Data-driven modeling of time-domain induced polarization

TL;DR

This paper introduces a novel, data-driven approach using variational autoencoders to model and analyze time-domain induced polarization data, providing new insights and tools for geophysical applications without relying on traditional parametric models.

Contribution

It develops a deep VAE model trained on extensive IP data, enabling unsupervised data processing, synthetic data generation, and outlier detection, challenging traditional IP modeling assumptions.

Findings

VAE effectively models extensive IP data without manual labeling.

A single scalar parameter suffices to encode IP data variability.

Latent space correlates strongly with average chargeability.

Abstract

We present a novel approach for data-driven modeling of the time-domain induced polarization (IP) phenomenon using variational autoencoders (VAE). VAEs are Bayesian neural networks that aim to learn a latent statistical distribution to encode extensive data sets as lower dimension representations. We collected 1 600 319 IP decay curves in various regions of Canada, the United States and Kazakhstan, and compiled them to train a deep VAE. The proposed deep learning approach is strictly unsupervised and data-driven: it does not require manual processing or ground truth labeling of IP data. Moreover, our VAE approach avoids the pitfalls of IP parametrization with the empirical Cole-Cole and Debye decomposition models, simple power-law models, or other sophisticated mechanistic models. We demonstrate four applications of VAEs to model and process IP data: (1) representative synthetic data generation, (2) unsupervised Bayesian denoising and data uncertainty estimation, (3) quantitative evaluation of the signal-to-noise ratio, and (4) automated outlier detection. We also interpret the IP compilation's latent representation and reveal a strong correlation between its first dimension and the average chargeability of IP decays. Finally, we experiment with varying VAE latent space dimensions and demonstrate that a single real-valued scalar parameter contains sufficient information to encode our extensive IP data compilation. This new finding suggests that modeling time-domain IP data using mathematical models governed by more than one free parameter is ambiguous, whereas modeling only the average chargeability is justified. A pre-trained implementation of our model -- readily applicable to new IP data from any geolocation -- is available as open-source Python code for the applied geophysics community.