balancing and restoration

20

Chapter ................................

Balancing and restoration

Restoring a geologic cross-section or map to its original, pre-deformational

state is an important part of making a structural interpretation. We want to be

able to restore our deformed section to a geologically feasible undeformed

section. For simplicity, we usually assume that either length or area (or volume in

three-dimensional analyses) is preserved. If preserved, the section is balanced,

meaning that length, area or volume of the restored section “balances” that

of the strained section (the interpretation). Such exercises were first performed

in areas of contraction, and are now routinely applied to extensional areas.

Balancing puts important constraints on geologic interpretations, although

there is no guarantee that a balanced section is correct. In this chapter we

look at the basic premises and methods for balancing and restoration,

mostly in sections and map view, and point out some of their usefulness

and shortcomings.

396 Balancing and restoration 20.2 Restoration of geologic sections 396

20.1 Basic concepts and definitions

The uncertainties contained in any geologic data set always

likely as possible. Only when we have demonstrated that a

geologic section can be restored to a reasonable pre-deform-

ational state does the section balance.

give room for many different interpretations. The principle

known as Occam’s Razor suggests that we should favor

simple explanations and models, and this also holds true

in the business of balancing geologic sections: If we were to

take into account every little detail we would meet technical

difficulties or simply find ourselves using our time very

inefficiently. Even though a simple approach to restoration

may give obvious inconsistencies or errors, it may still give

valuable information about the deformation in question.

Let us now discuss what balancing and restoration

actually means. Balancing adjusts a geologic interpretation

so that it not only seems geologically reasonable in its

present state, but also is restorable to its pre-deformational

state according to some assumptions about the deform-

ation. Thus, balancing is a method that adds realism to our

sections and maps. A balanced section must be admissible,

meaning that the structures that it contains are geologically

reasonable both with respect to each other and to the

tectonic setting, and restorable (retrodeformable).

Restoration involves taking a section or map and

working back in time to undeform or retrodeform it. In

terms of the deformation theory discussed in Chapter 2,

this is the same as applying the reciprocal or inverse

deformation matrix D 1, except that the deformation

does not have to be, and in general is not, a linear trans-

formation. We must decide whether the deformation can

be explained by rotation, translation, simple shear, flexural

A geologic section is not proven balanced until an

acceptable restored version is presented.

Technically, we are not necessarily concerned with the

deformation history or sequence of restorational actions;

only the deformed and undeformed stages are compared.

We can thus isolate different components of the deform-

ation, such as rigid rotation, fault offset (block transla-

tions) and internal deformation of fault blocks (ductile

strain, also called distortion). It is also possible to start

with an undeformed model and deform it until reaching

something that looks like the interpreted section. This is

not called balancing, but forward modeling.

There are several reasons why balancing and restor-

ation are increasingly used. They help ensure that the

interpretation is realistic and provide support for strain

estimates, for example by determining the amount of

extension or shortening along a cross-section. In the

1960s, Clarence Dahlstrom and others applied this tool

to reconstruct sections across the Canadian Rocky Moun-

tains of Alberta prior to contraction, and calculated the

amount of shortening involved. Later the same principles

were used in areas of extension, such as the Basin and Range

province and the North Sea basin. The Scottish geologist

Alan Gibbs was one of the first to apply the principles

of restoration to cross-sections from the North Sea rift.

flow or some combination of these. By applying reciprocal

versions of these deformations the deformed section or

map should be restored. Realistic restoration requires

compatibility between different elements of the section,

notably that layers within the section remain coherent.

This means that the restored section has no or a minimum

of overlaps and gaps, that fault offsets (except for those

from earlier phases) are removed and that sedimentary

layers are unfolded and rotated to planar and horizontal

layers. Hence, when restoring a previously undeformed

stratigraphic sequence:

A balanced section or map is not necessarily correct,

but is likely to be more correct than a section that

cannot be balanced.

Although the balancing of sections is most common,

restoration and balancing can be done in one, two and

three dimensions. One-dimensional restoration is known

as line restoration, two-dimensional restoration is most

commonly applied to cross-sections but can also be

applied to maps, while three-dimensional restoration

and balancing takes into account possible movements

We do not want to see overlaps, gaps, fault offsets, curved

layers and non-horizontal layers in the restored state.

