ALBERT

Description: The discontinuous Galerkin finite element method (DGM) is a promising algorithm for modelling wave propagation in fractured media. It allows for discontinuities in the displacement field to simulate fractures or faults in a model. Our approach is based on the interior-penalty formulation of DGM, and the fractures are simulated using the linear-slip model, which is incorporated into the weak formulation. On the other hand, the spectral element method (SEM) can be used to simulate elastic wave propagation in non-fractured media. SEM uses continuous basis functions which do not allow for discontinuities in the displacement field. However, the computation cost of DGM is significantly larger than SEM due primarily to increase in the number of degrees of freedom. Here we propose a hybrid Galerkin method (HGM) for elastic wave propagation in fractured media that combines the salient features of each of the algorithm resulting in significant reduction in computational cost compared to DGM. We use DGM in areas containing fractures and SEM in regions without fractures. The coupling between the domains at the interfaces is satisfied in the weak form through interface conditions. The degree of reduction in computation time depends primarily on the density of fractures in the medium. In this paper, we formulate and implement HGM for seismic wave propagation in fractured media. Using realistic 2-D/3-D numerical examples, we show that our proposed HGM outperforms DGM with reduced computation cost and memory requirement while maintaining the same level of accuracy.

Description: 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.

Description: Migration techniques are an integral part of seismic imaging workflows. Least-squares reverse time migration (LSRTM) overcomes some of the shortcomings of conventional migration algorithms by compensating for illumination and removing sampling artifacts to increase spatial resolution. However, the computational cost associated with iterative LSRTM is high and convergence can be slow in complex media. We implement pre-stack LSRTM in a deep learning framework and adopt strategies from the data science domain to accelerate convergence. The proposed hybrid framework leverages the existing physics-based models and machine learning optimizers to achieve better and cheaper solutions. Using a time-domain formulation, we show that mini-batch gradients can reduce the computation cost by using a subset of total shots for each iteration. Mini-batch approach does not only reduce source cross-talk but also is less memory intensive. Combining mini-batch gradients with deep learning optimizers and loss functions can improve the efficiency of LSRTM. Deep learning optimizers such as the adaptive moment estimation are generally well suited for noisy and sparse data. We compare different optimizers and demonstrate their efficacy in mitigating migration artifacts. To accelerate the inversion, we adopt the regularised Huber loss function in conjunction. We apply these techniques to 2D Marmousi and 3D SEG/EAGE salt models and show improvements over conventional LSRTM baselines. The proposed approach achieves higher spatial resolution in less computation time measured by various qualitative and quantitative evaluation metrics.