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The large spatial/temporal/frequency scale of geoscience and remote-sensing datasets causes memory issues when using convolutional neural networks for (sub-) surface data segmentation. Recently developed fully reversible or fully invertible networks can mostly avoid memory limitations by recomputing the states during the backward pass through the network. This results in a low and fixed memory requirement for storing network states, as opposed to the typical linear memory growth with network depth. This work focuses on a fully invertible network based on the telegraph equation. While reversibility saves the major amount of memory used in deep networks by the data, the convolutional kernels can take up most memory if fully invertible networks contain multiple invertible pooling/coarsening layers. We address the explosion of the number of convolutional kernels by combining fully invertible networks with layers that contain the convolutional kernels in a compressed form directly. A second challenge is that invertible networks output a tensor the same size as its input. This property prevents the straightforward application of invertible networks to applications that map between different input-output dimensions, need to map to outputs with more channels than present in the input data, or desire outputs that decrease/increase the resolution compared to the input data. However, we show that by employing invertible networks in a non-standard fashion, we can still use them for these tasks. Examples in hyperspectral land-use classification, airborne geophysical surveying, and seismic imaging illustrate that we can input large data volumes in one chunk and do not need to work on small patches, use dimensionality reduction, or employ methods that classify a patch to a single central pixel., Comment: 22 pages, 13 figures

This study focuses on inverting time-domain airborne electromagnetic data in 2D by training a neural-network to understand the relationship between data and conductivity, thereby removing the need for expensive forward modeling during the inversion process. Instead the forward modeling is completed in the training stage, where training models are built before calculating 3D forward modeling training data. The method relies on training data being similar to the field dataset of choice, therefore, the field data was first inverted in 1D to get an idea of the expected conductivity distribution. With this information, $ 10,000 $ training models were built with similar conductivity ranges, and the research shows that this provided enough information for the network to produce realistic 2D inversion models over an aquifer-bearing region in California. Once the training was completed, the actual inversion time took only a matter of seconds on a generic laptop, which means that if future data was collected in this region it could be inverted in near real-time. Better results are expected by increasing the number of training models and eventually the goal is to extend the method to 3D inversion., Comment: 4 pages, 5 figures, conference submission

Tracking a horizon in seismic images or 3D volumes is an integral part of seismic interpretation. The last few decades saw progress in using neural networks for this task, starting from shallow networks for 1D traces, to deeper convolutional neural networks for large 2D images. Because geological structures are intrinsically 3D, we hope to see improved horizon tracking by training networks on 3D seismic data cubes. While there are some 3D convolutional neural networks for various seismic interpretation tasks, they are restricted to shallow networks or relatively small 3D inputs because of memory limitations. The required memory for the network states and weights increases with network depth. We present a fully reversible network for horizon tracking that has a memory requirement that is independent of network depth. To tackle memory issues regarding the network weights, we use layers that train in a factorized form directly. Therefore, we can maintain a large number of network channels while keeping the number of convolutional kernels low. We use the saved memory to increase the input size of the data by order of magnitude such that the network can better learn from large structures in the data. A field data example verifies the proposed network structure is suitable for seismic horizon tracking.

Recently established equivalences between differential equations and the structure of neural networks enabled some interpretation of training of a neural network as partial-differential-equation (PDE) constrained optimization. We add to the previously established connections, explicit regularization that is particularly beneficial in the case of single large-scale examples with partial annotation. We show that explicit regularization of model parameters in PDE constrained optimization translates to regularization of the network output. Examination of the structure of the corresponding Lagrangian and backpropagation algorithm do not reveal additional computational challenges. A hyperspectral imaging example shows that minimum prior information together with cross-validation for optimal regularization parameters boosts the segmentation accuracy.

The large spatial/frequency scale of hyperspectral and airborne magnetic and gravitational data causes memory issues when using convolutional neural networks for (sub-) surface characterization. Recently developed fully reversible networks can mostly avoid memory limitations by virtue of having a low and fixed memory requirement for storing network states, as opposed to the typical linear memory growth with depth. Fully reversible networks enable the training of deep neural networks that take in entire data volumes, and create semantic segmentations in one go. This approach avoids the need to work in small patches or map a data patch to the class of just the central pixel. The cross-entropy loss function requires small modifications to work in conjunction with a fully reversible network and learn from sparsely sampled labels without ever seeing fully labeled ground truth. We show examples from land-use change detection from hyperspectral time-lapse data, and regional aquifer mapping from airborne geophysical and geological data.

Geological interpretation of seismic images is a visual task that can be automated by training neural networks. While neural networks have shown to be effective at various interpretation tasks, a fundamental challenge is the lack of labeled data points in the subsurface. For example, the interpolation and extrapolation of well-based lithology using seismic images relies on a small number of known labels. Besides well-known data augmentation techniques, as well as regularization of the network output, we propose and test another approach to deal with the lack of labels. Non learning-based horizon trackers work very well in the shallow subsurface where seismic images are of higher quality and the geological units are roughly layered. We test if these segmented and shallow units can help train neural networks to predict deeper geological units that are not layered and flat. We show that knowledge of shallow geological units helps to predict deeper units when there are only a few labels for training using a dataset from the Sea of Ireland. We employ U-net based multi-resolution networks, and we show that these networks can be described using matrix-vector product notation in a similar fashion as standard geophysical inverse problems., Comment: 7 pages, 5 figures

Neural-networks have seen a surge of interest for the interpretation of seismic images during the last few years. Network-based learning methods can provide fast and accurate automatic interpretation, provided there are sufficiently many training labels. We provide an introduction to the field aimed at geophysicists that are familiar with the framework of forward modeling and inversion. We explain the similarities and differences between deep networks to other geophysical inverse problems and show their utility in solving problems such as lithology interpolation between wells, horizon tracking and segmentation of seismic images. The benefits of our approach are demonstrated on field data from the Sea of Ireland and the North Sea., Comment: 8 pages, 5 figures

Detecting a specific horizon in seismic images is a valuable tool for geological interpretation. Because hand-picking the locations of the horizon is a time-consuming process, automated computational methods were developed starting three decades ago. Older techniques for such picking include interpolation of control points however, in recent years neural networks have been used for this task. Until now, most networks trained on small patches from larger images. This limits the networks ability to learn from large-scale geologic structures. Moreover, currently available networks and training strategies require label patches that have full and continuous annotations, which are also time-consuming to generate. We propose a projected loss-function for training convolutional networks with a multi-resolution structure, including variants of the U-net. Our networks learn from a small number of large seismic images without creating patches. The projected loss-function enables training on labels with just a few annotated pixels and has no issue with the other unknown label pixels. Training uses all data without reserving some for validation. Only the labels are split into training/testing. Contrary to other work on horizon tracking, we train the network to perform non-linear regression, and not classification. As such, we propose labels as the convolution of a Gaussian kernel and the known horizon locations that indicate uncertainty in the labels. The network output is the probability of the horizon location. We demonstrate the proposed computational ingredients on two different datasets, for horizon extrapolation and interpolation. We show that the predictions of our methodology are accurate even in areas far from known horizon locations because our learning strategy exploits all data in large seismic images., Comment: 24 pages, 13 figures