made with hands-on access to the outcrop.

4.1.2. Data entry A new OutcropStation can be added to an active Project by defining its position in the Location Map after which attribute information can be entered through a wizard (Fig. 7 I-IV). After finishing the specification of a new OutcropStation, an ‘Add new digitizing surface’ wizard appears and will ask for the baseline strike, height, length dip azimuth and angle to define the digitizing surface and a backdrop image of the outcrop (Fig. 7V). Entry of new Fractures and BedSurfaces onto the DigiSurface with backdrop image is done by activating one of the digitizing buttons (Fig. 7VI) that places a drawing cursor in the canvas. The digitizing of geometries can be performed by zooming in to a cm resolution, for instance to examine whether or not a fracture terminates at bedding interface scales, or zooming out to the full outcrop to capture the extent of large fractures that may cross the entire outcrop. Digitizing is finished after a right mouse click closure and filling in the attribute fields of a dialog page.

4.1.3. Data processing The workflow also includes a preliminary processing stage (Fig. 5III) that may even be done immediately in the field. Fracture spacing and length information is intrinsic to the digitized fracture geometries and becomes available by (spatial) data processing. Having access in the field to these and additional

Fig. 6. The main window of the Graphical User Interface (GUI) of DigiFract a menu bar with Session, Acquisition, Analysis and Help menu and corresponding functions. The central map window shows tabs to the Location Map, Digitizing Surface and Processing Output. (a) The Location Map is shown with a backdrop satellite image and outcrop locations for a loaded project. The ‘activeSession’ dock-menu ) located to the left of the main central window shows drop-down menus that allow the selection of an active Project, OutcropStation and DigiSurface. Other management functions can be found in the Session menu, including loading and saving of projects from Shapefile or PostgreSQL database sources. (b) The Digitizing Surface tab window with features of OutcropStation Lat12 in the Latemar Project Boro et al. (2012) (c) a Processing Output tab window with orientation plot.

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(I)click button

(II)

‘Capture Outcrop’

click location in ‘Location Map’canvas

(III)

(IV)

(V)

(VI)

digitize geologic features onto the DigiSurface

(VII)

Fig. 7. Overview of the DigiFract graphical user interface with dialogs for fracture and bedsurface data entry: the central map-window tab is set to the Digitizing Surface view when clicking ‘Capture Outcrop’ button (I), the location of the OutcropStation can selected in the map (II) and the ‘Add new outcrop’ wizard is launched for data entry. (III) New Outcrop wizard-page 1: define the basepoint (x,y,z) and baseline of the OutcropStation (strike and length). (IV) New Outcrop wizard-page 2: define outcrop attributes-Finish and continue with defining a new DigiSurface. (V) The ‘‘Add new DigiSurface’ wizard is launched, to define and georectify the backdrop image and the orientation of the ‘digitizing surface’. (VI) With the ‘digitizing surface’ defined, fractures can be digitized and attribute data defined in the ‘Add new fracture’ wizard.

