Geostatistical learning for seismic subsurface characterization

 This thesis contributes to the implementation of seismic inversion methodologies based on geostatistical modelling and deep learning methods, aiming to enhance petrophysical and facies predictions within probabilistic frameworks.
One significant challenge in geostatistical seismic inversion methods is predicting rocks’ permeability due to its high variability and weak correlation to seismic data. Chapter 3 proposes a geostatistical seismic inversion method integrating rock physics constraints in the objective function. This approach reproduces the statistical correlation of facies-dependent permeability, porosity, and acoustic impedance values inferred from well-log data through geostatistical simulations. By calculating permeability distributions from acoustic impedance realizations using a model based on rock physics principles, the method effectively integrates seismic data and penalizes inconsistencies between geostatistical simulations and expected rock physics. Application on synthetic and real data demonstrates improved correlation between permeability spatial distribution and seismic reflection data.
The research in Chapter 4 tackles the limitations of using a pre-calibrated, facies-dependent, rock physics model without an uncertainty estimation in geostatistical seismic inversion. The work proposes a geostatistical seismic AVA inversion method with self-updating of elastic properties based on rock physics modeling. The uncertainty is modelled for each elastic property estimate as by a parametric distribution. At each iteration, the petrophysical properties are modelled through geostatistics, while the elastic properties are sampled from a multi-Gaussian distribution locally defined by the rock physics model estimate and prior uncertainty. The parameters of this distribution are locally updated using auxiliary information from each iteration. Synthetic and real case examples illustrate improved accuracy and comparable uncertainty quantification compared to baseline methods.
In Chapter 5 deep learning for stochastic inversion is investigated to overcome limitations in uncertainty quantification for facies-dependent properties. Two deep neural networks, a variational autoencoder and a generative adversarial network, are proposed for generative tasks, to model simultaneously spatial patterns of facies and of collocated acoustic impedance. The training data used combines geostatistical simulations of facies based on multiple point statistics and co-located simulations of acoustic impedance based on two-points statistics. Both networks show the ability to honor these patterns accurately, generating spatial models from a low-dimensional latent space. Using an inference method based on variational inference, the neural transport method proposed by Levy et al. (2023), both networks were tested for seismic data inversion in synthetic scenarios. The results show that the inversion is accurate and significantly faster than inference methods based on sampling (e.g., based on Markov chain Monte Carlo).
Chapter 6 addresses computational costs of two-step inversion approaches in stochastic inversion with deep learning. A method based on a generative adversarial network architecture is proposed to infer the distribution of facies in a single training step, considering uncertainty in both facies and facies-dependent properties. The network learns the properties spatial patterns from a training dataset of geostatistical realizations of facies and collocated facies-dependent subsurface parameters. Applications on synthetic and real case scenarios of fullstack seismic data inversion show that the network predicts a non-parametric posterior distribution matching the desired target.
The methods proposed use different approaches for the prediction of multiple subsurface properties. Future work should consider the integration of the different approaches proposed, to obtain faster and more accurate solutions to the inverse problems. For example, deep learning solutions, proposed of fullstack seismic data inversion, can be extended to AVA inversion by designing networks able to generate multivariate petrophysical properties. Moreover, further research can focus on the integration of rock physics modeling uncertainty quantification for deep-learning-based inversion methods, in both parametric (two-steps) and non-parametric (single step) approaches. Finally, the proposed inversion methodologies based on deep neural networks are demonstrated solely on 2-D case studies. Direct modeling of 3-D subsurface spatial features through these architectures is indeed possible but mainly limited by the large computing power required. The direct inversion of 3-D subsurface models would provide great improvements to subsurface properties predictions, in terms of geological plausibility, predictions accuracy and algorithms efficiency. As computational resource efficiency and deep learning algorithms advance, it will be possible to expand the research to 3-D case studies applications and more complex deep-learning-based solutions. Overall, these advancements are crucial for improving subsurface modeling and predictions and essential to natural resources exploration and environmental management tasks.