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