. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. ADJUSTMENT BY LEAST SQUARES 163 be accommodated to the particular degree of accuracy in adjustment which is considered worth while. Most practical geophysicists are agreed that an elaborate, ultra-precise least-square adjustment of their observations is an unwarranted expenditure of time and labour. On the other hand, some adjustment is obviously necessary. §3. THE NORMAL EQUATIONS In the terms used in treatises on the method of least squares3 we have given a series of "conditional" equati
. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. ADJUSTMENT BY LEAST SQUARES 163 be accommodated to the particular degree of accuracy in adjustment which is considered worth while. Most practical geophysicists are agreed that an elaborate, ultra-precise least-square adjustment of their observations is an unwarranted expenditure of time and labour. On the other hand, some adjustment is obviously necessary. §3. THE NORMAL EQUATIONS In the terms used in treatises on the method of least squares3 we have given a series of "conditional" equations (AB) = (ab), (BC) = (be), (CA) = (ea), -iS. Fig. 1 together with a series of "rigorous" equations (AB) + (BC) + (CA) = o, There is one conditional equation for every link in the network, and one rigorous equation for every independent polygon in the net- work. We shall assume that all the observations and link-increments such as (ab) have equal weight. For such a system of conditional and rigorous equations, the nor- mal equations for a least-square adjustment are obtained as follows. For each rigorous equation, provide an unknown multiplier or cor- relate m. The unknown increment (PQ), which occurs in one only of the conditional equations, namely (PQ) — (pq)=o, occurs also in at most two of the rigorous equations. For normally it will be a common section of the boundary of two adjacent polygons, , OPQR, SQPT, Figure 1, and at the extreme boundaries of the network one of these 1 E. T. Whittaker, and G. Robinson, The Calculus of Observations, chap. IX, and particularly §129, pp. 252-254 (1924). 823. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Society of Exploration Geophysicists. Tulsa
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