scholarly journals Ensemble-based uncertainty estimation in Full Waveform Inversion

2019 ◽  
Author(s):  
J Thurin ◽  
R Brossier ◽  
L Métivier
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Waveform Inversion ◽  
Uncertainty Estimation ◽  
Low Rank ◽  
Full Waveform Inversion ◽  
Acoustic Frequency ◽  
Full Waveform ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

SUMMARY Uncertainty estimation and quality control are critically missing in most geophysical tomographic applications. The few solutions to cope with that issue are often left out in practical applications when these ones grow in scale and involve complex modeling. We present a joint full waveform inversion and ensemble data assimilation scheme, allowing local Bayesian estimation of the solution that brings uncertainty estimation to the tomographic problem. This original methodology relies on a deterministic square root ensemble Kalman filter commonly used in the data assimilation community: the ensemble transform Kalman filter. Combined with a 2D visco-acoustic frequency domain full waveform inversion scheme, the resulting method allows to access a low-rank approximation of the posterior covariance matrix of the solution. It yields uncertainty information through an ensemble-representation, that can conveniently be mapped across the physical domain for visualization and interpretation. The combination of ensemble transform Kalman filter with full waveform inversion is discussed along with the scheme design and algorithmic details that lead to our mixed application. Both synthetic and field-data results are presented, along with the biases that are associated with the limited rank ensemble representation. Finally, we review the open questions and developments perspectives linked with data assimilation applications to the tomographic problem.

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

2020 ◽  
Vol 223 (2) ◽  
pp. 811-824
Author(s):  
Chao Huang ◽  
Tieyuan Zhu
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Waveform Inversion ◽  
Time Lapse ◽  
Uncertainty Estimation ◽  
Covariance Matrices ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Velocity Changes ◽  
Over Time

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

scholarly journals Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization

2017 ◽  
Vol 145 (11) ◽  
pp. 4575-4592 ◽  
Author(s):  
Craig H. Bishop ◽  
Jeffrey S. Whitaker ◽  
Lili Lei
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Satellite Data ◽  
Localization Length ◽  
Model Space ◽  
Ensemble Size ◽  
Length Scales ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Expanded Ensemble

To ameliorate suboptimality in ensemble data assimilation, methods have been introduced that involve expanding the ensemble size. Such expansions can incorporate model space covariance localization and/or estimates of climatological or model error covariances. Model space covariance localization in the vertical overcomes problematic aspects of ensemble-based satellite data assimilation. In the case of the ensemble transform Kalman filter (ETKF), the expanded ensemble size associated with vertical covariance localization would also enable the simultaneous update of entire vertical columns of model variables from hyperspectral and multispectral satellite sounders. However, if the original formulation of the ETKF were applied to an expanded ensemble, it would produce an analysis ensemble that was the same size as the expanded forecast ensemble. This article describes a variation on the ETKF called the gain ETKF (GETKF) that takes advantage of covariances from the expanded ensemble, while producing an analysis ensemble that has the required size of the unexpanded forecast ensemble. The approach also yields an inflation factor that depends on the localization length scale that causes the GETKF to perform differently to an ensemble square root filter (EnSRF) using the same expanded ensemble. Experimentation described herein shows that the GETKF outperforms a range of alternative ETKF-based solutions to the aforementioned problems. In cycling data assimilation experiments with a newly developed storm-track version of the Lorenz-96 model, the GETKF analysis root-mean-square error (RMSE) matches the EnSRF RMSE at shorter than optimal localization length scales but is superior in that it yields smaller RMSEs for longer localization length scales.

scholarly journals Estimating Surface Carbon Fluxes Based on a Local Ensemble Transform Kalman Filter with a Short Assimilation Window and a Long Observation Window

2017 ◽  
Author(s):  
Yun Liu ◽  
Eugenia Kalnay ◽  
Ning Zeng ◽  
Ghassem Asrar ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Grid Point ◽  
Carbon Fluxes ◽  
Transfer Model ◽  
Observation Window ◽  
Surface Carbon ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. We developed a Carbon data assimilation system to estimate the surface carbon fluxes using the Local Ensemble Transform Kalman Filter and atmospheric transfer model of GEOS-Chem driven by the MERRA-1 reanalysis of the meteorological fields based on the Goddard Earth Observing System Model, Version 5 (GEOS-5). This assimilation system is inspired by the method of Kang et al. [2011, 2012], who estimated the surface carbon fluxes in an Observing System Simulation Experiment (OSSE) mode, as evolving parameters in the assimilation of the atmospheric CO2, using a short assimilation window of 6 hours. They included the assimilation of the standard meteorological variables, so that the ensemble provided a measure of the uncertainty in the CO2 transport. After introducing new techniques such as variable localization, and increased observation weights near the surface, they obtained accurate carbon fluxes at grid point resolution. We developed a new version of the LETKF related to the Running-in-Place (RIP) method used to accelerate the spin-up of EnKF data assimilation [Kalnay and Yang, 2010; Wang et al., 2013, Yang et al., 2014]. Like RIP, the new assimilation system uses the no-cost smoothing algorithm for the LETKF [Kalnay et al., 2007b], which allows shifting at no cost the Kalman Filter solution forward or backward within an assimilation window. In the new scheme a long observation window (e.g., 7-days or longer) is used to create an LETKF ensemble at 7-days. Then, the RIP smoother is used to obtain an accurate final analysis at 1-day. This analysis has the advantage of being based on a short assimilation window, which makes it more accurate, and of having been exposed to the future 7-days observations, which accelerates the spin up. The assimilation and observation windows are then shifted forward by one day, and the process is repeated. This reduces significantly the analysis error, suggesting that this method could be used in other data assimilation problems.

Real Data Assimilation Using the Local Ensemble Transform Kalman Filter (LETKF) System for a Global Non-hydrostatic NWP model on the Cubed-sphere

2018 ◽  
Vol 54 (S1) ◽  
pp. 351-360 ◽  
Author(s):  
Seoleun Shin ◽  
Jeon-Ho Kang ◽  
Hyoung-Wook Chun ◽  
Sihye Lee ◽  
Kwangjae Sung ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Real Data ◽  
Ensemble Transform Kalman Filter ◽  
Cubed Sphere ◽  
Nwp Model ◽  
Ensemble Transform
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