Applied Geostatistics

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Applied Geostatistics
Geostatistical techniques are designed to
evaluate the spatial structure of a variable, or
the relationship between a value measured at a
point in one place, versus a value from another
point measured a certain distance away

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Ho in Spatial Statistics states that

• events,
• highs,
• lows,
• differences between
• evenly distributed
• Randomly arranged
• Illustrated on directional trend

Features
are
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We assume either
Randomization - the observed pattern is one of
many possible arrangements of the population or
Normalization the observations is a sample of a
larger population and it was obtained randomly
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We consider
Global statistics pattern across the whole of
the study area
Local statistics individuals relationship with
nearby features
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Spatial Mean

• The average x-coordinate and average y-coordinate
  for all features in the study area (or select
  set).
• Comparing changes in spatial distributions

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Central Feature

• The feature having the shortest total distance
  to all other features in the study area (or
  select set)
• Describes the most accessible feature

Mean
Center
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Standard Distance, Standard Deviational Ellipse

• The extent to which the distances between the
  mean center and the features vary from the
  average distance.
• The standard deviation of the features from the
  mean center separately for the X and Y coordinates

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Linear Directional Mean

• The angle of the line that represents the mean
  direction (or orientation )

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J I H B

G C F
D A E
Join Count

• Categorical (nominal) data
• Are values clustered or dispersed
• Easy to construct

First Order Neighbors Topology Binary
Connectivity Matrix
Distance Class Connectivity Matrix
A B C D E F G H I J
A B C D E F G H I J
A B C D E F G H I J
A B C D E F G H I J
1 connected, 0not connected
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Morans I Gearys C

• Continuous data
• Similarity of nearby features
• Single statistics summarizing pattern
• Doesnt indicate clustering of highs or lows

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General-G

• Continuous data
• Concentration of high/low
• Not so good if both highs and lows are
  clustered

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Nearest Neighbor

• Average distance between features
• Results may be biased by edge
• Evaluated with Z-score

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K-function, Ripleys-K

• Count of features within defined distances
• Concentration at a range of scale
• Edge plays an important role
• Evaluation through simulations for random
  distribution envelope