GIS Application to Regional Geological Structure Relationship Modelling Considering Semantics

International Journal of Geo-Information

Article GIS Application to Regional Geological Structure Relationship Modelling Considering Semantics

Handong He 1 ID , Di Hu 2,3,4,* and Guonian Lü 2,3,4

1 School of Resources and Environment, Anhui Agricultural University, Hefei 230036, China; [email protected] 2 Key Laboratory of Virtual Geographic Environment, Nanjing Normal University, Ministry of Education, Nanjing 210023, China; [email protected] 3 State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China 4 Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China * Correspondence: [email protected]; Tel.: +86-152-5099-2342

Received: 11 April 2018; Accepted: 6 July 2018; Published: 9 July 2018

Abstract: GIS modelling, which is often employed to establish the abstract structural forms of geological phenomena and their structural relationships, is of great importance for the expression and analysis of geological structures to describe and express such phenomena accurately and intuitively. However, current GIS modelling schemes value structural forms over structural relationships, and existing geological semantic expressions in the modelling of geological relationships are incomplete. Therefore, this paper categorizes geological relationships into three levels: geological phenomena, geological objects and geological spatial objects: (1) based on their deﬁnitions, this work categorizes geological relationships into internal composition relationships and external combined relationships for a total of two categories, eight classes and 27 small groups; (2) this work also improves the system with a total of 33 classiﬁed geological objects by transforming the relationships between geological phenomena into relationships between geological objects; and (3) based on the 27 small groups of geological relationships, through the corresponding geometric and semantic expressions between topological rules and geological rules and between relationship rules and geological rules, this work then expresses internal composition relationships as topological relationships between geological spatial objects and expresses external combined relationships as association relationships between geological spatial objects. A GIS model of geological relationships that integrates their geometries and semantics is then built. Finally, taking the Dagang-Danyang section of the Ningzhen mountains as an example, the results show that the proposed GIS modelling method can better store and express geological phenomena, geological objects and geological spatial objects in a way that integrates geometry and semantics.

Keywords: regional geological structure; geological relationship; semantics; object-orient; GIS modelling

1. Introduction The geographic information system (GIS) modelling [1] of geological phenomena is a method used to directly represent the abstract concepts of structural shapes and structural relationships of geological features [2] using GIS technology [3], which is vital for the expression and analysis of geological relationships. Structural shapes of geological features refer to the geometry features and spatial position features of geological phenomena. Structural relationships of geological features refer to the spatial constituents and the combined forms of geological phenomena, that is, the interior

ISPRS Int. J. Geo-Inf. 2018, 7, 267; doi:10.3390/ijgi7070267 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2018, 7, 267 2 of 21 constitution and exterior constitution. This method employs the GIS modelling of the geometrical features of geological structures and their relationships to reveal and visualize the spatial locations and geometries of geological phenomena using dots, lines, planes and other geometric objects [4–8]. To further understand this process, many geologists have performed detailed research on models of geological geometric features [9,10]; these models can be divided into several types: wire-frame models, surface models, voxel models, constructive solid geometry (CSG) models, boundary representation (B-rep) models, and hybrid models. Triangular irregular networks (TIN) [11], Tetrahedral network (TEN) [12], B-rep [13], and Generalized tri-prism (GTP) [14] models are commonly used for the fast and accurate geometrical construction [15] of specialized geological phenomena, although difficulties still exist in building spatial relationships between geometric objects. These models mainly focus on the geometry modelling of geological phenomena [16], and a few of them consider the relationships of geological phenomena in strata, but it cannot fully describe the geological relationships [17] between folds, faults, and strata, and it lacks corresponding description of geological semantics [18,19] for geometric elements in the modelling process. Geological relationship model places a particular emphasis on the relationships of constituents of geological phenomena such as folds, faults and strata, and the relationships of combined forms of different geological phenomena [20]. In GIS, the geological phenomena are abstracted as geological objects, and then are expressed through spatial relationships and semantic relationships of geological objects. The GIS modelling of geological relationships includes a geological semantic ontology model [21,22], a geological topological model [23], and a geometric model of geological boundaries. The geological semantic ontology model is employed to construct a concept system and hierarchical relationships [24–26] using geological concepts. This model is effective in describing semantics of geological phenomena, for it expresses the relationships of geological phenomena based on the relationships between semantic features and geometry features such as ‘part of’, ‘is-a’ and ‘instance-of’ but is weak at representing their spatial topological relations. This ontology model uses geological ontology to define the hierarchical relations between concepts of geological objects and relationships, clarifying semantic relationships between strata concepts, although it still needs further study on distinguishing geological spatial relations and building mapping of semantic and geometric features in geological relations. The geological topological model is used to represent the spatial relationships of geological objects via reflecting the topological relations among the geometric elements (including dots, lines and planes) of geological phenomena. This model is good in expressing spatial relationships of geological phenomena but lacks an explication of geological concepts [27] for spatial relationship and geological phenomena, or, in other words, it lacks a description of semantic relationships of geological phenomena. The geological topology model adopts GIS topological relations to express the interior constitution between geological phenomena while it lacks incidence relations to express exterior constitution of geological phenomena. The geological topological model is used to represent the spatial relationships among geological objects via reflecting the topological relationships among the geometric elements (including dots, lines and plane) of geological phenomena. This model is effective in expressing spatial relationships of geological phenomena but lacks an explication of geological concepts for spatial relationship and geological phenomena, or, in other words, it lacks a description of semantic relationships of geological phenomena. A geological topological model adopts GIS topological relationships to express the interior constitution between geological phenomena while it lacks incidence relations to express exterior constitution of geological phenomena. The geological boundary geometric model is mainly based on dots, lines and planes to establish the geometric boundary that satisfies geological body constraints and geological rules. When there are geological interfaces between geological bodies, such as unconformable contact and fault contact, the generally used methods to deal with the ‘polygon–polygon’ topological relations are surface cutting and surface adjusting in order to eliminate the inconsistency of geological surfaces. However, it is ISPRS Int. J. Geo-Inf. 2018, 7, 267 3 of 21 weak at describing topological relations such as ‘line–line’ and ‘line–polygon’ relations. The geological boundary geometric model is used to show well-defined surfaces, the effectiveness of their contact relation, and surfaces’ geometric consistency from the perspective of geological boundary layers [28] and surface layers [29]. With the attribute data of strata [30], this model can better express the geometric features, topological relationships and geological meanings for strata. However, the model ability to express the geological relationships for folds and faults is relatively weak. To sum up, this modelling focuses more on spatial relation expressions that describe topological relations of geometry objects such as dots, lines and planes and cannot fully explain the associated semantic relationships of geological phenomena. For instance, geological relations, such as conformable contact and intrusive contact, are expressed more comprehensively and more clearly when geological objects are abstracted and spatial relations as well as semantic relations between geological objects are fully expressed based on geological geometry modelling. Therefore, problems still exist in geological relations models: how to combine geological relations, topological relations and incidence relations when modelling; how to better describe interior constitution and exterior constitution of geological phenomena; and how to establish geological relationships as a whole. This paper aims to build a GIS model of geological relationships, regarding the problems in existing GIS models. Evidently, a comprehensive GIS model of geological relationships capable of expressing both geometric spatial relationships and geological meanings is lacking. Moreover, different issues are encountered within each of the existing models; for example, there are no corresponding expressions of spatial relationships and geological meanings, and the expressions used for geological relationships are incomplete. Therefore, to unify the geometric and semantic expressions for geological relationships via GIS methods [31], a geological relationship model that can combine geometric features with semantic expressions is proposed in this paper. Geological objects are used to express geological relationships whose geological meanings [32,33] can be divided into two parts: an interior constitution and an exterior constitution. Based on geometric objects, the interior constitution of geological phenomena is shown by their topological relationships, while the exterior constitution is shown via the syntagmatic relationship between geometric objects. The purpose of this model is to build a bridge between GIS and semantics of geological relationship described by geologists, which is significant for both GIS modelling and analysis in geological phenomena.

2. Geological Definitions and the Classification of Geological Relationships The geological relationships in this paper refer to the spatial constituents and the combined forms of three small-scale geological phenomena, namely, folds, faults, and strata, which compose the abovementioned interior constitution and exterior constitution of geological structures. The geological relationships that are represented by folds, faults and strata constitute basic geological structural units. To differentiate these relationships, different grown forms are used to establish their geology. Based on the descriptions [34] of geological phenomena [35] with natural language [36,37], this paper classifies [38,39] the relationships among these three phenomena into 33 types, as shown in Table1, by referring to following documents:

• GB/T9649 The terminology classiﬁcation codes of geology and mineral resources (containing GB/T 9649.1-35), • GB958-99 Geological legends used for regional geological maps, • DZ/T0001-91 Principles for regional geological surveys (1:50,000), • The Spatial Database of the Digital Geological Map by the China Geological Survey. ISPRS Int. J. Geo-Inf. 2018, 7, 267 4 of 21

Table 1. Classiﬁcation of geological phenomenon in regional geological structures.

