1. Description of folds
Matlab project
Ana Isabel Martínez Poza

2. The classification of the folds is important because the
structure produced by experimental models on deformed
layered can be compared with the theoretical models of
rock deformation and hence with the results on the
geological processes.
The following classification (Ramsay, 1967) offers a very
sensitive method for determining slight changes in the fold
geometry from layer to layer in a fold structure.

3. The geometrical classification of folds
This classification depends on the shape of the profile section of the folded layers.
The form of any one layer in the structure depends on the relationship of the bounding surfaces of the layer, and in particular, the relative rates of change of the inclination of these bounding surfaces.
There are several ways in which we can measure these relatives rates of change and hence describe the shape of the folded layer.
The successive positions of the fold hinges form an
important curved or plane surface known as the axial
surface.

4. we could make a complete and systematic description of the fold.
In each fold we can determinate various parameters of amplitude, wavelength,
rates of curvature and the size and curvature of the hinge zone for each surface. So
we could make a complete and systematic description of the fold.
Orthogonal thickness. In a cross section of any fold we can determine the thickness t∞ of the material between two folded surfaces by constructing tangents to each surface making an angle of 900-α with tha axial trace of the fold.
t0= hinge zone of the fold.
Thickness parallel to the axial surfaces, T. Describes the variation in thickness of the folded layers records the distance between the bounding the bounding surfaces measured in a direction parallel to the axial surface of the fold.
Lines of equal dip, or dip isogons. On the profile section of the fold it is possible to determine points on the folded surface which have the same slope. By joining points of the same slope on adjacent surfaces, we obtain lines of equal slope known as dip isogons.

5. There are three types of fold which we can consider
fundamental classes.
Their definition is based on the comparison of curvature
changes on adjacent surfaces in the folded layer:
Class 1: Folds with convergent dip isogons. Curvature of the inner fold arc always exceeds that of the outer arc.
Subclass 1A: Folds with strongly convergent dip isogons.
Subclass 1B: Parallel folds.
Subclass 1C: Folds with weakly convergent isogons.

6. Class 2: Folds with parallel isogons. Curvature of the
inner and outer arcs are
equal.
Class 3: Folds with divergent isogons. Curvature of the inner fold arc is always less than that of the outer arc

7. t’= tα / to T’= Tα/To
Tα= thickness of the fold in the parallel direction if the axis of the fold.
T0= thickness of the hinge of the fold
α= angle of inclination
tα= proportional thickness
to= thickness of the hinge of the fold

8.  Objetive: Anaylize this image and specially the folds marked in-- 
Objetive: Anaylize this image and specially the folds marked in
green.

9. Matlab approach
Using the edge-based approach and the morphological approach to decide which develop the best structure of the folds.
Edge-based
Morphological

10. Different filters to enhance the folds edges.
Best result:
Bottom hat
Skeleton
Image after several filters
Inverted image

11. Further coding Get the axial plane of the fold.
Get the tangent lines of the fold.
Get the thickness of the fold, tα, to, Tα and T0.
Get the inclination α.
In order to define the fold type.

12. Bibliography Folding and fracturing of rocks. John G. Ramsay (1967).
Matlab image tool box guide.