  Citation: Marques, C.R.; dos Santos, V.G.; Lunelli, R.; Roisenberg, M.; Rodrigues, B.B. Analysis of Deep Learning Neural Networks for Seismic Impedance Inversion: A Benchmark Study. Energies 2022, 15, 7452. https://doi.org/10.3390/ en15207452 Academic Editor: Hossein Hamidi Received: 7 June 2022 Accepted: 22 July 2022 Published: 11 October 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). energies Article Analysis of Deep Learning Neural Networks for Seismic Impedance Inversion: A Benchmark Study Caique Rodrigues Marques 1 , Vinicius Guedes dos Santos 1 , Rafael Lunelli 1 , Mauro Roisenberg 1, * and Bruno Barbosa Rodrigues 2 1 Computer Sciences and Statistics Department, Federal University of Santa Catarina, Florianópolis 88040-900, Brazil 2 Petrobras Research Center, Rio de Janeiro 20031-912, Brazil * Correspondence: mauro.roisenberg@ufsc.br Abstract: Neural networks have been applied to seismic inversion problems since the 1990s. More recently, many publications have reported the use of Deep Learning (DL) neural networks capable of performing seismic inversion with promising results. However, when solving a seismic inversion problem with DL, each author uses, in addition to different DL models, different datasets and different metrics for performance evaluation, which makes it difficult to compare performances. Depending on the data used for training and the metrics used for evaluation, one model may be better or worse than another. Thus, it is quite challenging to choose the appropriate model to meet the requirements of a new problem. This work aims to review some of the proposed DL methodologies, propose appropriate performance evaluation metrics, compare the performances, and observe the advantages and disadvantages of each model implementation when applied to the chosen datasets. The publication of this benchmark environment will allow fair and uniform evaluations of newly proposed models and comparisons with currently available implementations. Keywords: Deep Learning; deep neural networks; seismic impedance inversion; benchmark 1. Introduction Seismic inversion extracts quantitative reservoir rock and fluid properties from seismic reflection data [1]. Seismic reflection data are geophysical records obtained from the reflection of acoustic waves in the subsurface due to the different properties of the rocks and fluids contained therein. Seismic waves are artificially generated at the surface by a controlled energy source and their reflections are captured by sensors. These signals are then processed to create a seismic record [2,3]. There are two types of seismic inversion: stochastic and deterministic. In general, seismic inversion, in addition to reflection data, typically includes other reservoir mea- surements such as well logs and cores. Stochastic seismic inversion is a statistical process integrating well and seismic data, which generates multiple realizations. Deterministic seismic inversion returns only one realization, considered “optimal” [4]. In most cases, the seismic inversion problem is not well posed, i.e., it is not a linear problem with a single solution. Thus, different combinations of rocks and waves generate the same seismic record [1]. The applications of seismic inversion helps to predict rock and fluid properties that are needed for subsurface studies, allowing the construction of a detailed 3D petrophysical model [5]. In the gas and oil industry, seismic inversion is one of the most frequently used methods for reservoir characterization. It is essential to reduce the necessity for well drilling, which is an expensive and time-consuming process [6]. The more traditional approaches in seismic inversion involve creating rock models, testing their adherence to the obtained data, adjusting the model, and continuing iteratively Energies 2022, 15, 7452. https://doi.org/10.3390/en15207452 https://www.mdpi.com/journal/energies