Geological Geological Meaning References [40–44] Geological Phenomena Structure A geological fold occurs when one surface Hinge of fold, limb of fold, folding axis line, or a stack of originally flat and planar folding axis surface, fold (syncline and surfaces, such as sedimentary strata, anticline), anticlinorium, synclinorium, Folds are bent or curved as a result of permanent comb-like fold, wide-spaced synclines, deformation. A set of folds distributed on a linear fold, brachyaxis fold, structural dome ISPRS Int.regional J. Geo-Inf.scale 2018, 7 constitutes, x FOR PEER a REVIEW fold belt, 4 of 21 and structural basin ISPRS Int.a J. common Geo-Inf. 2018 feature, 7, x FOR of PEER orogenic REVIEW zones. 4 of 21 A faultTable is a planar1. Classification fracture of or geological discontinuity phenomenon in regional geological structures. Table 1. Classification of geological phenomenon in regional geological structures. Geologicalin a volume of rock, across which there has ◦ ◦ Geological Meaning References [40–44] Fault plane (<45 Geologicaland >45 Phenomena), fault wall GeologicalStructurebeen significant displacement along the Geological Meaning References [40–44] (hanging wall and Geological foot wall), Phenomena normal fault, Structurefracture A asgeological a result fold of occurs movements when one at surface the or a Hinge of fold, limb of fold, folding axis line, folding Astack geological of originally fold occurs flat and when planar one surfaces, surface or such a asreverse/thrust fault, wrench fault, Faults Earth’s surface. Large faults within the Hingeaxis surface, of fold, fold limb (s ynclineof fold, andfolding anticline), axis line, folding stacksedimentary of originally strata, flat are and bent planar or curved surfaces, as a suchresult as longitudinalof fault, transverse fault, diagonal Folds Earth’s crust result from plate tectonic axisanticlinorium, surface, fold synclinor (synclineium, and comb-like anticline), fold, sedimentarypermanent deformation. strata, are bent A set or ofcurved folds asdistributed a result offault, strike-slip fault, dip-slip fault, oblique Folds forces; the largest faults form the anticlinorium,wide-spaced synclines, synclinor linearium, comb-like fold, brachyaxis fold, fold, permanenton a regional deformation. scale constitutes A set aof fold folds belt, distributed a commonfault and bedding fault boundaries between plates such as wide-spacedstructural dome synclines, and structural linear fold, basin brachyaxis fold, onfeature a regional of orogenic scale constitutes zones. a fold belt, a common structural dome and structural basin subductionfeatureA faultzones ofis aorogenic planar or transformfracture zones. or discontinuity faults. in a Avolume fault is of a rock,planar across fracture which or discontinuitythere has been in a In geology and related fields, a stratum GeologicalFault plane boundary, (<45° and rock>45°), formationfault wall (hanging wall volumesignificant of rock, displacement across which along there the fracturehas been as a (plural: strata) is a layer of sedimentary boundary,Faultand foot plane fault wall), (<45°line, normal and stratum >45°), fault, fault reverse/thrust contact wall (hanging plane fault, wall significantresult of movements displacement at the along Earth’s the fracturesurface. asLarge a Faults rock or soil with internally consistent (conformableandwrench foot fault,wall), contact longitudinal normal and fault, unconformablefault, reverse/thrust transverse fault,fault, resultfaults ofwithin movements the Earth’s at the crust Earth’s result surface. from plate Large Faults wrenchdiagonal fault, fault, longitudinal strike-slip fault, fault, dip-slip transverse fault, fault, Strata characteristicsfaultstectonic within forces; that the the distinguish Earth’s largest crust faults result it fromform from the other plate contact), rock contact plane (intrusive rock, diagonaloblique fault fault, and strike-slip bedding fault, fault dip-slip fault, layers.tectonicboundaries The stratum forces; between the is largest the plates fundamental faults such formas subduction the unit sedimentary rock and igneous rock), fault oblique fault and bedding fault in a stratigraphicboundarieszones or transform between column faults. plates and such forms as subduction the contact plane, chronostratigraphic element, basis ofzonesInthe geology or study transform and of related stratigraphy. faults. fields, a stratum (plural: and lithostratigraphicGeological boundary, elementrock formation boundary, Instrata) geology is a layerand related of sedimentary fields, a stratum rock or (plural:soil with Geologicalfault line, stratum boundary, contact rock plane formation (conformable boundary, strata)internally is a consistentlayer of sedimentary characteristics rock that or soil distinguish with faultcontact line, and stratum unconformable contact plane contact), (conformable rock contact Strata internallyit from other consistent layers. Thecharacteristics stratum is thethat fundamental distinguish contactplane (intrusive and unconformable rock, sedimentary contact), rock rock and contact igneous Strata This paper chooses twoitunit from typical in othera stratigraphic layers. types The column of stratum geological and is theforms fundamental the structures,basis planerock), (intrusivefault including contact rock, plane, sedimentary eight chronostratigraphic secondary rock and igneous types and 27 types of geological relationships,unitof the in study a stratigraphic which of stratigraphy.are column widely and forms recognized the basis rock),element, in the fault and field contact lithostratigraphic of plane, geology chronostratigraphic element to perform a further of the study of stratigraphy. element, and lithostratigraphic element classification. In this paper, a geological relationship consists of geological constituents and their combined This paper chooses two typical types of geological structures, including eight secondary types forms. Specifically,and the This27 constituentstypes paper of chooses geological are two geologicalrelationships, typical types phenomena ofwhich geologic are alwidely structures, that possessrecognized including geometric in the eight field secondary meanings. of geology types to In terms of the classificationandperform consisting 27 types a further of ofgeological folds,classification. faultsrelationships, andIn this strata, whichpaper, these area geologicalwidely constituents recognized relationship can in be theconsists dividedfield ofof geologygeological into 10 to types of perform a further classification. In this paper, a geological relationship consists of geological main classes: hingeconstituents of fold and their fold, combined limb of forms. fold andSpecifically fold, folding, the constituents axis line, are faultgeological wall phenomena (hanging that wall) and constituentspossess geometric and their meanings. combined In termsforms. of Specifically the classifica, thetion constituents consisting ofare folds, geological faults phenomenaand strata, these that fault plane, faultpossessconstituents wall (foot geometric can wall) be meanings. anddivided fault intoIn terms plane, 10 types of conformablethe of classifica main classes:tion contact, consisting hinge of unconformable offold folds, and faultsfold, limband contact,strata, of fold these and intrusive contact, sedimentaryconstituentsfold, folding contact, canaxis and beline, divided faultedfault wall into contact. (hanging 10 types wall)Theof main and combined classes: fault plane, hinge forms fault of foldwall refer and(foot to fold, variouswall) limb and of combinationsfault fold plane, and of fold, folding axis line, fault wall (hanging wall) and fault plane, fault wall (foot wall) and fault plane, geological phenomenaconformable under contact, certain unconformable grouping conditions contact, intr andusive orders.contact, Bysedimentary pairing foldcontact, with and fold, faulted fold with conformablecontact. The combinedcontact, unconformable forms refer to variouscontact, combinationsintrusive contact, of geological sedimentary phenomena contact, under and faultedcertain stratum, fault withcontact.grouping fold, The fault conditions combined with and fault, forms orders. and refer By fault to pairing various with fold combinations stratum, with fold, 17 offold types geological with of stratum, combined phenomena fault formswith under fold, are certain fault generated, as shown in Tablegroupingwith2: anticlinorium, fault, conditions and fault andwith synclinorium, orders. stratum, By 17 pairing types linear offold co fold, mbinedwith brachyaxisfold, forms fold arewith generated, fold, stratum, structural faultas shown with dome, infold, Table fault structural 2: basin, longitudinalwithanticlinorium, fault, fault, transverse and faultsynclinorium, with fault, stratum,diagonal linear 17 typesfold, fault, ofbrachyaxis co horstmbined and fold,forms graben structuralare generated, structure, dome, as imbricateshownstructural in Table reversebasin, 2: fault, anticlinorium,longitudinal fault, synclinorium, transverse fault,linear diagonalfold, brachyaxis fault, horst fold, and structuralgraben structure, dome, imbricatestructural reversebasin, reverse/back-thrust fault, conjugate fault, strike-slip fault, dip-slip fault, oblique fault and bedding fault. longitudinalfault, reverse/back-thrust fault, transverse fault, fault, conjugate diagonal fault, fault, strike-slip horst and fault, graben dip-slip structure, fault, obliqueimbricate fault reverse and fault,bedding reverse/back-thrust fault. fault, conjugate fault, strike-slip fault, dip-slip fault, oblique fault and bedding fault. Table 2. Classification of geological relationships. Table 2. Classification of geological relationships. Table 2. Classification of geological relationships. Graphs References L1 L2 L3 Geological Meaning References [40–44] Graphs References L1 L2 L3 Geological Meaning References [40–44] [40–44] Graphs[40–44] References L1 L2 L3 The hinge Geological is where Meaning the flanks References join together. [40–44] The hinge is where the flanks join together. [40–44] Hinge of fold The hinge point is the point of minimum Hinge of fold TheThe hingehinge ispoint where is the the point flanks of join minimum together. radius (maximum curvature) along a fold. Hinge of fold Theradius hinge (maximum point is thecurvature) point of along minimum a fold. The limbradiusThe limb of (maximum a foldof a fold is a curvature)is portion a portion of along of strata strata a fold. that that is foldedTheis folded limb or bent ofor abent intofold into anis a an anticlineportion anticline of or strata or syncline that synclineisor folded that or thatconnects or bent connects intotwo anhorizontal two anticline horizontal or or parallel syncline or Fold Fold Limb ofLimb fold of fold parallelorportions that portions connects of strata of stratatwo of differenthorizontal of different levels or parallel levels(as a elementsFoldelements Limb of fold Geological Geological (as a monocline).portionsmonocline). of strata The The limbsof limbs different are are the levels the flanks flanks (as of a the elements phenomena Geologicalphenomena of themonocline).fold. fold. The limbs are the flanks of the

constituents phenomenaconstituents fold.The axial trace is the line of intersection of The axial trace is the line of intersection of constituents Thethe axialaxial surfacetrace is withthe line an yof other intersection surface of(i.e., Folding axis line the axial surface with any other surface (i.e., Folding axis line thethe axialground, surface side withof a mountain,any other surfaceor (i.e., Folding axis line the ground, side of a mountain, or thegeological ground, cross-section). side of a mountain, or geological cross-section). geologicalThe hanging cross-section). wall occurs above the fault Hanging wall Fault The hangingTheplane. hanging wall wall occurs occurs above above the the fault Fault HangingHanging wall wall Faultelements fault plane. elements Foot wall The footwall occurs below the fault plane. elements Foot wallFoot wall The footwall The footwall occurs occurs below below the the fault fault plane. plane.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 5 of 21

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 5 of 21 ISPRSISPRS Int.Int. J.J. Geo-Inf.Geo-Inf. 20182018,, 77,, xx FORFOR PEERPEER REVIEWREVIEWTable 2. Cont. 5 5 ofof 2121 ISPRSISPRS Int.Int. J.J. Geo-Inf.Geo-Inf. 20182018,, 77,, xx FORFOR PEERPEER REVIEWREVIEW 5 5 ofof 2121 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 5 of 21 ISPRS Int. J. Geo-Inf. 2018,, 7,, xx FORFOR PEERPEER REVIEWREVIEW Graphs References 5 5 ofof 2121 L1 L2 L3 Geological Meaning References [40–44] The geological boundary lies along the [40–44] Conformable contact TheThe geologicalgeological boundaryboundary lieslies alongalong thethe ConformableConformable contactcontact Theconformable geological contact boundary surface. lies along the Conformable contact conformableTheconformable geological contactcontact boundary surface.surface. lies along the

Conformable contact conformableThe geological contact boundary surface. lies along the Conformable The geological boundary lies along the

Conformable contact conformableThe geological contact boundary surface. lies along the Conformable contact conformable contact surface. contact conformable contact surface. conformable contact surface.

Unconformable The geological boundary lies along the UnconformableUnconformable TheThe geologicalgeological boundaryboundary lieslies alongalong thethe Unconformablecontact Theunconformable geological boundary contact surface. lies along the UnconformablecontactUnconformablecontact The geologicalunconformableTheunconformable geological boundary boundary contactcontactlies surface.surface. lies along along the the

contactUnconformable unconformableThe geological boundary contact surface. lies along the

contactUnconformable unconformableThe geological boundary contact surface. lies along the contact unconformable contact surface. contact unconformable contact surface.

contact unconformable contact surface.

Stratum The rock formation boundary slices the StratumStratum Intrusive contact TheThe rockrock formationformation boundaryboundary slicesslices thethe Stratum Stratumelements IntrusiveIntrusive contactcontact The rockThestratum. rock formation formation boundary boundary slices slices the elementsStratumelementsIntrusive Intrusive contact contact stratum.Thestratum. rock formation boundary slices the

elementsStratum Intrusive contact stratum.The rock formation boundary slices the elements the stratum.

elementsStratum Intrusive contact stratum.The rock formation boundary slices the elements Intrusive contact stratum.

elements stratum.

The stratum boundary slices the rock SedimentarySedimentary contactThe stratumTheThe stratumstratum boundary boundaryboundary slices slicesslices the thethe rockrock SedimentarySedimentary contactcontact Theformation. stratum boundary slices the rock contactSedimentary contactrock formation.formation.Theformation. stratum boundary slices the rock

Sedimentary contact formation.The stratum boundary slices the rock

Sedimentary contact formation.The stratum boundary slices the rock Sedimentary contact formation.

formation.

The rockThe formationrock formation boundary boundary is theis the fault FaultedFaulted contact contact TheThe rockrock formationformation boundaryboundary isis thethe faultfault FaultedFaulted contactcontact Thezone. rock formation boundary is the fault Faulted contact faultzone. Thezone. rock formation boundary is the fault

Faulted contact zone.The rock formation boundary is the fault

Faulted contact zone.The rock formation boundary is the fault Faulted contact zone.

zone.A compound anticline consisting of a series A compoundA compound anticline anticline consisting consisting of of a seriesa series A compound anticline consisting of a series AA compoundcompound anticlineanticline consistingconsisting ofof aa seriesseries of subordinateAof compoundsubordinate anticlines anticline anticlines andconsisting and synclines, synclines, of a series Anticlinorium ofAof compoundsubordinatesubordinate anticline anticlinesanticlines consisting andand synclines,synclines, of a series Fold and AnticlinoriumAnticlinoriumAnticlinorium ofA compoundsubordinate anticline anticlines consisting and synclines, of a series AnticlinoriumAnticlinorium wherewhereofAwhere the compoundsubordinate whole thethe wholewhole structureanticline anticlines structurestructure consisting has and hashas the synclines, thethe general of generalgeneral a series wherewhere thethe wholewhole structurestructure hashas thethe generalgeneral ofwhere subordinate the whole anticlines structure and has synclines, the general

of subordinate anticlines and synclines,

fold FoldFold andand Anticlinorium whereofcontour subordinate the of whole an arch. anticlines structure and has synclines, the general FoldFold andand contour of an arch. FoldFold andand Anticlinorium contourwherecontour the ofof whole anan arch.arch. structure has the general where the whole structure has the general foldfoldfold contourwhere the of wholean arch. structure has the general Fold and where the whole structure has the general foldFoldfold and contourA synclinorium of an arch. (plural synclinoriums or foldFold and A synclinoriumAcontourA synclinoriumsynclinorium of an (plural arch. (plural(plural synclinoriums synclinoriumssynclinoriums or oror foldFold and AcontourA synclinoriumsynclinorium of an arch. (plural(plural synclinoriumssynclinoriums oror fold SynclinoriumSynclinorium synclinoria)Asynclinoria) synclinorium isis aa large(plurallarge synclinesyncline synclinoriums withwith or fold SynclinoriumSynclinoriumSynclinorium synclinoria)synclinoria)Asynclinoria) synclinorium is a largeisis aa (plurallargelarge syncline synclinesyncline synclinoriums with withwith or Synclinorium synclinoria)A synclinorium is a large(plural syncline synclinoriums with or

A synclinorium (plural synclinoriums or superimposed smaller folds.

Synclinorium superimposedsuperimposedsynclinoria)superimposed smaller is a smallersmaller large folds. syncline folds.folds. with Synclinorium superimposedsynclinoria) is asmaller large syncline folds. with

Synclinorium synclinoria) is a large syncline with superimposedThe trend and plungesmaller offolds. linear features, superimposed smaller folds. TheThe trendtrend andand plungeplunge ofof linearlinear features,features, The trendThesuperimposedThe trendtrend and and plungeand plungesmallerplunge of linearof offolds. linearlinear features, features,features, Thesuperimposedsuch trend as the and axis plungesmaller of a fold, of folds. linear describing features, the Linear fold suchsuch asThesuch the trend asasaxis thethe and axisaxis of plunge a ofof fold, aa fold,fold, of describing linear describingdescribing features, the thethe LinearLinearLinear fold foldfold suchTheazimuth trend as the of and axisthe plungeline of a and fold, of its lineardescribing deviation features, thefrom Linear fold azimuthsuchazimuth as the ofof theaxisthe lineline of a andand fold, itsits describing deviationdeviation thefromfrom azimuth of the line and its deviation from

Linear fold azimuthsuch as the of theaxis line of a and fold, its describing deviation thefrom

Linear fold theazimuthsuchthethe horizontalhorizontalhorizontal as the of theaxis plane. plane.plane.line of a and fold, its describing deviation thefrom the horizontal plane. Linear fold the horizontaltheazimuththe horizontalhorizontal of plane. the plane. plane.line and its deviation from the horizontal plane.

azimuth of the line and its deviation from

the horizontal plane. the horizontal plane. theIn arched, horizontal fractured plane. and block-type basins, Brachyaxis fold In arched,InIn arched,arched, fractured fracturedfractured and andand block-type block-typeblock-type basins, basins,basins, BrachyaxisBrachyaxisBrachyaxis fold foldfold Inopen arched, brachyanticlines fractured and often block-type form. basins, Brachyaxis fold openInopen arched, brachyanticlinesbrachyanticlines fractured and oftenoften block-type form.form. basins, open brachyanticlines often form.

