Time‐lapse applications of electrical methods have grown significantly over the last decade. However, the quantitative interpretation of tomograms in terms of physical properties, such as salinity, temperature or saturation, remains difficult. In many applications, geophysical models are transformed into hydrological models, but this transformation suffers from spatially and temporally varying resolution resulting from the regularization used by the deterministic inversion. In this study, we investigate a prediction‐focused approach (PFA) to directly estimate subsurface physical properties with electrical resistance data, circumventing the need for classic tomographic inversions. First, we generate a prior set of resistance data and physical property forecast through hydrogeological and geophysical simulations mimicking the field experiment. We reduce the dimension of both the data and the forecast through principal component analysis in order to keep the most informative part of both sets in a reduced dimension space. Then, we apply canonical correlation analysis to explore the relationship between the data and the forecast in their reduced dimension space. If a linear relationship can be established, the posterior distribution of the forecast can be directly sampled using a Gaussian process regression where the field data scores are the conditioning data. In this paper, we demonstrate PFA for various physical property distributions. We also develop a framework to propagate the estimated noise level in the reduced dimension space. We validate the results by a Monte Carlo study on the posterior distribution and demonstrate that PFA yields accurate uncertainty for the cases studied.
Precision agriculture requires an understanding of yield variability. The objectives of this study were to (i) document the temporal and spatial variability of corn (Zea mays L.) silage yields on dairy farms in New York, and (ii) derive farm‐based management zones that account for both types of variability. Silage yield data from 847 fields (9084 ha; six farms) were collected by yield monitoring systems between 2015 and 2017. Raw yield data were cleaned of errors via a standardized postharvest data cleaning protocol. The whole‐farm area‐weighted average yield across years and the temporal SD of yield across years for fields with 3 yr of data were used to divide each field into 10‐ by 10‐m grid‐cells. Each grid‐cell was assigned a quadrant (Q), with Q1 and Q4 having consistently higher and lower yield than the farm average yield, respectively; Q2 having variable but higher yield than the farm average; and Q3 having variable and lower yield than the farm average. The evaluation showed variability in average yield per farm, yield per field, and within‐field yield, in addition to variability across years. Spatial and temporal variability were uncorrelated, suggesting that management zones need to consider both spatial and temporal variability. The area per farm classified as variable (Q2 and Q3) ranged from 30 to 44%, illustrating the importance of implementing precision agriculture technologies and in‐season management adjustments. Research is needed to determine the optimum number of zones per farm and the number of crop years to include in developing yield stability zones. Core Ideas Corn silage yield monitors collect relevant yield data for dairy farmers. Management zones can be developed from yield stability maps. Both temporal and spatial variability are important factors to consider. A yield‐stability‐based approach can generate precision management zones.
[1] We introduce a new strategy for integrating hydrologic process information as a constraint within hydrogeophysical imaging problems. The approach uses a basisconstrained inversion where basis vectors are tuned to the hydrologic problem of interest. Tuning is achieved using proper orthogonal decomposition (POD) to extract an optimal basis from synthetic training data generated by Monte Carlo simulations representative of hydrologic processes at a site. A synthetic case study illustrates that the approach performs well relative to other common inversion strategies for imaging a solute plume using an electrical resistivity survey, even when the initial conceptualization of hydrologic processes is incorrect. In two synthetic case studies, we found that the POD approach was able to significantly improve imaging of the plume by reducing the root mean square error of the concentration estimates by a factor of two. More importantly, the POD approach was able to better capture the bimodal nature of the plume in the second case study, even though the prior conceptual model for the POD basis was for a single plume. The ability of the POD inversion to improve concentration estimates exemplifies the importance of integrating process information within geophysical imaging problems. In contrast, the ability to capture the bimodality of the plume in the second example indicates the flexibility of the technique to move away from this prior process constraint when it is inconsistent with the observed ERI data.Citation: Oware, E. K., S. M. J. Moysey, and T. Khan (2013), Physically based regularization of hydrogeophysical inverse problems for improved imaging of process-driven systems, Water Resour. Res., 49,[6238][6239][6240][6241][6242][6243][6244][6245][6246][6247]
Bayesian Markov-chain Monte Carlo (McMC) techniques are increasingly being used in geophysical estimation of hydrogeologic processes due to their ability to produce multiple estimates that enable comprehensive assessment of uncertainty. Standard McMC sampling methods can, however, become computationally intractable for spatially distributed, high-dimensional problems. We have developed a novel basis-constrained Bayesian McMC difference inversion framework for time-lapse geophysical imaging. The strategy parameterizes the Bayesian inversion model space in terms of sparse, hydrologic-process-tuned bases, leading to dimensionality reduction while accounting for the physics of the target hydrologic process. We evaluate the algorithm on cross-borehole electrical resistivity tomography (ERT) field data acquired during a heat-tracer experiment. We validate the ERT-estimated temperatures with direct temperature measurements at two locations on the ERT plane. We also perform the inversions using the conventional smoothness-constrained inversion (SCI). Our approach estimates the heat plumes without excessive smoothing in contrast with the SCI thermograms. We capture most of the validation temperatures within the 90% confidence interval of the mean. Accounting for the physics of the target process allows the detection of small temperature changes that are undetectable by the SCI. Performing the inversion in the reduced-dimensional model space results in significant gains in computational cost.
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