Exploratory Spatial Data Analysis
Exploratory Spatial Data Analysis Optimising interpolation of E&P datasets Paola Peroni Exprodat Consulting Ltd February 2009
Presentation plan Exploratory Spatial Data Analysis: ESDA • A look at a common approach to interpolation • Geoscience knowledge & interpolation process • Dataset knowledge & interpolation process • The ESDA workflow
Sample dataset Depth of Eocene
Sample points
Original grid
Trend grid
Spline grid
Common interpolation workflow – use defaults Sample points
You don’t know much about your variable You choose the default options in E&P applications
Trend grid
But how much can you trust your predictions? You integrate the results into your GIS database
Which approach to interpolation?
Deterministic • Results used for quick assessment • Simple modelling • Speed of output
versus
Geostatistics • Results used in decision-making • Flexible modelling • Quantifies uncertainty
But…is it enough?
Informed approach: Include your geoscience knowledge and understand your data
Common approach: Use the defaults
Include geoscience knowledge
Look at your data!
Deterministic Approach Sample points
Palaeogeography
• Quick and dirty • Simple modelling and parameter adjustment • Limited estimation of uncertainty
Spline grid
Tool: Spatial Analyst
Geostatistical Approach • • • •
Sample points
Palaeogeography
ESDA
Numerous, sparse data Custom parameters Estimation of uncertainty Groundwork to be done….but it’s worth it!
Geostatistically interpolated grid
Tool: Geostatistical Analyst
ESDA tools
Exploratory Spatial Data Analysis (ESDA) Spatial instability (non-normality)
Directional components
Outliers
Spatial dependence
ESDA high-level workflow Investigate input data
Y N N
Y
Is the data normally distributed? Are there trends? Are there outliers? Are observations autocorrelated?
Results of geostatistical approach
Action N
Investigate distribution
Y
Model trend separately
Y
Correct/remove or isolate outliers
N
Use deterministic approach
Why investigate distribution? Investigate input data
Y N N
Y
Is the data normally distributed? Are there trends? Are there outliers? Are observations autocorrelated?
Results of geostatistical approach
Action Investigate distribution
N
•
• •
Some geostatistical interpolators require normallydistributed observations To provide insights of statistical parameters for modelling To identify sub-sets and anomalies
How? Histogram tool Count
286
Min
10.28
Max
1298.3
Mean
251.7
SD
143.78
Skewness
1.3921
Kurtosis
11.814
1st Quartile
166.31
Median 3rd Quartile
250.5 342
Why check for trends? Investigate input data
Action
Is the data normally distributed?
N
Are there trends?
Model trend separately
Y
Are there outliers?
•
Are observations autocorrelated?
•
Results of geostatistical approach
A long-range, slowly-varying drift is better modelled by an n-order polynomial To evaluate the deterministic vs. random, spatially autocorrelated component
How? Trend Analysis
Depth of Eocene layer Second order polynomial NW-SE
Why check for outliers? Investigate input data
Action
Is the data normally distributed? Are there trends?
N
Are there outliers? Are observations autocorrelated?
Y
Correct/remove or isolate outliers • •
Results of geostatistical approach
Sampling errors should be corrected Anomalies in spatial structure should be modelled separately
How? Histogram & S/CC Histogram
Semivariogram – Covariance Cloud
Why check for autocorrelation? Investigate input data
Action
Is the data normally distributed? Are there trends? Are there outliers?
Y
Are observations autocorrelated?
Use deterministic approach
N
• Results of geostatistical approach
•
Fundamental for geostatistical approach To help identify anisotropy
How? Semivariogram/Covariance Cloud
SCC computed in NW-SE direction
SCC computed in NE-SW direction
..so now for the results
Geostatistical approach Investigate input data
Detrending
Is the data normally distributed? Are there trends? Are there outliers? Semivariogram modelling
Are observations autocorrelated?
