Analysis of different gridding methods using “Surfer7”

MichiganTechnological

Universitypresentation byFehmi Kamcili

February 10, 2001

Fig.: Shaded Relief and Contour map

Analysis of different gridding methods using “Surfer7”

Table of content

• Introduction• Grid Files• Grid Methods

1. Inverse Distance to a Power; 2. Kriging;3. Minimum Curvature; 4. Modified Shepard’s Method; 5. Natural Neighbor; 6. Nearest Neighbor; 7. Polynomial Regression; 8. Radial Basis Function; 9. Triangulation w/ linear Interpolation

• Best Results• Conclusion

Introduction

• Surfer 7; Feb. 2000Surface mapping systemGolden Software, Inc.

• Differences in created grid-files visualized by overlaying wireframe and contour mapsFig.: Wireframe and Contour Map

• Vernon/Rosebuch oilfields in Isabella county, Michigan with 245 well Data-Points (Lat-Long of Top Dundee)

Analysis of different gridding methods using “Surfer7”

Grid Files

• gridding by specifing source file-Spreadsheets (Excel)-manually in Surfer (Worksheet)

• gridding method• accuracy of grid• faults and breaklines• creates “file.grd”Fig.: Contour and Post Map

Analysis of different gridding methods using “Surfer7”

Grid Methods

• Inv. Distance to power

• Kriging

• Minimum curvature

• Modified shepard’s

• Natural neighbor

• Nearest neighbor

• Polynomial regression

• Radial basis function

• Triangulation w/ linear interpolation

Fig.: Wireframe Map

Analysis of different gridding methods using “Surfer7”

Inverse Distance to a Power

• weighting average interpolator

• Power parameter between 1E-38 & 38 “0” = planar surface; great weighting power = less effect on points far from the grid node during interpolation

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Fig.: Power: 0.00001

Fig.: Power: 2

Analysis of different gridding methods using “Surfer7”

Inverse Distance to a Power

• exact or smoothing interpolator

• generate "bull's-eyes”-smoothing reduce this effect

• very fast method for gridding -till 500 Datapoints

Fig.: with smoothing: 0.01

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Analysis of different gridding methods using “Surfer7”

Kriging

• express trends suggested in your data

• Point or Block -Block is using average values- smoother; not perfect

• specify & add as many variogram-components as wished

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Fig.: Point Kriging

• by entering path & file name production estimated standard deviation grid

Analysis of different gridding methods using “Surfer7”

Minimum Curvature

• smooth but not exact• recalculation of grid

node values until reached less of max. Residual value, or max. Iteration

• Set Internal and Boundary Tension

• Relaxiation Factor

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Fig.: default

Analysis of different gridding methods using “Surfer7”

Modified Shepard’s Method

• Like IDP Method• exact or smoothing• Weighting and

Quadratic Neighbors parameters specifies size (number) of local neighborhood

• Fig.1: Q13/W19; Fig.2: Q40/W60

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Fig.: 1

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Analysis of different gridding methods using “Surfer7”

Natural Neighbor

• Natural Neighbor interpolation algorithm uses a weighted average of neighboring observations, where the weights are proportional to new added polygons

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Fig.: default

Analysis of different gridding methods using “Surfer7”

Nearest Neighbor

• assigns value of the nearest point to each grid node

• useful when data are already evenly spaced

• this method is effective for filling missing values

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Fig.: default

Analysis of different gridding methods using “Surfer7”

Polynomial Regression

• used to define large-scale trends & patterns

• not real interpolator (does not predict unknown Z values)

• Fig.1: Simple planar surface; Fig.2: Bi-linear saddle

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Fig.: 1

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Analysis of different gridding methods using “Surfer7”

Radial Basis Function

1. Inverse Multiquadric

2. Multilog

3. Multiquadric

4. Natural Cubic Spline

5. Thin plate Spline• 1.; 2.; 4.- error• 5.- good; 3.- best

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Fig.: 5. Thin plate spline

Analysis of different gridding methods using “Surfer7”

Radial Basis Function

• all exact interpolators+ smoothing factor

• = variogram in K.(mathematically specifies spatial variability of data set & resulting grid fileFig.: 3. Multiquadric

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Analysis of different gridding methods using “Surfer7”

Triangulation w/ linear Interpolation

• creates triangles by drawing lines between data points

• exact interpolator

• for evenly distributed data over grid area -sparse areas result in distinct triangular facets on map

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Fig.: default

Analysis of different gridding methods using “Surfer7”

Best Results

Kriging is exact, has many options & modifications,but needs knowledge

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Fig.: Point Kriging

Analysis of different gridding methods using “Surfer7”

Best Results

Radial Basis Function is exact, shows nice views & is uncomplicated

Fig.: Radial Basic Function; Multiquadric -2975

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Analysis of different gridding methods using “Surfer7”

Conclusion

• I did not consider all aspects & details• Surfer is very powerful for the 3D-Visualization• Surfer 7 works:

-fast & without consuming much disk space-uncomplicated with Object manager

• All processes (gridding, mapping) can be automated with writing programs in Visual Basic

• Help content is very useful & describes also background information

Analysis of different gridding methods using “Surfer7”