### Abstract

We use log permeability and porosity data obtained from single-hole pneumatic packer tests in six boreholes drilled into unsaturated fractured tuff near Superior, Arizona, to postulate, calibrate and compare five alternative variogram models (exponential, exponential with linear drift, power, truncated power based on exponential modes, and truncated power based on Gaussian modes) of these parameters based on four model selection criteria (AIC, AICc, BIC and KIC). Relying primarily on KIC and cross-validation we select the first three of these variogram models and use them to parameterize log air permeability and porosity across the site via kriging in terms of their values at selected pilot points and at some single-hole measurement locations. For each of the three variogram models we estimate log air permeabilities and porosities at the pilot points by calibrating a finite volume pressure simulator against two cross-hole pressure data sets from sixteen boreholes at the site. The traditional Occam's window approach in conjunction with AIC, AICc, BIC and KIC assigns a posterior probability of nearly 1 to the power model. A recently proposed variance window approach does the same when applied in conjunction with AIC, AICc, BIC but spreads the posterior probability more evenly among the three models when used in conjunction with KIC. We compare the abilities of individual models and MLBMA, based on both Occam and variance windows, to predict space-time pressure variations observed during two cross-hole tests other than those employed for calibration. Individual models with the largest posterior probabilities turned out to be the worst or second worst predictors of pressure in both validation cases. Some individual models predicted pressures more accurately than did MLBMA. MLBMA was far superior to any of the individual models in one validation test and second to last in the other validation test in terms of predictive coverage and log scores.

Original language | English (US) |
---|---|

Pages (from-to) | 863-880 |

Number of pages | 18 |

Journal | Stochastic Environmental Research and Risk Assessment |

Volume | 24 |

Issue number | 6 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### Keywords

- Airflow
- Bayesian model averaging
- Inverse modelling
- Maximum likelihood

### ASJC Scopus subject areas

- Environmental Engineering
- Environmental Science(all)
- Environmental Chemistry
- Water Science and Technology
- Safety, Risk, Reliability and Quality

### Cite this

*Stochastic Environmental Research and Risk Assessment*,

*24*(6), 863-880. https://doi.org/10.1007/s00477-010-0383-2

**Maximum likelihood Bayesian averaging of airflow models in unsaturated fractured tuff using Occam and variance windows.** / Morales-Casique, Eric; Neuman, Shlomo P; Vesselinov, Velimir V.

Research output: Contribution to journal › Article

*Stochastic Environmental Research and Risk Assessment*, vol. 24, no. 6, pp. 863-880. https://doi.org/10.1007/s00477-010-0383-2

}

TY - JOUR

T1 - Maximum likelihood Bayesian averaging of airflow models in unsaturated fractured tuff using Occam and variance windows

AU - Morales-Casique, Eric

AU - Neuman, Shlomo P

AU - Vesselinov, Velimir V.

PY - 2010

Y1 - 2010

N2 - We use log permeability and porosity data obtained from single-hole pneumatic packer tests in six boreholes drilled into unsaturated fractured tuff near Superior, Arizona, to postulate, calibrate and compare five alternative variogram models (exponential, exponential with linear drift, power, truncated power based on exponential modes, and truncated power based on Gaussian modes) of these parameters based on four model selection criteria (AIC, AICc, BIC and KIC). Relying primarily on KIC and cross-validation we select the first three of these variogram models and use them to parameterize log air permeability and porosity across the site via kriging in terms of their values at selected pilot points and at some single-hole measurement locations. For each of the three variogram models we estimate log air permeabilities and porosities at the pilot points by calibrating a finite volume pressure simulator against two cross-hole pressure data sets from sixteen boreholes at the site. The traditional Occam's window approach in conjunction with AIC, AICc, BIC and KIC assigns a posterior probability of nearly 1 to the power model. A recently proposed variance window approach does the same when applied in conjunction with AIC, AICc, BIC but spreads the posterior probability more evenly among the three models when used in conjunction with KIC. We compare the abilities of individual models and MLBMA, based on both Occam and variance windows, to predict space-time pressure variations observed during two cross-hole tests other than those employed for calibration. Individual models with the largest posterior probabilities turned out to be the worst or second worst predictors of pressure in both validation cases. Some individual models predicted pressures more accurately than did MLBMA. MLBMA was far superior to any of the individual models in one validation test and second to last in the other validation test in terms of predictive coverage and log scores.

AB - We use log permeability and porosity data obtained from single-hole pneumatic packer tests in six boreholes drilled into unsaturated fractured tuff near Superior, Arizona, to postulate, calibrate and compare five alternative variogram models (exponential, exponential with linear drift, power, truncated power based on exponential modes, and truncated power based on Gaussian modes) of these parameters based on four model selection criteria (AIC, AICc, BIC and KIC). Relying primarily on KIC and cross-validation we select the first three of these variogram models and use them to parameterize log air permeability and porosity across the site via kriging in terms of their values at selected pilot points and at some single-hole measurement locations. For each of the three variogram models we estimate log air permeabilities and porosities at the pilot points by calibrating a finite volume pressure simulator against two cross-hole pressure data sets from sixteen boreholes at the site. The traditional Occam's window approach in conjunction with AIC, AICc, BIC and KIC assigns a posterior probability of nearly 1 to the power model. A recently proposed variance window approach does the same when applied in conjunction with AIC, AICc, BIC but spreads the posterior probability more evenly among the three models when used in conjunction with KIC. We compare the abilities of individual models and MLBMA, based on both Occam and variance windows, to predict space-time pressure variations observed during two cross-hole tests other than those employed for calibration. Individual models with the largest posterior probabilities turned out to be the worst or second worst predictors of pressure in both validation cases. Some individual models predicted pressures more accurately than did MLBMA. MLBMA was far superior to any of the individual models in one validation test and second to last in the other validation test in terms of predictive coverage and log scores.

KW - Airflow

KW - Bayesian model averaging

KW - Inverse modelling

KW - Maximum likelihood

UR - http://www.scopus.com/inward/record.url?scp=77954416510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954416510&partnerID=8YFLogxK

U2 - 10.1007/s00477-010-0383-2

DO - 10.1007/s00477-010-0383-2

M3 - Article

AN - SCOPUS:77954416510

VL - 24

SP - 863

EP - 880

JO - Stochastic Environmental Research and Risk Assessment

JF - Stochastic Environmental Research and Risk Assessment

SN - 1436-3240

IS - 6

ER -