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C O N T E N T S 1. INTRODUCTION 2. DATA TO BE MAPPED 3. MANUAL CONTOURING 4. COMPUTER CONTOURING 5. USE OF STRUCTURAL MAPS IN THE DETERMINATION OF GROSS ROCK VOLUME 6. ISOPACHS 7. GRID MANIPULATION 8. FAULT MAPPING 7 7 Mapping

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  • Well Control11

    C O N T E N T S

    1. INTRODUCTION

    2. DATA TO BE MAPPED

    3. MANUAL CONTOURING

    4. COMPUTER CONTOURING

    5. USE OF STRUCTURAL MAPS IN THEDETERMINATION OF GROSS ROCK VOLUME

    6. ISOPACHS

    7. GRID MANIPULATION

    8. FAULT MAPPING

    77Mapping

  • 12

    LEARNING OBJECTIVES:In this Chapter, we introduce the reader to the concept of mapping of subsurface data.Maps are two-dimensional representations of three-dimensional surfaces and theseare extensively used in the Petroleum Industry to locate wells and determine the sizeof hydrocarbon accumulations. By the end of this chapter the reader will be able todraw, read and understand oilfield maps

    Specific learning objectives for the student are:

    1. To be able to construct a contour map of spatial data using manual and mechanicalcontouring

    2. To state the advantages and disadvantages of computer and manual mappingtechniques

    3. To describe a computer grid and explain how these can be manipulated

    4. To appreciate "good" and "poor" maps from the type and density of the input data.

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 3

    INTRODUCTION

    Maps are a 2-D plan view representation of an area. The mapped area, in an oil or gasfield context, is usually the agreed limits of the field. Oilfields often straddle a numberof exploration licences, county boundaries or even national borders. Governmentsusually require fields to be developed as a single entity. When a field straddles alicence boundary, the interested parties negotiate the technical procedures for inter-preting the size and the proportions of the field. These procedures determine how logsshould be interpreted, what correlations are agreed, how maps should be generated,etc, etc.) and determine the companies percentage of costs and revenues associatedwith the development of the field through a process of unitisation. Field mapstherefore stop just outside the field boundaries (artificially, as the geological horizonprobably extends) and wells or other data outside will only be incorporated if includedin the unitisation agreement.

    Geologists and geophysicists are adept map makers and map readers and are verygood at picturing in their mind, the 3-D relationships expressed by the 2-D represen-tations. This visualisation is greatly helped by the ability of modern mapppingpackages to display 3-D surfaces which can be rotated and viewed from anyperspective. These highly coloured images may be deceptive - as they rely heavily onthe quality of the underlying data - and could mislead the viewer into considering thefield structure as a very well described object. This Chapter will help the PetroleumEngineer to appreciate some of the pitfalls in maps.

    Maps are the primary vehicles to summarise, interpret and communicate spatial data.Relationships are shown on maps by contours. Contouring is the drawing of lines ofequal value through a discrete data set of values at a few points and can be done eithermanually or by computers. Contour lines describe a surface (Figure 1). Computermapping in the oil industry is a major activity, assisted by many software packages.

    Subsurface mapping is the interpretation of the form of a continuous surface (orvariable) from a few isolated data points. To illustrate the challenge this provides, trycontouring the elevation data on the base map in Fig 2a, on a regular 2km grid.

    Data Point

    Contour Line

    Contour ValueValue of a

    Property at a Data Point

    4040

    4050

    50

    30

    30

    30

    20Figure 1Discrete data points and aset of contour lines showingthe form of a surfacethrough those points

  • 14

    160 225 245 270 160

    230 270 390 330 190

    305 440 360 200 170

    370 550 285 200 170

    410 280 200 230 250

    300 250 270 250 370

    Figure 2aA regular 2 x 2 km grid ofelevation data (values areheight above sea level inmetres). This is a base map(See solutions for contourmap)

