Reducing equivalence effect in vertical electrical sounding interpretation using a wavelet-based convolutional neural network

Abstract

Interpreting vertical electrical sounding data can be quite challenging due to its ambiguous and nonlinear nature. A significant issue in this interpretation is the equivalence phenomenon, where multiple resistivity-thickness models can correspond to the same set of recorded apparent resistivity data. This phenomenon complicates both traditional inversion methods and those utilizing neural networks. One way to mitigate these challenges is to establish an appropriate a priori model and incorporate constraints from geological information, such as borehole logs and field observations of exposed lithological sections. However, without such information, resolving these issues becomes difficult. In this study, we developed a wavelet-based convolutional neural network aimed at reducing the equivalence problem while estimating layer resistivities and thicknesses from provided apparent resistivities. This method utilizes the wavelet transform of apparent resistivity along with neural network convolutional layers, helping better identify features within the data and thereby addressing the equivalence issue more effectively. Additionally, since the method relies on a neural network, it does not require parameter estimation for each individual dataset; a single training session with suitable hyperparameters is sufficient for optimal performance. We trained and validated the model using both clear and noise-contaminated synthetic datasets and tested it with various synthetic and real datasets. The results indicate that the proposed model performs acceptably even in the presence of Gaussian random noise.