Neural network modeling and an uncertainty analysis in Bayesian framework: a case study from the KTB borehole site

Abstract

A new probabilistic approach based on the concept of Bayesian neural network (BNN) learning theory is proposed for decoding litho‐facies boundaries from well‐log data. We show that how a multi‐layer‐perceptron neural network model can be employed in Bayesian framework to classify changes in litho‐log successions. The method is then applied to the German Continental Deep Drilling Program (KTB) well‐log data for classification and uncertainty estimation in the litho‐facies boundaries. In this framework, a posteriori distribution of network parameter is estimated via the principle of Bayesian probabilistic theory, and an objective function is minimized following the scaled conjugate gradient optimization scheme. For the model development, we inflict a suitable criterion, which provides probabilistic information by emulating different combinations of synthetic data. Uncertainty in the relationship between the data and the model space is appropriately taken care by assuming a Gaussian a priori distribution of networks parameters (e.g., synaptic weights and biases). Prior to applying the new method to the real KTB data, we tested the proposed method on synthetic examples to examine the sensitivity of neural network hyperparameters in prediction. Within this framework, we examine stability and efficiency of this new probabilistic approach using different kinds of synthetic data assorted with different level of correlated noise. Our data analysis suggests that the designed network topology based on the Bayesian paradigm is steady up to nearly 40% correlated noise; however, adding more noise (∼50% or more) degrades the results. We perform uncertainty analyses on training, validation, and test data sets with and devoid of intrinsic noise by making the Gaussian approximation of the a posteriori distribution about the peak model. We present a standard deviation error‐map at the network output corresponding to the three types of the litho‐facies present over the entire litho‐section of the KTB. The comparisons of maximum a posteriori geological sections constructed here, based on the maximum a posteriori probability distribution, with the available geological information and the existing geophysical findings suggest that the BNN results reveal some additional finer details in the KTB borehole data at certain depths, which appears to be of some geological significance. We also demonstrate that the proposed BNN approach is superior to the conventional artificial neural network in terms of both avoiding “over‐fitting” and aiding uncertainty estimation, which are vital for meaningful interpretation of geophysical records. Our analyses demonstrate that the BNN‐based approach renders a robust means for the classification of complex changes in the litho‐facies successions and thus could provide a useful guide for understanding the crustal inhomogeneity and the structural discontinuity in many other tectonically complex regions.