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 5

    160 225 245 270 160

    230 270 390 330 190

    305 440 360 200 170

    370 550 285 200 170

    410 280 200 230 250

    300 250 270 250 370

    Figure 2bThe portion of theOrdinance Survey Map ofthe Pentland Hills fromwhich the above data weretaken in figure 2a. Notethat several large features(e.g., Glencorse reservoir,Castlelaw Hill, CarnethyHill) do not appear on the2km contoured data. Forthe sense of scale, BlackHill and Capelaw Hill areapproximately the sameareal extent as some smallfields (e.g., Helder andHoorn Fields, respectively,in the Netherlands sector ofthe North Sea). ThePentland Hills as a whole( the high area marked onthe map as HILLS) aresimilar in scale to someMiddle Eastern oilfields(e.g., Dukhan Field inQatar).

  • 16

    2 DATA TO BE MAPPED

    Before one can start mapping the data need to be located on a 2-D plane (base mapfigure 2.1a). In vertical wells, the data is located at the well coordinates (usually notedas x and y). The depth in a well (or any other property) is denoted as z. The data arethen referenced to a 3-D coordinate system (x,y,z). The coordinate system used forthe map (in the x,y plane) can be geographics (longitude or lattitude in degrees,minutes, seconds), metres (using a Universal Transverse Mercator, UTM, projection),metres or feet using a local platform coordinates (displacement relative to an origin,usually the platform reference point) or some local national coordinate system (e.g.,Amersfoort in the Netherlands). In deviated wells, the data point is located at the x,ythat corresponds to the northing (mN) and easting (mE) relating to the appropriatemeasured depth in the well bore (derived from the well survey).

    The data to be mapped are conventionally referred to as z in this 3-D coordinatesystem. These data can be:

    depths to a horizon (feet or metres). These depths are always vertical and expressedrelative to a datum, usually mean sea level (MSL). True vertical depths (TVD) aretherefore negative (to express subsea depths below sea level, TVDSS) or positive(elevations above sea level);

    the thickness of an interval (feet or metres);

    a petrophysical parameter (porosity, permeability), pressure (at some datum e.g.,oil-water contact), initial production rate, depth to oil-water contact (may not behorizontal) to give some examples.

    Figures 2a to 2c illustrate the relationship between the complexity of a map and thenumber of data points available. Only a relatively simple map can be contoured andjustified from the 2km grid of data points, compared to the detail available on theEarths surface. However the data are mapped, the greater the data density, the greaterthe map complexity. In other words the more data you have (i.e., wells drilled), themore complicated and more precise (but rarely simpler!) the field maps are likely to become.

    Depth to a horizon and fault locations are mapped on a structure map. Contours ona structure map represent the depth (or elevation) at locations along the line. Alonga contour these values are constant (i.e., at the same depth or elevation). Walkingalong a contour line is walking along a constant (i.e., flat) elevation. This is equivalentto walking along structural strike. Walk at right angles to an elevation contour and onewill be walking up hill (up-dip) or down hill (down-dip). When contours are closetogether the dip is steep; when the contours are far apart this represents a gentle slope.The contour interval must be constant on a map.

    If stratigraphic thickness is mapped the contours are known as isopachs ("iso"- beingGreek for "same"). Likewise pressure maps have isobars; temperature maps,isotherms; and lithology maps, isoliths. Thickness data can be mapped vertically (i.e,thickness encountered in a vertical well) or stratigraphically (by correcting forstructural dip) (Fig. 3). Hence:

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 7

    Isopoachs: contours of true stratigraphic thickness (TST) Isochores: contours of true vertical thickness (TVT)

    True StratigraphicThickness (isopach)

    TST = TVT x cos

    True VerticalThickness (isochore)

    Geological field mapping at outcrop is largely a separate discipline from subsurfacemapping. Outcrop maps, however, are similar to a subcrop maps which show thedistribution of beds beneath an unconformity. If the Earth's current surface wascompletely buried underneath a new layer of rock the current outcrop map - surfacegeology map - would become the subcrop map at the base of the new unit. After all,the present land surface is a likely future unconformity! Subcrop maps show thegeological units below an unconformity. These can be used to predict the overlyingsand distribution as they often record the ancient topography and this will influencethe deposition of new reservoir material. Subcrop maps can be useful in determiningthe topography of an erosional surface - hard rocks being local highs and possiblysediment sources - soft rocks being more easily eroded into valleys.

