Principles of balanced cross sections The true section

Principles of ‘balanced’ cross sections • The true section is retrodeformable. • Any retrodeformable section is a possible model. Not unique however in general. • The ‘space’ of retrodeformable section is large. We need assumptions to limit possibilities: – Conservation of mass is often assumed to convert to conservation of volume (not correct in case of compaction or metamorphism). – if plane strain is assumed or if the structure is cylindrical, conservation of volume converts to conservation of area NB: Balanced = retrodeformable

Fold classification (Axial plane dip angle , Fold Tightness of folding Fold style, Thickness of folded beds) Axial plane dip angle: Upright Overturned Recumbent Fold tightness: Gentle (>90°), Open (90°), Tight, (<90) Isoclinal (~0°) gentle Parallel Fold style: parallel (=concentric) Similar N: Fold style classification relies on the relative thickness of the layers in the hinge vs the limbs, or equivalently on the relative curvature of the upper and lower bounding surfaces.

Parallel folding Parallel folds commonly form by a deformation mechanism called flexural slip, where folding is accommodated by motions on minor faults that occur along some mechanical layering -- usually bedding. Flexural-slip surfaces, which can be observed in core or outcrop, may vary in spacing from a few millimeters to several tens of meters in spacing. In that case of flexural slip folding there is conservation of bed length and of bed thickness

First define section and assemble the data. Two popular methods can then be used to construct balanced cross sections -The Busk Method (Busk, 1929) - The Kink Method

The Busk’ method… parallel and concentric folds

The Busk’ method…

The Kink method for a parallel fold… The kink method is based on the assumption of flexural slip folding in the limit where dip angles varie only across axial surfaces (it is equivalent to the Busk method with infinite curvature within dip domains and zero curvature within axial surface. γ -the axial surface bisects the angle between the fold limbs Axial angle : γ γ

Constructing a balanced crosssection from the kink method • Assemble data (surface and subsurface observations) • Define dip domains, positions and dip angles of axial surface. • Extrapolate at depth by trials and errors. (you will need an eraser, experience will help). • Test that the section is indeed retrodeformable.

The Kink method for a parallel fold… - where two axial surfaces intersect, a new axial surface is formed. Its dip angle bisects the dip angles of the adjacent dip domains

The Kink method for a parallel fold… - Dip angles are constant within dip domains separated by axial surfaces. -the axial surface bisects the angle between the fold limbs

The Kink method for a parallel fold… Holland, 1914

The kink method is more general than the Busk method (any curve can be divided in straight segments).

Decollement

Minimum Shortening: 17. 5 km This section is retrodeformable and is thus a plausible model (but not a unique solution). A balanced cross-section generally yields a lower bound on the amount of shortening (because of erosion)

Fault-bend folding (Rich, 1934)… Flat: Fault is parallel to bedding Ramp: Fault cuts trough bed

Fault-bend folding (Rich, 1934)… The non planar fault has a flat-ramp-flat geometry. Translation of the thrust sheet along that fault requires axial surfaces. Note the difference between the active and passive axial surfaces

Constructing a balanced crosssection from the kink method • Assemble data (surface and subsurface observations) • Define dip domains, positions and dip angles of axial surface. • Extrapolate at depth by trials and errors. (you will need an eraser, experience will help). • Test that the section is indeed retrodeformable.

Two possible interpretations of structural measurements at the surface and along an exploration well. Which one is most plausible?

Two possible interpretations of structural measurements at the surface and along an exploration well. ‘Flat’ in hanging wall does not match ‘Ramp’ in footwall ‘Flat’ in hanging wall matches ‘Flat’ in footwall

- A balanced cross section might be checked from comparing hangingwall and footwall cutoff angles. - A balanced cross section might be checked and eventually retrodeformed based on the principle of conservation of area and conservation of bed length

Curvimetric Shortening & planimetric shortening Curvimetric Shortening: Sc= Lc-l Planimetric shortening: Sa=Asr/h Structural relief: Asr Undeformed depth of decollement below bed: h Area of Shortening: A Conservation of area implies: A=Asr= Sc*h. NB: Both quantities refer to a particular bed.

Curvimetric Shortening & planimetric shortening Curvimetric Shortening: Sc= Lc-l Structural relief: Asr Depth of decollement below bed: h Area of Shortening: A Conservation of area implies: A=Asr= Sc*h Planimetric shortening: A/h=Asr/h Conservation of area and bed length implies : - curvimetric shortening = planimetric shortening - Asr should increase linearly with elevation above decollement.

Sc= 0, 95 km Asr/h=2. 6 km Sc= 0, 95 km Asr/h=0. 95 km If area and bed length is preserved during folding then b is the most plausible solution …or a is correct but some diapirism is involved

Equality of curvilinear and planimetric shortening can be used to either check the section or predict the depth to the decollement. Asr= Sc*h

Structural relief: Asr Equality of curvilinear and planimetric shortening can be used to either check the section or predict the depth to the decollement. NB: Be careful with the possibility of diapirism

Structural elevation in balanced cross sections: the problem of filling space

Fault-bend-folding +Imprication/Duplex…

Balanced cross-section across the Pine Mountain (Southern Appalachians) (Suppe, 1983)

Structural elevation in balanced cross sections: the problem of filling space

The Move software Midland Valley Ltd. MOVE is the core product of the Move Suite providing a powerful structural modelling environment. Move provides data integration, 2 D cross-section construction and 3 D model building and is the base for the specialist structural modules for 2 D and 3 D kinematic, geomechanical, fracture and sediment modelling. 2 D MOVE - removes deformation to restore the present day interpretation to its un-deformed state, adhering to line length and area balancing structural geology principles and taking into account the importance of geological time and its impact on the structure of today.

Klippe (Robinson, Geosphere, 2008)

Move-3 D