processing results is of great importance as quality control and evaluation of results may help to guide further acquisition. 4.2. DigiFract data processing 4.2.1. Orientation analysis Analysing orientation distributions is a common first step in the processing of fracture data in order to find the main directions and to establish fracture subsets (Kiraly, 1969; Fisher, 1993). DigiFract generates rose diagrams to study circular distribution of fracture azimuth and stereonet diagrams in which the spherical orientation of planes can be plotted (see Ortner et al., 2002 for handling of structural orientation data). Fig. 8a depicts a rose diagram with the circular distribution for 942 fracture strike directions for outcrops from the Latemar case study Boro et al. (2012). The data shows a bimodal distribution with two dominant (and roughly perpendicular) fracture sets with respective strike directions of 0701–2501 for set A and 1601–3401 for set B. This distribution may be expressed according to a Von Mises probability density function, which is a circular analogue to a normal density distribution for linear data (Fisher, 1993; Borradaile, 2003). Fig. 8b displays the poles of fractures together with the DigiSurface great-circles for the Lat2 and Lat12 outcrops from the same dataset. The orientation of the two DigiSurfaces roughly correspond to the average orientation of one fracture set and samples fractures of the other set. Only fractures that make a small angle with the DigiSurface cannot be sampled. Such orientation bias can be circumvent by acquisition on DigiSurfaces of variant orientations. Statistics on a sphere is best handled by converting the angular plane description to unit vectors. The mean value can be calculated as the normalized resultant vector (Fisher, 1993; Borradaile, 2003). The distribution of fracture planes on a sphere may be characterized as a normal unimodal distribution with rotational symmetry about an (lat,lon) axis (effective mean) and by a concentration parameter k or a95 confidence parameter. The a95 describes the radius of the 95% confidence cone around a mean orientation that plots as a small circle on the stereogram (Fig. 8b). Alternatively, the symmetry of the distribution of planes may occur around a girdle (i.e., Bingham distributions) (Fisher, 1993; Borradaile, 2003) and can be described by the girdle greatcircle and two concentration parameters that outline an ellipse on the stereonet. 4.2.2. Automated scan-line analysis Fracture analyses of stratified rocks typically involve the determination of densities or spacings along a scan-line (La Pointe and Hudson, 1985; Priest, 2004). DigiFract uses a digital scan-line that ‘scans’ the outcrops along a ‘trackline’ (Fig. 9a). The scan-line is placed at the base of a DigiSurface parallel to the bedding surface or semi-perpendicular to the mean orientation of a selected fracture-set and applies an orientation correction when necessary (Terzaghi, 1965). The scan-line walks with a given step-size upward through the outcrop (along the ‘trackline’) and determines the position of intersections with fractures relative to the stratigraphic succession (Fig. 9a). The number of fractures divided by the width of the scan-line as cropped by the outcrop boundary polygon sets the fracture density. The number of features (0-D) sampled in 1-D space (along the scan-line) is referred to as a P10 value (Dershowitz and Herda, 1992). The position of fracture intersection with scan-line are translated into fracture spacing distribution, the average of which is the reciprocal of the fracture density. Fig. 10 shows fracture densities and spacing distributions plotted against the stratigraphic succession of Latemar outcrop

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Fig. 8. DigiFract orientation data plots of fractures distribution from a case study in the Latemar, Dolomites, Italy Boro et al. (2012). (a) Rose diagram showing the two fracture sets and their respective circular mean (m) and circular standard deviations for the azimuth strike directions. The relative frequencies between the two sets are of minor relevance in this dataset and is mainly due to fact that set A was more easy to sample. (b) Stereonet diagram with DigiSurface plotted as great-circle and fractures with their poles for Lat2 and Lat12 outcrops for which Fisher and Bingham statistics are given.

between interface 5 and 6 (number of fractures over scan-line length¼32/13.4 m). Values lower than 1.0 fracture per meter are found between interfaces 7 and 8 in bed VIII. Better insight in the spread is given by plotting spacing distances between each two adjacent fractures that intersect the scan-line (Fig. 10e). Mean and standard deviation of fracture spacing distances are plotted for each scan-line position. The closest spaced fractures occur between interface 5–6 and 12–17 with an average distance of 0.4–0.6 m (i.e., the reciprocal of 2.4 fractures per m between interfaces 5–6). Finally, the stratigraphic levels with smaller mean spacing (m) also show a smaller standard deviation (s) and indicate a more evenly distributed spacing with less spreading about the mean. This pattern may be further outlined by studying the coefficient of variation (s/m) and depends on the type of probability density distribution of the spacings (e.g., normal, log-normal, exponential or power-law distribution) (Bonnet et al., 2001).

Fig. 9. Data processing examples: (a) Automatic scan-line approach. (b) Scanwindow for deriving termination of fractures at bedding interface (I) or for calculating the total fracture length (P21) within a (stratigraphic) unit area (II). (c) Scan-window for deriving fracture intensities on pavement (sub-horizontal) surfaces.

