Abstract. The simulation of seismic waves is a core task in many geophysical applications. Numerical methods such as finite difference (FD) modelling and spectral element methods (SEMs) are the most popular techniques for simulating seismic waves, but disadvantages such as their computational cost prohibit their use for many tasks. In this work, we investigate the potential of deep learning for aiding seismic simulation in the solid Earth sciences. We present two deep neural networks which are able to simulate the seismic response at multiple locations in horizontally layered and faulted 2-D acoustic media an order of magnitude faster than traditional finite difference modelling. The first network is able to simulate the seismic response in horizontally layered media and uses a WaveNet network architecture design. The second network is significantly more general than the first and is able to simulate the seismic response in faulted media with arbitrary layers, fault properties and an arbitrary location of the seismic source on the surface of the media, using a conditional autoencoder design. We test the sensitivity of the accuracy of both networks to different network hyperparameters and show that the WaveNet network can be retrained to carry out fast seismic inversion in the same media. We find that are there are challenges when extending our methods to more complex, elastic and 3-D Earth models; for example, the accuracy of both networks is reduced when they are tested on models outside of their training distribution. We discuss further research directions which could address these challenges and potentially yield useful tools for practical simulation tasks.
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale, propagating and oscillatory nature of its solutions, and it is unclear how well they perform in this setting. We use a deep neural network to learn solutions of the wave equation, using the wave equation and a boundary condition as direct constraints in the loss function when training the network. We test the approach by solving the 2D acoustic wave equation for spatially-varying velocity models of increasing complexity, including homogeneous, layered and Earth-realistic models, and find the network is able to accurately simulate the wavefield across these cases. By using the physics constraint in the loss function the network is able to solve for the wavefield far outside of its boundary training data, offering a way to reduce the generalisation issues of existing deep learning approaches. We extend the approach for the Earth-realistic case by conditioning the network on the source location and find that it is able to generalise over this initial condition, removing the need to retrain the network for each solution. In contrast to traditional numerical simulation this approach is very efficient when computing arbitrary space-time points in the wavefield, as once trained the network carries out inference in a single step without needing to compute the entire wavefield. We discuss the potential applications, limitations and further research directions of this work.
Abstract. The simulation of seismic waves is a core task in many geophysical applications. Numerical methods such as Finite Difference (FD) modelling and Spectral Element Methods (SEM) are the most popular techniques for simulating seismic waves in complex media, but for many tasks their computational cost is prohibitively expensive. In this work we present two types of deep neural networks as fast alternatives for simulating seismic waves in horizontally layered and faulted 2D acoustic media. In contrast to the classical methods both networks are able to simulate the seismic response at multiple locations within the media in a single inference step, without needing to iteratively model the seismic wavefield through time, resulting in an order of magnitude reduction in simulation time. This speed improvement could pave the way to real-time seismic simulation and benefit seismic inversion algorithms based on forward modelling, such as full waveform inversion. Our first network is able to simulate seismic waves in horizontally layered media. We use a WaveNet network architecture and show this is more accurate than a standard convolutional network design. Furthermore we show that seismic inversion can be carried out by retraining the network with its inputs and outputs reversed, offering a fast alternative to existing inversion techniques. Our second network is significantly more general than the first; it is able to simulate seismic waves in faulted media with arbitrary layers, fault properties and an arbitrary location of the seismic source on the surface of the media. It uses a convolutional autoencoder network design and is conditioned on the input source location. We investigate the sensitivity of different network designs and training hyperparameters on its simulation accuracy. We compare and contrast this network to the first network. To train both networks we introduce a time-dependent gain in the loss function which improves convergence. We discuss the relative merits of our approach with FD modelling and how our approach could be generalised to simulate more complex Earth models.
The lunar permanently shadowed regions (PSRs) are expected to host large quantities of water-ice, which are key for sustainable exploration of the Moon and beyond. In the near future, NASA and other entities plan to send rovers and humans to characterize water-ice within PSRs. However, there exists only limited information about the small-scale geomorphology and distribution of ice within PSRs because the orbital imagery captured to date lacks sufficient resolution and/or signal. In this paper, we develop and validate a new method of post-processing LRO NAC images of PSRs. We show that our method is able to reveal previously unseen geomorphological features such as boulders and craters down to 3 meters in size, whilst not finding evidence for surface frost or near-surface ice. Our post-processed images significantly facilitate the exploration of PSRs by reducing the uncertainty of target selection and traverse/mission planning.
Recently, learning-based approaches have achieved impressive results in the field of low-light image denoising. Some state of the art approaches employ a rich physical model to generate realistic training data. However, the performance of these approaches ultimately depends on the realism of the physical model, and many works only concentrate on everyday photography. In this work we present a denoising approach for extremely low-light images of permanently shadowed regions (PSRs) on the lunar surface, taken by the Narrow Angle Camera on board the Lunar Reconnaissance Orbiter satellite. Our approach extends existing learning-based approaches by combining a physical noise model of the camera with real noise samples and training image scene selection based on 3D ray tracing to generate realistic training data. We also condition our denoising model on the camera's environmental metadata at the time of image capture (such as the camera's temperature and age), showing that this improves performance. Our quantitative and qualitative results show that our method strongly outperforms the existing calibration routine for the camera and other baselines. Our results could significantly impact lunar science and exploration, for example by aiding the identification of surface water-ice and reducing uncertainty in rover and human traverse planning into PSRs.
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