Brachyaxis fold openIn arched, brachyanticlines fractured and often block-type form. basins,

FoldFold andand Brachyaxis fold openIn arched, brachyanticlines fractured and often block-type form. basins, Fold and Fold andFoldFold andand Brachyaxis fold open brachyanticlines often form.

stratumstratum open brachyanticlines often form. Fold and stratumFoldstratum and stratum stratumFold and stratumFold and AnAn anticlineanticline structurestructure whosewhose aspectaspect ratioratio isis stratum Structural dome An anticlineAnAn anticlineanticline structure structurestructure whose whosewhose aspect aspectaspect ratio ratioratio is isis stratumStructural StructuralStructural dome domedome Ansmaller anticline than structure3:1 whose aspect ratio is Structural dome smallersmallerAnsmaller thananticline thanthan 3:1 structure3:13:1 whose aspect ratio is

Structural dome smallerAn anticline than structure3:1 whose aspect ratio is

Structural dome smallerAn anticline than structure3:1 whose aspect ratio is Structural dome smaller than 3:1

smaller than 3:1

Geological GeologicalGeological GeologicalGeological AA synclinesyncline structurestructure whosewhose aspectaspect ratioratio isis phenomenaphenomena Structural basin A synclineAA synclinesyncline structure structurestructure whose whosewhose aspect aspectaspect ratio ratioratio is isis phenomenaGeologicalphenomena StructuralStructuralStructural basin basinbasin Asmaller syncline than structure 3:1 whose aspect ratio is Geological phenomenaGeologicalCombined Structural basin smallersmallerAsmaller syncline than thanthan 3:1 structure 3:13:1 whose aspect ratio is Combined Asmaller syncline than structure 3:1 whose aspect ratio is Combined Combinedphenomena A syncline structure whose aspect ratio is Combined Structural basin smallerA syncline than structure 3:1 whose aspect ratio is Combined phenomenaCombined Combinedphenomena Structural basin A syncline structure whose aspect ratio is Structural basin smaller than 3:1 phenomena formsCombinedphenomenaformsforms Structural basin smaller than 3:1 formsCombinedforms smaller than 3:1 Combined smallerControlled than by 3:1 a structural trap, an orebody Combined Controlled by a structural trap, an orebody formsCombined Controlled by a structural trap, an orebody Combined forms ControlledControlledControlled by a byby structural aa structuralstructural trap, trap,trap, an anan orebody orebodyorebody forms Controlledlocatedlocated inin thethe by corecorea structural ofof aa brachyanticlinebrachyanticline trap, an orebody oror aa forms locatedlocatedlocatedControlledlocated in the ininin core thethethe by corecorecorea of structural a ofofof brachyanticline aaa brachyanticlinebrachyanticlinebrachyanticline trap, an orebody or ororor a aaa Longitudinal fault locatedControlledpitching in part the by of corea structurala plunging of a brachyanticline trap, anticline an orebody or a LongitudinalLongitudinalLongitudinal fault faultfault pitching pitchinglocatedpitching part in part ofpart the a of of plungingcore aa plungingplunging of a brachyanticline anticline anticlineanticline or a Longitudinal fault pitchinglocatedintersectedlocatedintersected inin part thethe byby of core core aa ahigh-anglehigh-angle plunging ofof aa brachyanticlinebrachyanticline anticlinelongitudinallongitudinal oror aa Longitudinal fault intersectedintersectedintersectedpitchingintersected by part a bybyby high-angle of aaa high-angleahigh-anglehigh-angle plunging longitudinallongitudinalanticlinelongitudinal Longitudinal fault intersectedpitchingfault. part by of a ahigh-angle plunging longitudinalanticline fault.intersectedfault. by a high-angle longitudinal longitudinalfault.intersectedintersectedfault. fault. byby aa high-anglehigh-angle longitudinallongitudinal Afault.intersectedA transformtransform by faultfault a high-angle oror transformtransform longitudinal boundaryboundary isis Fault and Afault.A transformtransform faultfault oror transformtransform boundaryboundary isis FaultFault andand A transformAfault.a platetransform boundary fault fault ortransform whereor transform the motion boundary boundary is is is Fault andFaultfold and aAa plateplatetransform boundaryboundary fault wherewhereor transform thethe motionmotion boundary isis is foldFaultfold and Transverse fault a plateaApredominantly plate boundarytransform boundary fault where horizontal. whereor transform the the motion It motion ends boundary isabruptly is is fold foldFault and TransverseTransverse faultfault predominantlyapredominantly plate boundary horizontal.horizontal. where the ItIt motion endsends abruptlyabruptly is foldFault and TransverseTransverse faultfault predominantlyapredominantly plate boundary horizontal.horizontal. where the ItIt motion endsends abruptlyabruptly is fold Transverse fault predominantlyandaand plate isis connectedconnected boundary horizontal. totowhere anotheranother Itthe ends transformmotiontransform abruptly is fault,fault, fold Transverse fault andpredominantlyand isis connectedconnected horizontal. toto anotheranother It transformtransform ends abruptly fault,fault, Transverse fault and isandpredominantlya connectedspreading is connected ridge, to horizontal. another to or another a subduction transform It transform ends abruptly zone. fault, fault, aanda spreadingspreading is connected ridge,ridge, to oror another aa subductionsubduction transform zone.zone. fault, aanda spreadingspreading is connected ridge,ridge, to oror another aa subductionsubduction transform zone.zone. fault, a spreadingAaandA spreading diagonaldiagonal is connected ridge, fault faultridge, or strikesstrikesto aor another subduction a subduction obliquelyobliquely transform zone. oror zone. fault, AaA spreading diagonaldiagonal fault faultridge, strikesstrikes or a subduction obliquelyobliquely oror zone. Diagonal fault Aadiagonally spreadingdiagonal tofault ridge, the strikes strike or a subduction ofobliquely the adjacent or zone. DiagonalDiagonal faultfault A diagonaldiagonallyAdiagonally diagonal fault totofault strikes thethe strikes strikestrike obliquely ofofobliquely thethe adjacentadjacent or or Diagonal fault diagonallyArocks. diagonal tofault the strikesstrike ofobliquely the adjacent or Diagonal fault rocks.diagonallyrocks. to the strike of the adjacent DiagonalDiagonal fault fault diagonallyrocks.diagonallyrocks. to the to strikethe strike of theof the adjacent Diagonal fault Controlledrocks.diagonallyControlled bytoby the normalnormal strike faultsfaults of the (growth(growth adjacent faults),faults), adjacentControlledrocks.Controlled rocks. byby normalnormal faultsfaults (growth(growth faults),faults), Horst and graben Controlledrocks.they assume by the normal general faults characteristics (growth faults), of HorstHorst andand grabengraben theyControlledthey assumeassume by thethe normal generalgeneral faults characteristicscharacteristics (growth faults), ofof Horststructure and graben ControlledtheyControlledhorst–graben assume by normal by the or normal semihorst–semigrabengeneral faults faults characteristics (growth (growth faults), faults), of structureHorststructure and graben horst–grabentheyhorst–graben assume the oror semihorst–semigrabengeneralsemihorst–semigraben characteristics of Horststructure and graben theyhorst–graben assume the or generalsemihorst–semigraben characteristics of

Horst and graben they assume the general characteristics of Fault and structureHorst and graben horst–grabenthey assume theor semihorst–semigrabengeneral characteristics of

FaultFault andHorstand Horst and graben and graben they assumetheystructures. assume the generalthe general characteristics characteristics of of FaultFault andand structure structures.horst–grabenstructures. or semihorst–semigraben fault structure structures.horst–graben or semihorst–semigraben faultFaultfault andstructure structure horst–grabenhorst–graben or or semihorst–semigraben fault faultFaultfault and structures.Reverse faults with the same occurrence faultFault and Imbricate reverse semihorst–semigrabenReversestructures.Reverse faultsfaults withwith the structures.the samesame occurrenceoccurrence fault ImbricateImbricate reversereverse Reversestructures.and hanging faults walls with thrustingthe same upwardsoccurrence fault Imbricatefault reverse andReverseand hanginghanging faults wallswalls with thrusting thrustingthe same upwardsupwardsoccurrence faultImbricatefault reverse andReversesuccessively. hanging faults walls with thrusting the same upwardsoccurrence faultImbricate reverse Reversesuccessively.andsuccessively. faults hanging with walls the thrusting same occurrence upwards Fault and ImbricatefaultImbricate reverse reverse successively.andsuccessively. hanging walls thrusting upwards fault and hangingand hanging walls walls thrusting thrusting upwards ISPRS Int.fault J. Geo-Inf. 2018,fault 7, x FORfault PEER REVIEW successively. 6 of 21 upwardssuccessively. successively.

A tearA faulttear fault intersected intersected by by a low-angle a low-angle

normalnormal fault fault or thrust or thrust fault fault can can form form some some Reverse/back-thrustReverse/back-thrust traps,traps, e.g., ae.g., trap-door a trap-door structural structural trap. trap. Two Two fault fault reversereverse faults faults with with the the same/different same/different tendenciestendencies are accompanied are accompanied by by an an anticline. anticline.

ConjugateConjugate fault fault Made Made up of up two of two groups groups of conjugateof conjugate faults. faults.

In a strike-slip fault (also known as a wrench fault, tear fault or transcurrent fault), the fault surface (plane) is usually Strike-slip fault nearly vertical, and the footwall moves laterally (i.e., sinistrally or dextrally) with very little vertical motion. Dip-slip faults can be either normal Fault and (extensional) or reverse. In a normal fault, stratum the hanging wall moves downward relative Dip-slip fault to the footwall. A reverse fault is the opposite of a normal fault, i.e., the hanging wall moves up relative to the footwall. A fault that has a component of dip-slip and Oblique fault a component of strike-slip. A bedding fault is a fault plane parallel to Bedding fault the bedding.

3. Modelling Methods for Geological Relationships

3.1. Modelling Approaches A GIS model for a geological relationship is based on semantics [45,46], and it integrates geological geometrical features and relationships to unify the geometry, semantics, and geological structures [47]. This paper generalizes geological phenomena into three levels of geological objects and then into geological spatial objects based on both the structured text expressions of geological spatial relationships presented in Ref. [42] and the geological modelling methods for geological information (e.g., geological geometries, semantics and relationships) from Ref. [44]. At the first level, the geological relationships of regional geological structures are divided into the interior constitutions and exterior constitutions of three geological phenomena: folds, faults and strata. At the second level, geological objects are used to express those geological relationships, which can then be generalized to represent the relationships between geological objects. At the third level, geological spatial objects are used to reveal geological structures. Therefore, the relationships between geological objects can be generalized to determine the spatial relationships and incidence relations between geological spatial objects, as shown in Figure 1. Based on the semantic classification rules for regional geological structures [38], this paper designs a classification system for multi-layer [48] geological objects with discernable relationships to improve the original rules. Object-oriented modelling is used, and 33 types of object elements and geometric expressions are designed based on four geometry types: points, polylines, polygons, and polycurves. The 33 types of geological objects created from combinations of folds, faults and strata are stored in the datasets of fold objects, fault objects and stratum objects. In a data model, a geometric element can be divided into different subtypes via a description of its concept. For example, folds include synclines and anticlines; fault walls include hanging walls and foot walls; fault surfaces include those with dips of <45° and >45°; geological boundaries include conformable lines and unconformable lines; rock formation contacts are classified by the presence of metamorphic rock, sedimentary rock and igneous rock. In this paper, textual and numeral coding methods are used to assign values to the subtypes, thereby ensuring the data integrity.

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 6 of 21

ISPRS Int. J. Geo-Inf. 2018, 7, 267 A tear fault intersected by a low-angle 6 of 21 normal fault or thrust fault can form some Reverse/back-thrust traps, e.g., a trap-door structural trap. Two fault reverse faults with the same/different Table 2. tendenciesCont. are accompanied by an anticline.

Graphs References L1 L2Conjugate L3 fault Geological Made up Meaning of two groups References of conjugate [40– 44faults.] [40–44] In a strike-slipIn a strike-slip fault fault (also (also known known as as a a wrenchwrench fault, fault, tear faulttear fault or transcurrent or transcurrent fault),fault), the fault the fault surface surfac (plane)e (plane) is usuallyis usually Strike-slipStrike-slip fault fault nearlynearly vertical, vertical, and and the footwallthe footwall moves moves laterallylaterally (i.e., sinistrally(i.e., sinistrally or dextrally) or dextrally) with with very littlevery verticallittle vertical motion. motion. Dip-slipDip-slip faults faults can becan either be either normal normal Fault andFault and (extensional)(extensional) or reverse. or reverse. In aIn normal a normal fault, fault, stratum stratum the hangingthe hanging wall wall moves moves downward downward relative relative Dip-slipDip-slip fault fault to theto footwall. the footwall. A reverse A reverse fault fault is theis the

oppositeopposite of a normalof a normal fault, fault, i.e., i.e., the the hanging hanging wall moveswall moves up relative up relative to the to the footwall. footwall. A fault that has a component of dip-slip and Oblique fault A fault that has a component of dip-slip Oblique fault a component of strike-slip. and aA component bedding fault of strike-slip.is a fault plane parallel to Bedding fault A beddingthe bedding. fault is a fault plane parallel to Bedding fault the bedding. 3. Modelling Methods for Geological Relationships

