1. Spatial analysis in GIS

2. Geology of Petroleum Systems 2
GIS for mineral and hydrocarbon exploration
Used for integrating data (map layers) to identify most prospective areas ∫
Integrating function
linear or non-linear
parameters
Stratigraphic hydrocarbon traps occur where reservoir facies pinch into impervious rock such as shale, or where they have been truncated by erosion and capped by impervious layers above an unconformity.
Output mineral potential map
Grey-scale or binary
Input spatial datasets
Categoric or numeric
Binary or multi-class

3. Geology of Petroleum Systems 3
Data Types
Nominal/categorical
Ordinal
Interval
Ratio
Nominal data are items which are differentiated by a simple label, usually a name.
May have numbers assigned to them. This may appear ordinal but is not.
Nominal items are usually categorical, in that they belong to a definable category.
Can be counted, but not ordered or measured.
Ordinal data can be ranked (put in order) or have a rating scale attached.
Can be counted and ordered, but not measured.
Interval data is where the distance between any two adjacent units of measurement (or 'intervals') is the same but the zero point is arbitrary.
Ratio data are measured in terms of the ratio between a magnitude of a continuous quantity and a unit magnitude of the same kind. The zero value is absolute
Stratigraphic hydrocarbon traps occur where reservoir facies pinch into impervious rock such as shale, or where they have been truncated by erosion and capped by impervious layers above an unconformity.

4. Geology of Petroleum Systems 4
Data Types
Parametric vs. Non-parametric
Interval and ratio data are parametric, and are used with parametric tools in which distributions are predictable (e.g.,  Normal).
Nominal and ordinal data are non-parametric, and do not assume any particular distribution. They are used with non-parametric tools such as the histogram.
Stratigraphic hydrocarbon traps occur where reservoir facies pinch into impervious rock such as shale, or where they have been truncated by erosion and capped by impervious layers above an unconformity.
4’ 7” ’ ’5” ’10’ 6’3” ’8”
4’ 7” ’ ’5” ’10’ 6’3” ’8”
Height of women
Height of men
Normal distribution – parameters are mean and standard deviation

5. Geology of Petroleum Systems 5
Data Types
Continuous and Discrete
Continuous measures are measured along a continuous scale.
Discrete data have a set of fixed values.
Discreet data
Continuous data
Stratigraphic hydrocarbon traps occur where reservoir facies pinch into impervious rock such as shale, or where they have been truncated by erosion and capped by impervious layers above an unconformity.

6. Multi-class/continuous and binary data
Binary magnetic map
Binary Geological map
Multiclass

7. What is GIS? GIS = Geographic Information System
Links databases and maps
Manages information about places
Helps answer questions such as:
Where is it?
What else is nearby?
Where is the highest concentration of ‘X’?
Where can I find things with characteristic ‘Y’?
Where is the closest ‘Z’ to my location?

8. Definition of GIS (Ron Briggs, UT Dallas)
A system of integrated computer-based tools for end-to-end processing (capture, storage, retrieval, analysis, display) of data using location on the earth’s surface.
set of integrated tools for spatial analysis
encompasses end-to-end processing of data
capture, storage, retrieval, analysis/modification, display
uses explicit location on earth’s surface to relate data
aimed at decision support, as well as on-going operations and scientific inquiry
Because of the link between spatial locations and non-spatial data, it is possible to apply non-spatial statistical modeling methods to spatial data 4

9. SPATIAL DATA MODELS What do you mean by spatial data?
How real world spatial data are represented? How would you represent a real world river? Land-use?

10. SPATIAL DATA TYPES Spatial data comes in three basic forms: Map data
Attribute data
Image data

11. SPATIAL DATA TYPES SPATIAL DATA MODELS Two models: Vector model
Spatial data come in three basic forms:
Map data 
Attribute data
Image data
SPATIAL DATA MODELS
Two models:
Vector model
Raster model

12. Vector Model: Map data
Map data contains the location and shape of geographic features. Maps use three basic shapes to present real-world features:
points,
lines, and
areas (called polygons/regions). 