In practice we will not be able to perfectly restore sections

or maps, at least not if the deformation is complex, but these

are our basic goals during restoration. In other words, we

want our restored section or map to look as realistic and

in all three dimensions.

20.2 Restoration of geologic sections

The simplest form of restoration is to reconstruct how

a mapped straight line was oriented and located before

the deformation started. Such simple one-dimensional


(a)

(b)

Extension

BOX 20.1 CONDITIONS FOR BALANCIN G OF CROSS-

SECTIONS

Geologically sound interpretation.

Plane strain deformation.

Figure 20.1 The concept of one-dimensional restoration

where the marker is horizontal. In this case the line

segments can be moved along the fault traces until they form

a continuous layer. The extension is found by comparing

the undeformed and the deformed states.

considerations are typically done to stratigraphic markers

observed or interpreted in cross-section, and the principle

is illustrated in Figure 20.1 for a horizontal marker hori-

zon. Taking into account fault geometry or two or more

stratigraphic markers turns section balancing into two

dimensions.

Systematic section balancing was first applied in the

Canadian Rockies in Alberta in the 1950s and 1960s,

where petroleum-oriented structural geologists balanced

thrusted and folded stratigraphic markers and recon-

structed their pre-deformational lengths. The basic prem-

ises were that bed length and bed thickness measured

normal to bedding remain constant. This works well

for the Alberta sections, because much of the defor-

mation in this area is localized to weak shale layers. This

localization caused detachment faulting and folding by

the flexural slip mechanism, which preserves layer thick-

ness. The stratigraphic markers were mapped through

traditional fieldwork, while modern mapping also relies

on remote data, including seismic line interpretation

with supporting well data. One-dimensional restoration

can be done in any direction, and the outcome is the

amount of extension or contraction in that direction. In

general section restoration, however, the principal prem-

ises are that we study sections that contain the displace-

ment vector or the maximum and/or minimum principal

axes of the strain ellipsoid, and that the strain is plane

(Box 20.1). These premises are sufficiently fulfilled in

many (but far from all) contractional and extensional

regimes that line balancing becomes meaningful.

The section must contain the tectonic transport

direction.

The choices of deformation (vertical shear, rigid

rotation etc.) must be reasonable and based

on the general knowledge of deformation in the

given tectonic setting.

The result must be geologically reasonable,

based on independent observations and

experience.

will move into and out of the section, implying that

lengths and areas will change. It is possible to account

for such strain if the bulk strain can be estimated,

but then we are into the more complex case of three-

dimensional restoration. In this section we will restrict

ourselves to plane strain cases. An important implica-

tion of this is that if we use one-dimensional restoration

in a region of non-plane strain, the resulting interpreta-

tion will be incorrect.

Rigid block restoration The simplest case of section restoration is where fault

blocks behave as rigid blocks during deformation, so that

only rigid rotation and translation is involved. Previously

undeformed sedimentary layers then end up as straight

lines in the section (planar in three dimensions), while

fault traces can be curved. The domino system in

Figure 20.2a is an example where both offset (transla-

tion) and rotation (anticlockwise) are involved. Each

block can be restored by rotating the section so that

the layers become horizontal, before removing the fault

offsets. This can readily be done by means of a pair of

scissors, or by using a computer drawing program.

Section balancing generally requires plane strain and

orientation in the main displacement direction.

If strain is not plane, so that there is a strain com-

ponent perpendicular to the section studied, material

Before starting, pin one of the two ends and use that

pinpoint as the point of reference. The outcome is not

only the extension, but also the initial dip of the faults

and the amount of block rotation. This is a simple

example of constant length restoration. When using


two or more horizons we see that rigid block restoration

also preserves area.

Constant length and area Assuming that the marker is restored to its initial length

means that it has been extended or shortened only

salt de collement, and therefore well-suited for constant

length restoration.

Constant length restoration works well when our layers

are straight and horizontal (Figures 20.1 and 20.2a).

