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有直观、容易理解的方式帮助学生理解outcropted地层学的三角面吗?

我发现很难教大学生使用遥感图像的三角面判断沉积地层的倾斜方向。有直观的方式,可以帮助吗?

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这是一个故事的两个三维坐标系统。你可能需要一个侧线如果你的学生不熟悉的概念三维坐标系统,三维向量,三维点和交叉的产品,和坐标系统之间的转换。下图描绘了两个这样的坐标系统,用斧子在蓝色和红色,[!(两套三维正交轴)[1]][1]我表示其中一个坐标系统的东部,北,坐标系统(简称ENU表示),与单位向量\帽子E(东),美元\帽子N(北),美元和美元\帽子U $(),和其他倾斜,罢工和外法线坐标系(dsn),与单位向量\帽子d (dip)美元,美元\帽子新元(罢工),和帽子\ N美元((向外)正常)。上面的图,想象蓝色向量对应的三东,北,而红色的三个向量相应下降,罢工,(向外)正常。作为一个老师,你很可能希望创建一个更好的图,与标签。存在奇点问题与这两组坐标系统。东/北/没有意义在地球的两极,水平方向都是南在北极和南极北端。浸渍/攻击/正常没有意义无论表面是平的。我将忽略这些问题。 (Bonus question for your students: Address those singularities.) One way to define local ENU coordinate system for a point on the surface of the Earth is to use the Earth's reference ellipsoid. The "up" unit vector is normal to the ellipsoid, with "up" pointing outward. The east unit vector is orthogonal to the $\hat U$ unit vector and the Earth's rotation axis. Use the cross product and divide by the norm. The north unit vector is the cross product of the up and east unit vectors. Regarding the dip/strike/normal coordinate system, one direction, the outward normal, can be determined from the coordinates of the three points in a triangle in a vector-based triangular network digital elevation model. The coordinates of the three points in a triangle ($\vec A$, $\vec B$, $\vec C$) are supposed to be arranged such that $(\vec B - \vec A)\times (\vec C - \vec B)$ points outward. This points in the direction of $\hat n$: $\hat n = \frac{(\vec B - \vec A)\times (\vec C - \vec B)}{||(\vec B - \vec A)\times (\vec C - \vec B)||}$. Aside: This is not always the case; there are DEMs that do not follow this rule. Those are DEMs one should toss in the nearest digital trashcan.)There are also some DEMs that do follow this rule but occasionally have triangles whose outward normal has a downward rather than upward component. An example is an extremely detailed DEM that models not only the topside but also the underside of an overhang. Satellite-based DEMS typically don't do this as satellites cannot see the underside of an overhang. (Extra credit: Have your students address such cases!) We're looking for $\hat s$ and $\hat d$, the unit vectors that point in the strike and dip direction. Both of these vectors lie in the plane of the triangle formed by $\vec A$, $\vec B$, and $\vec C$. This means that both $\hat s$ and $\hat d$ are normal to the outward normal $\hat o$. The strike vector is horizontal, which means that it is also normal to the unit upward normal. To find $\hat s$, compute the cross product of $\hat U$ and $\hat n$ and normalize. (Note: Normalization is impossible if $\hat U \times \hat n \equiv 0$. This only happens if $\hat n$ is parallel or antiparallel to $\hat U$, in which case strike and dip are not well-defined.) Finally, the dip unit vector, which is what we're after, is the cross product of the strike and outward normal unit vectors: $\hat d = \vec s \times \vec n$. Bonus: Ask your students to show that if $\hat d$ exists, it always has a downward component. [1]: https://i.stack.imgur.com/wBsBC.png

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