13. Vector Model
The spatial locations of features are defined on the basis of coordinate pairs.
These can be discrete, taking the form of points (Point or Node data) or lines (Arc or polyline data) or areas (Area or polygon data)
Attribute data pertaining the individual spatial features is maintained in an external database.
Topology – A set of rules that models how points, lines and polygons share geometry and are related to each other.
Area
Population

14. SPATIAL DATA MODELS: Vector Model
ROCK

15. VECTOR MODEL
A Polygon describes a geographic feature that is characterized by a boundary, whether natural, or artificial, such as the boundaries of countries, states, cities, census tracts, postal zones, and market areas or rock types
Points represent anything that can be described as an x, y location on earth’s surface, for example, mineral deposits, gas fields
Lines objects described by length only (zero width) such as faults, streets, highways, and rivers

16. SPATIAL DATA TYPES: Image data (Raster Model)
Image data ranges from satellite images, digital elevation models, potential field data data and aerial photographs to scanned maps (maps that have been converted from printed to digital format).
We can represent point, line and polygon data in image form

17. SPATIAL DATA MODELS: Raster Model
Every cell represents a unit area on the ground. All unit areas are equal
The smaller the area the cells represent, the larger the resolution.
Cell values represent a specific property of the ground in that unit area:
For example,
Surface reflectance
Magnetic field
Gravity field
Elevation
Rock type
The values can nominal, ordinal, interval or ratio, they can be integers or floating points.
Georeferenced
10 m x 10 m grid cell

18. SPATIAL DATA MODELS: Raster Model
Most spatial analysis are done in raster format because it facilitates mathematical calculations, e.g.,
INGRID1/ INGRID 2
INGRID1 * INGRID 2

19. VECTOR TO RASTER CONVERSION
The area of interest is covered by a fine mesh or matrix of grid cells and the surface attribute value occurring at the centre of each cell point is recorded as the value for that cell. 1 2 3 1 2 3 Id
Type
Area 1
Granite 25 2
Sandstone 63 3
Limestone 42 1 2 3

20. Raster to vector conversion (Digitization)
However, often it is necessary to convert raster to vector format, and then back to the raster format (why??)
For vectorization, trace the boundaries using a digitizing tablet/on-screen.
Essentially, the X,Y coordinates of features are stored

21. SPATIAL DATA TYPES: Attribute Data
Attribute (tabular) data is the descriptive data that GIS links to map features.
Attribute data is collected and compiled for specific areas like states, census tracts, cities, and so on and often comes packaged with map data.

22. PROCESSING & INTERPRETATION
GEOPROCESSING IN GIS
Processing of spatial data to derive predictor map layers
Primary data
Geological map
Structural map
Remote sensing
Geophysical data
geochemical
Derivative (Input) layers
Proximity to granites
Proximity to deep faults
Proximity to fold axes
Reactive rocks
Competency differences
Alteration
Metal anomalies
PROCESSING & INTERPRETATION

23. GEOPROCESSING IN GIS Querying and conditional evaluation
Density calculations
Distance calculations
Interpolation
Reclassification

24. QUERYING INGIS
Query by attributes
Query by location

25. SELECT BY ATTRIBUTES
SQL is used for selecting features in a map layer by attributes that full-fill specified condition.
for example,
SELECT * FROM MapLayer WHERE “field1”>= 10
OPTIONS:
NEW_SELECTION
ADD_TO_SELECTION
REMOVE_FROM_SELECTION
SUBSET_SELECTION
SWITCH_SELECTION
IMPORTANT OPERATORS =
>
<
<>
>=
<=
LIKE
AND OR
NOT

