316 



SHALLOW-WATER REVERBERATION 



ments made with the two different transducer orien- 

 tations in the same or similar areas, it should be pos- 

 sible to obtain some information about the angular 

 dependence of m". The following paragraphs describe 

 briefly the analysis of these data made in reference 2; 

 it is convenient to begin by considering the 0-degree 

 data. 



For the purpose of analyzing the 0-degree data, the 

 reverberation records obtained were segregated into 

 nineteen groups, each group comprising at least nine 

 records of bottom reverberation taken at nearly the 

 same time on a single day over one of six bottom 

 areas. The records were then measured and averaged 

 over the group to give the mean reverberation ampli- 

 tude, and the average reverberation level was plotted 

 against range for each group. Typical curves ob- 

 tained are shown in Figure 7. These curves extend 

 only to the range at which the reverberation becomes 

 comparable to the recording background. On each 

 curve in Figure 7 is shown the range at which the 

 6-degree ray struck the bottom, as computed from 

 the measured BT pattern. The high levels of the first 

 plotted points at 100-yd range in the curves of 

 Figure 7 are due to surface reverberation. 



These reverberation curves for horizontal trans- 

 ducers were then compared with equation (54) of 

 Chapter 12, by using 4 db per kyd for the absorption ; 

 in addition, the anomaly due to refraction was com- 

 puted from the ray diagram drawn from the BT 

 pattern, according to the methods described in Chap- 

 ter 3. The total correction for the anomaly was 

 found to be small for ranges corresponding to the re- 

 verberation peak. The average magnitude of twice the 

 anomaly correction for those ranges was only 2.5 db; 

 but the uncertainty in the transmission anomaly led 

 to uncertain values of m" corresponding to the 

 reverberation at longer ranges. Nevertheless, by us- 

 ing the data and comparing with equation (54) of 

 Chapter 12, it was possible in this way to obtain for 

 each group of records a curve for m", the bottom 

 scattering coefficient, as a function of the range of 

 the reverberation. At each range the incident grazing 

 angle of the ray reaching the bottom was computed 

 from the refraction diagram. However, from these 

 curves of m" against range, as explained in more de- 

 tail later, the value of m" was accurately determi- 

 nable only for grazing angles on the bottom very 

 nearly equal to the grazing angle of the central ray 

 of the main beam. This angle, for all the horizontal 

 projector curves studied in reference 2, lay between 

 9 and 13 degrees. It is clear therefore that determina- 



tion of the angular dependence of m" was not possible 

 from the 0-degree data alone. 



By using the 30-degree data, however, the value of 

 in" when the grazing angle on the bottom is equal to 

 30 degrees may readily be determined. With this 

 transducer orientation, the rays in the main beam are 

 only slightly bent by the temperature gradients. Thus 

 they strike the bottom at angles that can be cal- 

 culated directly from the geometry. Furthermore, 

 since the rays are only slightly bent, the transmission 

 anomaly due to refraction can be ignored. By using 

 equation (54) of Chapter 12, then, and by assuming 

 A equal to 4 db per kyd, the values of yn" at a grazing 

 angle of 30 degrees were determined from comparison 

 with the observed data. This comparison was made 

 on the assumption that the maximum amplitude of 

 bottom reverberation on the 30-degree records cor- 

 responded to scattered sound returning along the 

 central ray of the main beam; this assumption is 

 justified from the qualitative discussion in Section 

 15.1. 



The average scattering coefficients determined 

 from these analyses of the data in reference 2 are 

 shown in Table 2. The 10 log m" values in Table 2 



Table 2. Average values of m" for various bottom areas. 



are of course averages of the values obtained from 

 the nineteen groups into which the original data were 

 subdivided. That is, each group gave a value of 

 10 log m" for a definite bottom type, and the entries 

 in Table 2 are each averages over all the groups per- 

 taining to one particular bottom type. 



In interpreting these average scattering coefficients, 

 it should be remembered that the 0-degree data were 

 obtained with a horizontal transducer near the sur- 

 face so that an important part of the received bottom 

 reverberation reached the transducer along paths re- 

 flected from the ocean surface. As a result, the values 

 of 10 log m" inferred from comparison of the 0-de- 

 gree data with equation (54) of Chapter 12 are 6 db 

 greater than the true value of the bottom scattering 



