Matheus Klatt’s research while affiliated with Brazilian Center for Research in Physics and other places

The study of thin sections provides crucial information about the structure of sedimentary rocks. Different properties, such as mineral composition, texture, grain morphology, presence of clay minerals, and porosity level, can be derived from thin section analysis. These features directly determine the quality of crude reservoirs. In this context, manual grain identification from petrographic thin sections usually demands considerable time and effort, so machine learning and image processing techniques have become more frequent in the last few years. Obtaining large and reliable labeled data sets for supervised learning workflows is a complex and critical process. We devise a completely unsupervised approach for granulometric classification using thin section images. The introduced workflow first pre-processes the thin section image by denoising and dividing it into different image patches. In the second stage, the image patches are used to train an unsupervised convolutional neural network. Then, the trained network segments the grains in each patch of the pre-processed image. The training strategy uses transfer learning to guarantee the same initialization parameters of the neural network while processing the image patches. Next, a watershed transform is applied to recover the borders of the segmented grains. Finally, a granulometric calculation and classification process is performed by considering the grain contours restored through the implemented methodology. The results obtained with the proposed algorithm are concordant with those obtained from the analysis of sieved thin sections derived from controlled experiments in the laboratory.

Delimiting salt inclusions from migrated images during the velocity model building flow is a time‐consuming activity that depends on highly human‐curated analysis and is subject to interpretation errors or limitations of the images and methods available. We propose a supervised deep learning based method to include three‐dimensional salt geometries in the velocity models. We compare two convolutional networks – based on the U‐Net architecture – which can process three‐dimensional seismic data. One architecture uses three‐dimensional convolutional kernels, and the other has convolutional long short‐term memory units. Each architecture requires specific preprocessing steps which affects their training and predictive performance. Both proposed architectures use subsurface offset gathers obtained from reverse time migration with an extended imaging condition as input and are trained to predict the salt inclusions. The velocity model used in migration is a reasonable approximation of sediment velocity but without salt inclusions. Thus, the migration model and, consequently, the migrated images are inaccurate due to the absence of the salt inclusion in the model using just the sediment velocity information for the segmentation. A similar salt inclusion methodology was previously validated for two‐dimensional approaches; we extend it to the three‐dimensional case. Our approach relies on subsurface common image gathers to focus the sediments' reflections around the zero offset and spread salt reflections' energy over large subsurface offsets. The results show that both proposed network models can accurately delineate the salt bodies in the test models, but when evaluating the trained networks for the three‐dimensional SEG/EAGE salt model, the architecture with convolutional long short‐term memory units has proven to generalize better.

Full-Waveform Inversion (FWI) is the current standard method to determine final and detailed model parameters to be used in the seismic imaging process. However, FWI is an ill-posed problem that easily achieves a local minimum, leading the model solution in the wrong direction. Recently, some works proposed integrating FWI with Convolutional Neural Networks (CNN). In this case, the CNN weights are updated following the FWI gradient, defining the process as a Physics-Informed Neural Network (PINN). FWI integrated with CNN has an important advantage. The CNN stabilizes the inversion, acting like a regularizer, avoiding local minima-related problems and sparing an initial velocity model in some cases. However, such a process, especially when not requiring an initial model, is computationally expensive due to the high number of iterations required until the convergence. In this work, we propose an approach which relies on combining supervised learning and physics-informed by using a previously trained CNN to start the DL-FWI inversion. Loading the pre-trained weights configures transfer learning. The pre-trained CNN is obtained using a supervised approach based on training with a reduced and simple data set to capture the main velocity trend at the initial FWI iterations. The proposed training process is different from the initial works on the area which obtained the velocity model from the shots in supervised learning tasks, and that required a large amount of labelled data to ensure reasonable model predictions. We investigated in our approach two CNN architectures, obtaining more robust results and a reduced number of parameters when using a modified U-Net. The method was probed over three benchmark models, showing consistently that the pre-training phase reduces the process’s uncertainties and accelerates the model convergence using minimal prior information. Besides, the final scores of the iterative process are better than the examples without transfer learning. Thus, transfer learning solved one main limitation of the previous PINN approaches: the unfeasible number of iterations when not using an initial model. Moreover, we tested the method using data with low-frequency band limitations, since the lack of low frequencies is a common issue within real seismic data. The inversion converges to reasonable results probing the method’s robustness with restricted frequency content.

An accurate velocity model is essential to make a good seismic image. Conventional methods to perform Velocity Model Building (VMB) tasks rely on inverse methods, which, despite being widely used, are ill-posed problems that require intense and specialized human supervision. Convolutional Neural Networks (CNN) have been extensively investigated as an alternative to solve the VMB task. Two main approaches were investigated in the literature: supervised training and Physics-Informed Neural Networks (PINN). Supervised training presents some generalization issues since structures, and velocity ranges must be similar in training and test set. Some works integrated Full-waveform Inversion (FWI) with CNN, defining the problem of VMB in the PINN framework. In this case, the CNN stabilizes the inversion, acting like a regularizer and avoiding local minima-related problems and, in some cases, sparing an initial velocity model. Our approach combines supervised and physics-informed neural networks by using transfer learning to start the inversion. The pre-trained CNN is obtained using a supervised approach based on training with a reduced and simple data set to capture the main velocity trend at the initial FWI iterations. We show that transfer learning reduces the uncertainties of the process, accelerates model convergence, and improves the final scores of the iterative process.

