The document describes methods for constructing block diagrams and fold cross-sections from geological field data. It discusses the Busk method, which uses concentric cylinders to reconstruct folds by varying curvature between dip measurements. However, this assumes constant layer thickness and parallel folding, which is unrealistic. The kink method is now more common, approximating folds as zones of constant dip between measurements. Cross-sections must be modified by hand to match both dip data and observed stratigraphy at the surface, rather than relying purely on geometric constructions below ground.

1. Page1
Block Diagram
A block diagram is a sketch of a relief model—in particular, a representation of a
landscape in a perspective projection. Lobeck (1958), perfecting the art of block diagram
construction, defined these illustrations as plane figures that represent an imaginary rectangular
block of the Earth's crust in what appears as a three-dimensional perspective. The top of the
block gives a bird's-eye view of the ground surface, and the side gives the underlying geologic
structure. These three-dimensional landscape models, when suitably cut and placed, enable
examination of the surface and two of the lateral faces. Different types of block diagrams have
been developed (Monkhouse and Wilkinson, 1971), but most are based on the simple isometric
diagram that is prepared from a series of profiles. The need for these pseudo-three-dimensional
diagrams is, according to Lawrence (1971), often encountered in the interpretation of
landforms.
BUSK METHOD OF FOLD CONSTRUCTION
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.

2. Page2
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 clings 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 are 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 impossible.
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 appearing 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.

3. Page3
Kink Method
PURPOSE
Deformation of the Earth's surface is one of the most visible results of
activetectonics, but it is not the whole story. Some faults (“buried reverse faults”) can
causelarge earthquakes (for example, the 1994 Northridge earthquake that struck
the LosAngelesregion)eventhoughtheyneverbreakthesurface.Twoofthemostusefultoolsforstudying faults that
do not break the surface are 1) balanced cross sections, and 2)retrodeformation. This
exercise will acquaint you with these two tools and show you howtheycanbeappliedtoproblemsinactivetectonics,
activefolding,andearthquakehazard.
How the Kink Method Works
It's fairly common for folds to exhibit uniform dips for a wide interval and then change
dip abruptly. In other words the fold exhibits a series of kinks rather than smooth curvature.
We can approximate such folds using the kink method. It is a bit more common these days for
folds to be represented this way than with the Busk or arc method.
The basic method is to allow each dip measurement to define a zone where the dip is
constant. The boundaries of the dip zones are the lines that bisect angles between adjacent dips.
The example below begins with three different ways to find the bisector.
The actual point here the fold kinks may not coincide exactly with the bisector. Why
should it? If you have two dips at points 1 and 2, the change in dip could come anywhere
between them, and is not necessarily going to coincide with a line halfway between the two
dips. This method, like all fold construction techniques, is an approximation.
Tying the Diagram to Reality
It is virtually certain when you draw a cross section using strictly geometric methods
that the contacts will not match exactly with their predicted positions. There are many reasons
why not:
 The units will not be uniform in thickness
 There are small construction errors
 Dips are not uniform from place to place
 Dip measurements have small errors
 Folds do not have ideal geometrical shapes.

4. Page4
Here we have indicated the
stratigraphy. It is virtually
certain when you draw a cross
section using strictly geometric
methods that the contacts will not
match exactly with their predicted
positions.
What we need to do now is redraw
the folds so the cross-section
matches both the dips and the
stratigraphy.
Here the cross section lines are
subdued.
Most of the time you can modify
the fold shapes by hand to match
the stratigraphy without too much
trouble. Modified contacts are in
black.
Do not get distracted by your dip symbols or stratigraphic colors. The only requirement is that
the stratigraphy and dips match on the surface. Be prepared to modify the colors and depart
from the dips below the surface if it's called for. Compare the two diagrams above to see that
this was actually done.