    3 MANUAL CONTOURING

    There are five golden rules of contouring (Tearpock and Bischke, 1991):

    A contour line cannot cross itself or any other contour. A contour cannot merge with contours of same or different values A contour must pass between points whose values are lower and higher than its own

    value A contour line of a given value is repeated to indicate reversal of slope A contour line must close within mapped area or end at edge of map

    Other useful guidelines are:

    Maintain a constant contour interval clearly marked by with regular values Include a scale bar. A graphic scale bar is more important than the actual scale (ie.

    1 to 100000 - one unit on the map is equal to 100000 units on the ground) as mapsare often reduced on a photocopier or projected on a screen

    Hachures(small tick marks on one side of the contour) inwards around closed lowsand outwards around closed highs, or "HIGH" and "LOW", "THICK" and "THIN"annotation also help the reader get the right perspective. On coloured maps lightcolours can represent highs or thins, dark colours thicks or lows.

    Figure 3True vertical thickness andtrue stratigraphic thickness

  • 18

    Start contouring where there is maximum control data Start with simplest contouring that honours the data Always contour in pencil (it is very difficult to get it right first time!)

    There are a two alternative methods of contouring commonly encountered. We canillustrate this with the following example data set (Fig. 4a from Tearpock and Bischke,1991):

    130

    210

    190240

    163

    150

    85

    51

    62

    80

    116

    190 225

    178

    257

    205

    Mechanical contouring or triangulationProcedure (refer to Figure 4b).1. Drawlines between the points subdividing the area into triangles. Try to make thesetriangles as close to equilateral triangles as is possible. This is triangulation.2. Choose a contour interval. Take the maximum value, subtract the minimum value,divide by a convenient number between 5 and 8. Round up to a simple value (1000,500, 100, 25, 10, 1, 0.5, etc...). Choose the actual contours values at simple roundnumbers. (every 10, 50, 100, etc.) 3. Subdivide the sides of the triangles into appropriate divisions to identify theintersection of any contour lines passing between the points4. Join up the points of equal value5. Contours are the lines connecting points of equal value.

    Figure 4aAn irregular data set ( fromTearpock and Bischke1991)

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 9

    Triangulation assumes dip is constant between data points and any change occurs atthe control points (Fig. 4b). Using a ruler the map will appear as a series ofinterlocking triangles. The basic assumption that dip is constant is normally invalid,therefore the contouring is not "correct". However, it can be a useful techniquebecause it does not require interpretation. Mechanical contouring allows littlegeological interpretation and thus, because no two geologists are likely to exactlyagree on any interpretation, is often used in unitisation to remove perceived humanerror.

    130

    210

    190240

    163

    15085

    51

    62

    80

    116

    190 225

    178

    257

    205

    200200

    100

    100 150

    200

    150

    85

    225

    CONSTRUCTIONLIN ES

    PARALLELCONTOURS

    EQUILATERALTRIANGLE }

    FITTING A PLANE TO 3 POINTS

    200150

    100

    Interpretive contouringIn the most rigorous application of interpretive contouring, the procedure is the sameas mechanical contouring - except that no triangles are constructed and no ruler isused. In that respect, the resulting map would look like a mechanical contoured map,but with rounded contours. Many would argue that this map is the "correct" map forthe data. That is quite a different map from the map of the property, for which the datarepresent a few samples. This can be tested with the data in Figure 2a. A triangulatedmap of the data is not one that could be followed when out hill walking!

