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Direct prediction of temperature from time-lapse ERT using Bayesian Evidential Learning : extension to a 4D experiment

(2018)
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Abstract
The use of geophysical methods to characterize subsurface properties has significantly grown in the last decade. Although geophysics can bring relevant spatial and temporal information on subsurface processes, the quantitative interpretation and integration in models remain difficult. Indeed, standard deterministic solutions suffer from (excessive) smoothing and spatially variable resolution, whereas joint or coupled inversions remain difficult to apply in complex cases. Hermans et al. (2016) proved using cross-borehole ERT that physical properties distribution could be directly retrieved from data using Bayesian Evidential Learning (BEL). BEL uses a series of prior models to derive a direct relationship between data and forecast in a reduced dimension space. This can be challenging when the prediction becomes more complex with higher dimensions. In this contribution, we extend the work of Hermans et al. (2016) to a full 4D experiment (3D + time). We demonstrate that the shape and amplitude of the temperature plume can be retrieved, with uncertainty quantification, during a push-pull experiment using surface ERT. We analyze the robustness of the solution using a synthetic benchmark. The results indicate that the median of the posterior is very close to the true temperature distribution. The relative error increases at the edge of the temperature plume where the change of temperature is limited. This is related to the limited resolution of geophysics and the process of dimension reduction. We also investigate how discrete cosine transform can improve the dimension reduction process without altering the final prediction. Finally, we show that BEL is able to retrieve the spatio-temporal variability of the plume, while the smoothness constraint inversion fails to accurately image the corresponding contrast, largely underestimating the amplitude of the temperature change. BEL is therefore a well-suited framework for the interpretation of 4D geophysical data avoiding the drawbacks of standard deterministic solutions. Hermans, T., Oware, E., & Caers, J. (2016). Direct prediction of spatially and temporally varying physical properties from time-lapse electrical resistance data. Water Resources Research, 52, 7262-7283.

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Chicago
Hermans, Thomas, Nicolas Compaire, and Nolwenn Lesparre. 2018. “Direct Prediction of Temperature from Time-lapse ERT Using Bayesian Evidential Learning : Extension to a 4D Experiment.” In .
APA
Hermans, Thomas, Compaire, N., & Lesparre, N. (2018). Direct prediction of temperature from time-lapse ERT using Bayesian Evidential Learning : extension to a 4D experiment. Presented at the AGU Fall Meeting 2018.
Vancouver
1.
Hermans T, Compaire N, Lesparre N. Direct prediction of temperature from time-lapse ERT using Bayesian Evidential Learning : extension to a 4D experiment. 2018.
MLA
Hermans, Thomas, Nicolas Compaire, and Nolwenn Lesparre. “Direct Prediction of Temperature from Time-lapse ERT Using Bayesian Evidential Learning : Extension to a 4D Experiment.” 2018. Print.
@inproceedings{8586803,
  abstract     = {The use of geophysical methods to characterize subsurface properties has significantly grown in the last decade. Although geophysics can bring relevant spatial and temporal information on subsurface processes, the quantitative interpretation and integration in models remain difficult. Indeed, standard deterministic solutions suffer from (excessive) smoothing and spatially variable resolution, whereas joint or coupled inversions remain difficult to apply in complex cases. Hermans et al. (2016) proved using cross-borehole ERT that physical properties distribution could be directly retrieved from data using Bayesian Evidential Learning (BEL). BEL uses a series of prior models to derive a direct relationship between data and forecast in a reduced dimension space. This can be challenging when the prediction becomes more complex with higher dimensions. In this contribution, we extend the work of Hermans et al. (2016) to a full 4D experiment (3D + time). We demonstrate that the shape and amplitude of the temperature plume can be retrieved, with uncertainty quantification, during a push-pull experiment using surface ERT. We analyze the robustness of the solution using a synthetic benchmark. The results indicate that the median of the posterior is very close to the true temperature distribution. The relative error increases at the edge of the temperature plume where the change of temperature is limited. This is related to the limited resolution of geophysics and the process of dimension reduction. We also investigate how discrete cosine transform can improve the dimension reduction process without altering the final prediction. Finally, we show that BEL is able to retrieve the spatio-temporal variability of the plume, while the smoothness constraint inversion fails to accurately image the corresponding contrast, largely underestimating the amplitude of the temperature change. BEL is therefore a well-suited framework for the interpretation of 4D geophysical data avoiding the drawbacks of standard deterministic solutions.
Hermans, T., Oware, E., \& Caers, J. (2016). Direct prediction of spatially and temporally varying physical properties from time-lapse electrical resistance data. Water Resources Research, 52, 7262-7283.
},
  author       = {Hermans, Thomas and Compaire, Nicolas and Lesparre, Nolwenn},
  location     = {Washington DC},
  title        = {Direct prediction of temperature from time-lapse ERT using Bayesian Evidential Learning : extension to a 4D experiment},
  year         = {2018},
}