Migração reversa no tempo por filtros mínimos quadrados de única iteração com uso de redes neurais convolucionais no domínio da transformada Curvelet

Abstract

The concept of deblurring filters is a novel approach to the least-squares migration, trying to achieve similar results but with only one iteration, without resorting to computationally expensive iterative methods. There have been several studies proposing different solutions to this problem, such as using Fourier-based transforms and neural networks. In the end, all of them try to achieve some sort of reparametrization and deblurring of the image by using those new parameters, to approximate the inverse of the Hessian. This technique is not new, being employed in digital cameras to filter the blur inherent to the equipment by using a similar concept. This dissertation studies the use of the U-Net neural network topology, applied to the curvelet transform domain and to patches in the spatial domain. The U-Net is a specific type of convolutional neural network (CNN) that has encoding and decoding blocks, which enhances its ability to recognize features at different scales. By applying it to the curvelet domain, which is separated by scale, angle, and location, it has the opportunity to better grasp different aspects of the same features. The idea is to train the network to match the pair of remigrated and migrated images, and then apply it to the migrated image. Our research shows that training the U-Net deep learning model in the curvelet domain can improve resolution at the deep regions of the migrated seismic section.% However, is very susceptible to noise, and seems to work on marine data better. This is one of the very few recent studies attempting to use neural networks in the curvelet transform domain, and a lot of research is still needed to fully grasp what are the possibilities of using such a technique.The filter based in the U-Net network was tested on two synthetic data sets (Marmousi and Sigsbee), presenting encouraging results, on top of showing that the network application after the training process produced a seismic image with better resolution compared to the conventionally migrated section.