3. Modelling Methods3.1. Modelling for GeologicalApproaches Relationships A GIS model for a geological relationship is based on semantics [45,46], and it integrates 3.1. Modelling Approaches geological geometrical features and relationships to unify the geometry, semantics, and geological A GIS modelstructures for a [47]. geological This paper relationshipgeneralizes geological is based phenomena on semantics into three levels [45 ,of46 geological], and it objects integrates and then into geological spatial objects based on both the structured text expressions of geological geological geometricalspatial relationships features andpresented relationships in Ref. [42] toand unify the geological the geometry, modelling semantics, methods for andgeological geological structures [47]. Thisinformation paper generalizes(e.g., geological geological geometries, phenomena semantics and intorelationships) three levels from ofRef. geological [44]. At the objects first and then into geologicallevel, spatial the geological objects relationships based on of both regional the structuredgeological structures text expressions are divided ofinto geological the interior spatial constitutions and exterior constitutions of three geological phenomena: folds, faults and strata. At relationships presentedthe second in level, Ref. geological [42] and objects the geologicalare used to express modelling those geological methods relationships, for geological which can information then (e.g., geological geometries,be generalized semantics to represent and the relationships) relationships be fromtween Ref. geological [44]. At objects. the first At level,the third the level, geological relationships of regionalgeological geologicalspatial objects structures are used to are reveal divided geological into structures. the interior Therefore, constitutions the relationships and exterior between geological objects can be generalized to determine the spatial relationships and incidence constitutions of three geological phenomena: folds, faults and strata. At the second level, geological relations between geological spatial objects, as shown in Figure 1. objects are used to expressBased on those the semantic geological classification relationships, rules for re whichgional cangeological then structures be generalized [38], this topaper represent the relationshipsdesigns between a classification geological system objects. for multi-layer At the third[48] geological level, geological objects with discernable spatial objects relationships are used to reveal geologicalto structures. improve the Therefore,original rules. the Object-oriented relationships modell betweening is used, geological and 33 types objects of object can elements be generalized and geometric expressions are designed based on four geometry types: points, polylines, polygons, and to determine thepolycurves. spatial relationshipsThe 33 types of geological and incidence objects created relations from combinations between geologicalof folds, faults spatialand strata objects, as shown in Figureare1 stored. in the datasets of fold objects, fault objects and stratum objects. In a data model, a Based on thegeometric semantic element classification can be divided rules into for regionaldifferent subtypes geological via structuresa description [ 38of ],its this concept. paper For designs example, folds include synclines and anticlines; fault walls include hanging walls and foot walls; a classification systemfault surfaces for multi-layer include those [ 48with] geological dips of <45° objectsand >45°; with geological discernable boundaries relationships include conformable to improve the original rules.lines Object-oriented and unconformable modelling lines; rock is used,formation and contacts 33 types are of classified object elementsby the presence and geometric of expressions are designedmetamorphic based rock, onsedimentary four geometry rock and igneous types: ro points,ck. In this polylines, paper, textual polygons, and numeral and coding polycurves. methods are used to assign values to the subtypes, thereby ensuring the data integrity. The 33 types of geological objects created from combinations of folds, faults and strata are stored in the datasets of fold objects, fault objects and stratum objects. In a data model, a geometric element can be divided into different subtypes via a description of its concept. For example, folds include synclines and anticlines; fault walls include hanging walls and foot walls; fault surfaces include those with dips of <45◦ and >45◦; geological boundaries include conformable lines and unconformable lines; rock formation contacts are classified by the presence of metamorphic rock, sedimentary rock and igneous rock. In this paper, textual and numeral coding methods are used to assign values to the subtypes, thereby ensuring the data integrity. ISPRS Int. J. Geo-Inf. 2018, 7, 267 7 of 21

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 7 of 21

Figure 1. Modelling solutions of geological relationships at three levels. Figure 1. Modelling solutions of geological relationships at three levels. Environmental Systems Research Institute (ESRI) contains two object-oriented database modelling software programs: ArcGIS Case Tools and ArcGIS Diagrammer. ArcGIS Case Tools is used with ArcGIS Desktop and Office Visio. First, a database model is built using Office Visio. This model is then used to export an X Exrensible Markup Language (XML) file to ArcGIS, and the data

ISPRS Int. J. Geo-Inf. 2018, 7, 267 8 of 21

Environmental Systems Research Institute (ESRI) contains two object-oriented database modelling ISPRSsoftwareISPRS Int. Int.J. Geo-Inf. J. programs: Geo-Inf. 2018 2018, 7, x, ArcGIS 7FOR, x FOR PEER CasePEER REVIEW REVIEW Tools and ArcGIS Diagrammer. ArcGIS Case Tools is used 8 of with 8 21 of 21 ISPRSISPRSISPRSISPRS Int.Int. Int.Int. J.J. Geo-Inf.Geo-Inf. J.J. Geo-Inf.Geo-Inf. 20182018 2018,, 77,, ,x,x 7 FORFOR,, xx FORFOR PEERPEER PEERPEER REVIEWREVIEW REVIEWREVIEW 8 8 ofof 8 8 2121 ofof 2121 ArcGIS Desktop and Office Visio. First, a database model is built using Office Visio. This model is structurestructurethenstructure used isis toisautomaticallyautomatically exportautomatically an X Exrensiblegenerated.generated. generated. Markup ArcGISArcGIS ArcGIS LanguageDiDi agrammerDiagrammer (XML) is isthe file the toproduction ArcGIS,production and tool thetool used data used by structure byGIS GIS professionalsisprofessionals automatically to tocreate, generated. create, edit edit and ArcGIS and analyse analyse Diagrammer geograph geograph isicic the databaseicdatabaseic productiondatabasedatabase structures.structures. structures.structures. tool used DatabaseDatabase DatabaseDatabase by GIS structuresstructures professionals structuresstructures areare areare to renderedrenderedcreate,rendered edit inin inthethe and the formform analyse form ofof ofeditableeditable geographic editable graphics,graphics, graphics, database asas structures. asshownshown shown inin DatabaseinTableTable Table 3.3. Using structures3.Using Using thethe the arecataloguecatalogue catalogue rendered windowwindow inwindow the form inin in ArcCatalogueofArcCatalogue editable graphics, or orArcMap, ArcMap, as shown these these in documents Table documents3. Using can can the be catalogue beexported exported window or orimported imported in ArcCatalogue into into the the geographic or geographic ArcMap, database.thesedatabase. documents Because Because ArcGIS can ArcGIS be Case exported Case Tools Tools or needs imported needs to workto intowork withwith the withwith geographicOfficeOffice OfficeOffice Visio,Visio, Visio,Visio, database. ArAr cGISArArcGIScGIS DiagrammerDiagrammer Because Diagrammer ArcGIS isis moremoreis Casemore convenientconvenientToolsconvenient needs forfor tofor modellingmodelling work modelling with purposes.purposes. Office purposes. Visio, ArcGISArcGIS ArcGIS DiagrammerDiagrammer DiagrammerDiagrammer modelsmodels ismodels more variousvariousconvenient various interfaces,interfaces, interfaces, for modelling suchsuch such asas asobjects,objects, purposes. objects, falsefalseArcGISfalse alarms,alarms, alarms, Diagrammer modellingmodelling modelling models areas,areas, areas, variousunifiedunified unified interfaces,modellingmodelling modelling such languagelanguage languagelanguage as objects, (UML)(UML) (UML)(UML) false previews,previews, alarms,previews,previews, modellingobjectobject objectobject attributes,attributes, attributes,attributes, areas, unified andand andand previews.modellingpreviews. There languageThere are are various (UML) various previews, defined defined objectobjects objects attributes, (e.g., (e.g., collected andcollected previews. data, data, dot There dot elements, elements, are various image image defined datasets, datasets, objects relations,relations,(e.g.,relations, collected andand and geometricgeometric data,geometric dot networks)networks) elements, networks) that imagethat that allowallow datasets,allow useruser userss relations, totos performtoperform perform and basicbasic geometric basic operations,operations, operations, networks) suchsuch such thatasas asmodifyingmodifying allow modifying users names,tonames, perform adding adding basic fields fields operations, and and elements elements such,, and asand,, andand modifying exportingexporting exportingexporting names, XMLXML XMLXML filesfiles adding filesfiles thatthat thatthat fieldscancan cancan bebe and bebesubsequentlysubsequently subsequentlysubsequently elements, and editededited editededited exporting withwith withwith ArcGISXMLArcGIS filesDesktop. Desktop. that can be subsequently edited with ArcGIS Desktop.

TableTableTable 3. 3.EditableEditable 3.Editable EditableEditable graphicsgraphicsgraphics graphicsgraphics inin in Diagrammer. Diagrammer.ininDiagrammer. Diagrammer.Diagrammer. GraphicsGraphicsGraphics in in in PalettePalettePalette SymbolSymbolSymbol GraphicsGraphics in in DiagrammerDiagrammerDiagrammer Meaning Meaning Meaning PalettePalette SymbolSymbol DiagrammerDiagrammer DiagrammerDiagrammer Meaning Meaning DiagrammerDiagrammerDiagrammer

RedRed arrows arrows describe describe “relationships”. “relationships”. LinkLink mode mode RedRed arrowsRed arrows arrowsdescribe describe describe “relationships”. “relationships”. “relationships”. LinkLinkLinkLink mode modemode mode

Black arrows denote “contains”. BlackBlack arrows arrows denote denote “contains”. “contains”.

Black arrows denote “contains”. BlackBlack arrowsBlack arrows arrowsdenote denote “contains”. denote “contains”. “contains”. Black arrows denote “contains”.

A collectionA collectionA collection of geographic of geographic of geographic features features with features with the thesame with same the same Feature classes A collectionA collection of geographic of geographic features features with with the thesame same FeatureFeatureFeature classesclasses classes Feature classes polygonpolygonpolygon geometry, geometry, geometry, attributes, attributes, attributes, and and spatial spatial and reference. spatial reference. reference.

polygon geometry, attributes, and spatial reference.

A collectionA collection of geographic of geographic feature feature classes classes stored stored A collectionA collectionA collection of geographic of geographic of geographic feature feature classes feature classes stored stored classes stored togethertogethertogethertogethertogether thatthat thatthat shareshare thatshareshare thethe share thethesamesame samesame the spatialspatial spatialspatial same reference;reference; spatial reference;reference; thatthat reference; thatthat is,is, is,is, that DatasetDatasetDataset together that share the same spatial reference; that is, Dataset theytheytheythey shareshareis, shareshare they aa coordinatecoordinate aa share coordinatecoordinate a system, coordinatesystem, system,system, andand andand their system,their theirtheir featuresfeatures featuresfeatures and fall theirfall fall fall they they share share a coordinate a coordinate system, system, and and their their features features fall fall within within a common a common geographic geographic area. area. withinwithin featuresa common a common fall geographic within geographic a area. common area. geographic area.

TheThe arrangement arrangement that that constrains constrains how how point, point, line, line, and and TopologyTopology TheThe arrangementThe arrangement arrangement that that constrains constrains that constrains how how point, point, how line, line, point,and and line, TopologyTopologyTopologyTopology

polygon features share a geometry. polygonpolygon features features share share a geometry. a geometry.

and polygon features share a geometry. polygon features share a geometry.

An Anitem item in Geodatabase in Geodatabase that that stores stores information information about about RelationshipRelationship An Anitem Anitem in itemGeodatabase in Geodatabase in Geodatabase that that stores stores that information information stores information about about RelationshipRelationshipRelationship

a relationship. a relationship. a relationship. a relationship. a relationship. a relationship. a relationship. a relationship. a relationship. a relationship. a relationship.about a relationship.

a relationship.

A subsetA subset of feature of feature class class or objects or objects in a in table a table that that share share SubtypeSubtype A subsetA subsetA of subset feature of feature of class feature class or objects or class objects orin a objects in table a table that in that ashare table share that SubtypeSubtypeSubtypeSubtype

the same attributes. the same attributes. the same attributes. the same attributes. the same attributes. the same attributes. the same attributes. the same attributes. the sharesame attributes. the same attributes. the same attributes. the same attributes.

the same attributes.

BasedBasedBased on on onthe the the classiﬁcationsclassifications classifications of of geological ofgeologicalgeological geologicalgeological phenomena phenomenaphenomena phenomenaphenomena and theirandand andand relationshiptheirtheir theirtheir relationshiprelationship relationshiprelationship with natural withwith withwith languagesnaturalnatural naturalnatural languageslanguagesfoundlanguageslanguages in thefoundfound foundfound previous inin ininthethe section,thethe previousprevious previousprevious the object-orientedsection,section, section,section, thethe thethe objeobje [49objeobject-orientedct-oriented] methodct-oriented is [49][49] used [49] methodmethod with method ArcGIS isis isusedused Diagrammerused withwith with ArcGISArcGIS ArcGIS [50] to DiagrammerconstructDiagrammer complicated [50] [50] to toconstruct construct geological complicated complicated objects and geological their geological topological objects objects relationships.and and their their topological Additionally,topological relationships. relationships. relationship Additionally,associationAdditionally, rulesrelationship relationship are built, association and association a geological rules rules relationshipare are bu ilt,built, ilt, ilt,andand dataandand aa modelgeologicalgeologicalaa geologicalgeological integrating relationshiprelationship relationshiprelationship geometric datadata datadata attributes modelmodel modelmodel integratingintegratingandintegratingintegrating semantics geometricgeometric geometricgeometric is designed. attributesattributes attributesattributes The andand modelling andand semanticssemantics semanticssemantics process isis designed. isis designed. is as follows: The The modelling modelling process process is asis follows:as follows: • • BasedBased on onthe the geological geological meaning, meaning, design design the the geom geometricetric types, types, feature feature class class names, names, and and subtypes subtypes • • BasedBasedBased on on onthe thethe geological geologicalgeological meaning, meaning,meaning, design designdesign the thethe geom geometricgeometricetric types, types,types, feature featurefeature class classclass names, names,names, and andand subtypes subtypessubtypes forforfor aa geologicalgeological a geological object.object. object. • for a geological object. •• • If thereIf there exists exists a topological a topological relationship relationship between between geological geological objects objects (geological (geological object object subtypes), subtypes), • If IfthereIf there there exists exists exists a topological a a topological topological relationship relationshiprelationship between betweenbetween geological geologicalgeological objects objectsobjects (geological (geological(geological object objectobject subtypes), subtypes),subtypes), confirmconfirm the the topological topological name name and and the the rules rules of ofthe the topological topological relationship. relationship. Then, Then, store store the the confirmconﬁrmconfirm the the the topological topological topological name name andand and thethe rulesthe rules rules of of the ofthe topological the topological topological relationship. relationship. relationship. Then, Then, storeThen, store the store feature the the featurefeature classes classes related related to theto the topological topological relati relationshiponship and and set set the the parameters parameters in Geodatabase.in Geodatabase. featureclassesfeature classes related classes related to related the to topological theto the topological topological relationship relati relationship andonship set and the and set parameters set the the parameters parameters in Geodatabase. in Geodatabase.in Geodatabase. • • • • IfIf ananIf anassociationassociation association existsexists exists betweenbetween between geologicalgeological geological objects,objects, objects, confirmconfirm confirm thethe the relationrelation relation namename name andand and rule,rule, rule, andand and storestore store thethethethe originorigin originorigin classclass classclass andand andand destinationdestination destinationdestination classclass classclass inin Geodatabase.inGeodatabase.in Geodatabase.Geodatabase.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 9 of 21

• If an association exists between geological objects, conﬁrm the relation name and rule, and store the origin class and destination class in Geodatabase.

