Short-cuts on wave refraction computation

Abstract

SynopsisIt is shown how to get rid of iterative process to compute waveZengths and how the ceZerities and their derivatives can be computed in terms ofwaveZengths for any depth~ without using hyperboZic functions. -BackgroundIt is well known that the pressure wave records have a strong attenuation of the high frequency components of the wave train, and that such records can not b~ corrected in the time domain. In fact the Corrections would be feasible in the frequency domain, after the Fourier analysis of the pressure records, in terms of the frequency of the Fourier lines. Such corrections are usually computed iteratively because they are given in terrns of the wavelength which is the independent variable in the frequency equation. This problem was solved using polynomia~s and we can show that a similar solution can be found to compute celerities.According to the wave linear theory the celerity corresponding to a wave number k and a depth d is given by c = ~f tanh (kd).In addition for deep seas expression (la) can be changed into we obtain tanh (kd). The main problem ~s now to solve this equation for z. Since the series development of tanh z converges for