In many cases deformed layers are curved, and the concept

of constant length becomes questionable.

through the discrete formation of observable separations

or overlaps. This is the basis for constant length restor-

ation (or constant length balancing), which is commonly

and conveniently applied during section restoration, very

useful when a quick restoration is needed. It is frequently

used to restore fold-and-thrust belts, not only in the

Canadian Rocky Mountains, but in almost any region

dominated by thin-skinned tectonics. Figure 20.3 shows

an example from the Zagros fold-and-thrust belt of

Iran, which is one of several areas controlled by a weak

(a) Rotated layers (domino system)

(b) Non-planar layers (soft domino system)

(c) Non-planar layers, pure shear system

Figure 20.2 (a) Rotated layers can be restored by rigid

rotation and removal of fault displacement if layers are unfolded.

(b) and (c) Folded layers must be restored by a penetrative

(ductile) deformation such as vertical or inclined shear.

When deformed line segments are curved, we have

a component of ductile strain, and rigid body rotation

cannot restore the line.

It is still possible that the lengths of the lines are

preserved during folding – it all depends on the way that

strain accumulates. If the line lengths should change, area

may still be preserved, and in that sense constant area

restoration can be said to be somewhat more robust

and applicable. Area balancing makes sense: if we shrink

a section in one direction we somehow have to increase

it by the same amount in the other direction. Using

Figure 20.4b as an example, areas A and B have to be

equal. This is true even if layers change length and thick-

ness, as long as there is no compaction and no movement

in or out of our section. Area balancing also has implica-

tions for depth of detachment estimates. For example,

the area C in Figure 20.4c equals area D in the same

figure. If we know the extension (horizontal displacement

of the hanging wall) we can easily estimate the depth at

which the listric fault flattens out. The same is the case for

the fault-propagation fold shown in Figure 20.4b.

Flexural slip

Preservation of line length and bed thickness makes res-

toration simple. Flexural slip preserves both, as folding of

layers by flexural slip implies slip parallel to bedding only.

12 13

Paleocene– Lower Miocene

5 1 2 0

–5

–10 km

7 11

4 5 8 10

6 9

14 Cretaceous

Permo-Jurassic Cambrian

16

15

17

85 km

1

100 km

2 4 5 7

3 6

8 10 11

9

12 13 14

15 16

17

Figure 20.3 Cross-section through the Zagros fold-and-thrust belt. The section was balanced using the so-called sinuous bed

method, which involves measuring the lengths of the top and bottom of each formation between faults and matching ramp

and flat lengths on a restored section with those on the deformed section while maintaining bed thickness (constant area).

Numbers are added to help correlate the two sections. Modified from McQuarrie (2004).


(a) (a) Present

(b)

Area A

(b) Restored

Area B

(c)

Area A = area B

Area C Area D

Figure 20.5 Constant length and thickness was assumed

during this restoration. Each hanging-wall line was

straightened by rotation of individual segments and moved

left to match the stratigraphy in the footwall, consistent

with flexural slip restoration.

Area C = area D

Figure 20.4 Constant area balancing of sections in the

transport direction. (a) Undeformed section, (b) fault-

propagation fold, (c) listric extensional fault. Note that bed

length changes if internal strain is shear but not if the

mechanism is flexural slip or flexural shear.

If the strain is distributed we have flexural shear, still with

the shear plane along bedding.

In a contractional regime layer-parallel simple shear

is very common, as slip or shear easily localize to mech-

anically weak layer interfaces. Even if layers start to fold,

layer-parallel slip or shear can create flexural slip or flex-

ural shear folds – i.e. fold mechanisms that preserve both

layer length and area.

Flexural slip and flexural shear preserve layer length

and bed thickness, and therefore also area.

Flexural slip is convenient when modeling or balancing

contractional structures such as fault-bend folds and fault-

propagation folds. Fault-bend folds can be explored by

moving a paperback book or pile of papers over a ramp.

Drawing squares with circles on the side of the paper

pile shows how strain accumulates without changing the

length of the papers.

Restoration can be done by means of a ruler or

thread by measuring the length of each marker in the

deformed section. The markers are moved to their

original cut-off points (locations where they were cut

off at the ramp) and straightened while bed thickness is

maintained, as done in Figure 20.5. If bed thickness

changes in the deformed section, the flexural slip method

alone will not give the correct restored section. A similar

method can be used to restore flexural slip folds, such as

de collement folds.

