GRC 2003: Great Basin Geothermal GIS

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Estimation of Undiscovered Resources using a
Degree of Exploration Model in combination with
Data Driven Models such as Weights of Evidence
and Logistic Regression
Mark Coolbaugh, Gary Raines Great Basin Center
for Geothermal Energy, University of Nevada,
Reno, USA
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This study was the result of trying to address
two challenges in Natural Resource Modeling
1) How can we deal with the effect of
exploration when predicting undiscovered
resources?
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This study was the result of trying to address
two challenges in Natural Resource Modeling
1) How can we deal with the effect of
exploration when predicting undiscovered
resources?
2) When do evidence layers bias the model?
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This study was the result of trying to address
two challenges in Natural Resource Modeling
1) How can we deal with the effect of
exploration when predicting undiscovered
resources?
2) When do evidence layers bias the model?
a) How do we know if the problem exists (i.e. is
there a correlation)? b) How can we quantify
it? c) How can we correct for it?
evidence pattern
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Two - Step Approach
1) Build a degree-of-exploration model
2) Mathematically combine exploration model with
evidence in order to - assess exploration
bias - predict undiscovered resources
evidence pattern
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Degree-of-Exploration Model
1) Difficult to build 2) Often it must be
qualitative in nature 3) Argument when
estimating undiscovered resources, it is better
to try than not to try
shades of red and blue represent differing
degrees of exploration
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Initial Weights-of-Evidence Model used 4 evidence
layers


Weights-of-Evidence Posterior Probability
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Degree-of-Exploration Map built with information
on groundwater table depth, aquifers, and wells

6,600 wells

Geothermal Grad Wells
Water Table


160,000 wells
Degree-of-Exploration Map built using Fuzzy Logic
Carbonate aquifer
Other Wells
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Many options are available for building a
degree-of-exploration map
Variables used in this model - type of
wells - depth of wells - water
table depth - carbonate aquifer
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The degree-of-exploration model was
mathematically intersected with the initial
weights-of-evidence model to estimate
undiscovered resources

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Degree-of-Exploration Model
Undiscovered Resources
W of E Model
(1) AI AE AU (2) PIprior (NT unit cell) /
AI (3) PEprior (NT unit cell) / AE (4)
PEprior PIprior / ( AE/AI) (5) WIi,j ? ln
(Ni/NT) / (AIi/AI) j (6) WEi,j ? ln (Ni/NT) /
(AEi/AE) j (7) WEi,j ? ln (AIi/AI) /
(AEi/AE) x (Ni/Nt) / (AIi/AI) j (8) WEi,j ?
WIi,j ln (AE/AI) / (AEi/AIi)j (9) PU
PEpost (1 - fE)
Results estimated that 3.2 times more
undiscovered than known geothermal systems exist
in NV (geothermal systems defined as having
temperatures ? 100C)
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Intersection of Degree-of-Exploration Model with
Weights-of-Evidence Model
Simple Case Binary Exploration Model consisting
of perfectly explored and perfectly unexplored
areas
Recalculate Prior Probability for Explored area
(rises) Recalculate individual weights of
evidence for explored area (can go up or
down) Extrapolate probabilities into unexplored
area using unique conditions table
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Intersection of Degree-of-Exploration Model with
Weights-of-Evidence Model
General Case Gradational Exploration Model
includes partially explored areas
An area considered to be 70 explored would
have 70 of its area assigned to a conceptual
explored study area, and 30 assigned to a
conceptual unexplored study area (even though
we cant say exactly which parts of this area are
explored or unexplored)
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Weights-of-Evidence Formulas
Prior Probability, where AI AE AU PIprior
(NT unit cell) / AI PEprior (NT
unit cell) / AE PEprior PIprior / ( AE/AI)
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Weights-of-Evidence Formulas
Weights of Evidence (using density
simplification) WIi,j ? ln (Ni/NT) / (AIi/AI)
j WEi,j ? ln (Ni/NT) / (AEi/AE) j
WEi,j ? ln (AIi/AI) / (AEi/AE) x
(Ni/NT) / (AIi/AI) j WEi,j ? WIi,j ln
(AE/AI) / (AEi/AIi)j
If the evidence pattern is better explored than
average, then the weight in the explored area
will go down relative to a model without
exploration. If it is less well explored than
average, the explored weight will go up relative
to a model without exploration.
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WEi,j ? WIi,j ln (AE/AI) / (AEi/AIi)j
This term approximately compensates for
exploration bias
If the evidence pattern is better explored than
the study area as a whole, then the weight in the
explored area will go down relative to the model
without exploration. If it is less well explored
than average, the explored weight will go up
relative to a model without exploration.
evidence pattern
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In the geothermal example, all positive weights
declined after accounting for exploration bias
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Past Exploration focused on areas predicted by
the Weights-of-Evidence Model
Red higher degree of exploration
Warmer colors more favorable
Weights-of-Evidence Model
Degree-of-Exploration Model
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The Degree-of-Exploration model can be used to
compensate for exploration bias while predicting
the undiscovered resource base

x
Initial WofE Model
Degree-of-Exploration Model
Undiscovered Resources
(1) AI AE AU (2) PIprior (NT unit cell) /
AI (3) PEprior (NT unit cell) / AE (4)
PEprior PIprior / ( AE/AI) (5) WIi,j ? ln
(Ni/NT) / (AIi/AI) j (6) WEi,j ? ln (Ni/NT) /
(AEi/AE) j (7) WEi,j ? ln (AIi/AI) /
(AEi/AE) x (Ni/Nt) / (AIi/AI) j (8) WEi,j ?
WIi,j ln (AE/AI) / (AEi/AIi)j (9) PU
PEpost (1 - fE)
Results estimated that 3.2 times more
undiscovered than known geothermal systems exist
in NV (geothermal systems defined as having
temperatures ? 100C)
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Degree-of-Exploration Model
1) Qualitative Assessment of Undiscovered
Resources 2) Assessment of Possible
Exploration Bias - Qualitative correction for
this bias 3) Adaptable to other data-driven
models - e.g., Logistic Regression 4) GIS
makes it easy to assess multiple scenarios
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The End