Kinematic Porosity and Heteroscedasticity in Hard Rock Terrains

Extreme variability and its role in hydrogeology

Land and Water Resources EngineeringRobert Earon

• Changing Climate• Limited Storage• Increasing residency near coast• Heteroscedasticity

There is no annual shortage of water in Sweden.Problems arise due to temporal distribution of meteoric water and water storage.

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Grou

ndw

ater

Leve

l (m

und

er G

roun

d Su

rfac

e)

Glacial Till

Hard Rock

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity

Range

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Nugget

Sill

Spatial AnisotropyIntroduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Spatial AnisotropyIntroduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Spatial AnisotropyIntroduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity in spatial variance

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity in spatial variance

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Heterogeneity in spatial variance

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

• ANOVA, t-test both indicate samples significantly (sig.<0.000) different

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Multivariate Approach to Groundwater Resources

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Multivariate Approach to Groundwater ResourcesGroup GRP Range Group Median1 -0.75>GRP 3.96 l/hr, m

2 -0.75<GRP<-0.5 4.09 l/hr, m

3 0.5<GRP<0 6.08 l/hr, m

4 0<GRP 6.36 l/hr, m

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3

2

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01 2 3 4

GRP Group

LN(S

C)

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Kinematic Porosity

• Based on simple fracture geometry (Carlsson and Olsson, 1993)

• Relationship between fracture spacing, relation to measurement face, average angle between fractures, average estimated hydraulic aperture

• Relatively simple to collect data• Influenced by surficial physical factors (weathering)

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Kinematic Porosity

Area Rock typeFracture frequencyNa (m-1) 𝜖 eg

(m)λ

Kinematic porositynk

Median capacity(lit/hr)

Älgö Granite 2.13 1.5 0.001 0.25 0.08 % 375

Älgö Gneiss-granite 1.87 1.75 0.001 0.2 0.065 % 200

Älgö Sedimentary gneiss 1.57 1.5 0.001 0.2 0.05 % 100

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

• Kinematic porosity maps correlated to specific capacity maps (sig. = 0.003) but have a very low correlation coefficient (0.2)

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Review

• Heterogeneity places a high burden on point estimates for regional or even local characterization

• Heterogenic, anisotropic variability implies caution should be taken when applying statistical tools

• From the standpoint of limited-resource hydrogeological investigation, plausibility of applying and developing other tools

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks

Questions?

Introduction PossibilitiesHeterogeneityAnistropy Concluding Remarks