One‐dimensional prestack seismic waveform inversion using ensemble kalman filter

2008 ◽  
Author(s):  
Long Jin ◽  
Mrinal. K. Sen ◽  
Paul. L. Stoffa
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Waveform Inversion ◽  
One Dimensional ◽  
Seismic Waveform

Dual state-parameter optimal estimation of one-dimensional open channel model using ensemble Kalman filter

2013 ◽  
Vol 25 (4) ◽  
pp. 564-571 ◽  
Author(s):  
Rui-xun Lai ◽  
Hong-wei Fang ◽  
Guo-jian He ◽  
Xin Yu ◽  
Ming Yang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Open Channel ◽  
Channel Model ◽  
State Parameter ◽  
Optimal Estimation ◽  
One Dimensional

One-Dimensional Soil Moisture Simulation Using Ensemble Kalman Filter

2012 ◽  
Vol 212-213 ◽  
pp. 177-180
Author(s):  
Xiao Lei Fu ◽  
Zhong Bo Yu ◽  
Yu Li ◽  
Hai Shen Lv ◽  
Di Liu ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Soil Layer ◽  
Model Parameters ◽  
Deep Soil ◽  
One Dimensional ◽  
Initial Soil Moisture ◽  
Initial Soil

Data assimilation is a method which integrates model and observation. In hydrology, ensemble Kalman filter (EnKF) as a sequential data assimilation method is often used to correct model parameters, thus improve the simulated accuracy. In this study, we conduct one numerical experiment to predict soil moisture using the one-dimensional soil moisture system based on ensemble Kalman filter and Simple Biosphere (SiB2) Model at Meilin study area, China. The simulated period is divided into two parts: 0-60h and 60-240h. The results show that EnKF is an efficient method in assimilating the soil moisture, especially in soil surface layer and deep soil layer; in addition, the efficiency of EnKF depends on the selection of initial soil moisture profile. With different initial soil moisture profiles, the performance of EnKF is different at the first few assimilated time, but with time grows, it can improve the simulated accuracy significantly.

Correction of pumping station parameters in a one-dimensional hydrodynamic model using the Ensemble Kalman filter

2019 ◽  
Vol 568 ◽  
pp. 108-118 ◽  
Author(s):  
Xiaohui Lei ◽  
Yu Tian ◽  
Zhao Zhang ◽  
Lingling Wang ◽  
Xiaohua Xiang ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Hydrodynamic Model ◽  
Ensemble Kalman Filter ◽  
One Dimensional ◽  
Pumping Station

The Ensemble Kalman Filter for Continuous Updating of Reservoir Simulation Models

2005 ◽  
Vol 128 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Yaqing Gu ◽  
Dean S. Oliver
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Water Saturation ◽  
State Variables ◽  
Time Step ◽  
Two Phase ◽  
One Dimensional ◽  
Reservoir State

This paper reports the use of ensemble Kalman filter (EnKF) for automatic history matching. EnKF is a Monte Carlo method, in which an ensemble of reservoir state variables are generated and kept up-to-date as data are assimilated sequentially. The uncertainty of reservoir state variables is estimated from the ensemble at any time step. Two synthetic problems are selected to investigate two primary concerns with the application of the EnKF. The first concern is whether it is possible to use a Kalman filter to make corrections to state variables in a problem for which the covariance matrix almost certainly provides a poor representation of the distribution of variables. It is tested with a one-dimensional, two-phase waterflood problem. The water saturation takes large values behind the flood front, and small values ahead of the front. The saturation distribution is bimodal and is not well modeled by the mean and variance. The second concern is the representation of the covariance via a relatively small ensemble of state vectors may be inadequate. It is tested by a two-dimensional, two-phase problem. The number of ensemble members is kept the same as for the one-dimensional problem. Hence the number of ensemble members used to create the covariance matrix is far less than the number of state variables. We conclude that EnKF can provide satisfactory history matching results while requiring less computation work than traditional history matching methods.

scholarly journals Comparison of data assimilation methods based on the classical, ensemble and local Kalman filter by the example of the advection equation and Lorenz system

