Experimental Design Applied to Borehole DC Resistivity

1
Experimental Design Applied to Borehole DC
Resistivity

• Darrell Coles
• Frank Dale Morgan

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The Experimental Problem
3
All Experiments Are Not Equal
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Objective

• Explore the systematic design of experiments
  optimized for individual settings

Intent
Produce the highest quality inversion image
possible.
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Outline

• Framing the Experimental Design
• ED as an Optimization Problem
• Information
• Sequential ED Methodology
• Results
• Conclusion

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Framing Experimental Design
Forward Operator
Inverse Problem
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ED as an Optimization Problem
Computationally expensive
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Sensitivities as Information
Information Model Sensitivity
Absolute Sensitivities for Three Different Data
Stations
Log10 Sensitivity
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Information Complementarityand Magnitude
Consider the model sensitivity vectors of two
data stations
q ? information complementarity
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Sequential ED Method
Design experiments sequentially
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Sequential ED Method
Design experiments sequentially
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2D Borehole
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The Study Model
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Case 1

• Random Versus Designed Experiments

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Monte Carlo Performance Curves
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Monte Carlo Performance Curves
Homogeneous Target!
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Pseudosection Survey
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Top/Bottom Sweep Survey
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Computational Expense
Design Computational Expense
40
35
30
25
20
15
CPU Time (s)
10
5
0
0
20
40
60
80
100
120
140
Number of Observations
20
Designed Survey Homogeneous Model
Observation Number
1
2
3
4
5
6
7
8
9
10
1
1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
1
2
3
4
Electrode
5
6
7
Electrode Number
8
9
10
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Case 2

• Two-Stage Adaptive Experimental Design

Invert-Design-Invert
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Two-Stage Adaptive ED Example
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Case 3

• In-line Adaptive Experimental Design

Sub-invert
Design
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In-line Adaptive ED
Total CPU Time 261 seconds
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Conclusion

• Demonstrated a fast, sequential ED algorithm
  based on information complementarity and
  magnitude
• Two-stage AED works best faster, more accurate
• Tradeoff between image accuracy and additional
  computational expense of ED