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Register a new userA dual formulation of wavefield reconstruction inversion for large-scale seismic inversion
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Most of the seismic inversion techniques currently proposed focus on robustness with respect to the background model choice or inaccurate physical modeling assumptions, but are not apt to large-scale 3D applications. On the other hand, methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously bogged down by local minima and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting model or inaccurate physics when compared to full waveform inversion. The method is based on a dual (Lagrangian) reformulation of the classical wavefield reconstruction inversion, whose robustness with respect to local minima is well documented in the literature. However, it is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation. The proposed reformulation allows the deployment of state-of-the-art time-domain finite-difference methods, and is computationally mature for industrial scale problems.
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We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping. The original method was formulated in the frequency domain with acoustic isotropic physics. However, frequency-domain modeling requires sophisticated iterative solvers that are difficult to scale to industrial-size problems and more realistic physical assumptions, such as tilted transverse isotropy, object of this study. The work presented here is based on a recently proposed dual formulation of wavefield reconstruction inversion, which allows time-domain propagator that are suitable to both large scales and more accurate physics.
Achieving desirable receiver sampling in ocean bottom acquisition is often not possible because of cost considerations. Assuming adequate source sampling is available, which is achievable by virtue of reciprocity and the use of modern randomized (simultaneous-source) marine acquisition technology, we are in a position to train convolutional neural networks (CNNs) to bring the receiver sampling to the same spatial grid as the dense source sampling. To accomplish this task, we form training pairs consisting of densely sampled data and artificially subsampled data using a reciprocity argument and the assumption that the source-site sampling is dense. While this approach has successfully been used on the recovery monochromatic frequency slices, its application in practice calls for wavefield reconstruction of time-domain data. Despite having the option to parallelize, the overall costs of this approach can become prohibitive if we decide to carry out the training and recovery independently for each frequency. Because different frequency slices share information, we propose the use the method of transfer training to make our approach computationally more efficient by warm starting the training with CNN weights obtained from a neighboring frequency slices. If the two neighboring frequency slices share information, we would expect the training to improve and converge faster. Our aim is to prove this principle by carrying a series of carefully selected experiments on a relatively large-scale five-dimensional data synthetic data volume associated with wide-azimuth 3D ocean bottom node acquisition. From these experiments, we observe that by transfer training we are able t significantly speedup in the training, specially at relatively higher frequencies where consecutive frequency slices are more correlated.
Seismic inversion and imaging are adjoint-based optimization problems that processes up to terabytes of data, regularly exceeding the memory capacity of available computers. Data compression is an effective strategy to reduce this memory requirement by a certain factor, particularly if some loss in accuracy is acceptable. A popular alternative is checkpointing, where data is stored at selected points in time, and values at other times are recomputed as needed from the last stored state. This allows arbitrarily large adjoint computations with limited memory, at the cost of additional recomputations. In this paper we combine compression and checkpointing for the first time to compute a realistic seismic inversion. The combination of checkpointing and compression allows larger adjoint computations compared to using only compression, and reduces the recomputation overhead significantly compared to using only checkpointing.
Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exaspirated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train Neural Operators on an ensemble of simulations performed with random velocity models and source locations. As Neural Operators are grid-free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the methods applicability to seismic tomography, using reverse mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.
Inspired by recent work on extended image volumes that lays the ground for randomized probing of extremely large seismic wavefield matrices, we present a memory frugal and computationally efficient inversion methodology that uses techniques from randomized linear algebra. By means of a carefully selected realistic synthetic example, we demonstrate that we are capable of achieving competitive inversion results at a fraction of the memory cost of conventional full-waveform inversion with limited computational overhead. By exchanging memory for negligible computational overhead, we open with the presented technology the door towards the use of low-memory accelerators such as GPUs.
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