In extensional regimes, layer-parallel shear can also

occur, but less commonly. This is so because slip most

likely initiates at 20–30 to s1 (Chapter 7), which is

vertical for extension and horizontal in the contractional

regime. Another mechanism is therefore commonly used

during restoration of extended sections, namely simple

shear across the layering.

Shear

Distributed simple shear is a concept that implies that

small-scale deformation can be treated as ductile deform-

ation, where layer continuity is preserved. The actual

small-scale deformation is not really important in this

context, and on a seismic section it is simply referred to

as subseismic (below the resolution of seismic reflection

profiles) or ductile. The goal is to apply simple shear to

account for the ductile deformation in the fault blocks,

as exemplified in Box 20.2. As we know from Chapter 15,

simple shear acting across layers rotates the layers and

changes their length, and heterogeneous simple shear

deflects or folds the layers. However, simple shear pre-

serves area, so the assumption of constant area in exten-

sional regimes is more realistic than that of preservation

of bed length.

400 20.2 Restoration of geologic sections 400

BOX 20.2 WHAT DOES V E RTICAL AND I NCLINED S HEAR REALLY MEAN?

The distributed or ductile deformation of layers in a deformed section can be modeled in many ways. It is

convenient to use simple shear, and the variables are shear strain and the inclination of the shear plane,

referred to as the shear angle. At the scale of a seismic or geologic section, we may not be able to see the

deformation structures that make a layer look non-planar. The structures may be subseismic faults,

deformation bands, extension fractures or microscale reorganization structures. Hence, the deformation

is ductile at our scale of observation, and the effects are modeled by simple shear.

It is sometimes claimed that the orientation of small faults in the hanging wall represents a guide to

the choice of shear angle. The two figures below show hanging walls with small-scale faults that are mostly

synthetic to the main fault. However, their arrangement calls for antithetic shear, as shown by yellow arrows.

These examples illustrate the difficulty involved in using small faults to determine the shear angle.

(a) Cloos (1968) Synthetic

faults

Antithetic

shear

(b) Fossen and Gabrielsen (1996) Antithetic

shear

(a) Translation

The classic use of (simple) shear in extensional

deformation is hanging-wall deformation above non-

planar normal faults, particularly listric extensional faults

of the kind shown in Figure 20.6. Constant-area deform-

ation of the hanging wall of a listric fault was first

modeled by means of vertical shear. This technique is

sometimes referred to as the Chevron construction,

named for the oil company that first utilized the method

(not to be confused with chevron folds mentioned in

(b)

Antithetic simple shear

Chapter 11). Vertical shear involves no extension or

shortening in the horizontal direction, but individual

layers will be extended, rotated and thinned.

It was soon realized that hanging-wall shear deform-

ation could deviate from vertical shear. Both antithetic

shear (shear plane dipping against the main fault) and

(c) Vertical simple shear

synthetic shear were evaluated. The differences between

the two are illustrated in Figure 20.6, which shows that

antithetic shear affects a larger part of the hanging wall

and implies less fault offset than vertical shear. Choosing

the right shear angle is not always easy, and we usually

(d) Synthetic simple shear

have to try a few different options to make a good choice.

It seems that antithetic shear with a shear angle of around

60 works well in many deformed hanging walls above

listric faults, while synthetic shear produces unrealistically

Figure 20.6 Deformation of the hanging wall above a listric

fault. (a) Pure translation. (b–d) Antithetic, vertical and synthetic

shear. Note the different hanging-wall geometries and the fact

that the shear only affects the left part of the hanging wall.

401 20.2 Restoration of geologic sections 401

(a)

(b)

(a)

(b)

–24° –10°

–6°

34/10–8

0° 10° 14° 18°

(c) Synthetic shear

2000 m

2200 m 2400 m

500 m

Figure 20.7 Local synthetic shear in the hanging wall to a

normal fault. The simple shear is related to the downward

steepening of the fault.

steep hanging-wall layers in many cases (Figure 20.6d).

Vertical shear may be more realistic when considering

large parts of the crust.

Synthetic shear works in cases where faults steepen

downward, either gradually (antilistric faults) or abruptly

as in Figure 20.7. Synthetic shear also applies in some

cases where a hanging-wall syncline is developed. How-

ever, in cases where the syncline widens upward, trishear

(Box 8.3) may be a more realistic alternative. An example

is shown in Figure 20.8, where forward trishear modeling

(a) reproduces the present section (b) quite well.

