DIDACTIC APROACH TO REGIONALIZATION OF THE FAULT PLANE (AS A FUNCTION OF THE PITCH ANGLE OF STRIATION LINEATION), USING TRIDIMENSIONAL MODELS AND TRIGONOMETRIC ANALYSIS TO DETERMINE THE SENSE OF SLIP

A methodology with didactical purposes, to calculate total slip of blocks truncated by fault planes is presented as an aid to teachers of Structural Geology courses. It is assumed that strike and dip, of faults and contacts are known, as well as plunge and direction, or pitch of the striation lineation. An algorithm is utilized to calculate the total slip from apparent separation shown in maps and sections, of truncated structural planes (contacts, faults, axial planes, etc.), assuming for simplicity smooth planar surfaces for faults and truncated planes. Assuming a given strike, apparent dip separations are visually analyzed in a stereographic net, and projected on 3-D models, constructed with the vertical profiles on the borders of those maps. The map and the profiles are then folded, to produce blocks that show the geometry of those structures. The discussion includes the cases where the strikes of faults and planes are not parallel.

The footwall block is arbitrarily kept fixed, and the hanging wall block allowed to move freely. The magnitude of the slip vector is visually analyzed on the fault profile. Three regions are recognized on the fault profile that allow to interpret the sense of the fault motion of the hanging wall block. It is first analyzed the cases where the strikes of fault and contact are orthogonal, and the apparent strike or dip separations are greater than zero. The evaluation of total slip is evaluated and the algorithm is tested in the 3-D models.

When fault planes and truncated contacts are not orthogonal, keeping one of the two fixed, and letting the strike and/or the dip of the other varies, apparent paradoxes occur in sections and profiles, which are discussed and explained with the models and algorithms deduced here.

When apparent separation is zero, the slip on the fault plane must occur along the cut off line of the truncated plane (i.e. intersection of the truncated plane with the fault plane). The solution requires another plane, whose apparent separation is not zero. The orientation and magnitude of the slip vector (total slip), is calculated with the same algorithm. Various scenarios and apparent paradoxes are discussed.

These cases demonstrate that the only way to evaluate the slip on a fault is through the visualization on the fault profile, of the pitch angles of cut off lines, and slip vector.