    The geologist has license to contour the best interpretation for the area whilsthonouring the data (Figure. 4c). The mechanical map can be used as a guide, however,the geologist is often employed to find the anomalies, that might be missed by previousdrilling activities. Interpretive contouring is the most acceptable and most commonlyused form of contouring (Tearpock and Bishke, 1991). Interpretative data allowsincorporation of soft data (e.g., paleo-shoreline, paleo-wind direction, etc) which isparticularly useful in isopachs or porosity maps as they may direct the developmentdrilling towards additional oil reserves.

    Figure 4bA map produced bymechanical contouring ortriangulation

  • 110

    140

    160

    220

    120

    140

    200

    240

    200

    60

    8 0

    4 COMPUTER CONTOURING

    Oil companies are among the largest markets for automatic data interpolation andplotting software. Computer contouring methods are totally consistent and providea counterbalance to overly interpretive mapping. Two types of computer mapping areencountered in the industry:

    Trend surface analysisThis technique employs a type of statistical regression technique. In much the sameway as a polynomial is fitted to pairs of x,y data in linear regression, a surface is fittedthrough a number of x,y,z data points. The goodness of fit of a trend surface can betested statistically, allowing some measure of the fit to the data. A minimum weightedleast squares (MWLS) procedure is commonly used to find the best trend surface fit.Note that computer methods only work with the data available, therefore it can becommon for dummy points to be added to get the map to look right.

    Computer methods need adequate control and are subject to edge effects (i.e., wherethere are few data towards the edge of the mapped area). Unsightly bulls-eyes alsooccur around anomalous data points or outliers, so these maps, tend to be used forguiding manual contouring. The appearance of computer drawn maps also dependson:

    the grid size employed the smoothing factor applied to the contours the contour interval the way discontinuities (such as faults) are handled

    Figure 4cMaps produced byinterpretive contouring( from Tearpock andBischke 1991)

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 11

    Grid size should be selected close to the average displacement between controlpoints. With these considerations, it can be seen that the appearance of a computergenerated map also depends on the operator, and, possibly, is not so free of "humanerror".

    KrigingA moving average method developed originally by the mining industry but iscommonly encountered in oilfield data situations. Kriging requires an understandingof the correlation length - this is the distance over which a data point has an influenceon the estimates. The determination of correlation lengths is covered more fully in thefollowing Chapter. The use of correlation length allows estimates of the value of aspatially distributed variable together with the probable error associated with theestimates. Essentially, maps near data points are less uncertain than those at a distancefrom a control point. For kriging to be an effective mapping tool in oil fields, however,the well control has to be dense and this technique is not often used in unitisation inthe North Sea (when wells are few and far between).

    The important contribution of computer mapping techniques are the systematicquantification of errors (by also mapping the possible deviations from the mappedsurface). Although useful, this alone is not sufficient reason for abandoning themanual methods. A computer generated map from the Tearpock and Bischke data setis shown (Figure 5). Note that the form of the map is close to the mechanicallygenerated map (Figure 4b) and quite different from the interpretive map (Figure 4c).Note that whilst these maps are all different - they are all consistent with the data! Itis an geological and/or engineering judgement which decides which is used. Fordrilling targets these various maps can be used to provide a range of depths orthicknesses, which can then be incorporated in the drilling programme.

    200

    200

    200

    100

    Figure 5Computer contoured data infigures 4a for comparisonwith figures 4b and 4c. Themap was prepared using theMWLS option inMacGridzo. (MWLS -Minimum Weighted LeastSquares)

  • 112

    5. USE OF STRUCTURAL MAPS IN THE DETERMINATION OFGROSS ROCK VOLUME

    The gross rock volume (GRV) is the total volume between the mapped surface thatdefines the top of the reservoir or potential reservoir and the hydrocarbon contact orexpected hydrocarbon contact. The GRV of a reservoir is determined from thestructural maps,

    manually - using a mechanical device known as a planimeter, or by by computer - by subtracting oil-water contact grid (surface) from top structure grid.