26. QUERY BY ATTRIBUTES SELECT * FROM GEOLOGY WHERE “ROCK” = ‘Dolerite’

27. QUERY BY ATTRIBUTES
Map of dolerite
ROCK

28. SELECT BY LOCATION
Used for selecting features from a map layer based on spatial relationship (adjacency, connectivity, containment) with another layer.
For example,
SELECT * FROM MapLayer1 CONTAINS MapLayer2
ArcGIS syntax:
SelectLayerByLocation MapLayer1 Type_of_relationship MapLayer2 Buffer_distance NEW_SELECTION
Types of spatial relationships that can be queried:
Intersect
Are within a distance of
Contain
Completely contain
Are within
Are completely within
Have their centroid in
Share a line segment with
Are identical to

29. SELECT BY LOCATION
SELECT * FROM GOLD_DEPOSITS WITHIN _ 1_km FROM FAULTS
Gold deposits within 1 km from Faults
Gold deposits
Faults

30. Density estimation
Density is defined as number of (point/line) features per unit area
Density surfaces show where point or line features are concentrated.
For example, you have a point shape file showing mineral deposit locations. You want to learn more about the metal distribution in the area.
Can be used for cluster studies (mineral deposits, population, roads/infrastructure, natural resources such as minerals, forest, agriculture etc., animal inhabitations, ecology…

31. Density estimation
Gold deposits
Distribution of gold

32. Density estimation Faults Faults
Fault density (distribution of faults)

33. Density estimation
Distribution of gold
Distribution of faults

34. Distance estimation
Euclidean distance is calculated from the center of the source cells to the center of each of the surrounding cells. True Euclidean distance is calculated to each cell in the distance functions.
For each cell, the distance is calculated to each source cell by calculating the hypotenuse, with the x-max and y-max as the other two legs of the triangle. This calculation derives the true Euclidean, not cell, distance. The shortest distance to a source is determined, and if it is less than the specified maximum distance, the value is assigned to the cell location on the output raster.

35. Distance estimation
Faults
Distance to faults

36. Distance estimation

37. GEOPROCESSING IN GIS
Interpolation: used for determining the unknown value at any point from the known values at the given sample points in the spatial neigbourhood.

38. Non-interpolative methods

39. Non-interpolative methods
Assign each sample point to a grid cell (or pixel).
Buffer the sample points.
Draw a Thiessen or Voronoi polygon around each sample point; assign the value at the sample point to the entire area within the Voronoi polygon.

40. Delaunay triangles
a Delaunay triangulation for a set of points is a triangulation of the points in such a way that no point is inside the circumcircle of any triangle.
Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation.

41. Voronoi polygons
Connecting the centres of the circumcircles produces the Voronoi polygons.
The property of a Voronoi ploygon of a point is that all points with that polygon are closest to that point.

42. Interpolation: Estimating values at points intermediate between sample points.
Triangulation
Inverse distance weighting
Natural Neighbours
Krigging

43. Triangulation Draw Delaunay triangles for all sample points FID X Y Z1 26 2 4 32 3 28 5 35 42 6 ? 5 5 4 4 6 6 3 3 2 2 1 1
The equation for every triangular facet is given by
z = a + bx + cy
where z is the value,
x and y are X and Y coordinates of a sample point, respectively,
a, b and c are unknown coefficients
Three unknown coefficients, three equations, hence the values of the coefficients can be estimated. Once you have coefficients, you can estimate values at any point within the triangle

44. Inverse distance weighing5 4 3 1 2 6 5 4 3 6 2 1
Where z is the value at the point i; w is the weight of i;
d(j,i) is the distance between the point i and the point j where the value needs to be calculated;
p is the power;
n is total number points in the neighbourhood with known values.
Point Z
Distance from 6 1 26
3.6 2 32
2.2 3 28
1.4 4 35 5 42

45. Natural neighbor
Natural neighbor interpolation finds the closest subset of sample points for the query point and applies weights to them based on proportionate areas.
Draw Vornoi polygons for all points (green colour)
Draw a Voronoi polygon around the point at which the value is to be determined (orange colour)
Apply weights to each point value in proportion to the area of intersection between the Voronoi polygon of that point and the the Voronoi polygon of the query point.
Aij is the area of intersection between the Vornoi polygons of the points i and j.