Trishear has no fixed shear angle, but involves a mobile

triangular deformation zone. The triangular zone is

attached to the fault tip and represents a ductile process

zone ahead of the fault. Trishear is an interesting model

that explains local drag structures and folding of layers

around faults, but is not applicable to entire regional

sections, as is vertical or inclined shear. However, it is

possible to combine general vertical shear throughout

a cross-section and apply local trishear to specific faults

within that section.

Figure 20.8 (a) Trishear applied to a gently dipping normal

fault that has propagated up-section. A hanging-wall syncline

forms. (b) Section from the Gullfaks Field, North Sea,

constrained by seismic and well data. Dip isogons (blue)

are based on dipmeter data and seismic interpretation.

Note the geometric similarities.

Other models

Other assumptions that have been used to model ductile

deformation of the hanging wall of non-planar faults

include constant displacement along the master fault

and constant fault heave. We have already seen in Chap-

ter 8 how displacement varies along faults, so although

these assumptions may work geometrically, they are geo-

logically unsound except for very special cases. However,

if the displacement on a given fault is much longer than

the section studied, the variation in displacement may

be relatively small, and constant displacement may be

an acceptable approximation. In general, the testing of

different assumptions during section restoration provides

alternative explanations, and their differences highlight

the uncertainties involved.

The effect of compaction

Constant area implies that area is conserved even though

the shape of a given area may change during deformation.

However, compaction (vertical shortening) of sediments

402 Balancing and restoration 20.3 Restoration in map view 402

a0

f0

A Figure 20.10 Posttectonic compaction is largest in the upper

part of a sedimentary sequence. The reduction of the dip of the

faults will therefore be greater in the shallow part. An initially

straight fault will therefore flatten towards the top due to

differential compaction.

a

Rigid

f

tan(a)

= tan(a0)

B

1–f0

1– f

Rigid

Figure 20.11 If the hanging wall compacts more than the

footwall, a compaction syncline forms. In the example shown

Figure 20.9 The effect of compaction on the geometry of

synsedimentary faults (growth faults). The fault dip lowers

with depth because of the downward-increasing compaction.

Knowledge of the original porosity can be used to calculate the

original fault dip at any point along the fault. f0 is typically

around 0.4 (40%) for sandstone and 65–70% for clay. Note that

there may be other reasons why some faults flatten with depth.

may occur during as well as after tectonic deformation,

decreasing the area seen in vertical sections. The effect of

compaction on faults and folds is significant where sedi-

mentary sequences are deformed at shallow depths, prior

to burial and lithification. Growth faults in delta settings

are a realistic example, relevant to places such as the Gulf

of Mexico. The primary effect is shown schematically in

Figure 20.9, where the fault dip can be seen to decrease

downward, solely as a result of compaction.

Compaction also has a geometric effect on newly

formed faults in a sedimentary sequence. This is illustrated

in Figure 20.10, where the upper parts of the initially

straight faults become flattened and the faults slightly

antilistric. This effect is due to differential compaction,

here the hanging wall is assumed to be rigid while hanging-wall

layers compact from 50% in the topmost layer down to 10%

in the lower layer above the rigid basement.

where shallow layers compact more than the already com-

pacted deeper layers.

Another compaction-related effect relates to the fact

that sand compacts less than mud and clay. Clay has an

initial porosity close to 70%, while that of sand is around

40%. So, if a fault forms in a recently deposited sand–

clay sequence, subsequent compaction will give the fault

a lower dip in the more compacted clay layers than in

sand layers.

There is also the effect of differential compaction on

each side of a fault. If the offset on a fault becomes large,

say some hundred meters or more, then the hanging-wall

layers will compact more than those in the adjacent

footwall, simply because the footwall layers have already

been compacted to a larger extent or are crystalline rocks.

For dipping extensional faults, the result is a hanging-

wall syncline, as shown in Figure 20.11.


45° antithetic shear

Vertical shear

Figure 20.12 Example of a curved hanging-wall layer.

The shape of the layer reflects the fault geometry at depth,

but the choice of shear angle influences the estimated fault

geometry. From White et al. (1986).

