ORIENTATIONS AND ROTATIONS

1.	The following data (using the GSC ‘right-hand rule’ for planes) represent the strikes and dips of bedding planes across a fold (these data are real):

	308	59	265	35	326	89	278	31	152	81	154	83	155	78	169	49	312	64	319	69	278	29	255	30	241	28	219	33	197	38	193	43	182	52	179	57	175	58	179	56

	Plot the poles to bedding on an equal-area (Schmidt) stereogram, construct the π -plane, and determine the trend and plunge of the fold axis (to the nearest 5°  of trend and plunge).  Provide a key that indicates the different symbols used.

2.	Imagine that a vein (strike and dip of 184 46) was observed at the location of the first bedding measurement (308 59).  If the vein predates folding, then what was its orientation when formed?  Explain in words how to go about ‘unfolding’ bedding to answer this question, and show the procedure on a stereogram (separate from the one used in problem 1).  Label appropriately.

3.	Derive the transformation matrix for down-plunge projection along a fold axis having a trend of  and a plunge of .  I did the first part in class, but repeat that part of the derivation and use it as the start (first half) of the complete derivation.  Simplify your results so that both steps of rotation are included in a single transformation matrix.  This will require matrix multiplication; remember to multiply in the correct order.

4.	Use the Excel spreadsheet ‘down_plunge_proj’ (on web) and your results from problems 1 and 3 to calculate the down-plunge projection of the data provided and decode the hidden message.  The spreadsheet is set up so that all you need to enter is information in the yellow cells: the trend and plunge of the fold-axis, and the formulas for each of the nine components of the transformation matrix (note that Excel requires angles in radians, already calculated for you).  Data (x-y-z) are already entered, transformation of data (x”-y”-z”) is already calculated, and graphs are already set up for plan view (x-y) and profile-plane projection (y”-z”).  Nothing on the graphs requires modification!

Extra credit:  Derive the transformation matrix for a general rotation of angle  about an axis having a trend of  and a plunge of .