Iterated extended Kalman filter method for time‐lapse seismic full waveform inversion

Uncertainty quantification in the context of seismic imaging is important for interpretinginverted subsurface models and updating reservoir models. The limited illumination, noisydata and poor initial model in the seismic full waveform inversion (FWI) lead to inversionuncertainties. This is particularly true for anisotropic elastic FWI, which suffers from extra parameter trade-off problems. In this work, we address the uncertainty quantificationof anisotropic elastic FWI problem in the framework of Bayesian inference. Specially, weestimate the uncertainties of the subsurface elastic parameters in the Bayesian anisotropicelastic FWI by combining the iterated extended Kalman filter with an explicit representation of the sensitivity matrix with Green’s functions. The sensitivity matrix is based onthe integral equation approach, which is also within the context of nonlinear inverse scattering theory. We give the results of numerical tests with examples for anisotropic elasticmedia. They show that the proposed Bayesian inversion method can provide reasonablereconstructed results for the elastic coefficients of the stiffness tensor and the framework issuitable for accessing the uncertainties.

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Time-lapse full waveform inversion plus extended Kalman filter for high-resolution seismic models and uncertainty estimation

10.1190/segam2019-3215954.1 ◽

2019 ◽

Author(s):

Chao Huang ◽

Tieyuan Zhu

Keyword(s):

Kalman Filter ◽

High Resolution ◽

Extended Kalman Filter ◽

Waveform Inversion ◽

Time Lapse ◽

Uncertainty Estimation ◽

Full Waveform Inversion ◽

Full Waveform ◽

Seismic Models

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Full waveform inversion based on the ensemble Kalman filter method using uniform sampling without replacement

Science Bulletin ◽

10.1016/j.scib.2019.01.021 ◽

2019 ◽

Vol 64 (5) ◽

pp. 321-330 ◽

Cited By ~ 8

Author(s):

Jian Wang ◽

Dinghui Yang ◽

Hao Jing ◽

Hao Wu

Keyword(s):

Kalman Filter ◽

Ensemble Kalman Filter ◽

Waveform Inversion ◽

Filter Method ◽

Full Waveform Inversion ◽

Sampling Without Replacement ◽

Uniform Sampling ◽

Full Waveform ◽

Kalman Filter Method

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

Geophysical Journal International ◽

10.1093/gji/ggaa337 ◽

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.

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Performance evaluation of GPS / BDS combined single-point positioning based on RTKLIB

E3S Web of Conferences ◽

10.1051/e3sconf/202016503009 ◽

2020 ◽

Vol 165 ◽

pp. 03009

Author(s):

Li Yan-yi ◽

Huang Jin ◽

Tang Ming-xiu

Keyword(s):

Kalman Filter ◽

Extended Kalman Filter ◽

Single Point ◽

Least Square Method ◽

Least Square ◽

Filter Method ◽

Single System ◽

Positioning Error ◽

Dual Mode ◽

Kalman Filter Method

In order to evaluate the performance of GPS / BDS, RTKLIB, an open-source software of GNSS, is used in this paper. In this paper, the least square method, the weighted least square method and the extended Kalman filter method are respectively applied to BDS / GPS single system for data solution. Then, the BDS system and GPS system are used for fusion positioning and the positioning results of the two systems are compared with that of the single system. Through the comparison of experiments, on the premise of using the extended Kalman filter method for positioning, when the GPS signal is not good, BDS data is introduced for dual-mode positioning, the positioning error in e direction is reduced by 36.97%, the positioning error in U direction is reduced by 22.95%, and the spatial positioning error is reduced by 16.01%, which further reflects the advantages of dual-mode positioning in improving a system robustness and reducing the error.

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