Most balancing programs utilize compaction curves for

various lithologies that remove the effect of compaction

during restoration.

Finding fault geometry from

hanging-wall layers

At shallow levels in rift systems it is common to see

reflectors in seismic sections offset by a fault, while the

fault geometry at depth remains unclear. However, the

direct relationship between fault geometry and layer

geometry provides important insight into fault geometry

at depth. Where the hanging-wall reflectors are curved,

the fault is also likely to be curved. Hence, we can use the

shape of the layers to calculate the shape of the fault and,

in the case of a rollover structure, to estimate the depth

to the detachment.

between the blocks reflects the amount of extension. The

map pattern with all the different fault blocks is reminis-

cent of a jigsaw puzzle, and the restoration involves

putting the pieces back to their pre-deformational posi-

tions (Figure 20.13b). The goal is to restore the puzzle to

the state where the number of openings and overlaps is

minimized, either manually or by computer. If the blocks

involve no internal deformation and the layering is hori-

zontal, reconstruction is, at least in principle, relatively

simple.

For the common situation where layers are dipping,

rigid-body rotation of the blocks may be necessary to

obtain horizontal layering. If layers are non-planar, then

the surface should be unfolded or additional errors will be

introduced. The choice of strain model may not be easy –

should we project the material points on the folded surface

to the horizontal plane by means of oblique shear, vertical

shear or some other transformation? If constant surface

area is assumed, a flexural slip fold model is implied.

Even if such uncertainties and inaccuracies cannot be

dealt with to the full extent, the outcome of map restor-

ation is often quite useful. The displacement field emerges

by connecting the locations of points before and after

deformation, as shown in Figure 20.13c for our example.

The orientation of displacement vectors allows the distinc-

tion between plane and non-plane strain (parallel dis-

placement vectors versus diverging vectors, respectively)

and an assessment of the influence of gravity spreading

There is a direct relationship between fault geometry

and hanging-wall strain for non-planar faults.

We do, however, need to choose a model for the

hanging-wall strain, and the result will be different for

synthetic, vertical and antithetic shear angles. Vertical

shear gives a deeper detachment than antithetic shear,

as illustrated in Figure 20.12, but the amount of exten-

sion involved will be greater for antithetic shear. If we

have information from both hanging-wall and fault

geometries, we can find the shear angle that best balances

the section. For many cases, a 60 antithetic shear angle is

found, supporting the antithetic shear model.

20.3 Restoration in map view

A mapped horizon that has been affected by extensional

faulting is portrayed as a series of isolated fault blocks,

by contractional faulting as overlapping fault blocks, or a

combination of both. If we consider the case of exten-

sional faulting shown in Figure 20.13a, the separation

during deformation. Additionally, non-plane strain means

that area will not be conserved in any cross-section

through the deformed volume, and cross-sections cannot

be correctly balanced: If we create an interpretation that

does balance, it must be wrong! If the strain is plane,

then sections chosen for cross-section balancing must be

oriented parallel to the displacement vectors. Map restor-

ation allows us to more accurately choose this direction.

Some important outcomes from map restoration

include the following. Relative movement of points on

each side of faults will give the local displacement vector

of the fault (Figure 20.13d) or, if layers are not horizon-

tal, the horizontal component of the displacement

vectors. The nature of slip (dip-slip, oblique-slip, strike-

slip etc.) on faults is thereby revealed and the number of

rotation of blocks about the vertical axis also emerges

from map restoration (Figure 20.13e). The amount of

strain in any horizontal direction will also be apparent.

Finally, the gap and/or overlap areas provides an idea

about the consistency of the restoration and reliability of

the interpretation.


(a) (b) (c)

N

(d)

Gullfaks Field

1 km

(e)

Restored

42% area difference

Displacement

field

Fault

movements

Block rotation

13° –> 4°

4° –> 0.5°

0.5° –> –0.5°

–0.5° –> –4°

–4° –> –27°

Figure 20.13 Balancing of the Statfjord Formation map of the Gullfaks Field. (a) Present situation. (b) Restored version.

(c) Displacement field relative to westernmost block. (d) Fault slip. (e) Rotation about vertical axis. From Rouby et al. (1996).