3.2. Modelling for Composition Relationships of Geological Phenomena The modelling of the composition relationship of geological phenomena is performed via the ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 9 of 21 constructionISPRS of aInt. model J. Geo-Inf. based2018, 7, x FOR on PEER ten geologicalREVIEW relationships: hinge of fold and fold, 9limb of 21 of fold ISPRSISPRS Int. Int. J. J. Geo-Inf. Geo-Inf. 2018 2018, ,7 7, ,x x FOR FOR PEER PEER REVIEW REVIEW 9 9 of of 21 21 and fold, folding axis line, fault wall (hanging wall) and fault plane, fault wall (foot wall) and fault 3.2. Modelling for Composition Relationships of Geological Phenomena plane, conformable3.2.3.2. ModellingModelling contact, forfor CompositionComposition unconformable RelatiRelationshipsonships contact, ofof GeologicalGeological intrusive PhenomenaPhenomena contact, sedimentary contact, and faulted The modelling of the composition relationship of geological phenomena is performed via the contact. This modellingTheThe modellingmodelling approach ofof thethe composition includescomposition three relationshiprelationship aspects: ofof geological thegeological design phenomenaphenomena of the corresponding isis performedperformed viavia topological thethe construction of a model based on tenten geologicalgeological relationships:relationships: hingehinge ofof foldfold andand fold,fold, limblimb ofof foldfold description inconstructionconstruction the composition ofof aa modelmodel relationship, basedbased onon tenten geologicalgeological the building relationships:relationships: of thetopological hingehinge ofof foldfold relationship andand fold,fold, limblimb logicalofof foldfold model, and fold, folding axis line, fault wall (hanging wall) and fault plane, fault wall (foot wall) and fault andand fold,fold, foldingfolding axisaxis line,line, faultfault wallwall (hanging(hanging wall)wall) andand faultfault plane,plane, faultfault wallwall (foot(foot wall)wall) andand faultfault and the developmentplane, conformable of topological contact, unconformable rules. contact, intrusive contact, sedimentary contact, and plane,plane, conformableconformable contact,contact, unconformableunconformable contact,contact, intrusiveintrusive contact,contact, sedimentarysedimentary contact,contact, andand Duringfaulted the modelling contact. This of modelling the geological approach relationships, includes three aspects: certain the rules design are of the necessary corresponding for the data faultedfaulted contact.contact. ThisThis modellingmodelling approachapproach includesincludes threethree aspects:aspects: thethe designdesign ofof thethe correspondingcorresponding topologicaltopological descriptiondescription inin thethe compositioncomposition relationshrelationship,ip, thethe buildingbuilding ofof thethe topologicaltopological relationshiprelationship model to complytopologicaltopological with descriptiondescription the real geological inin thethe compositioncomposition situation. relationshrelationsh The constitutionip,ip, thethe buildingbuilding of ofof geological thethe topologicaltopological phenomena relationshiprelationship describes logicallogical model,model, andand thethe developmentdevelopment ofof topologicaltopological rules.rules. geometric topologicallogicallogical model,model, relationships andand thethe developmentdevelopment between ofof topologicaltopological geological rules.rules. objects. Therefore, mechanisms are required During the modelling of the geological relationships, certain rules are necessary for the data DuringDuring thethe modellingmodelling ofof thethe geologicalgeological relationrelationships,ships, certaincertain rulesrules areare necessarynecessary forfor thethe datadata to describe themodel geological to comply ruleswith the and real topologies geological situat to ensureion.ion. TheThe that constitutionconstitution the topological ofof geologicalgeological relationships phenomenaphenomena in the modelmodel toto complycomply withwith thethe realreal geologicalgeological situatsituation.ion. TheThe constitutionconstitution ofof geologicalgeological phenomenaphenomena model complydescribes with geometric the semantic topological descriptions relationships of betwee realn geological geological objects. relationships, Therefore, mechanisms as shown are in Table4. describesdescribes geometricgeometric topologicaltopological relationshipsrelationships betweebetweenn geologicalgeological objects.objects. Therefore,Therefore, mechanismsmechanisms areare required to describe the geological rules and topologies to ensure that the topological relationships Based on Geodatabaserequiredrequired toto describedescribe topological thethe geologicalgeological rules, this rulesrules paper andand topolotopolo designsgiesgies to ato seriesensureensure ofthatthat rules. thethe topologicaltopological These include, relationshipsrelationships for example, inin thethe modelmodel complycomply withwith thethe semanticsemantic descriptionsdescriptions ofof realreal geologicalgeological relationships,relationships, asas shownshown inin description rulesinin thethe formodelmodel topological complycomply withwith relationships thethe semanticsemantic descriptionsdescriptions (such as lines ofof realreal and geologicalgeological planes) relationships,relationships, and geological asas shownshown relationships inin Table 4. Based on Geodatabase topological rules, this paperpaper designsdesigns aa seriesseries ofof rules.rules. TheseThese include,include, TableTable 4.4. BasedBased onon GeodatabaseGeodatabase topologicaltopological rules,rules, thisthis paperpaper designsdesigns aa seriesseries ofof rules.rules. TheseThese include,include, (such as conformablefor example, contacts). description Furthermore, rules for topological corresponding relationships descriptions (such as lines and should planes) exist and for geological the geological forfor example,example, descriptiondescription rulesrules forfor topologicaltopological relatirelationshipsonships (such(such asas lineslines andand planes)planes) andand geologicalgeological rule statingrelationships “The boundary (such as of conformable a polygon contacts). (or conformable Furthermore, contact corresponding surface) descriptions should should coincide exist with the relationshipsrelationships (such(such asas conformableconformable contacts).contacts). FurtFurthermore,hermore, correspondingcorresponding dedescriptionsscriptions shouldshould existexist for the geological rule stating “The boundary of a polygon (or conformable contact surface) should line elementforfor (geological thethe geologicalgeological boundary)” rulerule statingstating “The and“The theboundaryboundary topological ofof aa polygonpolygon rule (or(or stating conformableconformable “Boundary contactcontact mustsurface)surface) be shouldshould covered by”. coincide with the line element (geological boundary)” and the topological rule stating “Boundary Consequently,coincidecoincide a mechanism withwith thethe lineline is constructedelementelement (geological(geological forthe boundabounda correspondingry)”ry)” andand thethe topologicaltopological topological rulerule description statingstating “Boundary“Boundary found in the must be covered by”. Consequently, a mechanism isis constructedconstructed forfor thethe correspondingcorresponding topologicaltopological mustmust bebe coveredcovered by”.by”. Consequently,Consequently, aa mechanismmechanism isis constructedconstructed forfor thethe correspondingcorresponding topologicaltopological compositiondescription relationships. found in the composition relationships. descriptiondescription foundfound inin thethe compositioncomposition relationships.relationships.

Table 4. CorrespondingCorresponding topologicaltopological descriptionsdescriptions inin thethe compositioncomposition relationships.relationships. Table 4. CorrespondingTableTable 4.4. CorrespondingCorresponding topological topologicaltopological descriptions descriptionsdescriptionsin inin thethe compositioncomposition relationships.relationships. relationships. Composition Meanings of Topological Rules Composition Geological Rules Meanings of Topological Rules Graphs CompositionRelationshipsCompositionComposition Geological Rules MeaningsMeaningsMeanings ofReference of Topologicalof Topological Topological [38] Rules Rules Graphs Relationships GeologicalGeologicalGeological Rules Rules Rules Reference [38] GraphsGraphs RelationshipsRelationshipsRelationships Rules ReferenceReferenceReference [38 [38] [38]]

Point features from one layer must Hinge of fold Every fold hinge (Point) must be properlyPoint Point features features from from one one layer layer must Hinge of fold Every fold hinge (Point) must be properly PointbePoint properly features features contained from from one one inside layer layer themust must Hinge of foldHingeandHinge Fold of of foldfoldEvery EveryinsideEvery fold foldthefold hinge foldhinge hinge( (PointPolygon ( (PointPoint) must)) ).must must be be be properly properlymust be be properly properly contained contained inside the and Fold inside the fold (Polygon). beareabe properly properly features contained contained from another inside inside layer. the the and Fold andand Fold Fold properlyinsideinside inside the the fold fold the ( (PolygonPolygon fold (Polygon).). ). insidearea the features area features from another from layer. areaarea features features from from another another layer. layer.

another layer.

Folding axis No axis (Polyline) can intersect with or A line feature from one layer must Folding axis No axis (Polyline) can intersect with or A line feature from one layer must FoldinglineFolding axis axis No axisNooverlapNo axis axis (Polyline (another(PolylinePolyline) canaxis)) can can intersect intersect intersect with with with or or A lineAnotA featureline line intersect feature feature from with from from one itself. one one layer layerlayer must must Folding axisline line overlap another axis not intersect with itself. lineline or overlapoverlapoverlap anotheranother another axis axis mustnotnot intersect intersect intersect with with with itself. itself. itself.

Every fold limb (Polyline) must be Line featuresLine features from from one one layer layer must Limb of fold EveryEvery fold fold limb limb (Polyline (Polyline) must) must be be Line features from one layer must Limb of foldLimb of fold EverycoveredEvery fold fold by limb limbthe fold( (PolylinePolyline (Polygon)) must must) element be be mustLinecoincideLine coincide features features with with from fromthe the boundaries one one layer layer must mustof the LimbandLimb Fold of of fold fold coveredcovered by theby the fold fold (Polygon (Polygon) ) element coincide with the boundaries of the and Fold and Fold coveredboundary.covered by by the the fold fold ( (PolygonPolygon)) element element boundariescoincideareacoincide features of with with the ofthe the area another boundaries boundaries features layer. of of the the andand Fold Fold elementboundary. boundary. area features of another layer. boundary.boundary. of anotherareaarea features features layer. of of another another layer. layer.

The boundaries of an area Hanging wallThe boundaryThe boundary of aof hanging a hanging wall wall (Polyline) The boundaries of an area feature Hanging wallHanging and wall The boundary of a hanging wall (Polylinefeature) The from boundaries one layer of an must area befeature HangingandHanging Fault wall wall( Polyline ThemustThe boundary boundary )be must covered be of of covereda bya hanging hanging a fault by planewall wall a fault ( (PolylinePolyline)) ThefromThe boundaries boundaries one layer must of of an an bearea area covered feature feature by Fault plane and Fault must be covered by a fault plane coveredfrom by one the layer line must features be covered of by andplaneand Fault Fault planemust(mustPolygon (Polygon be be covered covered). ). by by a a fault fault plane plane fromthefrom line one one features layer layer must must of another be be covered covered layer. by by plane (Polygon). anotherthe line layer. features of another layer. planeplane ((PolygonPolygon)). . thethe line line features features of of another another layer. layer.

The boundary of a foot wall (Polyline) The boundaries of an area feature Foot wall and The boundary of a foot wall (Polyline) The boundaries of an area feature Foot wall and ThemustThe boundary boundary be covered of of a bya foot foot a fault wall wall plane ( (PolylinePolyline )) ThefromThe boundaries boundaries one layer must of of an an bearea area covered feature feature by FootFaultFoot wall wallplane and and must be covered by a fault plane from one layer must be covered by Fault plane must(mustPolygon be be covered covered). by by a a fault fault plane plane fromthefrom line one one features layer layer must must of another be be covered covered layer. by by FaultFault plane plane (Polygon). the line features of another layer. ((PolygonPolygon)). . thethe line line features features of of another another layer. layer.

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 9 of 21

3.2. Modelling for Composition Relationships of Geological Phenomena The modelling of the composition relationship of geological phenomena is performed via the construction of a model based on ten geological relationships: hinge of fold and fold, limb of fold and fold, folding axis line, fault wall (hanging wall) and fault plane, fault wall (foot wall) and fault plane, conformable contact, unconformable contact, intrusive contact, sedimentary contact, and faulted contact. This modelling approach includes three aspects: the design of the corresponding topological description in the composition relationship, the building of the topological relationship logical model, and the development of topological rules. During the modelling of the geological relationships, certain rules are necessary for the data model to comply with the real geological situation. The constitution of geological phenomena describes geometric topological relationships between geological objects. Therefore, mechanisms are required to describe the geological rules and topologies to ensure that the topological relationships in the model comply with the semantic descriptions of real geological relationships, as shown in Table 4. Based on Geodatabase topological rules, this paper designs a series of rules. These include, for example, description rules for topological relationships (such as lines and planes) and geological relationships (such as conformable contacts). Furthermore, corresponding descriptions should exist for the geological rule stating “The boundary of a polygon (or conformable contact surface) should coincide with the line element (geological boundary)” and the topological rule stating “Boundary must be covered by”. Consequently, a mechanism is constructed for the corresponding topological description found in the composition relationships.

Table 4. Corresponding topological descriptions in the composition relationships.

Composition Meanings of Topological Rules Geological Rules Graphs Relationships Reference [38]

Point features from one layer must Hinge of fold Every fold hinge (Point) must be properly be properly contained inside the and Fold inside the fold (Polygon). area features from another layer.

