Cross Section Construction

1. Cross Section Construction • A big part of our task is to walk around collecting surface data, then we make a cross-section along lines that show near-surface structures and resources of interest

2. Our sections usually won’t run along true dip, so we must calculate and plot apparent dip, sometimes with vertical exaggeration.

3. Planar orientations • Over small distances, many geologic features are approximately planar Overturned Area Source: Tom Bean

4. Apparent Dip • True dip is measured perpendicular to strike. • On a vertical plane that is not perpendicular to strike, we measure apparent dip. It is less than true dip.

5. Vertical Distance to Plane • However, regardless of where the angles are measured, the drop from a line parallel to strike is the same.

6. Three methods for Apparent Dip • Geometric constructions • Trig Calculations • A Nomogram

7. Turn in your lab work • Your constructions and calculations to be turned in on the date specified. • We will use apparent dip data to construct a cross section.

8. Apparent Dip from Strike and True Dip Problem 1 Given: A coal bed has a strike and dip of N45E 35NW. Find: The apparent dip of the bed along a vertical section trending N90W. 1. Draw the strike N45E, then a perpendicular of arbitrary length. 2. Mark the far end o (origin). Draw the dip angle back toward the strike. Measure the length, here 2.03 units, say centimeters. 3. Draw the trend of the vertical wall N90W from point o till it hits the strike line. Drop a perpendicular with the same length, here 2.03 units. 4. Measure the apparent dip. It works because the central triangle is the surface, and both verticals must sink the same distance to the subsurface coal bed, because they start at the same strike line. Fold the triangles down; you’ll see it.

9. True Dip from Strike and Apparent Dip • Problem 2 • Given: A gold placer has a strike of E-W on a hilltop, and an apparent dip of 40o on the vertical hillside trending N35E. Find: True dip angle and quadrant. • Draw the E-W strike line, then a perpendicular N0oE. • Mark the far end o (origin). Draw the trend of the vertical wall N35E , then the apparent dip angle 40o. Measure the length, here 2.5697 units, say centimeters. • Measure the same distance away along the strike line, in the other direction shown. • Measure the angle, here 46o. It works because the central triangle is the surface, and both verticals must sink the same distance to the placer bed, which has its true dip perpendicular to the strike, and so must be at identical depths from any particular strike line. Cut out the figure, and fold the two outer triangles down.; you’ll see it.

10. Strike and true dip from two apparent dips • Given: 2 apparent dip angles and trends of 25o, S50E, and 35o, S20W, formed by excavating vertical cuts on the upper contact of a planar Copper Porphyry. • Find: Strike and true dip of this valuable deposit. • Draw lines along the first trend S50E, then draw the apparent dip angle (here 25o) away from the center as shown. At an arbitrary distance draw a perpendicular from the trend to the angle line. Measure the distance. • Draw similar lines for the second trend and angle. But draw the perpendicular where the length is the same. (this example 1.73 units) • Connect the two trend lines. That is the Strike, measure it. Here it is N 89W. • Drop a perpendicular from the origin to the strike, then measure off the same depth (here 1.73 units) to the planar deposit. Measure the angle subtended, that is the true dip, here 36o 30’.

11. Line of Section X-X’ Tan app dip = Tan true dip x sine angle strike to section

12. The equation on the previous slide can be arranged in the nomogram seen at left

13. Slide courtesy Steve Dutch X X’