A systematic approach to tuning a neural network model and its application in estimating layer parameters from VES Schlumberger data

Abstract

Interpretation of vertical electrical sounding (VES) data is inherently difficult due to its ambiguity and non-linear characteristics. Conventional least square-based methods rely on a well-defined apriori model, constrained by ground information (available borehole logs and field observations of exposed lithological sections) for meaningful interpretations. In this work, a back-propagation neural network-based model was developed to estimate layer resistivities and thickness from given apparent resistivities. The model was trained and validated on noise-infused synthetic datasets. Since the effectiveness and generalisation of any model depend on its hyperparameter settings, we investigated effective methods for estimating hyperparameters such as learning rate, momentum, model architecture and learning rate scheduling parameters. It is well known that the optimal values of hyperparameters are not entirely independent of each other. Thus, any change in one hyperparameter changes the optimal range of all other hyperparameters, and thus, tuning any hyperparameter individually is futile. This warrants a joint hyperparameter tuning along with network architecture, which was carried out using a modified version of meta-heuristic black hole algorithm. The modifications include randomly flipping one or more coordinates of the population stars (solutions) whose cost function was above a threshold value decided by a mutation rate parameter. This helped in boosting the exploration capability of the algorithm and prune trajectories with higher cost functions. It is demonstrated that with a finely tuned neural network model, reasonable resistivity model parameters which interpret the ground conditions fairly well could be obtained. The model was tested on resistivity-sounding data with associated borehole lithologs and was found to be giving reasonable results. The same model was used to estimate the overburden thickness consisting of topsoil and deposited silts in Bhadradri–Kothagudem district, India. The layer thickness was consistent with those seen in cutbanks in the area. The methods of optimal hyperparameter set estimation are not exclusive to this model and can be used to train models accomplishing other geophysical tasks.