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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 8540303, 14 pages
http://dx.doi.org/10.1155/2016/8540303
Research Article

Two-Dimensional Far Field Source Locating Method with Nonprior Velocity

1IOT Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221008, China
2School of Mathematics & Physics Science, Xuzhou Institute of Technology, Xuzhou 221008, China
3School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221008, China
4School of Mechanical Engineering, Nanjing University of Science & Technology, Nanjing 221000, China

Received 22 December 2015; Accepted 30 March 2016

Academic Editor: Anna Vila

Copyright © 2016 Qing Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Relative position of seismic source and sensors has great influence on locating accuracy, particularly in far field conditions, and the accuracy will decrease seriously due to limited calculation precision and prior velocity error. In order to improve the locating accuracy of far field sources by isometric placed sensors in a straight line, a new locating method with nonprior velocity is proposed. After exhaustive research, this paper states that the hyperbola which is used for locating will be very close to its asymptote when seismic source locates in far field of sensors; therefore, the locating problem with prior velocity is equivalent to solving linear equations and the problem with nonprior velocity is equivalent to a nonlinear optimization problem with respect to the unknown velocity. And then, this paper proposed a new locating method based on a one-variable objective function with respect to the unknown velocity. Numerical experiments show that the proposed method has faster convergence speed, higher accuracy, and better stability.