Data‐Worth Analysis for Heterogeneous Subsurface Structure Identification With a Stochastic Deep Learning Framework

Reliable characterization of subsurface structures is essential for earth sciences and related applications. Data assimilation‐based identification frameworks can reasonably estimate subsurface structures using available lithological (e.g., borehole core, well log) and dynamic (e.g., hydraulic head, solute concentration) observations. However, a reasonable selection of the observation type and frequency is essential for accurate structure identification. To achieve this, we extended a recently developed stage‐wise stochastic deep learning inversion framework by coupling it with non‐isothermal flow and transport simulations. With the extended framework, the worth of three common observations (hydraulic head, concentration, and temperature) are compared under different observation noise and frequency. The framework combines the emerging deep‐learning (DL)‐based framework with the traditional stochastic approaches. This combination makes it possible to simultaneously compare the ability of these two methods to assimilate observation data. Our results show that including at least one type of dynamic observation strongly improves subsurface structure identifiability and reduces the uncertainty. However, the DL‐based framework is able to identify subsurface structures more accurately than stochastic identification methods under the same scenarios. Assimilation of certain types of dynamic observations could reduce the prediction error for related dynamic responses, but not necessarily for other uncorrelated dynamic responses. Observation data worth is affected by the observation noise and frequency. High observation noise increases the uncertainty of the prediction and reduces the estimation accuracy. However, the higher observation frequency can significantly improve the temporal dynamic information of observations. This information can compensate for negative impacts of high observation noise. Obtaining realistic subsurface structures is crucial for earth sciences and other related applications, including groundwater management, geological carbon storage, radioactive waste disposal, and geothermal applications. This study extended a recently developed deep‐learning‐based identification framework to consider hydraulic head, concentration, and temperature observations. In addition, this framework combines the traditional method with recently popular deep learning framework. Through this framework, we study the effects of different observation types, noise, and frequency on subsurface structure identification, so as to guide the reasonable use of observations in practice to improve the accuracy of subsurface structure identification. Our results show that by applying some of the latest deep learning technologies, the framework can obtain more accurate subsurface structures. Through this original research, we recommend preferentially using observations that can directly inform the process of interest. When collecting more data, it is more important to focus on collecting higher quality data. Effects of the observation type, noise, and frequency are studied for subsurface structure identificationObservation data worth is influenced by observation noise and observation frequencyDynamic observations that can directly inform processes of interest should be preferentially assimilated Effects of the observation type, noise, and frequency are studied for subsurface structure identification Observation data worth is influenced by observation noise and observation frequency Dynamic observations that can directly inform processes of interest should be preferentially assimilated