Conservation of line length and bed thickness require a defined interplay between folding of the hangingwall and angle of a ramp with the following flat (the step down angle). The following displays show geometric mechanisms which may be used to explore the relation between the interlimb angle of the fold (gamma), the step down angle (phi) and the original dip of the hangingwall (theta).
One may distinguish between situations where the interlimb angle is known and situation where the fault angles are known. The first displays shows the solution to a fault bend fold where the interlimb angle is provided and the angle between the ramp and the following flat is constructed as an outcome. Conversely, the lower panel of the second display deals with the situation where one wants to determine the interlimb angle based on the fault angles. The upper panel of the second display is unconstrained and can be used to explore the sensitivity of changes in angles to a solution.
Move the red control points to change the geometry of the fold and the dip of the flat. You can read off and see the ramp angles which are required in FBF for this situation.
Use shift-leftclick and shift-mousewheel to pan and zoom. You can click on the upper left button to reset the construction.In the display below move the red point labelled MOVE to match cutoff_1 with cutoff_2. At this situation the fault-bend fold solution is given.
Match the red M point with orange N point on the lower panel to refine the solution there.
Use shift-leftclick and shift-mousewheel to pan and zoom.
The circle has the radius of the line length which needs to be preserved after material migrates through the active, anticlinal axial surface. The anticlinal fold axis is pinned to the fault bend and is bisecting the fold angle.
These two requirements define the geometry of the fault-bend fold. You can explore the system by moving blue points with the mouse. Hit the reset button in the upper right corner to get back to the initial geometry.
Details:
The gray line in the lower panel is the locus of all points which have same distance to the point MOVE as the point A has _and_ where gamma_1 equals gamma_2 as well. Where the gray locus intersects the ramp is the hangingwall cutoff of the the horizon which originally went through the fault bend.
Point N is an approximation of this intersection. It is defined as the intersection of an arc through points A, M and P, and the flat. M and P are arbitrary points on the locus line. Although N can be very close the intersection of the gray locus line with the ramp, it is necessary to have an almost exact match to arrive at an acceptable solution. By moving the point M to N, the approximation is refined and angles gamma_1 and gamma_2 become equal.
Andreas Plesch, Created with GeoGebra