20.4 Restoration in three dimensions

Map restoration is sometimes described as being three-

dimensional. However, true three-dimensional restoration

involves volume, and means simultaneous map-view and

cross-sectional restoration. Fault blocks are considered as

three-dimensional objects that can be moved around and

deformed internally, but not independently of each other.

Three-dimensional restoration is inherently complex, and

an in-depth treatment is beyond the scope of this book.

During three-dimensional restoration each surface is

mathematically treated as a mesh of triangles or other

polygons that can be deformed. Using vertical shear, it is

like holding a handful of pencils that connect the differ-

ent surfaces, where each pencil is free to move slightly

differently than its neighboring pencils. An advantage

of three-dimensional restoration is the opportunity to

account for non-plane strain. However, the many choices

involved and the time required to set up and run three-

dimensional restoration models makes simpler forms of

restoration more attractive. They may not be as accurate,

but they may provide very important information within

a reasonable time frame.

20.5 Backstripping

The restoration techniques discussed above are purely

kinematic and do not take into consideration the elastic

or isostatic response of the crust. This should be done

when large-scale restoration is performed. Backstripping

is a kind of isostatic restoration where the focus is on the

subsidence history of a basin by successively removing

sedimentary sequences and balancing isostasy. This type

of restoration is applied to rift basins to determine the

magnitude of lithospheric extension during rifting by

estimating the post-rift subsidence rate. The procedure

20.5 Backstripping 405 405 Balancing and restoration

Present

Postrift sequences Figure 20.14 Schematic

illustration of backstripping

of a section through a rift,

taking into consideration

flexural response (isostasy),

50 Ma

100 Ma

150 Ma

200 Ma:

End of rifting

Synrift sequence

25 km

compaction and thermal

subsidence. Sedimentary units

are successively removed to the

base of the postrift succession,

and the sections can be tested

against paleobathymetric

markers, such as eroded fault

crests. Based on Roberts

et al. (1993).

involves stepwise removal of gradually older stratigraphy,

correcting for compactional effects that can be calculated

from established compaction–depth curves, and adjusting

for subsidence caused by sediment loading. Just like the

geometric balancing discussed elsewhere in this chapter,

it can be done in one, two or, less commonly, three

dimensions. One-dimensional backstripping assumes Airy

isostasy while two- and three-dimensional backstripping

relies on flexural isostasy, where isostatic compensation

takes into account lateral variations in loading. Paleo-

bathymetric estimates are generally needed to constrain

previous stages of basin bathymetry.

We will not go into backstripping in any detail in this

book (see suggested reading below for a more detailed

treatment), but in general terms, modeling a cross-section

in a rift setting involves:

Removal of the water layer and computation of

the flexural isostatic response.

Removal of the youngest stratigraphic unit.

Decompaction of the remaining stratigraphy.

Calculation of the flexural isostatic response to removing

the sediment load.

Adding thermal uplift from an estimate of b and rift age.

This procedure is repeated for every stratigraphic unit to

the base of the postrift sequence, producing a series of

restored cross-sections. A schematic illustration is shown

in Figure 20.14.

20.5 Backstripping 406 406 Balancing and restoration

.S..u..m...

m...

a..r..y.............................................................................................

Restoration of sections and maps can be useful because it gives regional strain estimates and explores how well

different strain mechanisms can explain observed structures. If a section does not restore, both the interpretation

and the assumptions used during restoration should be critically evaluated. If a section or map is fully restored to a

geologically viable state the interpretation is balanced and sound, but not necessarily correct. Restoration is always

compromising the complexities of natural deformation and will never be correct in all detail, but is still quite useful as

long as this is kept in mind. Restoration can be done by means of paper and scissors, a drawing program on a computer

or special programs designed especially for restoration purposes. Important points to remember:

A balanced interpretation is one that has been restored to a geologically sound pre-deformational state.

A sound restored (undeformed) state generally implies horizontal sedimentary layers and no overlaps or open spaces

between fault blocks.

If basic assumptions made during restoration are sound, a balanced geologic interpretation is considered to be a more

likely interpretation.

There is always more than one restorable interpretation.

The conditions and assumptions used during restoration must be critically evaluated, using all available information

and experience.

