Title: Tensor-based reconstruction applied to regularized time-lapse data
SUMMARY
Repeatedly recording seismic data over a period of months or years is one way to identify trapped oil and gas and to monitor CO2 injection in underground storage reservoirs and saline aquifers. This process of recording data over time and then differencing the images assumes the recording of the data over a particular subsurface region is repeatable. In other words, the hope is that one can recover changes in the Earth when the survey parameters are held fixed between data collection times. Unfortunately, perfect experimental repeatability almost never occurs. Acquisition inconsistencies such as changes in weather (currents, wind) for marine seismic data are inevitable, resulting in source and receiver location differences between surveys at the very least. Thus, data processing aimed at improving repeatability between baseline and monitor surveys is extremely useful. One such processing tool is regularization (or binning) that aligns multiple surveys with different source or receiver configurations onto a common grid. Data binned onto a regular grid can be stored in a high-dimensional data structure called a tensor with, for example, x and y receiver coordinates and time as indices of the tensor. Such a higher-order data structure describing a subsection of the Earth often exhibits redundancies which one can exploit to fill in gaps caused by sampling the surveys onto the common grid. In fact, since data gaps and noise increase the rank of the tensor, seeking to recover the original data by reducing the rank (low-rank tensor-based completion) successfully fills in gaps caused by binning. The tensor nuclear norm (TNN) is defined by the tensor singular value decomposition (tSVD) which generalizes the matrix SVD. In this work we complete missing time-lapse data caused by binning using the alternating direction method of multipliers (or ADMM) to minimize the TNN. For a synthetic experiment with three parabolic events in which the time-lapse difference involves an amplitude increase in one of these events between baseline and monitor data sets, the binning and reconstruction algorithm (TNN-ADMM) correctly recovers this time-lapse change. We also apply this workflow of binning and TNN-ADMM reconstruction to a real marine survey from offshore Western Australia in which the binning onto a regular grid results in significant data gaps. The data after reconstruction varies continuously without the large gaps caused by the binning process.
Popa, Jonathan; Minkoff, Susan E.; Lou, Yifei(
, GEOPHYSICS)
null
(Ed.)
Seismic data are often incomplete due to equipment malfunction, limited source and receiver placement at near and far offsets, and missing crossline data. Seismic data contain redundancies because they are repeatedly recorded over the same or adjacent subsurface regions, causing the data to have a low-rank structure. To recover missing data, one can organize the data into a multidimensional array or tensor and apply a tensor completion method. We can increase the effectiveness and efficiency of low-rank data reconstruction based on tensor singular value decomposition (tSVD) by analyzing the effect of tensor orientation and exploiting the conjugate symmetry of the multidimensional Fourier transform. In fact, these results can be generalized to any order tensor. Relating the singular values of the tSVD to those of a matrix leads to a simplified analysis, revealing that the most square orientation gives the best data structure for low-rank reconstruction. After the first step of the tSVD, a multidimensional Fourier transform, frontal slices of the tensor form conjugate pairs. For each pair, a singular value decomposition can be replaced with a much cheaper conjugate calculation, allowing for faster computation of the tSVD. Using conjugate symmetry in our improved tSVD algorithm reduces the runtime of the inner loop by 35%–50%. We consider synthetic and real seismic data sets from the Viking Graben Region and the Northwest Shelf of Australia arranged as high-dimensional tensors. We compare the tSVD-based reconstruction with traditional methods, projection onto convex sets and multichannel singular spectrum analysis, and we see that the tSVD-based method gives similar or better accuracy and is more efficient, converging with runtimes that are an order of magnitude faster than the traditional methods. In addition, we verify that the most square orientation improves recovery for these examples by 10%–20% compared with the other orientations.
McKay, R.M.; De Santis, L.; Kulhanek, D.K.(
, Preliminary report)
null
(Ed.)
The marine-based West Antarctic Ice Sheet (WAIS) is currently retreating due to shifting wind-driven oceanic currents that transport warm waters toward the ice margin, resulting in ice shelf thinning and accelerated mass loss of the WAIS. Previous results from geologic drilling on Antarctica’s continental margins show significant variability in marine-based ice sheet extent during the late Neogene and Quaternary. Numerical models indicate a fundamental role for oceanic heat in controlling this variability over at least the past 20 My. Although evidence for past ice sheet variability has been collected in marginal settings, sedimentologic sequences from the outer continental shelf are required to evaluate the extent of past ice sheet variability and the associated oceanic forcings and feedbacks. International Ocean Discovery Program Expedition 374 drilled a latitudinal and depth transect of five drill sites from the outer continental shelf to rise in the eastern Ross Sea to resolve the relationship between climatic and oceanic change and WAIS evolution through the Neogene and Quaternary. This location was selected because numerical ice sheet models indicate that this sector of Antarctica is highly sensitive to changes in ocean heat flux. The expedition was designed for optimal data-model integration and will enable an improved understanding of the sensitivity of Antarctic Ice Sheet (AIS) mass balance during warmer-than-present climates (e.g., the Pleistocene “super interglacials,” the mid-Pliocene, and the late early to middle Miocene). The principal goals of Expedition 374 were to
• Evaluate the contribution of West Antarctica to far-field ice volume and sea level estimates;
• Reconstruct ice-proximal atmospheric and oceanic temperatures to identify past polar amplification and assess its forcings and feedbacks;
• Assess the role of oceanic forcing (e.g., sea level and temperature) on AIS stability/instability;
• Identify the sensitivity of the AIS to Earth’s orbital configuration under a variety of climate boundary conditions; and
• Reconstruct eastern Ross Sea paleobathymetry to examine relationships between seafloor geometry, ice sheet stability/instability, and global climate.
