Geology-informed Bayesian tomographic imaging using geochemical and seismic data

Abstract

Geoscientists study spatial variations in Earth’s properties like seismic velocity, geological age, or geochemical signature, crucial for various applications. These properties are represented by a model and parameter matrices, estimates at discrete locations are the values in a parameter matrix. However, data is often acquired in a different domain and the parameters of interested need to be inferred from that, such as estimating velocities from recorded arrival times. Estimating them from data is complex due to nonlinear problems, yielding multiple models and matrices fitting measured data.

Bayesian methods solve nonlinear problems by estimating a posterior probability distribution, incorporating data likelihood and prior distribution. Traditional prior distributions contain little structural geological information which results in a posterior distribution with samples of high probability but low geological plausibility. This thesis uses geological information derived from computational simulations as geological prior information. Resulting in a posterior distribution containing solely models that adhere to the geological simulations.

While the geological simulations herein are not compatible with all geological scenarios and do not fully represent geology, they do show what is possible using current Bayesian inversion and Machine Learning techniques. Therefore, the methods presented in this thesis serve as a proof of concept and can be improved by utilizing more accurate geological simulations.

Simulated models are parameterised using a Generative Adversarial Network (GAN), such that expensive simulations are only needed to establish the prior information and not during the Bayesian inversion.

This thesis focuses on rapid inversion of tomographic arrival time data using a fully neural network driven approach and shows that it is possible to estimate a geological posterior distribution in seconds which is comparable to a benchmark McMC estimate which takes days.

Furthermore, the thesis introduces a new method for geochemical correlation by utilizing geological prior information a fully Bayesian estimate of chronostratigraphic correlations is obtained even with large gaps in geochemical data due to geological erosion. What is more, the method allows estimating geochemical properties on a cross-section between the transects and provides full uncertainty information on all parameters.

Prior information formed by geological simulations can only support solutions where the true model is similar to those simulations. This thesis proposes an McMC starting model sampling strategy that utilizes the geological posterior estimates. This results in faster McMC convergence and fewer chains stuck in local minima at the expense of reduced geological realism.