𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Power law or power flaw?

✍ Scribed by Frank Pattyn; Wim Van Huele


Book ID
101219388
Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
168 KB
Volume
23
Category
Article
ISSN
0360-1269

No coin nor oath required. For personal study only.

✦ Synopsis


Since its introduction by Svensson in 1959, the power law curve y = ax b (where x and y are horizontal and vertical direction, respectively) has been widely used in morphological analysis of glacial trough cross-profiles. The numerical constants a and b are obtained by a linear regression analysis of the logarithmic form of the power law curve (ln y = ln a + b ln x). The value b then gives a measure for the form of the cross-section. However, over the years this form of the power law has endured a lot of criticism. This criticism is well founded, since this particular form of the power law is not suitable for curve fitting in morphological analyses. In this paper a general power law is proposed, of the form yy 0 = aο£Ίxx 0 ο£Ί b (where x 0 , y 0 are the coordinates of the origin of the cross-profile). A unique and unbiased solution for this equation is obtained with a general least-squares method, thereby minimizing the error between the cross-profile data and the curve, and not between the logarithmic transform of the data and its regression line. This provides a robust way to characterize trough cross-section forms.


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