To achieve these objectives, we will
• Use data and models to reconcile intervals of maximum Neogene and Quaternary Antarctic ice advance with far-field records of eustatic sea level change;
• Reconstruct past changes in oceanic and atmospheric temperatures using a multiproxy approach;
• Reconstruct Neogene and Quaternary sea ice margin fluctuations in datable marine continental slope and rise records and correlate these records to existing inner continental shelf records;
• Examine relationships among WAIS stability/instability, Earth’s orbital configuration, oceanic temperature and circulation, and atmospheric pCO2; and
• Constrain the timing of Ross Sea continental shelf overdeepening and assess its impact on Neogene and Quaternary ice dynamics.
Expedition 374 was carried out from January to March 2018, departing from Lyttelton, New Zealand. We recovered 1292.70 m of high-quality cores from five sites spanning the early Miocene to late Quaternary. Three sites were cored on the continental shelf (Sites U1521, U1522, and U1523). At Site U1521, we cored a 650 m thick sequence of interbedded diamictite, mudstone, and diatomite, penetrating the Ross Sea seismic Unconformity RSU4. The depositional reconstructions of past glacial and open-marine conditions at this site will provide unprecedented insight into environmental change on the Antarctic continental shelf during the early and middle Miocene. At Site U1522, we cored a discontinuous upper Miocene to Pleistocene sequence of glacial and glaciomarine strata from the outer shelf, with the primary objective to penetrate and date seismic Unconformity RSU3, which is interpreted to represent the first major continental shelf–wide expansion and coalescing of marine-based ice streams from both East and West Antarctica. At Site U1523, we cored a sediment drift located beneath the westerly flowing Antarctic Slope Current (ASC). Cores from this site will provide a record of the changing vigor of the ASC through time. Such a reconstruction will enable testing of the hypothesis that changes in the vigor of the ASC represent a key control on regulating heat flux onto the continental shelf, resulting in the ASC playing a fundamental role in ice sheet mass balance.
We also cored two sites on the continental slope and rise. At Site U1524, we cored a Plio–Pleistocene sedimentary sequence on the continental rise on the levee of the Hillary Canyon, which is one of the largest conduits of Antarctic Bottom Water delivery from the Antarctic continental shelf into the abyssal ocean. Drilling at Site U1524 was intended to penetrate into middle Miocene and older strata but was initially interrupted by drifting sea ice that forced us to abandon coring in Hole U1524A at 399.5 m drilling depth below seafloor (DSF). We moved to a nearby alternate site on the continental slope (U1525) to core a single hole with a record complementary to the upper part of the section recovered at Site U1524. We returned to Site U1524 3 days later, after the sea ice cleared. We then cored Hole U1524C with the rotary core barrel with the intention of reaching the target depth of 1000 m DSF. However, we were forced to terminate Hole U1524C at 441.9 m DSF due to a mechanical failure with the vessel that resulted in termination of all drilling operations and a return to Lyttelton 16 days earlier than scheduled. The loss of 39% of our operational days significantly impacted our ability to achieve all Expedition 374 objectives as originally planned. In particular, we were not able to obtain the deeper time record of the middle Miocene on the continental rise or abyssal sequences that would have provided a continuous and contemporaneous archive to the high-quality (but discontinuous) record from Site U1521 on the continental shelf. The mechanical failure also meant we could not recover sediment cores from proposed Site RSCR-19A, which was targeted to obtain a high-fidelity, continuous record of upper Neogene and Quaternary pelagic/hemipelagic sedimentation. Despite our failure to recover a shelf-to-rise transect for the Miocene, a continental shelf-to-rise transect for the Pliocene to Pleistocene interval is possible through comparison of the high-quality records from Site U1522 with those from Site U1525 and legacy cores from the Antarctic Geological Drilling Project (ANDRILL).
Hu, Yue; Work, Daniel B.(
, ACM Transactions on Knowledge Discovery from Data)
Event detection is gaining increasing attention in smart cities research. Large-scale mobility data serves as an important tool to uncover the dynamics of urban transportation systems, and more often than not the dataset is incomplete. In this article, we develop a method to detect extreme events in large traffic datasets, and to impute missing data during regular conditions. Specifically, we propose a robust tensor recovery problem to recover low-rank tensors under fiber-sparse corruptions with partial observations, and use it to identify events, and impute missing data under typical conditions. Our approach is scalable to large urban areas, taking full advantage of the spatio-temporal correlations in traffic patterns. We develop an efficient algorithm to solve the tensor recovery problem based on the alternating direction method of multipliers (ADMM) framework. Compared with existing l 1 norm regularized tensor decomposition methods, our algorithm can exactly recover the values of uncorrupted fibers of a low-rank tensor and find the positions of corrupted fibers under mild conditions. Numerical experiments illustrate that our algorithm can achieve exact recovery and outlier detection even with missing data rates as high as 40% under 5% gross corruption, depending on the tensor size and the Tucker rank of the low rank tensor. Finally, we apply our method on a real traffic dataset corresponding to downtown Nashville, TN and successfully detect the events like severe car crashes, construction lane closures, and other large events that cause significant traffic disruptions.
