arXiv subjects

Charles L. Bérubé

Publications and source records attributed to Charles L. Bérubé.

4 recordsLinked to original sources

arXiv2026

Learning relaxation time distributions from spectral induced polarization data with a complex-valued variational autoencoder

Spectral induced polarization (SIP) is a geophysical method used to characterize subsurface materials. It measures the frequency-dependent complex electrical resistivity of rocks and soils through the application of an alternating current. Debye and Warburg decompositions are standard methods for analyzing and interpreting SIP data, as they allow estimation of the relaxation time distribution (RTD) of geomaterials. However, conventional decomposition approaches treat measurements independently, work in real-valued spaces despite the complex-valued nature of SIP data, and provide limited uncertainty quantification. These limitations reduce the effectiveness of conventional decomposition on heterogeneous datasets. We reformulate the decomposition approach as an unsupervised machine learning problem and introduce a conditional variational autoencoder (CVAE) that learns a shared mapping from SIP datasets to continuous RTDs. The model is validated on a dataset comprising 140 laboratory and field SIP measurements of granular mixtures, sedimentary and igneous rock, and cementitious materials. The CVAE operates in complex-valued data space and achieves reconstruction errors of 0.53 % and 0.27 % for the imaginary and phase components of resistivity, respectively, with evidence of improvement over conventional methods at corresponding p-values of 0.007 and 0.06. The inferred RTDs are stable and physically consistent, and their total chargeability and mean relaxation time correlate with polarizable grain content and grain size, respectively, with coefficients of determination up to 0.98. An additional contribution of the proposed method is the learned latent representation, which organizes SIP spectra into a structured space. Unsupervised clustering in a two-dimensional projection of this space improves the silhouette score by nearly a factor of two relative to conventional RTD parameters.

physics.geo-ph↗

arXiv2024

Anisotropic induced polarization modeling with neural networks and effective medium theory

Accurately interpreting induced polarization (IP) data that reflects the inherent anisotropy of the Earth's crust requires anisotropic IP models. The Generalized Effective Medium Theory of Induced Polarization (GEMTIP) model effectively simulates the IP signatures of rocks containing polarizable minerals. A pivotal element of the GEMTIP model is calculating the depolarization tensor elements, an intensive task for anisotropic rocks because one must numerically solve six parametric integrals for each mineral inclusion. This study aims to streamline anisotropic IP simulations by extending the GEMTIP framework and introducing a machine learning approach to estimate the depolarization tensors. The theoretical contributions of this research are two-fold: (1) we augment the GEMTIP model to encompass anisotropic background conductivity and triaxial ellipsoidal inclusions, and (2) we reformulate the depolarization integrals to normalize their input and output variables, facilitating their estimation by neural networks. Validation against analytical solutions for spherical and spheroidal inclusions corroborates the accuracy of the neural network. Analyzing the neural network model, we find that the relationship between chargeability and polarizable inclusion content is increasingly uncertain for increasingly anisotropic rocks. A similar observation applies to the relationship between critical frequency and host rock conductivity. Moreover, the depolarization tensors are, on average, 56 % sensitive to inclusion anisotropy and 44 % sensitive to host rock conductivity anisotropy. Remarkably, our neural network drastically accelerates GEMTIP simulations--up to 100,000 times faster than numerical integration--without substantially sacrificing accuracy. This advancement is promising for efficient rock-scale IP modeling in complex and anisotropic geological settings.

physics.geo-ph↗

arXiv2022

Bayesian inference of petrophysical properties with generative spectral induced polarization models

Mechanistic induced polarization (IP) models describe the relationships between the intrinsic properties of geomaterials and their frequency-dependent complex conductivity spectra. However, the uncertainties associated with estimating petrophysical properties from IP data are still poorly understood. Therefore, practitioners rarely use mechanistic models to interpret actual IP data. We propose a framework for critically assessing any IP model's sensitivity and parameter estimation limitations. The framework consists of a conditional variational autoencoder (CVAE), an unsupervised Bayesian neural network specializing in data dimension reduction and generative modeling. We train the CVAE on the IP signatures of synthetic mixtures of metallic mineral inclusions in electrolyte-filled host geomaterials and describe the effect of data transformations on the model. First, the CVAE's Jacobian reveals the relative importance of each petrophysical property for generating spectral IP data. The most critical parameters are the conductivity of the host, the volumetric content of the inclusions, the characteristic length of the inclusions, and the permittivity of the host. The inclusions' diffusion coefficient, permittivity, and conductivity, as well as the host's diffusion coefficient, only have marginal importance for generative IP modeling. A parameter estimation experiment yields the standardized accuracy of petrophysical properties using various model constraints scenarios and corroborates the sensitivity analysis results. Finally, we visualize the effects of data transformations and model constraints on the petrophysical parameter space. We conclude that a common logarithm data transformation yields optimal parameter estimation results and that constraining the electrochemical properties of the geomaterial improves estimates of the characteristic length of its metallic inclusions and vice versa.

physics.geo-ph↗

arXiv2021

Data-driven modeling of time-domain induced polarization

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.

cs.LG↗