STRUCTURE GEOMETRY Lecture #12

Introduction• Geometrically geological structure element can be

assumed as planes and lines. • Plane or line is not always as boundary plane from rock’s

unit, but as an element that representing the rock or rock unit.

• Geometrically, plane or line is an element with attitude or definite orientation in space, and the relation between each other can be descript.

Bearing or azimuth, and inclination graphic coordinate.

• Plane structure (planar): bedding plane, foliation plane, fracture plane, fault plane, cleavage plane and etc.

Line structure (Linear): mineral lineation, fault, fold axes,

Coordinate Terms• Azimuth is general term for horizontal angle between line

with certain coordinate direction. The coordinate direction normally is the true north.

• Attitude: general orientation term for plane or line in space, and normally is related to the geographic coordinate and horizontal line. Attitude consist of direction component (bearing or azimuth) and dip/tendency (Inclination)

• Dip/tendency (Inclination) is the general term for vertical angle (measured from below) between the horizontal line with a plane or line.

Descriptive GeometryThree type of projection:Perspective projectionOrthographic projectionStereographic projection

Perspective Projection• Method of drawing an object on certain plane from certain

point of view. • The basic of this method is the view direction and the

chosen projection plane.• If seen the object from different distance and position, the

size and shape of the object is changing. • Helpful for structure geology phenomena identification in

field.

Orthographic Projection• Method of drawing an object, when each of the object

point is projected parallel one to another and perpendicular to the projection plane.

• The uses of this projection: To solve line length To solve area To solve angle between line and plane

All need scale

Stereographic Projection• An object (plane or line) being boundary by ball surface. • The cross section between the ball surface then being

projected on the equatorial plane which is divide the ball surface into two same size.

Plane

PlaneEquatoria

l

Point

Line

Lower Hemisphere

Big Circle

Resume• Generally, projection planes which is uses in descriptive

geometry is horizontal and vertical plane. • Horizontal plane known as map projection• Vertical plane known as cross sectional projection

• When the rotation done relatively to the fold line, the drawing of the plane projection from vertical to horizontal known as rotated projection.

• The line that connecting the point in the map projection to the equivalent point in the rotated projection known as connecting line.

• The connecting line has to be perpendicular with the cross fold line.

• Imagine a cube in the middle of a big box without base. • The cube can be projected to the top and 4 of the box

side. • The perpendicular between the top and each of the box

side is horizontal line and each edge of the box is the vertical line.

• Can been seen that when the box side being rotate to the horizontal fold line (all the box side on the horizontal plane).

• Two vertical projection plane which connected by the vertical fold line cannot be connected by the horizontal fold line.

• Therefore, the rotate projection from two plane cannot be connected by the connection line.

• Object from two rotated projection plane can be connected with the arc circle segment which known as connecting arc.

• The center point of the connecting arc located on the cross section of two perpendicular horizontal fold line.

Questions…