transport rates are high, the evolution of chan-
nels after individual earthquakes on centennial
time scales may better capture the geomorphic
process (fig. S3). Bedrock channels where sedi-
ment transport is not limiting may be better
modeled as detachment-limited kinematic waves
of erosion ( 17 – 19 ) with fault damage promoting
headward incision along the fault ( 2 , 20 ).
Up to this point in our analysis, we used the
avulsion threshold with respect to the present-
day channel geometry, independent of consid-
eration for its path and continued evolution.
Expandinghc(t)=h 0 +lvxt+ ···, whereh 0
reflects initial channel height or incision im-
mediately after an avulsion, andlis the dimen-
sionless ratio of apparent vertical to horizontal
motion in the fault plane at the avulsion node.
Topographic gradients translated along strike
and obliquity in slip (the ratio of strike-slip to
dip-slip motion) contribute tol. For the San
Andreas Fault, obliquity in slip rarely exceeds
10% ( 21 ). For sharp topographic elements
advected in front of the avulsion node,lmay
be much higher (e.g., an angle of repose slope
is approximately 35°, corresponding to a 70%
gradient) over relatively short distances. The
growth of the avulsion threshold, if sufficiently
high, may outpace channel aggradation (Fig. 4).
This results in persistent fault-parallel drain-
age, analogous to a river diverted by active up-
lift ( 22 ). In such cases the penultimate avulsion
may not occur at the avulsion node, where ag-
gradation is highest, but rather downstream,
where uplift wanes (e.g., figs. S40 and S41). Un-
like other fluvial environments susceptible to
frequentavulsion,suchasdeltasorfans( 10 ),
aggradation in offset channels is effectively
unbounded when there is sustained growth of
hc(t). Sedimentation can therefore far exceed
flow depths.
Introducing the time-dependent avulsion
threshold into Eq. 3 yields a limit,lc, in which
fluctuation inhcoutpaces aggradation,lc≈kS 02
16 vxh 0ð 5 ÞIfl>lc, channels are diverted along strike
( 15 ) (Fig. 4). For the channels we studied,lc
(estimated from Eq. 5) is typically on the order
of a few percent and is therefore sensitive to
near-fault topography, which may contribute
to the ubiquity of fault-parallel drainage on
the San Andreas Fault. Where near-fault relief
is high, the timing of avulsion is modulated by
the valley spacing or abandoned channels that
are advected along the fault ( 19 , 23 ). In the
Carrizo Plain, subdued near-fault topography
and nearly horizontal slip implies that the ratio
of vertical to horizontal motion rarely exceeds
the critical obliquitylcand results in abundant
cross-fault drainage. Along the Dragon’s Back,
however,l≈6% along a kilometer of the fault
( 24 ) is consistent with uncharacteristically
long channel offset and suppressed cross-fault
drainage (Fig. 1D and figs. S40 and S41). The
case ofl< 0 (downdropping) results in an
unstable channel geometry, which is likely to
develop alluvial fans where channels reset in
high-flow events ( 5 , 25 ). For large rivers, the
numeratorkS^20 of Eq. 5 is roughly two orders
of magnitude larger than the ephemeral chan-
nels of the Carrizo Plain ( 26 ), which suggests
that established fault-crossing rivers are less
susceptible to diversion. Therefore, major fault-
parallel drainages along strike-slip faults may
preferentially develop from the coalescence of
smaller tributaries.
The geometry of offset channels is the pro-
duct of an interactive fluvial-tectonic system.
In the Carrizo Plain, channels offset by the
San Andreas Fault provide an opportunity to
characterize the long-term evolution of chan-
nels under a simple forcing history. In these
reaches, the life span of fault-crossing chan-
nels is well described by a transport-limited
response culminating in avulsions. The con-
figuration of fault-crossing channels, readily
obtained from topography data, quantifiably
constrains the relative pace of the tectonic and
fluvial systems. Our analysis implies that the
geomorphology of strike-slip fault zones exists
in a careful balance where subtle changes to
the system can toggle drainage from fault-
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ACKNOWLEDGMENTS
We thank the members of the UCSC seismology laboratory
along with A. M. Rodriguez Padilla, A. Duvall, C. Abrahams,
D. Draper, and M. Oskin for providing thoughtful insight and
discussion.Funding:Supported by NASA FINESST fellowship
80NSSC19K1300 and the Southern California Earthquake
Center (contribution no. 11001). SCEC is funded by NSF
Cooperative Agreement EAR-1600087 and USGS Cooperative
Agreement G17AC00047.Author contributions:
Conceptualization, K.D.C., N.J.F., E.E.B.; data curation, K.D.C.;
formal analysis, K.D.C.; methodology, K.D.C., N.J.F., E.E.B.;
investigation, K.D.C., N.J.F., E.E.B.; visualization, K.D.C.;
funding acquisition, K.D.C., E.E.B.; supervision, N.J.F.,
E.E.B.; writing–original draft, K.D.C.; writing–review and
editing, K.D.C., N.J.F., E.E.B.Competing interests:To the
best of the authors’knowledge, we have no conflict of
interest publishing this research.Data and materials
availability:All data are available in the manuscript or the
supplementary materials. The data collected in this paper
are available in table S1. Figures were produced using QGIS
( 27 ) and MATLAB, with source code provided at https://
doi.org/10.5281/zenodo.4766502.SUPPLEMENTARY MATERIALS
science.sciencemag.org/content/373/6551/204/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S64
Table S1
References ( 28 – 33 )13 October 2020; accepted 18 May 2021
10.1126/science.abf2320SCIENCEsciencemag.org 9JULY2021•VOL 373 ISSUE 6551 207
AvulsionTimeAggradationt 1hc(t) t 2h 0DivertedCAvulsive
riticalFig. 4. Channel aggradation and relative vertical
motion along the fault.Aggradation at the
avulsion node is shown as a function of time for a
channel with an avulsion thresholdhc(t) that grows
with time. Timest 1 andt 2 represent the two
solutions to the quadratic form of the avulsion time
scale; however, only timet 1 is physically realized,
as the system resets once avulsion occurs. In detail,
aggradation exhibits jagged high-frequency fluctua-
tions representing cut-in-fill behavior but should be
well approximated as a smooth diffusive curve
on millennial time scales.
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