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
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
2560
2555
2555
2570
2570
2570
25802600
2570
2550
2540
2560
2590
2560
2550
2535
2550
2550
2560
2570
2580
2590
2570
2570
2560
2540
2535
2530
2530
2540
2540 25
45
2555
2535
2560
2575
2545
2570
2595
2545
2540
2540
2540
2560
2525
2530
2540
2570
2540
2550
2575
2600
2600
2610
2600
2630
2610
km
NN
EXERCISE 4
120
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
9750
0 1 2km
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
270 390 330 190
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