Folding axis No axis (Polyline) can intersect with or A line feature from one layer must line overlap another axis not intersect with itself.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 10 of 21

Every fold limb (Polyline) must be Line features from one layer must Limb of fold covered by the fold (PolygonTable) element 4. Cont. coincide with the boundaries of the and Fold boundary. area features of another layer. Composition Meanings of Topological Geological Rules Graphs Relationships Rules Reference [38] ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 10 of 21 The boundaries of an area Hanging wallThe boundaryThe boundary of aof foot a hanging wall wall (Polyline) The boundaries of an area feature Foot wall and feature from one layer must be and Fault (Polylinemust )be must covered be coveredby a fault by plane a fault from one layer must be covered by Fault plane covered by the line features of plane plane(Polygon (Polygon). ). the line features of another layer. The boundary of a conformable contact anotherThe boundaries layer. of an area feature Conformable (Polyline) must be covered by a geological from one layer must be covered by contact boundary (Polygon). the line features of another layer. The boundaries of an area The boundary of a conformable Conformable The boundary of a foot wall (Polyline) featureThe from boundaries one layer of an must area be feature Foot wall andcontact (Polyline) must be covered by contact must be covered by a fault plane coveredfrom by one the layer line must features be covered of by Fault plane a geological boundary (Polygon). (Polygon). anotherthe layer.line features of another layer.

The boundary of an unconformable contact The boundaries of an area feature Unconformabl (Polyline) must be covered by a geological from one layer must be covered by e contact The boundaries of an area boundaryThe boundary (Polygon of) an. unconformable the line features of another layer. Unconformable feature from one layer must be contact (Polyline) must be covered by contact covered by the line features of a geological boundary (Polygon). another layer.

The boundary of a stratum contact The boundaries of an area feature Intrusive The boundaries of an area (PolylineThe boundary) must be of covered a stratum by contact a rock from one layer must be covered by contact feature from one layer must be Intrusive contact boundary(Polyline (Polygon) must be). covered by a rock the line features of another layer. covered by the line features of boundary (Polygon). another layer.

The boundaries of an area TheThe boundary boundary of a of rock a rock contact contact (Polyline) The boundaries of an area feature Sedimentary feature from one layer must be Sedimentary contactplane(Polyline must be) plane covered must a geological be covered a from one layer must be covered by contact covered by the line features of boundarygeological boundary. (Polygon). the line features of another layer. (Polygon) another layer.

The boundaries of an area The boundary of a planar rock contact feature from one layer must be Faulted contact The(Polyline boundary) must of a beplanar covered rock bycontact a The boundaries of an area feature Faulted covered by the line features of (Polylinefaulted) linemust (Polygon be covered). by a faulted from one layer must be covered by contact another layer. line (Polygon). the line features of another layer.

Based on the ArcGIS Diagrammer Geodatabase model and according to the 10 topological relationshipsBased with on whichthe ArcGIS the geological Diagrammer objects Geodatabase comply, thismodel paper and builds according logical to modelsthe 10 topological for topological relationships with which the geological objects comply, this paper builds logical models for relationships between different or identical elements consisting of folds, faults and strata. Figure2 topological relationships between different or identical elements consisting of folds, faults and showsstrata. the Figure Geodatabase 2 shows datathe Geodatabase model of thedata topology model of ofthe folds, topology Figure of folds,3 shows Figure the 3 shows Geodatabase the dataGeodatabase model of the data topology model of ofthe fault topology elements, of fault andelements, Figure and4 Figureshows 4 theshows Geodatabase the Geodatabase data data model of stratummodel elements.of stratum elements.

Figure 2. Geodatabase data model of the topology of fold elements. Figure 2. Geodatabase data model of the topology of fold elements.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 11 of 21 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 11 of 21 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 11 of 21

Figure 3. Geodatabase data model of the topology of fault elements. Figure 3. Geodatabase data model of the topology of fault elements. Figure 3. Geodatabase data model of the topology of fault elements.

Figure 4. Geodatabase data model of the topology of stratum elements. Figure 4. Geodatabase data model of the topology of stratum elements. Based on Figurethe ArcGIS 4. Geodatabase Diagrammer data Geodatabase model of the model topology and of according stratum elements. to the 10 topological relationshipsBased on with the whichArcGIS geological Diagrammer objects Geodatabase comply, this model paper and builds according Geodatabase to the data 10 topologicalmodels for Basedrelationshipsthe topological on the with relationships ArcGIS which Diagrammergeological between objects different Geodatabase comply, or id thisentical model paper elements builds and according consistingGeodatabase of to folds,data the models 10faults topological and for relationshipsthestrata. topological Figure with 2 shows whichrelationships the geological Geodatabase between objects different data comply,model or idof entical thisfold paperelements, elements builds Figure consisting Geodatabase 3 shows of folds,the Geodatabase data faults models and for strata.data model Figure of 2 fault shows elements, the Geodatabase and Figure data 4 shows model the of foldGeodatabase elements, dataFigure model 3 shows of stratum the Geodatabase elements. the topological relationships between different or identical elements consisting of folds, faults and dataIn Figure model 2, of the fault feature elements, dataset and is Figure composed 4 shows of folds, the Geodatabase namely, folds, data fold model hinges, of stratum fold limbs, elements. and strata. Figure2 shows the Geodatabase data model of fold elements, Figure3 shows the Geodatabase Infolding Figure axes; 2, theanticlines feature and dataset synclines is composed are subtypes of folds, of a fold.namely, In Figure folds, 3,fold the hinges,feature folddataset limbs, consists and datafoldingof model faults, axes; of namely, fault anticlines elements, fault andplanes andsynclines and Figure fault are4 walls; subtypesshows faul the ofts a Geodatabasewith fold. dips In Figure of <45° data 3, andthe model feature>45° are of dataset stratum subtypes consists elements. of a In Figurefaultof faults,2 plane,, the namely, feature while hangingfault dataset planes walls is composed and and fault foot walls; ofwalls folds, faulare namely, tssubtypes with dips folds, of aof fault fold<45° wall. hinges, and In>45° Figure fold are limbs, subtypes4, the andfeature of folding a axes;faultdataset anticlines plane, consists while and of synclineshanging stratum walls elements, are and subtypes foot namely, walls of ageare fold.ological subtypes In boundaries, Figure of a fault3, the wall.rock feature Information Figure dataset 4, boundaries, the consistsfeature of faults,dataset namely, consists fault of planes stratum and elements, fault walls;namely, faults geological with boundaries, dips of <45 rock◦ and formation >45◦ are boundaries, subtypes of a fault plane, while hanging walls and foot walls are subtypes of a fault wall. In Figure4, the feature dataset consists of stratum elements, namely, geological boundaries, rock formation boundaries, ISPRS Int. J. Geo-Inf. 2018, 7, 267 12 of 21 fault lines, stratum contact planes, rock contact planes, fault contact planes, and chronostratigraphic and lithostratigraphic elements; conformable contacts and unconformable contacts are subtypes of stratum contact planes, and intrusive rocks, sedimentary rocks and igneous rocks are subtypes of rock contact planes. The semantics of red arrows constitute a “link mode” topological relation, and the semantics of black arrows constitute a “contains” relationship. Based on the description of geological relationships with natural languages, this paper follows classified geological rules to build logical models for each topological relationship through a Topology Rule. A Topology Rule includes the following key elements: OriginClassId, OriginSubtype, DestinationClassId, Destination, and TopologyRuleType. Take the conformable contact as an example: its OriginClassId is a stratum contact plane, its OriginSubtype is a conformable contact plane, its DestinationClassId is a geological boundary, and its TopologyRuleType is esriTRTAreaBoundaryCoveredByline, as shown in Figure5.

Figure 5. Procedure for building topological rules (an example of a conformable contact relationship).

3.3. Modelling of Association Relationships of Geological Phenomena The model of the association relationships of geological phenomena is constructed with the following 17 types of geological relationships: anticlinorium, synclinorium, linear fold, brachyaxis fold, structural dome, structural basin, longitudinal fault, transverse fault, diagonal fault, horst and graben structure, imbricate reverse fault, reverse/back-thrust fault, conjugate fault, strike-slip fault, dip-slip fault, oblique fault and bedding fault. This modelling scheme includes three aspects: the design of the corresponding description mechanism of the association relationships in combined relationships, the building of association models, and the development of association rules. In addition to a topological relationship, geological objects also contain an association relationship that is not afﬁliated with the geometric features; rather, this relationship reﬂects the association between geological phenomena. For example, an anticlinorium is made up of folds (synclines and anticlines); an anticlinorium or synclinorium refers to the anticlines or synclines in the limbs of the folds that are complicated by a series of secondary folds. Therefore, a corresponding mechanism is required to describe the association relationship in the combined relationship, ensuring that the association in the model complies with the semantic description of the real geological association, as shown in Table5. Based on the Geodatabase association relationship rules, this paper designs the origin class and destination class for elements, such as an anticlinorium and a fold, and association rules, such as one-to-many simple relationships, to build the corresponding description mechanism. ISPRS Int. J. Geo-Inf. 2018, 7, 267 13 of 21

Table 5. Corresponding description of the association relationship in each combined relationship.

L1 L2 L3 Origin Class Destination Class Association Rule ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW One-to-many 13simple of 21 Fold and Anticlinorium Anticlinorium Fold relationship fold One-to-many simple Table 5. Corresponding descriptionsynclinorium of the association synclinorium relationship in Foldeach combined relationship. relationship L1 L2 L3 Origin Class DestinStratumation Class contact AssociationOne-to-many Rule simple Linear fold Linear fold One-to-many simple Anticlinorium Anticlinorium Foldplane relationship Fold and relationship Stratum contact One-to-many simple fold Brachyaxis fold Brachyaxis fold One-to-many simple Fold and synclinorium synclinorium Foldplane relationship relationship stratum Structural Stratum contact One-to-manyOne-to-many simple simple StructuralLinear fold dome Linear fold Stratum contact plane dome plane relationshiprelationship Stratum contact One-to-manyOne-to-many simple simple BrachyaxisStructural fold basin BrachyaxisStructural fold basin Stratum contact plane Fold and plane relationshiprelationship stratum One-to-many simple Structural dome StructuralLongitudinal dome Stratum contact plane One-to-one simple Longitudinal fault Folding axis relationship fault relationship One-to-many simple Structural basin Structural basin Stratum contact plane Transverse One-to-onerelationship simple Fault and Transverse fault Folding axis Longitudinalfault One-to-onerelationship simple Association fold Longitudinal fault Folding axis relationship of fault One-to-onerelationship simple geological Fault and Diagonal fault Diagonal fault Folding axis One-to-one simple Transverse fault Transverse fault Folding axis relationship Associationphenomena fold relationship Horst and graben One-to-many complicated relationship of Fault wall Normal fault One-to-one simple Diagonalstructure fault Diagonal fault Folding axis relationship geological relationship phenomena Horst and graben One-to-manyOne-to-many complicated complicated Imbricate reverse faultFault Hanging wall wall Normal Reverse fault fault Fault and structure relationshiprelationship fault Reverse/back-thrust One-to-manyOne-to-many complicated simple Imbricate reverse fault HangingAnticline wall Reverse Reverse fault fault Fault and fault relationshiprelationship fault Reverse/back-thrust One-to-many simple Anticline Reverse fault One-to-many simple Conjugatefault fault Wrench fault Stratum line relationship relationship One-to-many simple Conjugate fault Wrench fault Stratum line Rock formation One-to-manyrelationship simple Strike-slip fault Strike-slip fault Rockcontact formation plane One-to-manyrelationship simple Strike-slip fault Strike-slip fault contactRock formationplane One-to-manyrelationship simple Fault and Dip-slip fault Dip-slip fault Rock formation One-to-many simple Dip-slip fault Dip-slip fault contact plane relationship Faultstratum and contact plane relationship stratum RockRock formation formation One-to-manyOne-to-many simple simple ObliqueOblique fault fault Oblique Oblique fault fault contactcontact plane plane relationshiprelationship RockRock formation formation One-to-manyOne-to-many simple simple BeddingBedding fault fault Bedding Bedding fault fault contactcontact plane plane relationshiprelationship

Based on the the ArcGIS ArcGIS Diagrammer Diagrammer Geodatabase Geodatabase mode model,l, this this paper paper builds builds anan element element dataset dataset to storeto store the the association association relationships. relationships. In Inthe the dataset, dataset, there there are are 17 17 relationship relationship classes classes following following the geological association rules rules used used to complete the model design for the association relationships of geological phenomena (such as an anticlinorium and a synclinorium), as shown in Figure6 6..

FigureFigure 6. LogicalLogical model model map map of of the the feature data datasetset for the combined relationships.

The associationassociation rulesrules shown shown in in Table Table4 are 4 are better better explained explained with with a UML a UML diagram diagram that clearly that clearly shows showsthe number the number of constraints. of constraints. Figure7 shows Figure the 7 associationshows the rulesassociation of an anticlinorium. rules of an anticlinorium. Its OriginClassId Its OriginClassId is an anticlinorium, and its DestinationClassId is a fold; its DestinationSubtype is an anticlinorium and synclinorium, and its association rule is one-to-many. Figure 8 shows the association rules of a synclinorium. Its OriginClassId is a synclinorium, and its DestinationClassId is a fold. Its DestinationSubtype is an anticlinorium and a synclinorium, and its association rule is one-to-many. The red arrows describe “origin” and “dest” associations, while black arrows denote a subtype feature “contained” within an anticlinorium and synclinorium.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 14 of 21 is an anticlinorium, and its DestinationClassId is a fold; its DestinationSubtype is an anticlinorium and synclinorium, and its association rule is one-to-many. Figure8 shows the association rules of a synclinorium. Its OriginClassId is a synclinorium, and its DestinationClassId is a fold. Its DestinationSubtype is an anticlinorium and a synclinorium, and its association rule is one-to-many. The red arrows describe “origin” and “dest” associations, while black arrows denote a subtype feature “contained” within an anticlinorium and synclinorium. ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 14 of 21

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 14 of 21

Figure 7. Association rule of an anticlinorium. Figure 7. Association rule of an anticlinorium. Figure 7. Association rule of an anticlinorium.