    Step 1. Calibrate planimeter

    Planimeter clock wise

    This angle should never get below 30degreesor exceed 160degrees

    Start point

    Known area1 sq.km.

    =247.1 acres

    Step 2. Planimeter each contour to create area vs height plot

    HIGH

    Dep

    th

    Area

    Step 3. Planimeter area vs height plot to get volume

    ........or count squares or use trigonometry

    The basic procedure for planimetering is given in Figure 6. The planimeter is used todetermine the total volume between the top reservoir surface and the hydrocarboncontact. This volume is usually known as the Gross Rock Volume (GRV). The useof the GRV in volumetrics is discussed in Chapter 9.

    The simplest structural maps are seen for simple anticlines. An anticline is anelongate stucture with dipping flanks in all directions. An example is shown in Figure7 of Helder Field in the Netherlands offshore area, the anticline is orientated fromnorthwest to southeast. The structure is cut by a number of small faults and one moremajor one running sub-parallel to the anticline. The thick Vlieland Sand is well inexcess of the height of the oil column, resulting in bottom water over the entire areaof the field as can be seen on the cross-section. From the map and a scale bar the area

    Figure 6Basic planimeter procedure.

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 13

    of the field can be determined. The determination of area is the first step towardsdetermining the volume of hydrocarbons that might be contained in the field (orprospect). This is illustrated in Figure 8 by the counting squares method.

    1420

    1410

    1420

    1425

    1400

    1400

    OWC

    1420

    A

    A'

    1400

    A A'1380

    1400

    1420(MSS) 1425

    OWC

    VERTICAL EXAGGERATION12.5 x HORIZONTAL

    Contour interval 10mDepths metres subsea (MSS)MAP ON TOP VLIELAND SANDSTONE

    1 km

    A A'

    NO VERTICAL EXAGGERATION

    2061 squares

    441 squares

    25 squares

    AREA = 1 sq. km.

    AREA = 2061 = 4.67 sq. km.441

    Figure 7Structural map on TopVlieland Sandstone forBlock Q/1, Netherlandsoffshore (Contour values inmetres). The cross -sectionA-A has been constructedat various verticalexaggerations.(From Roelofsen and DeBoer, in Spencer, 1991)

    Figure 8Outline of the Helder Fieldshowing the method ofcalculating area bycounting squares.Although this method is notused when other computermethods are available it isthe easiest way to representthe more sophisticatedprocedures and remains adefault technique to be usedwhen technology is notavailable.

  • 114

    6. ISOPACHS

    An isopach(s) of the reservoir producing horizon(s) is required to determine whetherthe oil column is thinner than the sand - in which case there will be bottom-water; orwhether the sand is thin, relative to the oil column, in which case there will be edgewater. If, as in the Helder case above, the sand or reservoir unit is very much thickerthan the oil-column then they are of less significance (-useful, nevertheless, for themodelling of the aquifer). In some fields, structure maps do not define the oilaccumulation, but the isopach does (eg., Figure 9 Hartzog Draw Field and Figure 10Indian Draw Field). In each example, the geometry of the contours is determined bythe sedimentological interpretation, helped and proven in these examples by the closeUS onshore well spacing. In the case of Indian Draw, the contours follow the shapeof a fluvial channel.

    2 km

    A A'

    50'

    0

    VERTICAL = 133 X HORIZONTAL

    PRODUCING WELLSDRY HOLES (NO RESERVOIR)

    2 km

    ONSHOREREGULARWELLSPACING

    A'

    A

    PALAEOSHORELINE

    0'

    50'

    0'

    Figure 9Net pay isopach(stratigraphic thickness ofproducing sand) of theShannon Sandstone,Hartzog Draw Field,Wyoming. Shape ofisopach reflects thepreservation along ancientshoreline. Close wellspacing is typical ofonshore developments.Note the lack of any faultsin this reservoir.(From Tillman andMartinsen in Tillman andWeber, 1987)

