The Earth’s subsurface is formed by different materials, mainly porous rocks possibly containing minerals and filled with salty water and/or hydrocarbons. The formations that these materials create are often irregular, appearing geometrically abrupt forms with different properties that are mixed within the same layer. One of the main objectives in geophysics is to determine the petrophysical properties of the Earth’s subsurface. In this way, companies can discover hydrocarbon reservoirs and maximize the production, and determine optimal locations for hydrogen storage or CO2sequestration. To achieve these goals, companies often record electromagnetic measurements using Logging While Drilling (LWD) instruments, which are able to record data while drilling. The recorded data is processed to produce a map of the Earth’s subsurface. Based on the reconstructed Earth model, the operator adjusts the well trajectory in realtime to further explore exploitation targets, including oil and gas reservoirs, and to maximize the posterior productivity of the available reserves. This realtime adjustment technique is called geosteering. Nowadays, geosteering plays an essential role in geophysics. However, it requires the capability of solving inverse problems in real time. This is challenging since inverse problems are often illposed. There exist multiple traditional methods to solve inverse problems, mainly, gradientbased or statisticsbased methods. However, these methods have severe limitations. In particular, they often need to compute the forward problem hundreds of times for each set of measurements, which is computationally expensive in threedimensional (3D) problems. To overcome these limitations, we propose the use of Deep Learning (DL) techniques to solve inverse problems. Although the training stage of a Deep Neural Network (DNN) may be timeconsuming, after the network is properly trained, it can forecast the solution in a fraction of a second, facilitating realtime geosteering operations. In the first part of this dissertation, we investigate appropriate loss functions to train a DNN when dealing with an inverse problem. Additionally, to properly train a DNN that approximates the inverse solution, we require a large dataset containing the solution of the forward problem for many different Earth models. To create such dataset, we need to solve a Partial Differential Equation (PDE) thousands of times. Building a dataset may be timeconsuming, especially for two and threedimensional problems since solving PDEs using traditional methods, such as the Finite Element Method (FEM), is computationally expensive. Thus, we want to reduce the computational cost of building the database needed to train the DNN. For this, we propose the use of refined Isogeometric Analysis (rIGA) methods. In addition, we explore the possibility of using DL techniques to solve PDEs, which is the main computational bottleneck when solving inverse problems. Our main goal is to develop a fast forward simulator for solving parametric PDEs. As a first step, in this dissertation we analyze the quadrature problems that appear while solving PDEs using DNNs and propose different integration methods to overcome these limitations.
Date of Award  2022 

Original language  English 

Awarding Institution   Universidad del País Vasco (UPV/EHU)


Deep Learning for Inverting Borehole Resistivity Measurements
Rivera Gonzalez, J. A. (Author). 2022
Doctoral thesis: Doctoral Thesis