Lat12 Boro et al. (2012). The plots outline changes in fracture density that correlate well with some of lithostratigraphic bed interfaces. The highest fracture density of 2.4 m  1 is recorded

4.2.3. Analysing fracture termination and bed-confinement The extent of fracture traces relative to the stratigraphic layering can have a strong influence on the interconnectivity between beds and fractures. DigiFract can examine the bed-confinement or through-going nature of fractures from fracture height distributions or by analysing spatial relationships between the terminations of fracture traces and stratigraphic units defined by polygons bounded by a base- and top-surface. DigiFract defines beds, or any other (stratigraphic) unit, based on a user defined subdivision that is stored in the StratUnit table (Fig. 2b). The polygon geometries are generated based on the assigned base and top bedding interfaces (Fig. 10b). Fractures with lengths substantially longer than the thickness of individual beds may interconnect multiple beds. This can be shown by plotting the fracture height distribution for each bed in a box-whisker plot together with the bed thickness (Fig. 11b). The notched box plot of, for instance, bed VI depict the lower quartile (Q1), median (Q2) and upper quartile (Q3) and shows how 25% of the fracture heights (Q1) fall within the thickness of the bed.

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Fig. 10. Plot of fracture statistics from scan-line against a stratigraphic section of outcrop Lat12 of the Latemar case study, with (a) scan line length (b) outcrop photo with fracture and bedding geometries (c) number of fractures (d) fracture density P(10) in 1/m (e) the average and standard deviation of the fracture spacing distribution in m.

Fig. 11. Plot of fracture statistics per bed (i.e., StratUnits in database) for the Lat12 outcrop of the Latemar case study. (a) stratigraphic subdivision (beds) (b) fracture height box plots relative to bedunit thickness, with median (Q2) and lower and upper quartiles (Q1 and Q3) and with outlier values plotted with þ(c) fracture countings within the bedunit that are confined at one or two extremities by the unit and countings of the terminations at the bed interfaces (d) P10 (density) distributions (from scan-line) grouped over stratigraphic unit as box plots together with P21 values per bedunit.

For bed VI, about 50% of the fractures (Q2) have heights that come fairly close to the bed thickness, whereas most other beds have a Q2 that is quite larger than the bed-thickness. This implies that these

fractures have heights larger than the bed thickness and therefore extend beyond the bed. The outliers of the height distribution are also plotted and show five fractures with a length 415 m that

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a powerlaw distribution: n(w) = A w -I

an exponential distribution: n(w) = A EXP(w / l)

a lognormal distribution: (see Bonnet et al., 2001)

histogram of spacings for all outcrops combined histogram of spacings for Lat12 outcrop

powerlaw with A = 0.15 ; I = -1.17 : n(w) = 0.03 w -1.62 exponential with A = 0.07; I = -6.74: n(w) = 0.05 EXP(w / -1.87)

frequency

frequency

log-normal with μ=2.1;σ = 0.79

fracture height distribution

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powerlaw with A = 0.03 ; I = -1.62 : n(w) = 0.03 w -1.62 exponential with A = 0.05; I = -1.87: n(w) = 0.05 EXP(w / -1.87) log-normal with σ=0.7;μ = 0.31; loc=0.16 log-normal with σ=0.7;μ = 0.51; loc=0.16

fracture spacing distribution (m)

Fig. 12. Frequency histogram from the total fracture population from the Latemar case study: (a) for fracture height distribution (b) for fracture spacing distribution.

appear consistently in box-whisker plots of the different beds and breach the entire succession of the outcrop. Fractures with heights that are smaller than the bed thickness are not necessarily confined by the unit. This is the case for unit VIII where relatively small fractures cut its upper boundary. Bed confinement and termination of fractures are best examined by topological operations that for instance use the geometric centre (centroid) and end points of fractures (Fig. 9b). A fracture may be defined as confined by a bed when the latter contains both the fracture’s centroid and its endpoints. The success of a bed-surface as fracture terminator can be captured by placing a scan-window around the interfaces (Fig. 9b–I) and counting the number of fracture terminations. Fig. 11c shows a bar-plot of the number of fracture start- and end-points that were counted in a scanwindow of 0.4 m height that was placed around each unit interface. Unit VI stands out with high numbers of fracture terminations at its lower and upper interface. Also the interfaces between the beds in the upper part of the succession coincide with high numbers of fracture terminations.