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 15

    1 km

    TURBIDITE CHANNEL SANDSTONE GEOMETRY

    LIMIT PRODUCTIVE ZONES

    N S

    LIMESTONE MARKER

    ZONES

    PRODUCTIVE

    LIMIT OF PRODUCTIVE ZONES

    N

    PAY THICKNESS IN FEET

    DOLOMITE

    ZONES

    PRODUCTIVE

    120 100

    40

    7. GRID MANIPULATION

    Often the top reservoir structure is mapped from seismic surveys and well control. Inmany cases, however, it is not possible to resolve the base of the reservoir unitseismically. If sufficient well data is available, however, the isopach can be used togenerate a base structure map. The simplified procedure is shown in Figure 11. A gridor contour map of sand thickness can be subtracted from the top structure map to givethe structure at the base of the reservoir. The area where the base of the reservoir isabove the hydrocarbon contact determines the area of no bottom water or completereservoir fill. The area where water underlies the hydrocarbon column (i.e., thereservoir sand is not full) the area around the edge of the field, where there is bottom-water, is sometimes known as the Feather edge.

    Figure 10Net pay isopach (above)and cross section (below)through the Indian DrawField, Wyoming. Isopachshows the preservation of achannel fill sandstone.(From Philips in Tillmanand Weber, 1987)

  • 116

    - 8300- 8200

    - 8100

    - 8325

    200

    150

    100

    50

    TOP STRUCTURE MAP PAY ISOPACH MAP

    - 8325

    -8300 - 200 = -8500

    -8300 - 100 = -8400

    OWC

    200

    150

    100

    50

    - 8300 - 8400

    - 8500

    Area of no bottom water

    BASE STRUCTURE MAP

    8. FAULT MAPPING

    In multi-reservoir, faulted fields (such as occur numerously in the Gulf Coast , US, theNiger, West Africa, and Mahakam, Indonesia, deltas) the juxtaposition of sand againstsand and sand against shale can determine the location and mapped extent of reserves(Figure 12). Detailed cross sections and fault plane maps (sections along the plane ofthe map showing juxtaposition of sands on upthrown and downthrown sides) can bevery useful to illustrate across-fault communication. These Fault Plane maps are alsoreferred to as Allan maps.

    Figure 11Determining the BaseStructure from TopStructure and ReservoirIsopach maps

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 17

    Figure 12Fault-plane map (Allenmap) to show juxtapositionof reservoir on either sideof the fault.

    A'

    B'

    A

    B

    A'

    B'

    A

    B

    A A'

    B B'

    B A'

    FAULT PLANE MAP

    UPTHROWN

    DOWNTHROWN

  • 118

    EXERCISES

    1. Collect together some spatial data and produce a hand drawn map - this could bea structure map, a topographic surface, an isopach, an isotherm, an isochore, an isobar,etc....

    2. Map the following x,y,z, data set on graph paper, using (a) triangulation and (b)interpretive contouring

    X Y Z10 5 714.5 35 721 20 1025 10 033 35 1136 20 1537 6 1750 10 2150 36 053 22 1560 33 13

    For the interpretive contouring assume Z is sand thickness and that the sand wasdeposited from the South East. (X is East, Y is North)

    3. Find a copy of an oilfield map and draw a cross section along a transect - at thecorrect aspect ratio and at a suitable vertical exagerration

    4. The data came from a simple anticlinal field. Contour at 10m intervals

    5. These data came from a regional seismic interpretation. You have been given thefault pattern. Contour the surface (250m contours interval) and highlight the shallowmost areas (these are prospects)

    Bibliography

    Davies. J.C., 1973, Statistics and Data Analysis in Geology, John Wiley & Sons, NewYork, 550p

    Spencer, A.M. 1991 Generation, accumulation and production of Europes hydro-carbons. EAPG Spec. Publ. 1, Oxford Univ. Press, Oxford, 459p.

