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Earth and Space Sciences · 术语表

什么是 Mean orientation (vector mean)？

又称： mean orientation

Definition 6.4 University Earth and Space Sciences — Year 1 · 第 6 章 — Field and Lab Methods I

For a plane of dip direction $\alpha$ and dip $\delta$ , let

\vec n = (\sin\delta\sin\alpha,\ \sin\delta\cos\alpha,\ \cos\delta)

be its upward unit normal in east, north and up components. The mean orientation (or vector mean) of $N$ readings of normals $\vec n_1, \dots, \vec n_N$ is the plane whose normal is $\vec m = \vec S/\|\vec S\|$ , where $\vec S = \sum_i \vec n_i$ is their resultant; $\bar R = \|\vec S\|/N$ is the mean resultant length. The mean dip direction and dip are $\bar\alpha = \operatorname{atan2}(S_E, S_N)$ and $\bar\delta = \arccos(S_U/\|\vec S\|)$ .

Twenty-five simulated readings of the bedding of the Varden east limb, whose model attitude is 080.7/12.2, each with errors of 3 standard deviation on both angles, rounded to the degree. Solid line: the mean; dashed: one standard deviation either side (080.8 ± 2.9 and 12.4 ± 2.1). The vector mean of the 25 readings is 080.9/12.3. — Twenty-five simulated readings of the bedding of the Varden east limb, whose model attitude is $080.7/12.2$ , each with errors of $3{}^{\circ}$ standard deviation on both angles, rounded to the degree. Solid line: the mean; dashed: one standard deviation either side ( $080.8 \pm 2.9$ and $12.4 \pm 2.1$ ). The vector mean of the 25 readings is $080.9/12.3$ .

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