ANSWERS TO "TEST YOUR KNOWLEDGE" ON PAGE 40
4. The answer is choice “b” or “false.” “Dendritic” patterns are typical of flat or gently sloping areas. “Trellis” patterns are characteristic of “ridge and valley” topography.
5. The answer is choice “a” or “The linear relationships between S1 vs. depth and S2 vs. depth are dissimilar with coefficients of cor- relation of considerably different magnitudes.”
From the original table of values presented in our question (Table 1), linear regression analyses were performed relating S1 vs. depth and S2 vs. depth. Results are summarized in Table 2 and graph shown below:
Table 2. Linear regression analyses of strength vs. depth contrasting the effects of pressure only and the effects of pressure plus temperature.
Linear regression analysis
Strength S1 in kb (y) vs. depth D in km (x)
Linear regression analysis
Strength S2 in kb (y) vs. depth D in km (x)
Key Parameter Equation
Coefficient of determination R2 Coefficient of correlation R
Standard error of estimate SEE Key Parameter Equation
Coefficient of determination R2 Coefficient of correlation R
Standard error of estimate SEE Strength in kilobars vs. Depth in kilometers Value
y = 0.479 * x + 9.7809 0.9492 0.974
3.9048 Value
y = 0.0095 * x + 8.0238 0.0148 0.122
2.7334
To reiterate, from the values summarized in Table 2, it is evident that choice “a” as presented in our question is correct, as the coef-
ficients of correlation calculated in the linear regression analyses of S1 vs. depth and S2 vs. depth vary significantly. (As a point of interest, it should be noted that the SEE values are much closer. This is a different issue not addressed at this point).
Choice “b” is incorrect, as it represents a parabola that is concave upward with its vertex (h, k) at (2, 5). A function of this type does not fit our data. Choice “c” is also erroneous. The brittle to ductile transition should occur at depths of about ±20 km. From
the data provided in table 1, the strength S2 decreases below 30 km where rock deformation is no longer within the zone of brittle behavior. Choice “d” is not correct either, as S2 values show a relatively narrow range between 9.55 and 10.60 kilobars.
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Jul.Aug.Sep 2024 • TPG 47
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