Solution of the Deconvolution Problem in the General Statement / Vasin V. V.,Skorik G. G. // PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. - 2017. - V. 297, l. 1. - P. S211-S222.

ISSN/EISSN:

0081-5438 / 1531-8605

Type:

Article

Abstract:

The deconvolution problem, which arises in the description of well testing processes, is formulated in the form of a Volterra equation of the first kind with discontinuous input data (the kernel is the flow rate and the right-hand side is the pressure change) characterized by large measurement errors. In addition, the solution of this equation has multiscale behavior in its domain. In this situation, the traditional solution algorithms for Volterra equations, as a rule, do not provide satisfactory results. To solve the problem, we use the variational regularization methods and construct a function basis (a system of exponents), which allows us to take into account in the algorithm all a priori constraints known for the desired solution. As a result, we form a family of approximate solutions that satisfies the conditions of smoothness and exactness required for the interpretation of well tests. For the constructed regularizing algorithms, we formulate convergence theorems and describe the details of numerical implementation.

Author keywords:

deconvolution problem; well test; Tikhonov regularization; method of quasisolutions; system of exponents; a priori constraints

DOI:

10.1134/S0081543817050236

Web of Science ID:

ISI:000410252500023

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	JUL
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1531-8605
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	vasin@imm.uran.ru skorik@imm.uran.ru
Funding-Acknowledgement	Russian Foundation for Basic Research {[}15-01-00629]
Funding-Text	This work was supported by the Russian Foundation for Basic Research (project no. 15-01-00629).
Number-of-Cited-References	18
Journal-ISO	Proc. Steklov Inst. Math.
Doc-Delivery-Number	FG4RG