Abstract
A review is presented of methods for estimating the dispersion law of a plane wave which is observed over time at a set of recorders located in an irregularly spaced array. The wave is represented by a signal, which may be either deterministic or random, plus noise which is represented by a stationary random process. The combination of several sets of observations for the one array and the estimation procedure when more than one signal is present are also discussed. A procedure which may give improved estimates for transient signals is introduced. An application of this procedure to some data and the results of some simulations are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bloomfield, P., 1976, Fourier analysis of time series: John Wiley, New York, 258 p.
Capon, J., 1969, High resolution frequency—wave number spectrum analysis: Proc. IEEE, v. 57, no. 8, p. 1408–1418.
Cox, D. R., and Hinkley, D. V., 1974, Theoretical statistics: Chapman and Hall, London, 511 p.
Goncz, J. H., and Hannan, E. J., 1975, New methods of estimating dispersion from stacks of surface waves: Bull. Seismological Soc. Amer., v. 65, no. 6, p. 1519–1529.
Groves, G. W., and Hannan, E. J., 1968, Time series regression of sea level on weather: Rev. Geophysics, v. 6, no. 2, p. 129–174.
Hamon, B. V., and Hannan, E. J., 1974, Spectral estimation of time delay for dispersive and non-dispersive systems: J. Roy. Statist. Soc. Ser. C, v. 23, no. 2, p. 134–142.
Hannan, E. J., 1970, Multiple time series: John Wiley, New York, 536 p.
Hannan, E. J., 1975, Measuring the velocity of a signal:in Perspectives in probability and statistics, Academic Press, New York, p. 227–237.
Marcus, M., and Minc, H., 1964, A survey of matrix theory and matrix inequalities: Allyn and Bacon, Boston, 180 p.
Moran, P. A. P., 1971, Estimating structural and functional relationships: J. Multiv. Analysis, v. 1, no. 2, p. 232–255.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cameron, M.A., Hannan, E.J. Measuring the properties of plane waves. Mathematical Geology 10, 1–22 (1978). https://doi.org/10.1007/BF01033296
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01033296