Figure 8. Association rule of a synclinorium. Figure 8. Association rule of a synclinorium. 4. Study and Discussion Figure 8. Association rule of a synclinorium. 4. StudyIn this and paper, Discussion the section from Dagang to Danyang in the Nanjing-Zhenjiang Mountains is used as the research area. Based on the ArcGIS Diagrammer Geodatabase model, the 4. Study andIn Discussionthis paper, the section from Dagang to Danyang in the Nanjing-Zhenjiang Mountains is object-oriented method is used to build a geological relationship model. With an XML workspace used as the research area. Based on the ArcGIS Diagrammer Geodatabase model, the Indocument this paper, as the the section working from document, Dagang the to Danyangelements, topology, in the Nanjing-Zhenjiang and associations of Mountains a geological is used as object-oriented method is used to build a geological relationship model. With an XML workspace relationship are stored prior to importing them into Geodatabase 10.2 to build the geological the researchdocument area. as Based the working on the ArcGISdocument, Diagrammer the elements Geodatabase, topology, and model, associations the object-oriented of a geological method relationship models that unify the geometrical features and semantics. is usedrelationship to build a geologicalare stored prior relationship to importing model. them With into an Geodatabase XML workspace 10.2 to documentbuild the geological as the working The key element of this study is to construct and store the topologies and associations of document,relationship the elements, models that topology, unify the and geometrical associations features of and a geologicalsemantics. relationship are stored prior to complicated geological relationships described by regional natural languages using GIS geometry The key element of this study is to construct and store the topologies and associations of importingand themsemantic into data Geodatabase and to further 10.2 create to comprehe build thensive geological expressions relationship for geological models objects. thatFor the unify the complicated geological relationships described by regional natural languages using GIS geometry geometricalstorage features of the model, and semantics.33 types of geometric and semantic properties must be designed. For example, and semantic data and to further create comprehensive expressions for geological objects. For the “OBJECTID”, “SHAPE”, “SHAPE_Length”, “Lithology”, “Axis length”, “Axis strike” and Thestorage key of element the model, of 33 this types study of geometric is to construct and semantic and properties store the must topologies be designed. and For example, associations of “Two-limb stratum” are all found for a folding axis in the fold dataset. Additionally, “OBJECTID”, complicated“OBJECTID”, geological “SHAPE”, relationships “SHAPE_Length”, described by“Lithology”, regional natural “Axis languageslength”, “Axis using strike” GIS geometry and and “SHAPE”, “SHAPE_Area”, “Stratum unit name”, “Stratum unit symbol”, “Stratum unit time” and semantic“Two-limb data and stratum” to further are createall found comprehensive for a folding axis expressions in the fold fordataset. geological Additionally, objects. “OBJECTID”, For the storage of “Stratum thickness” are found for a chronostratigraphic element in the stratum dataset. The field the model,“SHAPE”, 33 types “SHAPE_Area”, of geometric “Stratum and semantic unit name”, properties “Stratum must unit be symbol”, designed. “Stratum For example, unit time” “OBJECTID”, and names, types and features of a folding axis and chronostratigraphic element are shown in Figures 9 “Stratum thickness” are found for a chronostratigraphic element in the stratum dataset. The field “SHAPE”,and “SHAPE_Length”,10, respectively. “Lithology”, “Axis length”, “Axis strike” and “Two-limb stratum” are names, types and features of a folding axis and chronostratigraphic element are shown in Figures 9 all found for a folding axis in the fold dataset. Additionally, “OBJECTID”, “SHAPE”, “SHAPE_Area”, and 10, respectively. “Stratum unit name”, “Stratum unit symbol”, “Stratum unit time” and “Stratum thickness” are found

ISPRS Int. J. Geo-Inf. 2018, 7, 267 15 of 21 forISPRS a chronostratigraphic Int. J. Geo-Inf. 2018, 7, x FOR element PEER REVIEW in the stratum dataset. The ﬁeld names, types and features 15 of 21 of a ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 15 of 21 folding axis and chronostratigraphic element are shown in Figures9 and 10, respectively.

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 15 of 21

Figure 9. Feature field design of a fold axis. FigureFigure 9.9. FeatureFeature ﬁeldfield design of of a a fold fold axis. axis.

Figure 9. Feature field design of a fold axis.

Figure 10. Feature field design of a chronostratigraphic element. Figure 10. Feature field design of a chronostratigraphic element. Figure 10. Feature field design of a chronostratigraphic element. AA unified unified physical physical model modelFigure isis required10.required Feature field to store design the theof a compensationchronostratigraphic compensation and element. and association association relationships relationships of of A unified physical model is required to store the compensation and association relationships of geologicalgeological phenomena. phenomena.A unified physical BasedBased model on the is required ArcGIS to Distore Diagrammeragrammer the compensation Geodatabase Geodatabase and association model, model, relationships the the following following of five five geological phenomena. Based on the ArcGIS Diagrammer Geodatabase model, the following five classesclasses are are usedgeological used to achieve tophenomena. achieve unified Basedunified physical on thephysical ArcGIS storage: storage:Diagrammer Feature Feature Class,Geodatabase Class, Subtype, model, Subtype, Feature the following Feature Dataset, five Dataset, Topology, classes are used to achieve unified physical storage: Feature Class, Subtype, Feature Dataset, andTopology, Relationship.classes and Relationship.are These used classesto achieve These are unified usedclasses asphysical are shown used storage: inas Figureshown Feature 11in . FigureClass, Subtype,11. Feature Dataset, Topology,Topology, and Relationship. and Relationship. These These classes classes are are used used as as shownshown in in Figure Figure 11. 11.

Figure 11. Physical storage of the geological relationship model. Figure 11. Physical storage of the geological relationship model.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 16 of 21 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 16 of 21 ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 16 of 21 AccordingAccording to to thethe geological relationship relationship model model shown shown in inFigure Figure 11, the11, Feature the Feature Class Classstores stores33 According to the geological relationship model shown in Figure 11, the Feature Class stores 33 33types types of of geological geological features, features, the the Feature Feature Dataset Dataset stores stores the the datasets datasets for for folds, folds, faults, faults, strata strata and and associationtypes of geological relationships, features, the the Relationship Feature Dataset class ststoresores the 17 datasetstypes offor relationships,folds, faults, strataincluding and association relationships, the Relationship class stores 17 types of relationships, including anticlinorium anticlinoriumassociation relationships, and synclinorium, the Relationshipthe Subtype classclass ststoresores all 17 subtypes types of gerelationships,ological elements, including and and synclinorium, the Subtype class stores all subtypes of geological elements, and the Topology class theanticlinorium Topology class and storessynclinorium, the topological the Subtype relationships class st oresof folds, all subtypes faults and of strata. geological elements, and stores the topological relationships of folds, faults and strata. the TopologyThe geometrical class stores objects the in topological geological relationships objects of the of pansection folds, faults from and Dagang strata. to Danyang in the The geometrical objects in geological objects of the pansection from Dagang to Danyang in the Nanjing-ZhenjiangThe geometrical Mountain objects inare geolog expressedical objects in the ofmodel. the pansection Figures 12 from and 13Dagang are used to Danyangin the study in the of Nanjing-ZhenjiangregionalNanjing-Zhenjiang geological Mountain structureMountain aredata are expressed expressedto establish in in thethe model.modelmodel. of Figures Figures “fold”, 12 12“fault” and and 13 13and are are “strata”,used used in inthe in the orderstudy study toof of regionalexpressregional geological the geological geometric structure structure features data data of to the establish to establishthree thekinds modelthe of model objects of “fold”, of graphically. “fold”, “fault” “fault” and Figure “strata”,and 12 “strata”, shows in order inthe order toresults express to theofexpress geometric the integrated the featuresgeometric expression of thefeatures three of geometryof kinds the ofthree objects and kinds semant graphically. of objectsics for fold Figuregraphically. objects 12 shows with Figure thethe results12classify shows of standard thethe integrated results of expressiontheof the natural integrated of geometrylanguage expression andof fold semantics of (synclinegeometry for foldand and objectsanticsemantline) withics andfor the fold the classify objectsresults standard with for faultthe of classify theobjects, natural standard with language the of ofclassifythe fold natural (syncline standard language and of anticline) the of naturalfold and (syncline language the results and of for anticfaul faultt line)(wrench objects, and fault,the with results normal the classify for fault fault standard and objects, reverse of with the fault). natural the languageFigureclassify 13 ofstandard presents fault (wrench of the the resu fault,naturallts for normal language the stratigraphic fault of and faul reverset (wrenchobjects. fault). Infault, Figure Figure normal 13, 13 accordingpresentsfault and the toreverse resultsthe natural fault). for the stratigraphiclanguageFigure 13 of presents objects. geological Inthe Figure ageresu oflts 13the for, according regionalthe stratigraphic geolog to theical natural objects. structure language In Figureof Ning-Zhen of 13, geological according mountain age to of thearea, the natural regionalwith geologicalthelanguage classify structure of standard geological of Ning-Zhen from age new of the mountainto oldregional (sinian area, geolog system withical the, cambrian structure classifystandard system, of Ning-Zhen silurian from new mountain system, to old (sinianetc.), area, it with system,sets cambrianthethe stratigraphicclassify system, standard silurian object from element system, new etc.),classto old itto (sinian sets realize the system stratigraphicthe integrated, cambrian object expression system, element silurianof class geometry to system, realize and etc.), the semantics integrated it sets expressionforthe the stratigraphic geological of geometry objectage andof element stratigraphic semantics class for toobjects. realize the geological the integrated age of stratigraphicexpression of objects. geometry and semantics for the geological age of stratigraphic objects.

FigureFigure 12.12. Modelling of of fold fold and and fault fault objects. objects. Figure 12. Modelling of fold and fault objects.

Figure 13. Modelling of strata objects. Figure 13. Modelling of strata objects. Figure 13. Modelling of strata objects.

ISPRS Int. J. J. Geo-Inf. Geo-Inf. 2018,, 7,, x 267 FOR PEER REVIEW 17 of 21

The model shows geolocation relationships through topologies and various relationships. The The model shows geolocation relationships through topologies and various relationships. topology system is built as follows: The topology system is built as follows: • Three types of topological rules are established in the fold dataset: hinge of fold and fold, limb • Three types of topological rules are established in the fold dataset: hinge of fold and fold, limb of of fold and fold, and folding axis; fold and fold, and folding axis; • Two types of topological rules are established in the fault dataset: fault wall (hanging wall) and • faultTwo typesplane ofand topological fault wall rules(foot arewall) established and fault inplane; the fault dataset: fault wall (hanging wall) and • Fivefault planetypes andof topological fault wall (footrules wall) are andestablished fault plane; in the stratum dataset: conformable contact, • unconformableFive types of topological contact, intrusive rules are contact, established sedimentary in the contact stratum and dataset: faulted conformablecontact. contact, unconformable contact, intrusive contact, sedimentary contact and faulted contact. The association relationship system consists of 17 relationship rules: anticlinorium, synclinorium,The association linearrelationship fold, brachyaxis system fold, consists structural of 17 relationship dome, structural rules: anticlinorium, basin, longitudinal synclinorium, fault, transverselinear fold, brachyaxisfault, diagonal fold, structuralfault, horst dome, and structural graben basin, structure, longitudinal imbricate fault, transversereverse fault, fault, reverse/back-thrustdiagonal fault, horst fault, and graben conjugate structure, fault, imbricatestrike-slip reverse fault, dip-slip fault, reverse/back-thrust fault, oblique fault fault, and conjugate bedding fault.fault, strike-slip fault, dip-slip fault, oblique fault and bedding fault. Figure 14 shows the geological relationships of regional structures based on the geological relationships described within the MemoirMemoir on GeologyGeology ofof Nanjing-ZhenjiangNanjing-Zhenjiang Mountains. Figure 1414a–da–d show thethe relationshipsrelationships among among the the anticlinorium, anticlinorium, folding folding axis, axis, conformable conformable contact, contact, and faulted and contact,faulted whichcontact, are which all stored are all in stored the same in the data same model. data model.

(a) (b)

Figure 14. Geological relationships among regionalregional geological structures. (a) Jizhuang-Houzhuxiang anticlinorium; (b (b) )Jizhuang-Houzhuxiang Jizhuang-Houzhuxiang folding folding axis axis line; line; (c) (conformablec) conformable contact contact relationship; relationship; (d) faulted(d) faulted contact contact relationship. relationship.

ISPRS Int. J. Geo-Inf. 2018, 7, 267 18 of 21

1. Figure 14a shows the geometric expression of the anticlinorium. This model complies with the semantic description of the topological relationship that states “The anticlinorium is made up of some folds (syncline and anticline)” and the association rule of “one-to-many simple relationship”. 2. Figure 14b shows the geometric expression of the folding axis. This model complies with the semantic description of the topological relationship that states “The axis cannot intersect with or be covered by the geological boundary”, that is, the topological rule of “must not self intersect”. 3. Figure 14c shows the geometric expression of the conformable contact. This model complies with the semantic description of the topological relationship that states “The boundary of the conformable contact plane must be covered by the geological boundary”, that is, the topological rule of “Boundary must be covered by”. 4. Figure 14d shows the geometric expression of faulted contact. This model complies with the semantic description of the topological relationship that states “The boundary of the rock contact plane must be covered by a faulted line”, that is, the topological rule of “Boundary must be covered by”.