46. Krigging C ● w = D C-1 ● C ● w = D ● C-1 Or w = D ● C-1
The value at the queried point is given by:
Where zi are the values at sample points
wi are the weights of sample points
C ● w = D
C – Spatial covariance values between the pair of sample points
D – Spatial covariances between sample points and the point where the value is required to be estimated
C-1 ● C ● w = D ● C-1
Or w = D ● C-1

47. Krigging: Spatial covariance
Covariance between two variables x and y is given by
Measures the degree to which x co-varies with y
Moment of inertia measures the deviation from the perfect correlation
In the above equation, suppose we substitute zt for x and z(t+h) for y, where z is a spatial variable measured at a location t and at another location (t+h), where h is the separation distance called a shift or lag.
The spatial covariance of z with itself at separate distance of h can also be measured by γ, (or by C).

48. Krigging: Variograms
By changing the separation distance h (called lag or shift), a series of scatter plots can be generated showing how the variable z is correlated with itself as a function of h.
The plot of the moment of inertia as a function of h is called variogram, the plot with covariance is called autocovariance diagram
autocovariance diagram
Variogram
Range
Sill
Exponential model fitted to the scatter plot
Scatter plot
γ(h) = C0 if h =0
γ(h) = C0 + C1(1-exp(-3 h/a) ) if h >0
Sill and range are estimated so the model is a reasonable fit to the observed data

49. Krigging: Variogram Models

50. Krigging: Variogram Models

51. Krigging: Variogram Fitting a model to data
Longer range
smaller range

52. Krigging: Spatial covariance
Autocovariance diagram can be used to calculate covariance at different distances, hence different covariances in the equations below:
C ● w = D
The following equation is then used to estimate the value at the query point

53. 40 56 55 49 45 52 50 43 42 44 48
100 m
100 m
Elevation in Meters

54. Auto-covariance
Case 1: Shift of 100 meters X
Y = X+100

55. 40 56 55 49 45 52 50 43 42 44 48
100 m
100 m
Elevation in 100 meters

56. Auto-covariance Case 1: Shift of 100 meters X Y = X+100 40 42 43 X

57. 40 56 55 49 45 52 50 43 42 44 48
100 m
100 m
Elevation in 100 meters

58. Auto-covariance
Case 1: Shift of 100 meters X
Y = X+100 40 42 43 44 45

59. 40 56 55 49 45 52 50 43 42 44 48
100 m
100 m
100 m
100 m
Elevation in 100 meters

60. Auto-covariance Case 1: Shift of 100 meters X Y = X+100 40 42 43 44 4548 50 52

61. Auto-covariance Case 1: Shift of 100 metersX
Y = X+100 40 42 43 44 45 48 50 52 49 55 56
Mean X = Mean Y = Covariance = MOI = 6.71

62. Auto-covariance
Case 2: Shift of 200 meters X
Y = X+200

63. 40 56 55 49 45 52 50 43 42 44 48
200 m
200 m
Elevation in 100 meters

64. Auto-covariance
Case 2: Shift of 200 meters X
Y = X+200 40 44 45

65. 40 56 55 49 45 52 50 43 42 44 48
200 m
200 m
Elevation in 100 meters

66. Auto-covariance Case 2: Shift of 200 meters X Y = X+200 40 44 45 42 4849

67. Auto-covariance Case 2: Shift of 200 metersX
Y = X+200 40 44 45 42 48 49 55 56 43 50 52
Mean X = 43 Mean Y = Covariance = 8.718
MOI = 25.56

68. Auto-covariance Case 2: Shift of 300 metersX
Y = X+300 40 48 43 52 45 56
Mean X = Mean Y = 52 Covariance = MOI = 44.33

69. Auto-covariance Distance -vs- Covariance Distance Covariance 100 13.94
200
8.718
300
7.8889

70. Variogram sill range nugget effect Distance -vs- MOI Distance MOI 100
6.71
200
25.56
300
44.33
sill
range
nugget effect