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%.
Yin, Ziyi; Erdinc, Huseyin Tuna; Gahlot, Abhinav Prakash; Louboutin, Mathias; Herrmann, Felix J.(
, The Leading Edge)
Geologic carbon storage represents one of the few truly scalable technologies capable of reducing the CO 2 concentration in the atmosphere. While this technology has the potential to scale, its success hinges on our ability to mitigate its risks. An important aspect of risk mitigation concerns assurances that the injected CO 2 remains within the storage complex. Among the different monitoring modalities, seismic imaging stands out due to its ability to attain high-resolution and high-fidelity images. However, these superior features come at prohibitive costs and time-intensive efforts that potentially render extensive seismic monitoring undesirable. To overcome this shortcoming, we present a methodology in which time-lapse images are created by inverting nonreplicated time-lapse monitoring data jointly. By no longer insisting on replication of the surveys to obtain high-fidelity time-lapse images and differences, extreme costs and time-consuming labor are averted. To demonstrate our approach, hundreds of realistic synthetic noisy time-lapse seismic data sets are simulated that contain imprints of regular CO 2 plumes and irregular plumes that leak. These time-lapse data sets are subsequently inverted to produce time-lapse difference images that are used to train a deep neural classifier. The testing results show that the classifier is capable of detecting CO 2 leakage automatically on unseen data with reasonable accuracy. We consider the use of this classifier as a first step in the development of an automatic workflow designed to handle the large number of continuously monitored CO 2 injection sites needed to help combat climate change.
Popa, Jonathan, Minkoff, Susan E., and Lou, Yifei. Tensor-based reconstruction applied to regularized time-lapse data. Geophysical Journal International 231.1 Web. doi:10.1093/gji/ggac211.
Popa, Jonathan, Minkoff, Susan E., and Lou, Yifei.
"Tensor-based reconstruction applied to regularized time-lapse data". Geophysical Journal International 231 (1). Country unknown/Code not available: Oxford University Press. https://doi.org/10.1093/gji/ggac211.https://par.nsf.gov/biblio/10368614.
@article{osti_10368614,
place = {Country unknown/Code not available},
title = {Tensor-based reconstruction applied to regularized time-lapse data},
url = {https://par.nsf.gov/biblio/10368614},
DOI = {10.1093/gji/ggac211},
abstractNote = {SUMMARY Repeatedly recording seismic data over a period of months or years is one way to identify trapped oil and gas and to monitor CO2 injection in underground storage reservoirs and saline aquifers. This process of recording data over time and then differencing the images assumes the recording of the data over a particular subsurface region is repeatable. In other words, the hope is that one can recover changes in the Earth when the survey parameters are held fixed between data collection times. Unfortunately, perfect experimental repeatability almost never occurs. Acquisition inconsistencies such as changes in weather (currents, wind) for marine seismic data are inevitable, resulting in source and receiver location differences between surveys at the very least. Thus, data processing aimed at improving repeatability between baseline and monitor surveys is extremely useful. One such processing tool is regularization (or binning) that aligns multiple surveys with different source or receiver configurations onto a common grid. Data binned onto a regular grid can be stored in a high-dimensional data structure called a tensor with, for example, x and y receiver coordinates and time as indices of the tensor. Such a higher-order data structure describing a subsection of the Earth often exhibits redundancies which one can exploit to fill in gaps caused by sampling the surveys onto the common grid. In fact, since data gaps and noise increase the rank of the tensor, seeking to recover the original data by reducing the rank (low-rank tensor-based completion) successfully fills in gaps caused by binning. The tensor nuclear norm (TNN) is defined by the tensor singular value decomposition (tSVD) which generalizes the matrix SVD. In this work we complete missing time-lapse data caused by binning using the alternating direction method of multipliers (or ADMM) to minimize the TNN. For a synthetic experiment with three parabolic events in which the time-lapse difference involves an amplitude increase in one of these events between baseline and monitor data sets, the binning and reconstruction algorithm (TNN-ADMM) correctly recovers this time-lapse change. We also apply this workflow of binning and TNN-ADMM reconstruction to a real marine survey from offshore Western Australia in which the binning onto a regular grid results in significant data gaps. The data after reconstruction varies continuously without the large gaps caused by the binning process.},
journal = {Geophysical Journal International},
volume = {231},
number = {1},
publisher = {Oxford University Press},
author = {Popa, Jonathan and Minkoff, Susan E. and Lou, Yifei},
}
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