    Smith., D. 1980 Sealing and Nonsealing Faults in Louisiana Gulf Coast Salt Basin,AAPG Bulletin v.64, p145-172.

    Tearpock, D.J., and R.E.Bischke, 1991 Applied subsurface geological mapping.Prentice Hall, New Jersey, 646p.

    Tillman, R.W., and Weber, K.J., (eds) Reservoir Sedimentology SEPM specialpublication No. 40, Tulsa, Ok. 357p .

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 19

    0 1

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    EXERCISE 4

  • 120

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    CI = 250m

    NN

    EXERCISE 5

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 21

    SOLUTION Figure 2a (in text page 4)

    160 225 245 270 160

    230

    200

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    305 440 360 200

    200

    170

    370 550

    400

    300

    500

    285 200 170

    410 280 200 230 250

    300 250 270 250300

    370

  • 122

    SOLUTION EXERCISE 2

    40

    40 50 60

    30

    30

    20

    20

    20

    10

    100

    011

    0

    0

    7

    7

    10

    10

    13

    1515

    15

    5

    21

    17

    0

    y

    x

    Here I cheated because I knew the shape of thefeature before sampling the points. It illustrates howpoor maps can be using this technique with few data points.

  • 77Mapping

    Department of Petroleum Engineering, Heriot-Watt University 23

    SOLUTION EXERCISE 4

    H

    L

    H

    0 1

    C.I. = 10m

    2560

    2555

    2555

    2570

    2570

    2570

    25802600

    2570

    2550

    2540

    2560

    2590

    2560

    2550

    2535

    2550

    2550

    2560

    2570

    2580

    2590

    2570

    2570

    2570

    2560

    2540

    2535

    2530

    2530

    2525

    2520

    2530

    2540

    2540 25

    45

    2555

    2535

    2560

    2575

    2545

    2570

    2595

    2545

    2540

    2540

    2540

    2540

    2540

    2550

    2575

    2600

    2600

    2610 2600

    2630

    2610

    2570N

    2560

    2540

    N

  • 124

    1020

    010

    200

    1035

    0

    1060

    0

    9900

    1000

    010

    000

    1010

    098

    0010

    000

    1025

    0

    1040

    010

    100

    1000

    010

    00099

    50

    1010

    0

    1000

    0

    1000

    010

    100

    1010

    0

    1040

    0

    1040

    0

    1050

    0

    1050

    0 1025

    0

    1025

    0

    1000

    0

    1000

    010

    000

    1010

    010

    1501025

    0

    9900

    1000

    010

    250

    1030

    0

    9500

    96009800

    1010

    010

    000

    1000

    0

    9750

    9750

    9900

    9900

    9850

    0

    9800

    1010

    0

    1040

    010

    600

    1050

    0

    1070

    010

    400

    1025

    0

    1025

    0

    1025

    010

    400

    1025

    0

    9900

    1025

    0

    1015

    0

    1030

    099

    0010

    150

    1010

    0 1000

    0

    1000

    0

    1025

    0

    1030

    0

    1060

    0

    1075

    0

    1060

    010

    500

    1100

    010

    750

    1050

    0

    1040

    0

    1040

    0

    1060

    010

    500

    1020

    010

    100

    1000

    0

    1000

    9750

    9950

    9900

    9900

    9800

    9800

    9800

    9750 9750

    1000

    0

    1000

    0

    1000

    0

    1000

    0

    10000

    1000

    0

    9800

    9850

    1010

    0

    1005

    010

    250

    9900

    9750

    9750

    9250

    9250

    1040

    0

    1030

    095

    0095

    00

    9400

    9500

    1060

    0

    1075

    0

    1050

    0

    1035

    010

    500

    1025

    0

    H

    H

    H

    H

    HH

    H

    L

    L

    L

    9750

    0 1 2km

    CI = 250m

    NN

    SOLUTION EXERCISE 5