rel="nofollow" href="#ulink_9c5529c3-7cd2-5653-a7a1-666b90bb71d4">Figure 1.16) (Elliott et al. 1976; Watterson 1986; Scholz 2019), and various questions remain on the displacement–length relationships and fault growth mechanisms: faults rarely originate with their total length extent. This is the reason why we talk about “fault nucleation”. The rock block separation is supposed to initiate on a nucleus and extend in a certain direction. However, the mechanism and time–space evolution are not fully understood. In terms of normal faults in rifts, fault growth models can be divided into two categories: (1) the “propagating fault” or “isolated fault” model and (2) the “constant-length” fault model (Rotevatn et al. 2019). In the propagating fault model, the displacement synchronously increases and accordingly the fault grows in length (Cartwright et al. 1995; Walsh et al. 2003). On the other hand, with the constant-length model, the fault is supposed to reach almost its full length extent early in its evolution, and displacement occurs at later stages by successive increments (Jackson and Rotevatn 2013; Childs et al. 2017). Based on case examples, Jackson et al. (2017) show that normal fault growth may incorporate both models, with a predominance of the constant-length model and periods of minor fault-tip propagation and coeval displacement accumulation.
Figure 1.15. Illustration of normal faults: a) cartoon illustrating the fault core and damage zone (source: Yang et al. 2020); b) field observation photo by @Haakon Fossen from the Lærdal-Gjende normal fault, Norway and c) offshore seismic line, showing a series of normal faults with up to several km offset, North Sea (source: Haakon Fossen, available at: https://folk.uib.no/nglhe/
Figure 1.16a. Conceptual model of the development of normal fault systems. The isolated fault model shown is one of the main types: a) map view; b) strike projection; c) displacement–length (D–L) plots and d) basin geometry and syntectonic stratigraphic architecture (source: modified from Jackson et al. 2017)
Figure 1.16b. The constant length fault model, another commonly used modeling type: a) map view; b) strike projection; c) displacement-length (D–L) plots and d) basin geometry and syntectonic stratigraphic architecture (source: modified from Jackson et al. 2017)
Anderson’s law remains extremely elegant for studying fault dips. However, this theory is best applied to ideal cases with isotropic rocks and coaxial deformation (the stress axes do not rotate). However, in reality, fault blocks are often composite, with different rheology and lithology, and thus different mechanical strengths. Therefore, faults have various dips that cannot be explained by Andersonian mechanics and debates remain on various aspects of the theory, notably on the question of the activity of low-angle faults.
Figure 1.17. Schematic illustration of the formation of a low-angle fault (LANF) plane/detachment plane by rotation of higher-angle normal faults in the context of the development of a metamorphic core complex (source: based on a figure from J.P. Burg, after Buck 1988)
While the simple shear model of extension developed in the 1980s (e.g. Wernicke 1985), numerous observations of faults with very low-angle surfaces, but with apparent large-scale extension and significant amounts of displacement accumulated. This led to fundamental discussions on the feasibility of tectonic displacement along such low-angle surfaces. Faults were categorized as Andersonian and non-Andersonian, depending on whether they were “correctly” oriented with respect to the regional stress-field or not. Normal faults with an apparent dip-angle below 30° contradict Anderson’s fault theory and are often termed “non-Andersonian faults”. Doubts remained on the actual activity of such low-angle faults and it was regularly proposed that the low-angle normal faults (LANFs) are flexurally rotated segments of larger-scale complex fault systems and that the regional extension is actually operated on the higher-angle segments (>60°) (Figure 1.17), thereby respecting Anderson’s theory (Buck 1988). However, others argue that displacements on low-angle surfaces are possibly due to elevated pore fluid pressures and weakening factors (Wernicke 1981; Axen 1992; Scott and Lister 1992).
In rift and rifted margin studies, extension across the rift can be defined by the parameters beta factor (β), thinning factor (ε), elongation (e) or stretching factor (S) (McKenzie 1978; Hellinger and Sclater 1983; Davis Kusznir 2004; Reston 2007; Reston 2009; Reston and McDermott 2014). These terms are used to constrain the amount of extension accommodated over a certain area defined by section lengths before (L0) and after (Lf) the deformation episode (Figure 1.18). The initial and final crustal thicknesses (t0 and tf) can also be used to define the area that has extended.
The elongation is equivalent to:
The beta or stretching factor:
Thus, Lf = βL0, wherein β goes from 1 (Lf = L0) to infinity (Lf >> L0).
And the thinning factor:
Note that alternative definitions of these parameters have been proposed in the literature (and/or some relationships between L and t can be assumed). Therefore, to avoid any misunderstanding, special attention should be paid to the definition listed by the authors.
Figure 1.18. Illustration of the elongation, stretching and thinning factors
1.3.2.2. Detachment faults
“Detachment fault” is a term often used in rifted margin studies to refer to a specific fault plane that is distinguished from standard normal faults by its sub-regional to regional-scale geometry and low-angle apparent slip (Figure 1.19). First identified in the Basin and Range Province (Longwell 1945; Wernicke 1981), a series of publications in the 1980s and early 1990s proposed the occurrence of similar structures in other continental rifted margins (Wernicke 1985; Lister et al. 1986, 1991).
A detachment fault is a normal fault of very large-scale extent, accommodating significant displacements (tens of km), with a dip usually varying from higher angles at its breakaway
