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Correction: Zhang, H.; Zhang, X. Generalized Tikhonov Method and Convergence Estimate for the Cauchy Problem of Modified Helmholtz Equation with Nonhomogeneous Dirichlet and Neumann Datum. Mathematics 2019, 7, 667
Open AccessArticle

A New Method for De-Noising of Well Test Pressure Data Base on Legendre Approximation

by Fengbo Zhang 1,†, Yuandan Zheng 2,†, Zhenyu Zhao 3,4,* and Zhi Li 2
1
Zhanjiang Branch of CNOOC Ltd., Zhanjiang 524000, China
2
Faculty of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China
3
School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China
4
Southern Marine Science and Engineering Guangdong Laboratory (Zhanjiang), Zhanjiang 524088, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2019, 7(10), 989; https://doi.org/10.3390/math7100989
Received: 14 September 2019 / Revised: 13 October 2019 / Accepted: 15 October 2019 / Published: 18 October 2019
(This article belongs to the Special Issue Numerical Analysis: Inverse Problems - Theory and Applications)
In this paper, noise removing of the well test data is considered. We use the Legendre expansion to approximate well test data and a truncated strategy has been employed to reduce noise. The parameter of the truncation will be chosen by a discrepancy principle and a corresponding convergence result has been obtained. The theoretical analysis shows that a well numerical approximation can be obtained by the new method. Moreover, we can directly obtain the stable numerical derivatives of the pressure data in this method. Finally, we give some numerical tests to show the effectiveness of the method. View Full-Text
Keywords: well test data; noise; filtering method; LEGENDRE approximation well test data; noise; filtering method; LEGENDRE approximation
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Zhang, F.; Zheng, Y.; Zhao, Z.; Li, Z. A New Method for De-Noising of Well Test Pressure Data Base on Legendre Approximation. Mathematics 2019, 7, 989.

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