Section Restoration

Restoration (or check for viability) of a cross section is the actual process of pulling- back cross sections in contractional terrains and pushing forward cross sections in extensional terrains. Restoration is done on the restoration template, which should incorporate changes in stratigraphic thickness, unconformities and any structures believed to have been present prior to the deformational event which will be restored. Sections are sometimes partially restored, which means restoration to an earlier less deformed state. Regional sections should be fully restored. Except possibly for very simple structures, restored section should invariably accompany deformed-state section, if it is claimed that the section is balanced.

There are several reasons for restoring a section: (1) It is the ultimate test of whether the deformed-state section is reasonable or not. A cross section that does not restore is most likely a bad section. (2) The restored section gives us the original undeformed length and comparing it with the length in deformed-state cross section allows us to estimate total shortening (or extension). (3) The restoration process glaringly reveals commonly made mistakes and errors in section construction.

Restoration is not merely measuring lengths (or areas) in deformed-state section and stretching them out, and somehow matching them. Sections must always be sequentially restored, i.e., one fault should be restored at a time. This requires that we must always take into account the sequence of faulting. The displacement on a younger fault should be removed first before the displacement on an older fault is removed. Also, out-of-sequence thrusts should be restored first followed by restoration of in sequence thrusts. In other word, restoration of faults should be carried out in an order reverse of the order in which they form. At every stage of restoration, all the structures must essentially be admissible. If this not the case the section is not balanced even if the section can be restored to an undeformed state. Step-wise restoration has two

additional benefits: (1) it helps us understand how a fold-thrust belt evolves through space and relative time, and (2) burial and uplift history can be worked out that may be useful in understanding source-rock maturation and hydrocarbon migration and accumulation.

The iterative process involved in restoring a section to its undeformed state and then changing the original section if it does not restore can be tedious, frustrating and very time consuming. Therefore, it is important to spend the maximum time and effort to correctly construct the first section using forward-modelled structural geometry. This is because even minor changes in one part of the section will invariably result in changing the remainder of the section. The ultimate objective is to construct a geometrically reasonable cross section within a limited amount of time.

There are two methods of restoration: equal line-length restoration (also called sinuous bed method) and equal-area restoration. The methods are briefly discussed below.

16.1 Equal line-length restoration

This is the most commonly applied restoration method. Line-length restoration is used when it is believed that there has been no stratigraphic thickness changes as a result of deformation, in any of the stratigraphic horizons included in the cross section. In other words, the line lengths (i.e., contacts between stratigraphic units in 2D) remain constant through the deformation. We can restore sections merely by stretching out the lines to return them to regional level and dip. If thicknesses do not change during deformation, areas will also remain constant. Consequently, we do not need to compare areas of beds or thrust sheets. If the folds are kink style, bed lengths can be measured with a divider or a good-quality ruler. If the folds are concentric, the measurements obviously become more involved.

Before we start restoration a pin line and a loose line at either end of the section are to be established. The first step in the restoration is to match hangingwall cut-offs to respective footwall cut-offs, starting with the frontal thrust sheet if there is no out-of- sequence thrusting The measured bed lengths are then laid out as straight-line

segments. The ends of these straight-line segments then define the footwall trajectory of the second fault. This procedure is repeated successively for all the faults.

Fig. 16.1 shows a fault-bend fold. For the purpose of restoration two reference lines are chosen. The pin line and the loose lines are located in the leading and trailing edges, respectively. Point A was at the upper bend (A') before deformation, so A is pulled back to this point. In so doing, we also pull back the entire rock package as well as the reference lines. Now keeping the pin line fixed, we straighten all the lines keeping the length of the lines constant. In Fig. 16.2, there are two faults in the deformed section; fault 1 is younger and fault 2 is older. We first restore fault 1 and then restore fault 2 following the same procedure as in Fig. 16.1. Note that the dip of fault 2 has changed in restored section. One surprise is that we find significant layer- parallel simple shear in the restored section that is not obvious in the deformed-state section.

Loose line Pin line

A 1 2 3 4 5 6 A' 1' 2' 3' 4' 5' 6' Deformed _Restored

Figure 16.1. The line-length method of section restoration involving one fault.

L1 L1 L2 L2 2 1 2 1 θ1 θ2 θ3 θ1 ψ Shear

Loose line Pin line

Deformed Restored

Figure 16.2. The line-length method of section restoration involving two faults.

16.2 Equal area restoration

Area restoration is used in regions where it is believed that changes in bedding thickness have occurred as result of deformation. The changes in bedding thickness

must be the result of plane strain within the cross sectional plane in order for the area balancing to be valid. The changes in bedding thickness must not be result of material moving in and out the plane of section during deformation. Under this condition, if there has been no overall volume change then the cross-sectional area of any rock unit shown in the deformed-state cross section has not changed during deformation. However, line-lengths (e.g., distances between given thrust faults as measured along specific bedding planes) may have changed. In such a situation, areas of rocks and not line lengths are measured for the purpose of restoration.

A = 3.2 sq. km X Y 1 2 3 4 A = 2.0 sq. km X' 1' 2' 3' 4' Y' A = 3.2 sq. km

Figure 16.3. Equal-area method of restoration (adapted after Marshak and Woodward, 1988).

Equal-area restoration involves measurement of area (A) of the deformed thrust sheet and the original thickness (t) of the unit. Assuming plane strain, the restored average length (L) is given by A/t. Fig. 16.3 shows general methodology of area restoration. The shaded unit in the rather unusual-looking ramp anticline has

undergone extreme thickening and has an area of 3.2 km2_{. We take the thickness at the}

trailing edge as the original thickness. The line-length restoration of the shaded unit

results in an area of 2.0 km2_{, which is about 38% too small. In order to keep the area}

constant, the undeformed length of the unit must be increased as shown in the lower diagram.

16.3 The key-bed method

Mitra and Namson (1989) pointed out that area restoration does not ensure that the units are balanced or the fault trajectories in the restored section are geologically reasonable. This is because only one average length is calculated for each unit and the top and bottom of the unit are assumed to be equal to the average length. This makes the undeformed sheet to be a parallelogram.

X' Y' W' Z' A2 A2 A2 A1 A1 A1 L_2k L_2k L_1a L_1a L_1k L_1k L_2a L_2a X Y W Z X W Y* Z* L₂ L₁ L_d

Deformed section

Area restoration