2018 ◽  
pp. 507-515
Author(s):  
Д.А. Ростилов ◽  
М.Н. Кауркин ◽  
Р.А. Ибраев
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Lorenz System ◽  
Parallel Implementation ◽  
Advection Equation ◽  
Ensemble Kalman Filters ◽  
One Dimensional ◽  
The Mean ◽  
The Lorenz System

Статья посвящена сравнению трех методов усвоения данных наблюденй: фильтр Калмана (Kalman Filter, KF), ансамблевый фильтр Калмана (Ensemble Kalman Filter, EnKF) и локальный фильтр Калмана (Local Kalman Filter, LKF). Выполнены численные эксперименты по усвоению синтетических данных этими методами в двух разных моделях, описываемых системами дифференциальных уравнений. Первая описывается одномерным линейным уравнением адвекции, а вторая - системой Лоренца. Проведено сравнение средних ошибок и времени исполнения этих методов при различных размерах модели, которые согласуются с теоретическим оценками. Показано, что вычислительная сложность ансамблевого и локального фильтров Калмана растет линейно с увеличением размера модели, в то время как у первого метода эта сложность растет со скоростью куба. Рассмотрена эффективность одной из возможных параллельных реализаций локального фильтра Калмана. The paper is devoted to the comparison of three data assimilation methods: the Kalman Filter (Kalman Filter, KF), the ensemble Kalman Filter (EnKF), and the local Kalman Filter (LKF). A number of numerical experiments on data assimilation by these methods are performed on two different models described by systems of differential equations. The first one is a simple one-dimensional linear equation of advection and the second one is the Lorenz system. The mean errors and the execution time of these assimilation methods are compared for different model sizes. The numerical results are consistent with the theoretical estimates. It is shown that the computational complexity of local and ensemble Kalman filters grows linearly with the size of the model, whereas in the classical Kalman Filter this complexity increases according to the cubic law. The efficiency of parallel implementation of the local Kalman filter is considered.

Application of the Ensemble Kalman Filter to a One-Dimensional Linear Advection Model

2015 ◽  
Vol 804 ◽  
pp. 287-290
Author(s):  
Somsiri Payakkarak ◽  
Dusadee Sukawat
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Weather Prediction ◽  
Atmospheric Model ◽  
Ensemble Member ◽  
Observation Data ◽  
State Estimate ◽  
One Dimensional ◽  
Weather Forecasts

Data assimilation is used in numerical weather prediction to improve weather forecasts by incorporating observation data into the model forecast. The Ensemble Kalman Filter (EnKF) is a method of data assimilation which updates an ensemble of states to provide a state estimate and associated error at each step. The atmospheric model that is used in this research is a one-dimensional linear advection model. This model describes the motion of a scalar field as it is advected by a known speed field. The result shows that by selecting appropriate initial ensemble, model noise and measurement perturbations, it is possible to achieve a significant improvement in the EnKF results. The accuracy of the EnKF increases when the number of ensemble member grows. That is, the larger ensemble sizes perform better than those of smaller sizes.

scholarly journals Parameter and State Estimation of One-Dimensional Infiltration Processes: A Simultaneous Approach

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 134 ◽  
Author(s):  
Song Bo ◽  
Soumya R. Sahoo ◽  
Xunyuan Yin ◽  
Jinfeng Liu ◽  
Sirish L. Shah
Keyword(s):  
Kalman Filter ◽  
Vadose Zone ◽  
Ensemble Kalman Filter ◽  
Water Movement ◽  
Richards Equation ◽  
Residual Soil ◽  
Simultaneous Approach ◽  
One Dimensional ◽  
Gravitational Forces ◽  
Infiltration Processes

The Richards equation plays an important role in the study of agro-hydrological systems. It models the water movement in soil in the vadose zone, which is driven by capillary and gravitational forces. Its states (capillary potential) and parameters (hydraulic conductivity, saturated and residual soil moistures and van Genuchten-Mualem parameters) are essential for the accuracy of mathematical modeling, yet difficult to obtain experimentally. In this work, an estimation approach is developed to estimate the parameters and states of Richards equation simultaneously. In the proposed approach, parameter identifiability and sensitivity analysis are used to determine the most important parameters for estimation purpose. Three common estimation schemes (extended Kalman filter, ensemble Kalman filter and moving horizon estimation) are investigated. The estimation performance is compared and analyzed based on extensive simulations.

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