of curvelinear functions to points in a plane. The advantage of alternative 

 functions would be that they could be used to estimate second and perhaps 

 higher derivatives of profile distribution as well as profile gradients. 



It may be pointed out that the straight line is the least expensive 

 function that can be fit to a set of points in a profile, in terms of the computer 

 time required to identify a union of regression curves on a profile data set and 

 perhaps in terms of the computer memory required to record the union as well . 

 A profile may be represented economically with N + 1 regression points for a 

 union of N regression lines, whereas more complicated methods would have to 

 be used to represent a union of N higher order regression curves. Moreover, a 

 solution has not been specified here to the problem of representing the union of 

 neighboring curve sets that do not intersect in the range of overlap, or which 

 intersect there more than once (Figure 10). 



The straight line probably constitutes a function of sufficient resolution 

 to represent standard scale mechanical BT profiles. It is doubtful that higher 

 order functions can be used advantageously to gain either precision or economy 

 of BT data representation. This is not to say that the straight line is the most 

 appropriate function for representing other kinds of profile data sets, however. 



E. Other Kinds of Profile Data Sets 



When applying this algorithm to the reduction of a profile data set it 

 is necessary to select a coordinate system that will appropriately relate measures 

 of profile interval to measures of profile amplitude. The choice of the bathy- 

 thermograph slide scale seems to be an obvious one in the case of the standard 

 mechanical BT. In general, the selection must be rendered on the basis of less 

 obvious criterion. 



As is the case for the mechanical BT, gradient features of a profile, 

 rather than individual trace values, may be worth preserving. In order to 

 record these features with reasonable fidelity it may be necessary to record 

 individual trace values to tolerances that would seem unrealistic considering 

 instrument inaccuracy. Evidently, when one sensor is used to measure a 

 profile, instrument error over the profile range may be regarded as systematic. 

 That is, the sensor tends to stay inaccurate by the same amount over short time 

 intervals during the measurement of the profile. These inaccuracies may 

 accumulate over an extended time period or with changing circumstances, as 

 is evidenced by the hysteresis in a typical BT profile trace. 



Accordingly, it may be suggested that the coordinate scale be designed 

 to reflect the sensitiyity, rather than the absolute accuracy, of the profile 



19 