4.2.4. Fracture area distribution and scan-window analyses In addition to describing fracture distributions along scanlines, analyses that use a scan-window can calculate fracture areal densities (P20) or intensity (P21) per unit area (Dershowitz and Herda, 1992). The first is defined by the number of fractures and the latter by the sum of fracture trace lengths that are contained by the scan-window and divided over its area. A moving (rectangular) scan-window is a well suited method for analysing sub-horizontal pavement surfaces (Fig. 9c). For this show-case, scan-window analyses are performed for each of the above described beds (Fig. 9b–II). Fig. 11d shows the P21 values for each of the beds of outcrop Lat12, outlining the intensity of fracturing by total fracture trace lengths that are contained and normalized by the bed area. The beds with high fracture densities in Fig. 10d also exhibit high P21 values. For instance, bed VI and bed XIII and higher exhibit fracture areal densities above 2.0 m/m2. Fig. 11d also shows box-whisker plots

of the distribution in P10 fracture density values from Fig. 10d that are wrapped per bed. 4.2.5. Subset and grouped distribution analyses The scan-line and scan-window typically walk over DigiSurface per outcrop. The fracture-set may comprise the total set of fractures captured in a DigiSurface or consists of a subset, for instance when the rose and stereonet diagrams outline a non-unimodal distribution. Our use of a database management system and a well-implemented data model supports the use of query statements (SQL) that return subsets without altering the dataset itself (i.e., no subsets as separate data files). The queries are based on logic/algebraic conditions on attributes, for instance all fractures of which type ¼ ¼ ‘joint’ or quality ¼ ¼ ‘good’ or fracture.dipdir4220 and o290. Queries that are executed by SQL statements on a DBMS can also reference to relational crosslinked tables and access attributes that are held by parent or child classes/tables. For instance, a SQL statement can call the outcrop and project information through the DigiSurface identifier that cross-links the different tables. In addition to per-outcrop analyses, total distribution of fracture spacings and lengths for the same study area can be grouped and frequency distribution can be analysed and plotted. Fig. 12 shows a frequency histogram of the total fracture population from the Latemar case study. Fracture heights less than 5 m show increasing frequencies from 0.1 to 0.7 for successively smaller fractures. Fractures with heights above 5 m occur with low frequencies ( o0.02). Trends in such histograms may be described by exponential, log-normal or power-law distributions (Baecher, 1983; Odling et al., 1999; Bonnet et al., 2001).

5. Conclusions This study shows the advantage of direct digital acquisition of the fractures spatial relationships in the field with our newly developed DigiFract software. The software has been used by a variety of researchers and students during various projects on the

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Tata anticline in Morocco, on a siliciclastic succession in Jordan and on the Latemar carbonate platform in the Dolomites (North Italy). Our experience is that a strongly customized acquisition and processing workflow can be designed with a user-friendly and intuitive QGIS environment and by using a variety of open source Cþþ and python libraries. This workflow enables us to capture fracture geometries during the acquisition stage and derive distribution statistics and plots during subsequent data processing. Digitizing fractures as 2D GIS geometries helps performing scan-line and scanwindow analyses by using a variety of spatial and topological operations from open-source libraries. This meets well the aim to enhance the acquisition and processing workflow of geologic outcrop data as proxy for fractured reservoir characterization. Future development will address the possibility to represent the digitizing surfaces as an irregular surface description from optical remote sensing technology and to capture 3D geometries.

Acknowledgements The development of DigiFract was steered over multiple fracture studies. Most invaluable are the financial support from Statoil, TOTAL NL and ExxonMobil that enabled the allocation of development time for the first author and development support. ExxonMobil Upstream Research Company by name of Susan Agar is thanked for including this development within the Research Alliance on ‘Fundamental Controls on Flow in Carbonates’—(FC)2 and continuous support Nils de Reus is thanked for his development help. Colleagues and students, Jose´ Taal-van Koppen, Herman Boro, Geertje Strijker, Stefan Luthi, Jeroen v.d. Vaart and Kevin Bisdom are thanked for their (user) input during the development of early proto-type to current version.

Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.cageo.2012.10.021.

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