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Neural network has been successfully used for field-scale temperature estimation based on resistivity data. Although the methodology is able to estimate temperature distribution based on geophysical data with a limited number of temperature data, it has also been shown that the estimation accuracy can decrease as distance increases from temperature measurements. In this letter, we developed a resistivity-based neural kriging approach to improve the accuracy of estimated temperatures. The neural kriging method in this letter incorporated a variogram of temperature data, which constrained the spatial distribution of temperature. We examined the accuracy of standard neural network approaches, as well as the neural kriging approach, using a cross-validation test. The examination showed that when neural kriging was used, the estimation error and variogram error were reduced by 6%-87% and 191%-285%, respectively. The improvement was also significant at areas distant from well logs. The pattern of estimated temperatures matched the underlying geology and was in accordance with previous studies. The proposed methodology can incorporate other types of geophysical data for estimating other physical parameter distributions.
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Ishitsuka et al. (2018) studied this question.
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