Science - USA (2021-07-09)

streams ( 7 , 8 ). He noted that offset increases
channel length without changing the drop in
elevation (Fig. 1A), thus reducing channel gra-
dients in fault-crossing reaches. Where a chan-
nel enters a fault zone, the shallowing slope
associated with a reduction in sediment trans-
port causes deposition on the channel floor
( 9 ). Wherever the combined depth of aggrad-
ing sediment and water approaches the height
of local topographic barriers, flow is suscepti-
ble to diversion in a sudden abandonment of
thechannel,knownasanavulsion( 10 ). Flow
then incises a new channel in the steepest
descent direction, typically orthogonal to the
fault trace. In this way, avulsion resets the
offset and orientation of fault-crossing chan-
nels ( 2 , 7 ) (Fig. 1B). The upstream bend locally
incurs the most pronounced change in chan-
nel slope and therefore marks an avulsion
node, a persistent point for subsequent avul-
sions to occur (Fig. 1C), much in the same way
that the backwater length scale in lowland
coastal rivers controls the location of geo-
logically persistent flow deceleration, sedi-
mentation, and therefore chronic avulsion in
deltas ( 11 ). Trenching and geochronology along
channels in the Carrizo Plain corroborate re-
peated cycles of aggradation, avulsion, and in-
cision ( 4 , 7 ).
The importance of sedimentation in the life
span of fault-crossing channels suggests that
bedload transport, rather than the stream’s
ability to erode the bed, limits their long-

term evolution. In a transport-limited chan-

nel, the rate of aggradation,va[L/T], impli-

citly determines the time required for a channel

to avulse,tc[T]:

hcðÞ¼tc ∫

tc

0

vaðÞtdt ð 1 Þ

( 12 ), where the avulsion thresholdhc(t) is

the net height of aggraded sediment required

for the channel to overflow its container,

which may be either a bank or a valley wall.

Equation 1 evaluates the avulsion threshold

at the time of avulsion,tc; before this point

in time, aggradation in active channels can

never exceed the threshold. Throughout, the

value ofhc(t) may vary as a result of dip-slip

along the fault, or because of advection of

topographic features such as shutter ridges,

depressions, or abandoned channel heads.

We first expand Eq. 1 with particular con-

sideration of aggradation at the avulsion node

and examine how the present-day geometry

constrains and validates it, and then explore

the influence of the avulsion threshold’s time

dependence. If we assume bedload transport

capacity to be linearly related to channel slope,

then the rate of erosion or aggradation [L/T] is

proportional to a change in slope in the chan-

nel profile ( 13 ),

va¼k

@S

@x

ð 2 Þ

wherexis the distance along the channel

profile [L],Sis the channel slope, andkis a

diffusivity coefficient [L^2 /T]. The diffusiv-

ity coefficient represents the volumetric sedi-

ment transport capacity per unit channel

width and slope. A channel conveying more

sediment has a higher diffusivity coefficient

and adjusts more rapidly to perturbations

in the channel slope.

The channel elevation profile allows for use-

ful approximations of the right side of Eq. 2

(Fig. 1E). For a narrow fault zone, offset intro-

duces a fault-parallel segment with slopeSf,

whichismuchsmallerthantheoriginalslope

S 0 ,suchthatDS=Sf–S 0 ≈–S 0 approximates

the slope change without aggradation. In re-

sponse, a wedge of sediment near the avulsion

nodegrowsasasymmetricdiffusivepulse.We

define its horizontal half-width at the time

of avulsion aslcand thus approximate the

channel response leading up to the avulsion

as–k(@S/@x)≈k(S 0 /lc).

To relate Eq. 1 and Eq. 2, we castlcin terms

of the initial channel slopeS 0 and the avulsion

threshold heighthc. After aggradation to the

threshold level, the riseS 0 lcaccommodates

twice its original run, recovering half the orig-

inal slope (Fig. 1E). This leads to the relation-

shipS 0 /2≈hc/lcor, equivalently,lc≈ 2 hc/S 0 , an

approximation that is consistent with measure-

ments of millennial-scale slope changes along

alluvial rivers induced by check-dams ( 14 ) and

holds when channel response is rate-limiting

SCIENCEsciencemag.org 9JULY2021•VOL 373 ISSUE 6551 205

Wallace

Creek

Recently

avulsed

dobs

Active

channel

dc

vx

Avulsion

node vx

dobs(abandoned)

Abandoned

channel

vx

dobs(active)

Dragon's Back

S 0

~S 0 /2

hc

Avulsion node

Eroding

Fault parallel

Aggrading

lc

L dobs v

x

AggradationTime

hc

tc

Aggrading

Eroding

vx

D E

A B C

Fig. 1. The life span of fault-crossing channels.(AtoD) Hillshading ( 28 ) illustrates,
in progressive stages, (A) an offset channel, (B) a recently avulsed or reset channel
at the critical offsetdc, and (C) a subsequently offset channel. (D) Large fault-parallel
drainage along the advection path from the Dragon’s Back. In this case, the
penultimate avulsion caused a pulse of incision due to the resulting steeper gradient.
Locations for (A) to (D) are shown in fig. S4. (E) Idealized elevation profile of an

offset channel (shown in plan view in the upper inset), with a reachLand offsetdobs,

undergoing horizontal fault slipvx. Offset introduces a fault-parallel segment with

near-horizontal slope (black dotted lines); the channel responds evolving with time

(gray dotted lines) up until its current geometry (bold line). Avulsion occurs at time

tcif aggradation approaches the threshold heighthc(lower inset), which can be related

to the upstream aggradation length scalelcand the initial slopeS 0 (gray triangle).

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