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We present a new method to obtain dynamic body force at virtual interfaces to reconstruct shear wave motions induced by a source outside a truncated computational domain. Specifically, a partial differential equation (PDE)-constrained optimization method is used to minimize the misfit between measured motions at a limited number of sensors on the ground surface and their counterparts reconstructed from optimized forces. Numerical results show that the optimized forces accurately reconstruct the targeted ground motions in the surface and the interior of the domain. The proposed optimization framework yields a particular force vector among other valid solutions allowed by the domain reduction method (DRM). Per this optimized or inverted force vector, the reconstructed wave field is identical to its reference counterpart in the domain of interest but may differ in the exterior domain from the reference one. However, we remark that the inverted solution is valid and introduce a simple post-process that can modify the solution to achieve an alternative force vector corresponding to the reference wave field. We also study the desired sensor spacing to accurately reconstruct the wave responses for a given dominant frequency of interest. We remark that the presented method is omnidirectionally applicable in terms of the incident angle of an incoming wave and is effective for any given material heterogeneity and geometry of layering of a reduced domain. The presented inversion method requires information on the wave speeds and dimensions of only a reduced domain. Namely, it does not need any informa- tion on the geophysical profile of an enlarged domain or a seismic source profile outside a reduced domain. Thus, the computational cost of the method is compact even though it leads to the high-fidelity reconstruction of wave re- sponse in the reduced domain, allowing for studying and predicting ground and structural responses using real seismic measurements.
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Reconstruction of Sparsely Sampled Seismic Data via Residual U-Net
Reconstruction of sparsely sampled seismic data is critical for maintaining the quality of seismic images when significant numbers of shots and receivers are missing.We present a reconstruction method in the shot-receiver-time (SRT) domain based on a residual U-Net machine learning architecture, for seismic data acquired in a sparse 2-D acquisition and name it SRT2D-ResU-Net. The SRT domain retains a high level of seismic signal connectivity, which is likely the main data feature that the reconstructing algorithms rely on. We develop an “in situ training and prediction” workflow by dividing the acquisition area into two nonoverlapping subareas: a training subarea for establishing the network model using regularly sampled data and a testing subarea for reconstructing the sparsely sampled data using the trained model. To establish a reference base for analyzing the changes in data features over the study area, and quantifying the reconstructed seismic data, we devise a baseline reference using a tiny portion of the field data. The baselines are properly spaced and excluded from the training and reconstruction processes. The results on a field marine data set show that the SRT2D-ResU-Net can effectively learn the features of seismic data in the training process, and the average correlation between the reconstructed missing traces and the true answers is over 85%.
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- Award ID(s):
- 1832197
- PAR ID:
- 10296119
- Date Published:
- Journal Name:
- IEEE Geoscience and Remote Sensing Letters
- ISSN:
- 1545-598X
- Page Range / eLocation ID:
- 1 to 5
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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PurposeTo develop a strategy for training a physics‐guided MRI reconstruction neural network without a database of fully sampled data sets. MethodsSelf‐supervised learning via data undersampling (SSDU) for physics‐guided deep learning reconstruction partitions available measurements into two disjoint sets, one of which is used in the data consistency (DC) units in the unrolled network and the other is used to define the loss for training. The proposed training without fully sampled data is compared with fully supervised training with ground‐truth data, as well as conventional compressed‐sensing and parallel imaging methods using the publicly available fastMRI knee database. The same physics‐guided neural network is used for both proposed SSDU and supervised training. The SSDU training is also applied to prospectively two‐fold accelerated high‐resolution brain data sets at different acceleration rates, and compared with parallel imaging. ResultsResults on five different knee sequences at an acceleration rate of 4 shows that the proposed self‐supervised approach performs closely with supervised learning, while significantly outperforming conventional compressed‐sensing and parallel imaging, as characterized by quantitative metrics and a clinical reader study. The results on prospectively subsampled brain data sets, in which supervised learning cannot be used due to lack of ground‐truth reference, show that the proposed self‐supervised approach successfully performs reconstruction at high acceleration rates (4, 6, and 8). Image readings indicate improved visual reconstruction quality with the proposed approach compared with parallel imaging at acquisition acceleration. ConclusionThe proposed SSDU approach allows training of physics‐guided deep learning MRI reconstruction without fully sampled data, while achieving comparable results with supervised deep learning MRI trained on fully sampled data.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/LGRS.2020.3035835