...e..v..i.e..w....

q..u...e..s.t..i.o..n..s........................................................................

1. What are the two most basic conditions that must be fulfilled for section balancing to make sense?

2. What is the difference between restoration and forward modeling?

3. What is meant by ductile strain in restoration?

4. What is the most common model for ductile strain in section restoration?

5. How could we restore a folded layer?

6. What information can map-view restoration give?

E-MODULE

The e-learning module called Balancing and

restoration is recommended for this chapter.

Further reading 407

FURTHER READING

General

Rowland, S. M. and Duebendorfer, E. M., 2007, Structural

Analysis and Synthesis. Oxford: Blackwell Science.

Contraction

Dahlstrom, C. D. A., 1969, Balanced cross sections.

Canadian Journal of Earth Sciences 6: 743–757.

Hossack, J. R., 1979, The use of balanced cross-sections

in the calculation of orogenic contraction: a review.

Journal of the Geological Society 136: 705–711.

Mount, V. S., Suppe, J. and Hook, S. C., 1990, A forward

modeling strategy for balancing cross sections. American

Association of Petroleum Geologists Bulletin 74: 521–531.

Suppe, J. 1983, Geometry and kinematics of fault-bend

folding. American Journal of Science 283, 684–721.

Woodward, N. B., Gray, D. R. and Spears, D. B., 1986,

Including strain data in balanced cross-sections.

Journal of Structural Geology 8: 313–324.

Woodward, N. B., Boyer, S. E. and Suppe, J., 1989,

Balanced Geological Cross-sections: An Essential Technique

in Geological Research and Exploration. American

Geophysical Union Short Course in Geology, 6.

Extension

de Matos, R. M. D., 1993, Geometry of the hanging wall

above a system of listric normal faults – a numerical

solution. American Association of Petroleum Geologists

Bulletin 77: 1839–1859.

Gibbs, A. D., 1983, Balanced cross-section construction

from seismic sections in areas of extensional tectonics.

Journal of Structural Geology 5: 153–160.

Morris, A. P. and Ferrill, D. A., 1999, Constant-thickness

deformation above curved normal faults. Journal of

Structural Geology 21: 67–83.

Nunns, A., 1991, Structural restoration of seismic and

geologic sections in extensional regimes. American

Association of Petroleum Geologists Bulletin 75: 278–297.

Westaway, R. and Kusznir, N., 1993, Fault and bed

“rotation” during continental extension: block

rotation or vertical shear? Journal of Structural Geology

15: 753–770.

Withjack, M. O. and Peterson, E. T., 1993, Prediction of

normal-fault geometries – a sensitivity analysis.

American Association of Petroleum Geologists Bulletin

77: 1860–1873.

Salt structures

Hossack, J., 1993, Geometric rules of section balancing

for salt structures. In M. P. A. Jackson, D. G. Roberts

and S. Snelson (Eds.), Salt Tectonics: A Global Perspective.

Memoir 65. American Association of Petroleum

Geologists, pp. 29–40.

Rowan, M. G., 1993, A systematic technique for sequential

restoration of salt structures. Tectonophysics 228: 331–348.

Map and three-dimensional restoration

Rouby, D., Fossen, H. and Cobbold, P., 1996, Extension,

displacement, and block rotation in the larger Gullfaks

area, northern North Sea: determined from map view

restoration. American Association of Petroleum Geologists

Bulletin 80: 875–890.

Rouby, D., Xiao, H. and Suppe, J., 2000, 3-D Restoration

of complexly folded and faulted surfaces using multiple

unfolding mechanisms. American Association of

Petroleum Geologists Bulletin 84: 805–829. Backstripping

Roberts, A. M., Yielding, G. and Badley, M. E., 1993,

Tectonic and bathymetric controls on stratigraphic

sequences within evolving half-graben. In G. D. Williams

and A. Dobb (Eds.), Tectonics and Seismic Sequence

Stratigraphy. Special Publication 71, London: Geological

Society, pp. 81–121.

Watts, A. B., 2001, Isostasy and Flexure of the Lithosphere.

Cambridge: Cambridge University Press.

balancing and restoration

Documents

balanced section

strained section

geologic interpretations

restored section balances

feasible undeformed

geologic crosssection

deformation history

deformation theory