From a geometric perspective, the geographic expressions of geological objects can effectively reﬂect the geometric features of folds, faults and strata. From a topological perspective, such expressions can reveal the spatial relationships among real geological phenomena and store the topological relationships found between geological objects. From a relationship perspective, such expressions can effectively represent the composition relationships of real geological phenomena at a macroscopic level and store their association relationships. From a semantic perspective, such expressions can correspondingly show the topological and relation rules to store and express geological relationships via GIS data. The results show that this GIS modelling method can better store and express geological phenomena, geological objects and geological spatial objects in a way that integrates their geometry and semantics.

5. Conclusions Our GIS modelling method integrating geometry and semantics uses object-oriented technology via a Geodatabase spatial data model supported by a standard relation database. Our method uses the ArcGIS Diagrammer Geodatabase model and designs relationships via modelling in consideration of geological semantics. This paper aims to build a GIS model of geological relationships, regarding the problems in existing GIS models. The purpose of this model is to build a bridge between GIS and semantics of geological relationship described by geologists, which is signiﬁcant for both GIS modelling and analysis in geological phenomena. The construction of the data model mainly includes the following key aspects:

1. Based on the geological deﬁnitions, the model categorizes geological relationships as internal composition relationships and external combined relationships, resulting in a total of two categories, eight classes and 27 small groups. 2. The corresponding descriptions of topological rules are designed for each composition relationship, and the corresponding descriptions of association rules are designed for each association relationship. 3. The model then expresses the internal composition relationships as topological relationships between geological spatial objects, thereby defining the Origin, Dest and TopologyRuleType for each Topology Rule, and expresses the external position relationships (i.e., combined relationships) as association relationships between geological spatial objects, thereby defining the Origin, Dest and RelationRuleType for each Relationship Class.

The results show that this GIS modelling method can better store and express geological phenomenon, geological objects and geological spatial objects in a way that integrates their geometry and semantics. ISPRS Int. J. Geo-Inf. 2018, 7, 267 19 of 21

This paper discusses the geological relationships of three geological phenomena, namely, folds, faults and strata, based on their geological definitions and develops an expression that unifies the geometries and semantics of those relationships. A GIS model that can unify the geometries and semantics of geological relationships has the following features: 1. Define and classify the geological relationships. Explain the geological phenomena and their relationships based on their geological meanings. 2. Generalize the three levels of geological relationships from geological phenomena to geological objects and geological spatial objects to construct their interior constitution expressions by topological relationships and their exterior constitution expressions by association relationships between spatial objects. 3. According to this study, the developed model can express geological meanings and store geometric elements, and it can show the corresponding geological relationships well. Some issues still persist that must be investigated through further research: 1. Based on the relationship classification system of multiple tectonic scales (such as tectonics, regional structures, and microstructures), GIS modelling could be used to study the geological relationships at multiple dimensions and scales and unify the levels of spatial expression. 2. Using the geological rules of geological relationships as the platform for recognition and judgement, the GIS model could be used to recognize and judge the relationships of complicated structures.

Author Contributions: H.H. designed the research flow and wrote the manuscript. D.H. performed the data analysis of the study. G.L. contributed significantly to the conception of the study and constructive discussion. All authors read and approved the final manuscript. Funding: National Natural Science Foundations of China; The Key Project of Natural Science Foundation of the Anhui Higher Education Institutions: (No. 41601412, 41771421); (No. KJ2016A222). Conflicts of Interest: The authors declare that they have no conflict of interest.

References

1. Wu, L.; Zhang, R.; Qi, Y. 3D geoscience modelling and virtual mine system. Acta Geod. Cartogr. Sin. 2002, 1, 28–33. 2. Scheck-Wenderoth, M.; Lamarche, J. Crustal memory and basin evolution in the Central European Basin System—New insights from a 3D structural model. Tectonophysics 2005, 397, 143–165. [CrossRef] 3. Qiang, W.; Hua, X. Three-dimensional geological modeling and its application in digital mine. Sci. China Earth Sci. 2013, 43, 1996–2006. 4. Cheng, P.; Gong, J. Design of three-dimensional spatial datamodel and its data structure in geological exploration engineering. Acta Geod. Cartogr. Sin. 2001, 1, 74–81. 5. Yu, J.; Wu, L.; Zi, G.; Guo, Z. SDOG-based multi-scale 3D modeling and visualization on global lithosphere. Sci. China Earth Sci. 2012, 5, 755–763. [CrossRef] 6. Raiber, M.; White, P.A.; Daughney, C.J.; Tschritter, C.; Davidson, P.; Bainbridge, S.E. Three-dimensional geological modelling and multivariate statistical analysis of water chemistry data to analyse and visualize aquifer structure and groundwater composition in theWairau Plain, Marlborough District, New Zealand. J. Hydrol. 2012, 436, 13–34. [CrossRef] 7. Natali, M.; Klausen, T.G.; Patel, D. Sketch-based modelling and visualization of geological deposition. Comput. Geosci. 2014, 67, 40–48. [CrossRef] 8. Turner, A.K. Challenges and trends for geological modelling and visualisation. Bull. Eng. Geol. Environ. 2006, 65, 109–127. [CrossRef] 9. Li, Z.; Pan, M.; Han, D. Three dimensional structural modeling technique. Earth Sci. 2016, 12, 2136–2146. 10. Guo, J.; Wu, L.; Zhou, W.; Jiang, J.; Li, C. Towards automatic and topologically consistent 3D regional geological modeling from boundariesand attitudes. ISPRS Int. J. Geo-Inf. 2016, 5, 17. [CrossRef] 11. Wang, R.-H.; Li, Y.-S. Introduction and determination of borderline virtual boreholes in 3D modeling of complicated geological bodies. Acta Geod. Cartogr. Sin. 2007, 4, 468–475. ISPRS Int. J. Geo-Inf. 2018, 7, 267 20 of 21

12. Li, Q.; Li, D. Reserch on the conceptual frame of the integration of 3D spatial data model. Acta Geod. Cartogr. Sin. 1998, 4, 325–330. 13. Zhong, D.; Zhang, X.; Ao, X.; Wang, X.; Tong, D.; Ren, B. Study on coupled 3D seepage and stress fields of the complex channel project. Sci. China Technol. Sci. 2013, 11, 1193–1201. [CrossRef] 14. Chen, X.; Wu, L.; Che, D. 3D modeling method of geological bodies including faults based on borehole data. Coal Geol. Explor. 2005, 33, 5–8. 15. Zhang, S.; Zhou, C.; Zhang, J.; Chen, X. A ubiquitous knowledgeable data representation model (UKRM) for three-dimensional geographic information systems (3D GIS). Sci. China Earth Sci. 2016, 2, 214–228. [CrossRef] 16. He, H.D. Research on Regional Geological Structure, Semantic Parsing and Object Modeling; Nanjing Normal University: Nanjing, China, 2014. (In Chinese) 17. An, C.; Zhan, L.; Xinzhong, W. Automatic construction of topological relationship of 3D geological blocks based on stratified geological structure. Acta Geod. Cartogr. Sin. 2012, 1, 147–151. 18. Wu, L.; Xu, L.; Che, D. Stratum-ontology and its application in borehole data integration. Geomat. Inf. Sci. Wuhan Univ. 2008, 2, 144–148. 19. Du, Q.; Ren, F. Representation of spatial information in natural languag. Geomat. Inf. Sci. Wuhan Univ. 2014, 6, 682–688. 20. Calcagno, P.; Chilès, J.P.; Courrioux, G.; Guillen, A. Geological modelling from field data and geological knowledge: Part I. Modelling method coupling 3D potential-field interpolation and geological rules. Phys. Earth Planet. Inter. 2008, 171, 147–157. [CrossRef] 21. Wu, C.; He, Z.; Weng, Z. Property, classification and key technologies of three-dimensional geological data visualization. Geol. Bull. China 2011, 5, 642–649. 22. Amorim, R.; Brazil, E.V.; Samavati, F.; Sousa, M.C. 3D geological modeling using sketches and annotations from geologic maps. In Proceedings of the 4th Joint Symposium on Computational Aesthetics, Non-Photorealistic Animation and Rendering, and Sketch-Based Interfaces and Modeling, New York, NY, USA, 8–10 August 2014. 23. Zlatanova, S.; Rahman, A.; Shi, W. Topological models and frameworks for 3D spatial objects. Comput. Geosci. 2004, 30, 419–428. [CrossRef] 24. Perrin, M.; Mastella, L.; Morel, O. Geological time formalization: An improved formal model for describing time successions and their correlation. Earth Sci. Inf. 2011, 11, 81–96. [CrossRef] 25. Adaly, S.; Bouqata, B.; Marcus, A. A day in the life of a metamorphic. In Proceedings of the IEEE 29th International Conference on Data Engineering Workshops, Brisbane, Australia, 8–12 April 2013. 26. Mastella, L.S.; Ait-Ameury, Y.; Jean, S. Semantic exploitation of persistent metadata in engineering models: Application to geological models. In Proceedings of the Third International Conference on Research Challenges in Information Science, Fez, Morocco, 22–24 April 2009. 27. Hou, W.; Liu, X.; Wu, X. Geo-ontology logical structure and development technology for 3D geology modeling. Geogr. Geo-Inf. Sci. 2009, 1, 27–31. 28. Yao, M.; Li, A.B.; Chen, Y.; Wu, C.Y. An automatic method for creating the geological boundary layer. J. Geo-Inf. Sci. 2017, 19, 326–335. 29. Guo, J.; Wu, L.; Zhou, W. Automatic ore body implicit 3D modeling based on radial basis function surface. J. China Coal Soc. 2016, 8, 2130–2135. 30. Li, W.J.; Shi, Y.L.; Hu, D. A geological map edge matching method based on considering attributes elements. Metal Mine 2017, 6, 132–136. 31. Gong, J.; Li, X.; Wu, H. Spatiotemporal data model for real-time GIS. Acta Geod. Cartogr. Sin. 2014, 3, 226–232. 32. Keßler, C.; Raubal, M.; Wosniok, C. Semantic rules for context-aware geographical information retrieval. In Proceedings of the 4th European Conference on Smart Sensing and Context, Guildford, UK, 16–18 September 2009; Springer: Guildford, UK, 2009. 33. Bazire, M.; Brézillon, P. Understanding context before using it. In Modeling and Using Context; Dey, A., Kokinov, B., Leake, D., Turner, R., Eds.; Springer: Berlin/Heidelberg, Germany, 2005. 34. China Geological Survey. DD2006-06, Digital Geological Map Database Standards; China Geological Survey: Beijing, China, 2006. 35. Li, C.; Lv, X.; Liu, C.; Li, F.; Li, J.; Liu, Y. The architecture of geological survey intelligent space. Acta Geod. Cartogr. Sin. 2015, 1, 143–151. ISPRS Int. J. Geo-Inf. 2018, 7, 267 21 of 21

36. Lomotey, R.K.; Deters, R. Terms mining in document-based NoSQL: Response to unstructured data. In Proceedings of the 3rd IEEE International Congress on Big Data, BigData Congress, Anchorage, AK, USA, 27 June–2 July 2014. 37. Sirsat, S.R.; Chavan, V.; Deshpande, S.P. Mining knowledge from text repositories using information extraction: A review. Sadhana 2014, 39, 53–62. [CrossRef] 38. He, H.; Di, H.; Lu, G. GIS data modeling of a regional geological structure by integrating geometric and semantic expressions. Acta Geod. Cartogr. Sin. 2017, 8, 1058–1068. 39. Wu, L.; Xue, L.; Li, C. A geospatial information grid framework for geological survey. PLoS ONE 2015, 10. [CrossRef][PubMed] 40. Hu, M.; Liao, T. Structural Geology; Petroleum Industry Press: Beijing, China, 2007. (In Chinese) 41. Zeng, Z.X.; Fan, G.M. Structural Geology; China University of Geosciences Press: Wuhan, China, 2008. (In Chinese) 42. Pollard, D.D.; Fletcher, R.C. Fundamentals of Structural Geology; Cambridge University: Cambridge, UK, 2005. 43. Neville, J.P.; John, W.C. Analysis of Geological Structures; Cambridge University: Cambridge, UK, 1990. 44. Davis, G.H.; Reynolds, S.J. Structural Geology of Rocks and Regions; John Wiley & Sons: Hoboken, NJ, USA, 1996. 45. Zhang, X.Y.; Zhang, C.J.; Zhu, S.N. Annotation for geographical spatial relations in Chinese text. Acta Geod. Cartogr. Sin. 2012, 3, 468–474. 46. Vockner, B.; Mittlböck, M. Geo-enrichment and semantic enhancement of metadata sets to augment discovery in geoportals. ISPRS Int. J. Geo-Inf. 2014, 3, 345–367. [CrossRef] 47. Lu, G.; Yuan, L.; Yu, Z. Surveying and mapping geographical information from the perspective of geography. Acta Geod. Cartogr. Sin. 2017, 10, 1549–1556. 48. Zhu, Q.; Hu, M. Semantics-based LOD models of 3D house property. Acta Geod. Cartogr. Sin. 2008, 4, 514–520. 49. Zambelli, P.; Gebbert, S.; Ciolli, M. Pygrass: An object oriented python Application Programming Interface (API) for Geographic Resources Analysis Support System (GRASS) Geographic Information System (GIS). ISPRS Int. J. Geo-Inf. 2013, 2, 201–219. [CrossRef] 50. Hu, Y.; Janowicz, K.; Prasad, S.; Gao, S. Enabling semantic search and knowledge discovery for arcgis online: A linked-data-driven. In Proceedings of the 18th AGILE International Conference on Geographic Information Science, AGILE 2015, Lisbon, Portugal, 9–12 June 2015; Kluwer Academic Publishers: Lisbon, Portugal, 2015.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).