TABLE IV. The measured rms values of 

 travel time and intensity. 



Frequency (nominal) 4 kHz 8 kHz 



Travel time 

 Intensity 



0.384 0.374 msec 

 5.2 5.7 dB 



satisfactory for the off-axis rays but for near-axis rays 

 the theory seems to overestimate the size of the fluctua- 

 tions; in particular, the ±1° rays are predicted to have 

 fluctuations that are larger by a factor of two to three 

 than the "experiment" shows. This discrepancy is pos- 

 sibly related to the fact that we use the linear approxi- 

 mation to the dispersion [Eq. (92)], or that the WKB ap- 

 proximation underlying the theory does not allow the re- 

 duction in vertical displacement near the boundaries, 

 or to the two-dimensional character of the "experi- 

 ment, " or, finally, to the failure of the expansion in 

 power of acoustic wavelength over the vertical correla- 

 tion length of the fluctuations at this wavelength. 



IX. SINGLEPATH EXPERIMENT ON COBB 

 SEAMOUNT 



Ewart'' has measured amplitude and phase (transit 

 time) fluctuations between a fixed transmitter and re- 

 ceiver on Cobb Seamount (46°46' N, 130°47' W). The 

 sound axis is shallow, 400 m, as is characteristic of 

 high latitude. Setting I = - 0. 4 km in Eq. (84), we con- 

 struct a ray path through source and receiver (both at 

 1000 m depth) separated by 17.2 km, with a lower turn- 

 ing point at a depth of 1350 m, in agreement with ray 

 tracing based on locally measured sound profiles (Fig. 

 4, Ewart). Further, the measured niz) is very close 

 to our experimental model [Eq. (82)]. Ewart obtained 

 144. 5 h or records (with minor gaps) based on 8-cycle 

 pulses at 4166 Hz and 16-cycle pulses at 8333 Hz trans- 

 mitted alternately every 15. 7 sec. The measured rms 

 variations are given in Table IV. 



Ewart remarks on the strong tidal contribution to the 

 travel time spectra, and on the important effect on in- 

 tensity by sporadic multipaths associated with sound 

 velocity fine structure. We note that the results are 

 similar ^t the two frequencies (as expected); the rms 

 phase at 4 kHz is 3.84x10"* secx4166 Hz = 1.60 cycles. 



The maximum value of is 10"' (7 km from turning 

 point), so geometric optics applies, and according to 

 Eq. (118) 



{4,') = {{5C/Cfo){j-')q^BRF,{Q)=25l.'7rad^ 



for rms (6C/C)o = 4. 9x10"*, <;"'> = 0. 435, 9 = 1.745 

 xlO* radkm'Mfor 4166 Hz), B = lkm, i? = 20. 8 km, «„ 

 = 5.2x10"' sec"', u,„ = 1.06x10"* sec"' (46.75° latitude), 

 and Fi(0)=0. 38 (from a numerical integration). Thus 

 rms 1^=2.53 cycles, compared to 1.60 measured. 



Similarly the intensities are found from Eq. (120), 

 using A][ - x{R - x)/R which is appropriate for a single 

 lower loop. The result is <t^>- <l)^ = 0. 245, or 



(10/logl0)(0. 245)"^ = 2. 15 dB, 



as compared to the observed rms value of 5. 5 dB. (A 

 more accurate form for A'^, will increase the calculated 

 value slightly. ) Observations and computation of both 

 phase and intensity are roughly within a factor of 2 and 

 can be brought into better accord by increasing the 

 model parameter j^ (Table V). 



A more sensitive test consists of comparing com- 

 puted'^ and observed spectra (Fig. 7). The computed 

 phase spectrum is high, as expected from the rms val- 

 ues, but in the principal band between inertial and 

 buoyancy frequencies the computed u"' slope is reason- 

 ably consistent with the observed spectral slope. The 

 observed phase spectrum continues smoothly beyond the 

 computed n cutoff. Computed intensities completely 

 fail to account for the observed high frequencies, 

 Dashen (private communication) has demonstrated that 

 the high-frequency phases and intensities are due to in- 

 terference between "sporadic multipaths." (Ewart has 

 remarked on the occasional arrival of multiple pulses. ) 

 A discussion goes beyond the scope of this paper. " 



X. MULTIPATH EXPERIMENT MIMI 



The most persistent measurements of ocean propaga- 

 tion are the 406-Hz transmission of MIMl'* between 

 Eleuthera (Bahamas) and Bermuda. The measured <t)[t) 

 and c(/) are completely dominated by the effects of mul- 

 tipath interference, and are not simply related to the 

 <ti,(t) and (.,(/) along any singlepath ; with which our pa- 

 per is concerned. However, it is possible to use the 

 measured multipath spectra to infer rms 0, for a typi- 

 cal singlepath. '^ Results are given in Table VI. 



For a "back-of-the- envelope" comparison (after two 

 years) with our results we use the axial approximation 

 (105) in Eq. (102): 



< <^? ) = < (bC/C)l) <j"' > q^BR^i,noF2 



= 87T"2<(aC/C)|,„)0"'>9^Sfla.,.nolog"/'^in- 



(123) 

 Using 9 = 1701 rad km"' for 406 Hz, rms(6C/C)o = 4. 9 

 xlO"*, <;•"') = 0.435, B = lkm, a),„ = 7. 3x10"' sec"', «„ 

 = 5.2x10"' sec"', K = 1.9x10"' sec"' and Eq. (89), this 

 simple expression leads to excellent agreement with the 

 measurements (Table VI). For the surface limited ray 

 we use the apex approximation (106) with h =«o ^nd a 

 radius of curvature (R = 13.7 km [Eq, (85)] to obtain 



<<^2> = 8,r"2 (f 77)"= <(6C/C)^o><r' Vb"'<R'" 



per double loop, leading to somewhat larger values. 



Table VII summarizes a more precise calculation, 

 allowing for the proper "ray mix." From Eqs. (102) 

 and (103) 



229 



