A minimal number of line sets may be selected initially to cover a 

 profile using the following method. Identify the line set for the surface data 

 point. A, in the profile set (A, B, C, . .). Suppose that the last point in 

 this line set is the point N. Then identify the line set for point N, and so 

 on downward, until the profile data set is exhausted. 



Line sets may be said to "overlap" if they contain the same point. 

 They may be called "neighbors" if they contain neighboring points. Line 

 sets that overlap are neighbors, but not all neighboring line sets overlap. 

 The line sets selected to cover a profile by the method described here overlap. 

 TTiat is, for example, the line set defined for point A contains the point, N, 

 as does the line set defined for point N. A line set may have several neighbors, 

 including one that does not overlap. It would be advantageous to represent a 

 profile with neighboring line sets that do not overlap, but this is not always 

 possible. Accordingly, it is required to examine various combinations of line 

 sets for the sake of selecting neighboring sets to represent a profile with minimum 

 overlap . 



It is important to distinguish between a line set and the line of regression 

 on the set. The line set, a collection of discrete data points, conveys no infor- 

 mation at all about the depth intervals between points. The line of regression 

 is a continuous function without natural limits that articulates implicit assump- 

 tions about the intervals between the data points. It must be restricted exclusively 

 to depth intervals containing the line set upon which it regresses. It is therefore 

 convenient to consider a regression line as a line segment which extends to but 

 not across depths of points neighboring the line set (Figure 6(a)). So considered, 

 it is meaningful to refer to "neighboring" regression lines. It may be noted that 

 regression lines on neighboring line sets overlap the depth interval between the 

 two sets whether or not the line sets overlap. Hence, it is meaningful to refer 

 to this depth interval as the "range of overlap" between neighboring regression 

 lines. 



Suppose that neighboring line sets respectively contain points (A, B, C) 

 and (D, E, F). The range of overlap between regression lines on those two sets 

 is the depth interval between points C and D. The right limit of the range of 

 overlap may be identified as the depth of the point which neighbors the left- 

 set on the right, and the left limit may be identified as the depth of the point 

 which neighbors the right set on the left. When there is overlap between 

 neighboring sets the range of overlap will contain one or more data points. 

 Thus point E would be the right limit and point B the left limit of the range of 

 overlap between regression lines on sets (A, B, C, D) and (C, D, E, F), and 

 the range would contain points C and D. 



