Multimodal variational autoencoder for inverse problems in geophysics: application to a 1-D magnetotelluric problem

Estimating subsurface properties from geophysical measurements is a common inverse problem. Several Bayesian methods currently aim to find the solution to a geophysical inverse problem and quantify its uncertainty. However, most geophysical applications exhibit more than one plausible solution. Here, we propose a multimodal variational autoencoder model that employs a mixture of truncated Gaussian densities to provide multiple solutions, along with their probability of occurrence and a quantification of their uncertainty. This autoencoder is assembled with an encoder and a decoder, where the first one provides a mixture of truncated Gaussian densities from a neural network, and the second is the numerical solution of the forward problem given by the geophysical approach. The proposed method is illustrated with a 1-D magnetotelluric inverse problem and recovers multiple plausible solutions with different uncertainty quantification maps and probabilities that are in agreement with known physical observations.PDC2021-121093-I00 IA4TE

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

Physics-informed neural network for inverse modeling of natural-state geothermal systems

Predicting the temperature, pressure, and permeability at depth is crucial for understanding natural-state geothermal systems. As direct observations of these quantities are limited to well locations, a reliable method-ology that predicts the spatial distribution of the quantities from well observations is required. In this study, we developed a physics-informed neural network (PINN), which constrains predictions to satisfy conservation of mass and energy, for predicting spatial distributions of temperature, pressure, and permeability of natural-state hydrothermal systems. We assessed the characteristics of the proposed method by applying it to 2D synthetic models of geothermal systems. Our results showed that the PINN outperformed the conventional neural network in terms of prediction accuracy. Among the PINN-predicted quantities, the errors in the predicted temperatures in the unexplored regions were significantly reduced. Furthermore, we confirmed that the predictions decreased the loss of the conservation laws. Thus, our PINN approach guarantees physical plausibility, which has been impossible using existing machine learning approaches. As permeability investigations in geothermal wells are often limited, we also demonstrate that the resistivity model obtained using the magnetotelluric method is effective in supplementing permeability observations and improving its prediction accuracy. This study demonstrated for the first time the usefulness of the PINN to a geothermal energy problem

Advances in Magnetotelluric Modelling: Time-Lapse Inversion, Bayesian Inversion and Machine Learning

This thesis presents advancements to the area of magnetotelluric (MT) modelling. There are three main aims to this work. The first aim is to implement an inversion to model time-lapse MT data in a temporal dimension. The algorithm considers the entire dataset at once, with penalisations for model roughness in both the spatial and temporal dimensions. The inversion is tested on synthetic data, as well as a case-study from a coal-seam gas dewatering survey. Second is to explore the problem of nonuniqueness in MT data inversion by implementing a 1D Bayesian inversion using an efficient sampler. The implemented model includes a novel way of regularising MT inversion by allowing the strength of smoothing to vary between different models. The Bayesian inversion is tested on synthetic and case-study datasets with results matching known data. The third aim is to implement a proxy function for the 3D MT forward function based on artificial neural networks. This allows for rapid evaluation of the forward function and the use of evolutionary algorithms to invert for resistivity structures. The evolutionary search algorithm is tested on synthetic data sets and a case-study data set from the Curnamona Province, South Australia. Together, these three novel algorithms and software implementations represent a contribution to the toolkit of MT modelling.Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 201

A Review of Geophysical Modeling Based on Particle Swarm Optimization

This paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical felds are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefts and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle diferent data sets without conficting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the beneft of PSO practitioners or inexperienced researchers

The role of electrical anisotropy in magnetotelluric responses: From modelling and dimensionality analysis to inversion and interpretation

The study of electrical anisotropy in the Earth, defined as the electrical conductivity varying with orientation, has experienced important advances in the last years regarding the investigation of its origins, how to identify and model it, and how it can be related to other parameters, such as seismic and mechanical anisotropy. This paper provides a theoretical background and a review of the current state of the art of electrical anisotropy using electromagnetic methods in the frequency domain, focusing mainly on magnetotellurics. The aspects that will be considered are the modelling of the electromagnetic fields with anisotropic structures, the analysis of their responses to identify these structures, and how to properly use these responses in inversion and interpretation. Also, an update on the most recent case studies involving anisotropy is provided

The Barcelona International Conference on Advances in Statistics (BAS 2012) : Abstracts of communications

Conferència Organitzada per l'Escola Politècnica Superior, Universitat de Vic en col·laboració amb Servei d'Estadística de la Universitat Autònoma de Barcelona i CosmoCaixa Barcelona. Celebrada del 18 al 22 de juny de 2012 a Barcelon

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms