Structural Geology Stereographic Projections 4/20/2017 Surfaces, or a pole perpendicular to the surface, are oriented by their intersection with the surface of a bowl

4/20/2017 The Stereonet Grid. The stereonet grid is used as a protractor, and in structural geology, it is used to plot attitudes of planes and lines.

Plotting Planes using the Stereonet Grid. 4/20/2017 Plotting Planes using the Stereonet Grid. The stereonet grid is a protractor which can measure strike and dip, and trend (bearing and and plunge) – the attitude of lines and planes. Since the equatorial plane is horizontal, its edge (called the primitive great circle) measures the strike or bearing. The great circles can measure dip or plunge.

Plotting Planes using the Stereonet Grid. 4/20/2017 Plotting Planes using the Stereonet Grid. Plotting is done on transparent paper laid over the stereonet that can be rotated around a thumb tack poking up at the center of the net. A tick mark coinciding with the 0 on the primitive circle is labeled N. E, S and W occur at 90, 180 and 270o respectively.

1: Plotting a Plane using the Stereonet 4/20/2017 1: Plotting a Plane using the Stereonet Suppose a sandstone layer has strike and dip N80W 40S Visualize the plane in space and the way it cuts the sphere.

Plotting a Plane using the Stereonet 4/20/2017 Plotting a Plane using the Stereonet The layer is N80W, 40S Place the overlay on the net and mark N, S, E, & W on the overlay. With the overlay positioned with N at 0o, Count 80o CCW to N80W and place a tick mark showing the position of the strike.

Plotting a Plane using the Stereonet 4/20/2017 Plotting a Plane using the Stereonet The layer is N80W, 40S Next, rotate the transparency so the strike is at 0. Now you can find the great circle with the same dip (40) as the layer by counting 40 from the primitive circle along the 90 – 270 diameter. Make sure you count in from the primitive along the equator Now trace that great circle on the transparency and you have the projection of the layer plotted.

Plotting a Plane using the Stereonet 4/20/2017 Plotting a Plane using the Stereonet The layer is N80W, 40S Now, rotate the transparency back so North on the transparency coincides with 0 on the stereonet. The plot now shows the projected position of the layer in space.

2: Plotting a Line using the Stereonet 4/20/2017 2: Plotting a Line using the Stereonet The line is a fold axis at bearing S42W, plunge angle 38o Visualize the line in space plunging 38o to the SW

Plotting a Line using the Stereonet 4/20/2017 Plotting a Line using the Stereonet The line is a fold axis at S42W, 38o Next, place the overlay on the net and mark N, S, E, & W on the overlay. Locate S42W and make a tick mark at that position on the primitive circle.

Plotting a Line using the Stereonet 4/20/2017 Plotting a Line using the Stereonet The line is a fold axis at S42W, 38o Next, rotate the tick mark to either of the straight line axes of the net. Measure 38o along the line from the primitive circle and put a dot. This is the projection of the point where the line penetrates the sphere.

Plotting a Line using the Stereonet 4/20/2017 Plotting a Line using the Stereonet The line is a fold axis at S42W, 38o Finally, rotate the transparency so that North coincides with 0 on the stereonet. Check to make sure your dot is in the SW quadrant.

3: Plotting a Line on a plane 4/20/2017 3: Plotting a Line on a plane The plane (cleavage) is N70W 43 SW or (290, 43) The line (a mineral lineation) bears S20E or 160. Plot the plane and the line and find the plunge of the line. Visualize the problem: A plane (cleavage) with a line (lineation) lying in the plane.

Plotting a Line on a plane 4/20/2017 Plotting a Line on a plane The plane (cleavage) is N70W 43 SW or (290, 43) The line bears S20E Plot the plane on the overlay: Put a mark at 290

Plotting a Line on a plane 4/20/2017 Plotting a Line on a plane The plane (cleavage) is N70W 43 SW or (290, 43) The line has bearing S20E = 160o Next rotate the overlay to 0 or 180, then count in 43o along the equator to find the great circle that dips 43o to the SW. Trace the arc.

Plotting a Line on a plane 4/20/2017 Plotting a Line on a plane The plane (cleavage) is N70W 43 SW or (290, 43) The line has bearing S20E = 160o Rotate the overlay so that N is at 0. Mark the primitive at the bearing of the lineation, 160o.

Plotting a Line on a plane 4/20/2017 Plotting a Line on a plane The plane (cleavage) is N70W 43 SW or (290, 43) The line has bearing S20E = 160o Rotate the overlay so that the 160o mark is at the 0-180 axis of the net. The line from the center of the net to the 160 mark is the trend of the lineation. Where that trend line intersects the arc of the plane is the projection of the lineation that lies in the plane. The plunge on the lineation is measured from the primitive to the point on the arc.

Before we go on, let’s review Rake (aka Pitch)

The Rake of a Line on a plane 4/20/2017 The Rake of a Line on a plane The plane (cleavage) is N70W 43 SW or (290, 43) The line has bearing S20E = 160o We plotted the plane and the line. Rotate the transparency so the plane lies along a great circle. The rake is the angle measured from the primitive along the great circle, here 58o. b. Return the Transparency to North = 0o

4: Apparent Dip knowing True Dip 4/20/2017 4: Apparent Dip knowing True Dip The attitude of a dike is 205, 65 (N25E, 65SE). What is its apparent dip on a vertical quarry wall trending 350? Visualize the problem (a) and plot the dike (b)

Apparent Dip knowing true dip 4/20/2017 Apparent Dip knowing true dip The attitude of a dike is 205, 65 (N25E, 65SE). What is its apparent dip on a vertical quarry wall trending 350? Plot the quarry wall [c]. The intersection of the dike with the wall defines a line parallel to the apparent dip.

Apparent Dip knowing true dip 4/20/2017 Apparent Dip knowing true dip The attitude of a dike is 205, 65 (N25E, 65SE). What is its apparent dip on a vertical quarry wall trending 350? d. Rotate the transparency so the wall is along the axis. The apparent dip angle is from the primitive to the intersection, 52o.

True Dip from two Apparent Dips 4/20/2017 True Dip from two Apparent Dips Question: A layer intersecting a road cut trends 256, 32. The same layer intersects the road cut around a bend and trends 125, 27. What is the strike & dip of the layer? Visualize the problem (a) and then plot the intersections for the road cuts and the layer (b & c) Mark 256, rotate it to vertical Count in apparent dip 32o Mark 125, rotate it to vertical Count in apparent dip 27o

True Dip from two Apparent Dips 4/20/2017 True Dip from two Apparent Dips Question: A layer intersecting a road cut trends 256, 32. The same layer intersects the road cut around a bend and trends 125, 27. What is the strike & dip of the layer? Because the two road cut intersections lie on the dike, rotate the transparency so the two points line on the same great circle (d). Draw the great circle.

True Dip from two Apparent Dips 4/20/2017 True Dip from two Apparent Dips Question: A layer intersecting a road cut trends 256, 32. The same layer intersects the road cut around a bend and trends 125, 27. What is the strike & dip of the layer? That great circle is the attitude of the dike; measure its dip along the equator from the primitive to the great circle (d). Now rotate the transparency so that its N coincides with 0 on the net. Measure the strike and note its dip direction (e), here about N77W 54S