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The choice of geometric technique for reconstructing a fold must be governed by the reasonable assumption that the fold behaves in some geometrically ordered and well defined way. In the past such reconstructions have mostly been carried out assuming that all the layers in the structure retain their original thickness at all points in the fold, and that the fold style is parallel throughout. The basic method was suggested in a classic work on folding by Busk (1929). He developed a graphical procedure which allowed the curvature of the beds between any two adjacent dip observations to vary so that the two dips were tangent planes to concentric cylinders. Between two data points (e.g. band in Figure), the centre of curvature of the sector is established by finding the point of intersectioo of the two normals of the dip surfaces. In any sector of the structure the curvature varies from layer to layer, but along any one layer it is constant. Successive reconstructions of adjacent sectors between pair of dip observations, each with its own centre of curvature, enables a complete cross section of the structure to be establislied. Slight modifications of this general teclinique, were proposed by Coates (1945) as a result of his practical experience in the oil industry, and his technique is an improvement on the basic Busk method where there is a large amount of dip orientation data and where dips have consistently low values. The average dip of a fold sector is determined, and this value is extrapolated downwards along the bisectors of the mean dip tangents.

Constructions produced by the Busk method show a number of special geometric properties.

1. All layers in the fold retain constant orthogonal thickness irrespective of lithology.

2. Sudden clianges of curvature occur in any surface in the fold where it cuts a line perpendicular to an observed dip. In some positions in the structure these curvature changes arc very marked and give rise to cusp-like forms. Construction cusps of this type occur at different layer levels in the structure. On the inner arc of the cusps the arc lengths measured along any folded surface are smaller than those on the outside of the cusp.

3. The amplitude on the folds in successive layers always decreases away from the topographic surface where the prime data were collected.

4. At some positions in the structure geometrical incompatibility occurs and, over certain sectors, it is not always possible to retain constant layer thickness. At these positions Busk suggested that the folds become non-parallel and that limb thinning takes place; he suggested that freehand constructions should be used as there was no unique geometric solution to the problem by the methods previously 

used. He was clearly aware of the problems of thickness changes in folds but he thought that there were so many unknown factors that an exact geometric solution of the problem was too complicated or even


All the features listed above arise because of the assumptions on which the method is based are not applicable to most fold forms.

Folds with geometric charactenstics of the parallel 1B are generally uncommon. Folds which have geometry approximating to this style are most commonly found in single layer competent layers of ptygmatic structures, some multIlayered complexes where strong competence contrasts exist between the different components. In these multilayers parallel folds may occur in the most competent layer, especially where they are strongly laminated parallel to the contacts. In this case, however, the less competent layers take on forms of Class 3 folds. In multilayered Complexes which do not show strongly marked competence variations the folds alternate between Class IC and 3, often approaching to the similar (Class 2) form. The sudden changes in curvature which appear in these reconstructions are clearly an outcome of the methods used and become less pronounced as more data arc incorporated into the construction. A refinement of the Busk technique was suggested by Mertie (1940) in order to smooth the curvature changes along each folded surface. He described a method for establishing positions of continuously changing centres of curvature (an evolute), and how, from this, it is possible to construct the surfaces in the structure showing continuously changing curvature (an involute). This is an Improvement on the basic method of Busk, but it is still open 

to the criticism that the folding remains parallel throughout

the layers, and it still leads to the appearance of cuspate discontinuities at certain points In the sectIOn. Cuspate folds

are commonly observed in natural folds but they are always localized at special positins in the structure close to interfaces between materials of marked ductility constrast. This observation conflicts with the random location of cusps appcaring on the graphical constructions made by the Busk-Mertie methods, and which arise entirely as a result of geometric construction procedures. The changing amplitude of folds away from the data collection surface is an outcome of the assumption of parallelism of the folded layers. It has been suggested that the

change of shape downwards implies that the folds pass into

unfolded material, perhaps with an intervening decoupling surface or decollement horizon. The same geometric feature also appears in the sections in an upward direction, and so clearly this interpretation is unsound.