Unsupervised physics-based neural networks for seismic migration

Abstract

We have developed a novel framework for combining physics-based forward models and neural networks to advance seismic processing and inversion algorithms. Migration is an effective tool in seismic data processing and imaging. Over the years, the scope of these algorithms has broadened; today, migration is a central step in the seismic data processing workflow. However, no single migration technique is suitable for all kinds of data and all styles of acquisition. There is always a compromise on the accuracy, cost, and flexibility of these algorithms. On the other hand, machine-learning algorithms and artificial intelligence methods have been found immensely successful in applications in which big data are available. The applicability of these algorithms is being extensively investigated in scientific disciplines such as exploration geophysics with the goal of reducing exploration and development costs. In this context, we have used a special kind of unsupervised recurrent neural network and its variants, Hopfield neural networks and the Boltzmann machine, to solve the problems of Kirchhoff and reverse time migrations. We use the network to migrate seismic data in a least-squares sense using simulated annealing to globally optimize the cost function of the neural network. The weights and biases of the neural network are derived from the physics-based forward models that are used to generate seismic data. The optimal configuration of the neural network after training corresponds to the minimum energy of the network and thus gives the reflectivity solution of the migration problem. Using synthetic examples, we determine that (1) Hopfield neural networks are fast and efficient and (2) they provide reflectivity images with mitigated migration artifacts and improved spatial resolution. Specifically, the presented approach minimizes the artifacts that arise from limited aperture, low subsurface illumination, coarse sampling, and gaps in the data.

Accelerating Least Squares Imaging Using Deep Learning Techniques

“…Under the paradigm of theory guided data science, many researchers in the geophysics community are looking at ways of combining physics and machine learning [10][11][12][13][14][15][16][17]. These works, however were not extended to least-squares migrations.…”

Inversion using adaptive physics‐based neural network: Application to magnetotelluric inversion

“…The advantage of ML as an inversion scheme is the ability to derive a complex nonlinear mapping function from input data to output models by training a neural network Inverse modelling (Dawson et al, 1992;Lunz et al, 2018;Vamaraju and Sen, 2019) (Raissi et al, 2019b;Kahana et al, 2020;Colombo et al, 2021) and current study (Biswas et al, 2019;Fan and Ying, 2020;) Solve PDE (Lee and Kang, 1990;Dissanayake and Phan-Thien, 1994;Lagaris et al, 1998;Rudd and Ferrari, 2015;) (Raissi et al, 2017b;Yang et al, 2018;Raissi et al, 2019a;Zhu et al, 2019) (Chen et al, 2018;Raissi and Karniadakis, 2018;Mattheakis et al, 2019) Discover governing equation (Bongard and Lipson, 2007;Brunton et al, 2016;Raissi, 2018;Zhang and Ma, 2020) (Raissi et al, 2017a) (Udrescu and Tegmark, 2020) (Guo et al, 2018) without considering the influence of the initial model or calculating the gradient of the objective function in the deterministic inversion. The training phase in ML geophysical inversion aims to learn directly from the data about the pseudoinverse operator (Adler and Öktem, 2017).…”

“…ML inversions are traditionally solved using neural network techniques such as remote sensing of surface properties (Dawson et al, 1992) and seismic processing (Vamaraju and Sen, 2019). Table 1 shows a new trend to solve inverse problems by combining the advantages of deterministic inversion with neural network inversion.…”

Modeling of water waves and sediment transport using physics-based and machine learning methods

“…Thus, applying ML to obtain the solution to inverse problems would be desirable because it can execute faster than numerical models and simulate high-dimensional scenarios with a large amount of data. For instance, Collins et al (2020) (Pilozzi et al, 2018), seismic processing (Vamaraju and Sen, 2019), medical imaging (Lunz et al, 2018), and remote sensing of surface properties (Dawson et al, 1992), among others.…”