Growth of fault populations

Faults grow from micro-fractures or deformation band zones and accumulate displacement over time as deformation proceeds. Moreover, faults tend to nucleate at many different places as a region is critically stressed, for instance during rifting, and we refer to such groups of faults as fault populations. In general, many faults in a population soon become inactive and thus remain small. Others reach an intermediate stage before dying, while a few grow into long faults with large displacements. Hence, a fault population is always dominated by small faults, while additional long faults develop as strain accumulates. Faults are unlikely to grow as individual structures over a long period of time. As they grow, they are likely to interfere with nearby faults. In this way two faults can join to form a single and much longer fault. Growth by linkage is a very common mechanism that creates some of the most interesting and important structures in faulted regions.

Fault linkage and relay structures 

In a population where faults grow in length and height, faults and their surrounding stress and strain fields will locally interfere. Let us consider two faults whose tips approach each other during growth. Before the tips have reached each other (but after their strain fields have started to interfere) the faults are said to under lap. Once the tips have passed each other, the faults are overlapping. Under and overlapping faults are said to be soft linked as long as they are not in direct physical contact. Eventually the faults may link up to form a hard link. Under lapping faults “feel” the presence of a neighbouring fault tip in the sense that the energy required to keep the deformation going increases. The propagation rate of the fault tips in the area of under lap is thus reduced, which causes the local displacement gradient to increase. This results in asymmetric displacement profiles, where the maximum is shifted toward the overlapping tip. This asymmetric displacement distribution becomes more pronounced as the faults overlap and the layers in the overlap zone become folded. The folding is a result of ductile displacement transfer (relay) from one fault to the other and is directly related to the high displacement gradients in the overlapping tip zones. If the fault interference occurs perpendicular to the slip direction, which for normal and reverse faults means in the horizontal direction, and if the layering is subhorizontal, then the folding is well expressed in the form of a ramp-like fold. The fold itself is called a relay ramp and the entire structure is known as a relay structure. The ramp is a fold that may contain extension fractures, shear fractures, deformation bands and/or minor faults depending on the mechanical rock properties at the time of deformation. Eventually the ramp will break to form a breached relay ramp. The two faults are then directly connected and associated with an abnormally wide damage zone. Upon breaching there will be a displacement minimum at the location of the relay structure. The total displacement curve along the fault will therefore show two maxima, one on each side of the relay structure. As the deformation proceeds and the fault accumulates displacement, the displacement profile will approach that of a single fault, with a single, central maximum. However, the link is still characterized by the wide damage zone and a step in the horizontal fault trace. If the mapping is based on poorly constrained outcrop information or seismic data (which always have a resolution issue), a sudden change in strike may be the only indication of a breached ramp. Such steps, seen at many locations in the seismic interpretation, are therefore very important as they may hint at the locations of both breached and intact relay ramps. Bends and jogs of faults in map view are very common on many scales. The final fault geometry can be seen to be the result of interaction between individual fault segments through the creation and breaching of relay ramps. The curved fault pattern seen in map view is very similar to that displayed by much larger faults, such as the northern North Sea faults and the Wasatch Fault in Utah, so it seems likely that these large faults formed by fault linkage. Assuming that this analogy holds, we are now able to interpret a deformation history from the geometry of a dead fault system. It is clear that ramps come in any size and stage of development. It is also important to understand that relay ramps and overlap zones are formed and destroyed continuously during the growth of a fault population.

Fault growth by linkage involves the formation and destruction of relay structures, deviations from the ideal elliptical displacement distribution and generation of wide damage zones and fault bends at locations of linkage.

Relay ramp formed between two overlapping fault segments in Arches National Park, Utah.
Fault linkage in the slip direction 

Faults grow in the directions both normal and parallel to the slip direction and therefore interfere in both the vertical and horizontal directions. In the previous section we looked at the horizontal interaction of normal fault tips. Now we will look at the interference of normal fault tips in the vertical plane, i.e. parallel to the slip vector. Fault linkage is most commonly recognized and described in map view, but this is simply because they are easier to observe in map view. Tall vertical sections are less common than long horizontal exposures, and the continuity of good seismic reflectors in the horizontal direction makes it easier to map relays in map view than in the vertical direction. It takes a whole package of good reflectors to identify and map vertical overlap zones on seismic sections. There is therefore a good chance that vertical relay zones are under represented in seismic interpretations. Faults initiate after a certain amount of strain that depends on the mechanical properties (Young’s modulus, etc.). As strong rock layers start to fracture, weak rocks continue to accumulate elastic and ductile deformation. As these fractures grow into faults, they will interfere and connect. In many cases sandstones become faulted before shales. The process is similar to that occurring in map view, except that the angle between the displacement vector and the layering is different. The rotation depends on fault geometry and how the faults interfere. Restraining overlap zones are, in this connection, overlap zones with shortening in the displacement direction. In principle, volume reduction may accommodate the deformation within the zone. More commonly, however, the layers within the overlap zone rotate. Releasing overlap zones are zones where the fault arrangement and sense of displacement cause stretching within the overlap zone. Weak layers such as shale or clay layers are rotated within releasing overlap zones. If the overlap zone is narrow, such weak layers can be smeared along the fault zone. Field observations show that this is a common mechanism for the formation of clay smear in sedimentary sequences, but usually on too small a scale to be detected from seismic data. Such structures may cause faults to be sealing with respect to fluid flow, which can have important implications in petroleum or groundwater reservoirs.

The role of lithology 

Layering or mechanical stratigraphy is important as fault populations develop in layered rocks. The timing of fault formation in the different layers is one aspect, and the way that faults form (ordinary fracturing versus faulting of deformation band zones) is another. Mechanical stratigraphy simply implies that the rock consists of layers that respond mechanically differently to stress, i.e. they have different strengths and different Young’s moduli (E). In simple terms, some layers, such as clay or shale, can accommodate a considerable amount of ductile strain, while other layers, such as limestone or cemented sandstone, fracture at much lower amounts of strain. The result is that, in a layered sequence, fractures or deformation bands initiate in certain layers, while adjacent layers are unaffected or less affected by such brittle structures. So long as the deformation band or fracture grows within a homogeneous layer, a proportionality exists between maximum displacement, length and height. Once the fracture touches the layer boundaries it is called a vertically constrained fracture, and the fracture will only expand in the horizontal direction. This means that the fracture gets longer and longer while its height remains constant, i.e. its eccentricity increases. In fact, its shape is likely to become more rectangular than elliptical.
The moment a fracture is constrained, its area increases only by layer-parallel growth, and its displacement/ length (D/L) ratio becomes lower than what it was during its unconstrained growth history. In simple terms, this is because displacement scales with fracture area, and since the fracture area only increases along its length, the length has to increase at a faster rate relative to displacement. Eventually, if the fracture keeps accumulating displacement, it will break through the bounding interface and expand into the overlying/underlying layers. The D-L relationship will then return to its original trend. The same development is seen for deformation bands in sandstone-shale sequences. At a critical point the deformation band cluster in the sandstone is cut by a slip surface (fault) that extends into the over and/or underlying shale.
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