imaging. Conventional methods, like Tomography, Stereotomography, Migration Velocity Analysis (MVA) and Full-Waveform Inversion (FWI), obtain appropriate velocity models; however, they require intense and specialized human supervision and consume much time and computational resources. In recent years, some works investigated Deep Learning (DL) algorithms to obtain the velocity model directly from shots or migrated angle panels, obtaining encouraging predictions of synthetic models. This paper proposes a new flow to to recover structurally complex velocity models with DL. Inspired by the conventional geophysical velocity model building methods, instead of predicting the entire model in one step, we predict the velocity model iteratively. We implement the iterative nature of the process when, at each iteration, we train the DL algorithm to determine the velocity model with a certain level of precision/resolution for the next iteration; we name this process as Deep-Tomography. Starting from an initial model, that is an ultra-smooth version of the true model, Deep-Tomography is able to predict an appropriate final model, even in complete unseen during the training data, like the Marmousi model. When used as the initial model for FWI, the models estimated by Deep-tomography can also improve substantially the final results obtained with FWI.

Velocity models are crucial intermediate products generated in seismic data processing, and the model's accuracy is essential for constructing quality seismic images. Conventional approaches to velocity model building employ a family of inversion methods, among which are ray-based tomography and full-waveform inversion. These methods have been highly optimized throughout the years but are still heavily dependent on continuous human curation of the results, which leads to an overall high time cost, especially in areas with high structural complexity, such as those containing salt tectonics. We investigate a deep learning approach that accurately defines salt geometries for velocity model building. We train our convolutional neural network on synthetic shot gather data, explore a manner of leveraging information through summation of shot data, and demonstrate the influence that the choice of loss function has on the quality and aspect of predicted velocity models. Our Residual U-Net model trained on data containing only randomly shaped salt bodies can estimate geologically complex salt geometries such as those in 2D SEG/EAGE Salt Model slices. Our results show that deeper encoder-decoder models with shortcut connections resolve velocity model structures better than shallower models. Moreover, network models trained with a composite loss function - combining mean absolute error and the Multi-Scale Structural Similarity Index - better delineate the contours of areas with high-velocity contrast and better recover regions with a uniform velocity trend than network models trained with conventional loss functions like the mean squared error. The Residual U-Net and loss functions we employ are not task-specific and can be extended to other deep learning approaches to velocity model building.

Delimiting salt inclusions from migrated images is a time-consuming activity that relies on highly human-curated analysis and is subject to interpretation errors or limitations of the methods available. We propose to use migrated images produced from an inaccurate velocity model (with a reasonable approximation of sediment velocity, but without salt inclusions) to predict the correct salt inclusions shape using a Convolutional Neural Network (CNN). Our approach relies on subsurface Common Image Gathers to focus the sediments' reflections around the zero offset and to spread the energy of salt reflections over large offsets. Using synthetic data, we trained a U-Net to use common-offset subsurface images as input channels for the CNN and the correct salt-masks as network output. The network learned to predict the salt inclusions masks with high accuracy; moreover, it also performed well when applied to synthetic benchmark data sets that were not previously introduced. Our training process tuned the U-Net to successfully learn the shape of complex salt bodies from partially focused subsurface offset images.

The accurate and fast estimation of velocity models is crucial in seismic imaging. Conventional methods, like Tomography and Full-Waveform Inversion (FWI), obtain appropriate velocity models; however, they require intense and specialized human supervision and consume much time and computational resources. In recent years, some works investigated deep learning(DL) algorithms to obtain the velocity model directly from shots or migrated angle panels, obtaining encouraging predictions of synthetic models. This paper proposes a new flow to increase the complexity of velocity models recovered with DL. Inspired by the conventional geophysical velocity model building methods, instead of predicting the entire model in one step, we predict the velocity model iteratively. We implement the iterative nature of the process when, for each iteration, we train the DL algorithm to determine the velocity model with a certain level of precision/resolution for the next iteration; we name this process as Deep-Tomography. Starting from an initial model that roughly approaches the true model, the Deep-Tomography is able to predict an appropriate final model, even in complete unseen data, like the Marmousi model.

Delimiting salt inclusions from migrated images is a time-consuming activity that relies on highly human-curated analysis and is subject to interpretation errors or limitations of the methods available. We propose to use migrated images produced from an inaccurate velocity model (with a reasonable approximation of sediment velocity, but without salt inclusions) to predict the correct salt inclusions shape using a Convolutional Neural Network (CNN). Our approach relies on subsurface Common Image Gathers to focus the sediments' reflections around the zero offset and to spread the energy of salt reflections over large offsets. Using synthetic data, we trained a U-Net to use common-offset subsurface images as input channels for the CNN and the correct salt-masks as network output. The network learned to predict the salt inclusions masks with high accuracy; moreover, it also performed well when applied to synthetic benchmark data sets that were not previously introduced. Our training process tuned the U-Net to successfully learn the shape of complex salt bodies from partially focused subsurface offset images.