Stress, faults, and folds - Tectonic Geomorphology - page 83

have a coseismic displacement gradient that
is itself bow-shaped? In fact, the cumulative
displacement profile is predicted to be triangu-
lar for coseismic displacement patterns that are
either bow-shaped or box-like, whereby dis-
placement is uniform along most of the fault in
each seismic event. Studies of over 200 normal
faults in the Afar Depression near the southern
end of the Red Sea rift (Manighetti et al. , 2001)
reveal both triangular and semi-elliptical dis-
placement patterns, but these styles character-
ize only about 20% of all the faults (Fig. 4.10).
Symmetrical triangular profiles develop when
both tips of a fault progressively propagate out-
ward without restriction. Much more commonly,
however, barriers appear to impede propaga-
tion of either one or both tips of a fault.
Whenever a fault continues to accumulate dis-
placement without lengthening, the slip gradi-
ent becomes increasingly steep near the
restricted fault tip (Fig. 4.10). Thus, if barriers
remain effective in future earthquakes, the slip
profile evolves from triangular to more and
more semi-elliptical.
These models for fault profiles provide a
basis for interpretations of where faults freely
propagate, where barriers exist, and where
former barriers have been breached. They also
offer an attractive explanation for how the
theoretically predicted triangular slip profiles
evolve toward semi-elliptical ones. An impor-
tant implication from this study in Afar is that,
even if a fault is no longer lengthening, slip can
continue to accumulate (Manighetti et al. ,
2001). A key corollary is that, rather than stead-
ily growing, faults may lengthen to their full
lateral extent early in their history, as has been
documented in studies in which the chronolog-
ical history of fault growth is well constrained
(Walsh et al. , 2002).
For the faults cutting the Bishop Tuff
(Fig. 4.9), the maximum displacement ( D ) is
about 1-2% of the fault length ( L ). A compilation
of displacement data (Fig. 4.11) from a variety
of settings and different types of faults (Davis
et al. , 2005; Schlische et al. , 1996; Scholz, 2002)
suggests that predictable scaling relationships
exist between the length of a fault and the
maximum displacement. For faults longer than a

Displacement variations along a fault,
fault growth, and fault segmentation

Fault length and displacement variations

The concept of characteristic earthquakes
contrasts with studies suggesting that, as a fault
accumulates a greater total displacement, it
lengthens, such that, with each earthquake, the
rupture is extended a bit more. But, does
displacement vary systematically along a single
fault, or is it unpredictable? Do spatial variations
in total fault displacement provide insight into
how the fault grew over time? In order to collect
a robust data set on fault growth and displace-
ment, at least three attributes are desirable: a
widespread planar surface that can serve as a
marker against which to calibrate fault displace-
ments; a large array of faults offsetting the
surface; and an absence of significant post-
faulting erosion or deposition on the deformed
marker. By exploiting these characteristics, a
key study of fault growth (Dawers et al. , 1993)
was undertaken on the Bishop Tuff (Fig. 4.9E),
an extensive ashflow in eastern California that
is ∼ 770 ka (Bailey et al. , 1976; Crowley et al. ,
2007). The normal faults that offset this tuff
display similar displacement patterns for fault
lengths spanning about two orders of magnitude
(20-2000 m; Fig. 4.9A, B, and C). For all these
faults, the most rapid increases in displacement
occur nearer their tips than toward the central
part of the rupture, and for most faults, the
change in displacement with distance from a
fault tip is initially quite linear. The region of the
fault containing the maximum displacement
may show either broad, slowly varying displace-
ment, as is typical of the longer faults, or quite
abrupt changes, as is typical of the shorter faults.
The former display bow-shaped displacement
profiles (Fig. 4.9C), whereas the latter show
more triangular profiles (Fig. 4.9A).
The overall suite of faults cutting the Bishop
Tuff has a broadly bow-shaped or semi-elliptical
displacement profile (Fig. 4.9D), a shape that is
considered to characterize many faults that have
experienced numerous earthquakes. But, can
such a displacement profile be developed by
faults that lengthen with each earthquake and