Energy evaluation of wide-band SOFAR transmission

Abstract

Transmitted energy levels for wide-band $OFAR transmission are calculated for arbitrary sound-speed profries using ray-mode analysis [R. P. Porter, J. A½oust. Soc. Am. 54, 1081-1091 (1973)]. The analysis of the received field has been generalized to include arbitrary normal modes and range-varying, soundspeed profiles. It is shown that computations of wide-band propagation based on ray-mode analysis require an order of magnitude fewer calculations than do calculations by harmonic analysis. A computer code has been developed and used to estimate the wide-band loss for profiles from the Mediterranean and the North Atlantic. Comparisons with continuous tone, normal-mode calculations yield agreement to within 3 dB. Subject Classification: 30.20, 30.25' 20.20, 20.40. LIST OF SYMBOLS c(z), Co kO q R•, R} t To sound speed at depth z and at source depth z0 frequency dependence of source ray cycle length in the horizontal plane = w/c(z), wavenumber where c(z) is the sound speed wavenumber at depth z0 mode number, number of modes eigenray order = k(z)/ko, index of refraction referred to source depth slope for N •' -linear sound-speed profile cylindrical coordinates reflection coefficients looking up and down time arrival time of energy traveling at axial sound speed Co U W Zu, Zt Y o 7' r group velocity bandwidth of transmitted pulse upper and lower turning points at which • = k(z) scale height of phase integral vertical propagation constant phase integral of vertical propagation constant normalization factor horizontal propagation constant dispersive delay referred to T o = (t-To)/T o , relative dispersive delay pressure field ray exit angle from the source z-dependent eigenfunction for mode m pressure field spectrum circular frequency

Rays, Modes and Flux

“…Perhaps we may have the best of both worlds by building on the section 3.8 association of group velocity with a specific ray path. In another method we also have the best of both worlds through the simultaneous display of ray and mode effects (23,24). The flux approach is inapplicable here.…”

Guided acoustic waves in the ocean

“…Unfortunately this is a region of turning points for rays where their behaviour may not be entirely satisfactory, and one can overcome this by the technique (Leibiger and Lee, discussed by Jensen and Krol (1975)) of replacing each ray by a ray-modetype integral over a group of modes, though one immediately loses some of the point of economy in computation. Porter (1973b) and Porter and Leslie (1975) use a ray-mode analogy in which they can, at the same time, see the time dispersion associated with the ray arrivals and the frequency dispersion associated with the modes. No choice is needed in this approach!…”

The effect of internal waves on long range acoustic propagation in the ocean

“…It was apparent that the relationship between the induced refractive index is satisfied (Porter and Leslie, 1975). 'When this expression is not satisfie4 '…”