Results of geostatistical approach
Result of deterministic approach Original grid
Geoscience knowledge
Spline grid
Result of geostatistical approach Original grid
Geostatistical interpolator grid
Geoscience knowledge & ESDA
Standard error grid
…and comparing the models Spline grid
Geostatistical grid
Summarising
Summarising
Summarising
Paper Exploratory Spatial Data Analysis Optimizing interpolation of E&P datasets Available for download from:
www.exprodat.com
Thank you! Paola Peroni email:[email protected] web:www.exprodat.com
Datasets from the Millenium Atlas set of maps
Presentation plan Exploratory Spatial Data Analysis: ESDA • A look at a common approach to interpolation • Geoscience knowledge & interpolation process • Dataset knowledge & interpolation process • The ESDA workflow
Sample dataset Depth of Eocene
Sample points
Original grid
Trend grid
Spline grid
Common interpolation workflow – use defaults Sample points
You don’t know much about your variable You choose the default options in E&P applications
Trend grid
But how much can you trust your predictions? You integrate the results into your GIS database
Which approach to interpolation?
Deterministic • Results used for quick assessment • Simple modelling • Speed of output
versus
Geostatistics • Results used in decision-making • Flexible modelling • Quantifies uncertainty
But…is it enough?
Informed approach: Include your geoscience knowledge and understand your data
Common approach: Use the defaults
Include geoscience knowledge
Look at your data!
Deterministic Approach Sample points
Palaeogeography
• Quick and dirty • Simple modelling and parameter adjustment • Limited estimation of uncertainty
Spline grid
Tool: Spatial Analyst
Geostatistical Approach • • • •
Sample points
Palaeogeography
ESDA
Numerous, sparse data Custom parameters Estimation of uncertainty Groundwork to be done….but it’s worth it!
Geostatistically interpolated grid
Tool: Geostatistical Analyst
ESDA tools
Exploratory Spatial Data Analysis (ESDA) Spatial instability (non-normality)
Directional components
Outliers
Spatial dependence
ESDA high-level workflow Investigate input data
Y N N
Y
Is the data normally distributed? Are there trends? Are there outliers? Are observations autocorrelated?
Results of geostatistical approach
Action N
Investigate distribution
Y
Model trend separately
Y
Correct/remove or isolate outliers
N
Use deterministic approach
Why investigate distribution? Investigate input data
Y N N
Y
Is the data normally distributed? Are there trends? Are there outliers? Are observations autocorrelated?
Results of geostatistical approach
Action Investigate distribution
N
•
• •
Some geostatistical interpolators require normallydistributed observations To provide insights of statistical parameters for modelling To identify sub-sets and anomalies
How? Histogram tool Count
286
Min
10.28
Max
1298.3
Mean
251.7
SD
143.78
Skewness
1.3921
Kurtosis
11.814
1st Quartile
166.31
Median 3rd Quartile
250.5 342
Why check for trends? Investigate input data
Action
Is the data normally distributed?
N
Are there trends?
Model trend separately
Y
Are there outliers?
•
Are observations autocorrelated?
•
Results of geostatistical approach
A long-range, slowly-varying drift is better modelled by an n-order polynomial To evaluate the deterministic vs. random, spatially autocorrelated component
How? Trend Analysis
Depth of Eocene layer Second order polynomial NW-SE
Why check for outliers? Investigate input data
Action
Is the data normally distributed? Are there trends?
N
Are there outliers? Are observations autocorrelated?
Y
Correct/remove or isolate outliers • •
Results of geostatistical approach
Sampling errors should be corrected Anomalies in spatial structure should be modelled separately
How? Histogram & S/CC Histogram
Semivariogram – Covariance Cloud
Why check for autocorrelation? Investigate input data
Action
Is the data normally distributed? Are there trends? Are there outliers?
Y
Are observations autocorrelated?
Use deterministic approach
N
• Results of geostatistical approach
•
Fundamental for geostatistical approach To help identify anisotropy
How? Semivariogram/Covariance Cloud
SCC computed in NW-SE direction
SCC computed in NE-SW direction
..so now for the results
Geostatistical approach Investigate input data
Detrending
Is the data normally distributed? Are there trends? Are there outliers? Semivariogram modelling
Are observations autocorrelated?
Results of geostatistical approach
Result of deterministic approach Original grid
Geoscience knowledge
Spline grid
Result of geostatistical approach Original grid
Geostatistical interpolator grid
Geoscience knowledge & ESDA
Standard error grid
…and comparing the models Spline grid
Geostatistical grid
Summarising
Summarising
Summarising
Paper Exploratory Spatial Data Analysis Optimizing interpolation of E&P datasets Available for download from:
www.exprodat.com
Thank you! Paola Peroni email:[email protected] web:www.exprodat.com
Datasets from the Millenium Atlas set of maps
