CORRECTIONS OF SONIC DEPTHS DETERMINED ON BOARD THE CARNEGIE 

 ON ACCOUNT OF ERRORS IN THE TIMING 



Depth was measured on board the Carnegie by three 

 different methods, namely, by thermometers which were 

 reversed at a short distance from the bottom, by wire 

 soundings, and by sonic methods. The accuracy of 

 soundings by thermometers or wire has been discussed 

 and it has been shown that the depth obtained by ther- 

 mometers can be regarded as reliable within +0.5 per 

 cent: the depths by wire soundings are reliable within 

 + 2.0 per cent. 



The accuracy of the depths determined by the sonic 

 depth finder would be considerably greater thn.n th^.t of 

 the other methods, supposing that no instrumental er - 

 rors were present. Whether or not such errors oc- 

 curred can be decided by examining the cases in which 

 the depth was determined by thermometers or wire 

 sounding close to a locality where the depth was meas- 

 ured by the sonic method. When making such an exami- 

 nation one must expect considerable variation in the 

 results obtained by the different methods. This is part- 

 ly because of the limited accuracy of the wire soundings, 

 and partly because the sonic depth was not determined 

 simultaneously with the other determination, for which 

 reason irregularities of the bottom may give rise to 

 discrepancies. The mean values obtained by the differ- 

 ent methods, however, ought to agree if no systematic 

 errors occur in the sonic depths. 



When comparing the results by the different meth- 

 ods, it is to be noted that the timing of the sonic depth 

 finder was readjusted February 19, 1929, and the com- 

 parison, therefore, must be made separately for the 

 periods before and after this date. Table 1 gives the 

 approximately simultaneous values of sonic depths and 

 depths determined either by thermometers or by wire. 

 The latter two are entered under the heading "true 

 depth." The depths by thermometers have been en- 

 tered, if available, because of the greater accuracy. 

 The sonic depths entered in the table are derived from 

 those sonic soundings which were made at the shortest 

 distances from the locations at which the depths were 

 determined by other methods. The last two columns of 

 the table give the ratios between the true depths and the 

 sonic depths, that is, the factor by which the sonic depth 

 must be multiplied to obtain the true depth. The factors 

 are arranged according to the character of the bottom. 

 The bottom was regarded as being fairly regular when 

 the difference between the two nearest sonic depths was 

 less than 100 meters and the resulting factors are en- 

 tered in the first of the last two columns. The bottom 

 was regarded as irregular when the difference between 

 the two nearest sonic depths exceeded 100 meters, and 

 the resulting factors are entered in the last column. 



It is seen that the sonic depths usually are greater 

 than the depths by thermometers or wire. The bottom 

 was extremely irregular or the wire depth was uncertain 

 in a few outstanding cases, as is evident from the foot- 

 notes to the table. Omitting the nine cases indicated by 

 these footnotes, fifty-nine approximately simultaneous 

 values of sonic depths and thermometer or wire depths 

 remain for comparison, twelve of which were obtained 

 before, and forty-seven after, the readjustment of the 

 timing February 19, 1929. The further discussion will 

 be based on these fifty-nine cases only. 



During the first period, using all twelve values, the 

 mean sonic depth is 2871 meters, the mean true depth is 

 2683 meters, and the timing factor is 0.935. Using only 

 the eight cases in which the depth was determined by 

 means of thermometers, the mean sonic depth is 2327 

 meters, the mean true depth is 2197 meters, and the 

 timing factor is 0.944. 



The available data are much greater for the second 

 period and a more detailed comparison between the 

 sonic depths and the depths obtained by other methods 

 can be made. The data of table 1 have been summarized 

 in table 2, which gives the ratios between true depth and 

 sonic depth for a number of different groups. The mean 

 ratios were derived both from the mean depths and by 

 forming the means of the single ratios. In the latter 

 case the probable error of the mean value has been in- 

 dicated. 



From table 2 it is evident that the mean value of the 

 ratio is practically independent of the grouping and also 

 that the mean ratio, which is computed from the single 

 ratios, agrees with the ratio of the mean depths. The 

 latter feature shows that the ratio is nearly independent 

 of depth. The mean errors in the last column show that 

 the scattering of the single values of the ratio is smaller 

 when the bottom is regular than when it is irregular, and 

 also that the scattering is smaller when the true depth 

 was determined by thermometers instead of by wire. 

 Both these features should be expected. The irregular 

 variations of the bottom and the greater error of the 

 wire depths give rise to greater discrepancies. 



From the preceding discussion it appears that the 

 depths which were determined by means of the sonic 

 depth finder during the period from February 19 to No- 

 vember 18, 1929 must be multiplied with a constant fac- 

 tor in order to give the true depth and the same evident- 

 ly applies to the first period from May 13, 1928 to Feb- 

 ruary 19, 1929. Considering that the most consistent 

 results were obtained by comparison with depths which 

 were determined by thermometers when the bottoff was 

 fairly regular, the following correction factors have 

 been adopted for the soundings taken with the sonic depth 

 finder: (1) May 13, 1928 to February 19, 1929, correc- 

 tion factor 0.944 and (2) February 19 to November 18, 

 1929, correction factor 0.964. The probable error of 

 the latter factor is not greater than +0.003, but the 

 probable error of the former is perhaps +0.009. 



The instrumental error which makes application of 

 these corrections to the sonic depths necessary must 

 arise from an error of timing of the system. An error 

 in the timing would lead to error in the sonic depth, 

 which would be approximately proportional to the depth 

 and therefore could be approximately eliminated by 

 multiplication of the computed sonic depth with a con- 

 stant factor. The fact that the correction factor was 

 evidently changed when the timing was readjusted also 

 indicates that the discrepancies arise from errors in 

 timing. An error in timing should strictly be eliminated 

 by correcting the time of echo before computing the 

 sonic depth, but it can be shown that only an insignificant 

 error is introduced by computing the sonic depth on the 

 basis of the observed time of echo and correcting this 

 computed depth by multiplication by a constant factor. 



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