构造地质学双语 2 stereographic

上课时候请带直尺，铅笔，透明纸（能看到下面字迹的就可以）

chapter 2 Stereographic Projection

Stereographic Projection（赤平投影）is a method of representing and interpret ing orientational data (such as the dips of bedding planes or joints). There are two parts to the concept.

Firstly consider the idea that any direction can be represented as a point on a hemisphere. We will concentrate on 'lower hemisphere projection' which means that we will consider our hemisphere to be convex down like a grapefruit half in a bowl. If you wish to represent the direction of a mine drift (tunnel) that dips down at an angle of 25 degrees towards the east then imagine the tunnel passing through the centre of an enormous grapefruit half. It will pass out through the skin on the east side of the fruit. If we draw the grapefruit (skin) half from above then this point will represent the direction of the direction of the drift. The skin will be a circle and the point will lie between its easterly margin and the centre. If you wish to represent a plane rather than a line then you must consider this passing though the grapefruit centre. The result will be a line on the grapefruit resembling a line of longitude on map of the world. It is indeed referred to as a Great Circle

Hint: 1. The stereographic projection, in geometry, is a particular mapping

it preserves neither distances nor the areas of figures.

Stereographic projection is a method used in crystallography and structural geology to depict the angular relationships between crystal faces and geologic structures, respectively. Here we discuss the method used in crystallography, but it is similar to the method used in structural geology

Angular relationships between points can only be measured on Great Circles.

The second problem is how to transfer lines (conceptually) drawn on a hemisphere or grapefruit onto a flat page or computer screen. There are two methods. Equal Angle projection ensures that, measured along great circles, the size of an angle is proportional to its separation on the plot. Equal area projection ensures that if two regions have the same area plotted on the hemisphere then they will be the same size on the plot.

I.Stereographic Projections

a) Two types

1. Equal-area (Schmidt)（施米特网）

2. Equal-angle (Wulff)（吴氏网）

b) Equal-angle stereonets are used in crystallography（结晶学）because the plotted angular relationships are preserved, and can be measured directly from the stereonet plot.

c) Equal-area stereonets are used in structural geology because they present no statistical bias when large numbers of data are plotted. On the equal-area net area is preserved so, for example, each 2° polygon on the net has the same area.

d) In structural geology the stereonet is assumed to be a lower-hemisphere projection（下半球投影）since all structural elements are defined to be inclined below the horizontal.

II. Elements of the Stereonet

a) The outer perimeter of the stereonet is termed the primitive（基圆）. The primitive is always a perfect circle. Usually the diameter of the primitive is some convenient length, such as 10 cm.

b) The north pole of the stereonet is the upper point where all lines of longitude converge. The south pole is the equivalent lower convergence point.

c) Lines that run from the north to south pole of the stereonet are termed great circles（大圆）and are analogous to lines of longitude on a globe. The lines of longitude can be visualized as forming from planes that strike due north and intersect the lower hemisphere at 2°increment s. The bolder lines are 10°increments. It is possible to measure the true dip of a plane only along the east-west line. There is one great circle that is a straight line- it runs directly from the north to south polar position.

d) Circular arcs that run east-west are termed small circles（小圆）. Small circles