Dating offset fans along the Mojave section of the San Andreas fault using
cosmogenic 26Al and 10Be
A. Matmon†
D.P. Schwartz
U.S. Geological Survey, 345 Middlefield Rd., Menlo Park, California 94025, USA
R. Finkel
S. Clemmens
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
T. Hanks
U.S. Geological Survey, 345 Middlefield Rd., Menlo Park, California 94025, USA
ABSTRACT
Analysis of cosmogenic 10Be and 26Al in
samples collected from exposed boulders (n
= 20) and from buried sediment (n = 3) from
offset fans along the San Andreas fault near
Little Rock, California, yielded ages, ranging
from 16 to 413 ka, which increase with distance from their source at the mouth of Little
Rock Creek. In order to determine the age of
the relatively younger fans, the erosion rate
of the boulders and the cosmogenic nuclide
inheritance from exposure prior to deposition in the fan were established. Cosmogenic nuclide inheritance values that range
between 8.5 × 103 and 196 × 103 atoms 10Be g–1
quartz were determined by measuring the
concentrations and ratios of 10Be and 26Al in
boulders (n = 10) and fine sediment (n = 7) at
the outlet of the present active stream. Boulder erosion rate, ranging between 17 and
160 mm k.y.–1, was estimated by measuring
10
Be and 26Al concentrations in nearby bedrock outcrops (n = 8). Since the boulders on
the fans represent the most resistant rocks in
this environment, we used the lowest rate for
the age calculations. Monte Carlo simulations
were used to determine ages of 16 ± 5 and 29
± 7 ka for the two younger fan surfaces.
Older fans (older than 100 ka) were dated
by analyzing 10Be and 26Al concentrations in
buried sand samples. The ages of the three
oldest fans range between 227 ± 242 and 413
± 185 ka. Although fan age determinations
are accompanied by large uncertainties, the
results of this study show a clear trend of
†
E-mail: [email protected].
increasing fan ages with increasing distance
from the source near Little Rock Creek and
provide a long-term slip rate along this section of the San Andreas fault.
Slip rate along the Mojave section of the
San Andreas fault for the past 413 k.y. can
be determined in several ways. The average
slip rate calculated from the individual fan
ages is 4.2 ± 0.9 cm yr–1. A linear regression
through the data points implies a slip rate of
3.7 ± 1.0 cm yr–1. A most probable slip rate of
3.0 ± 1.0 cm yr–1 is determined by using a χ2
test. These rates suggest that the average slip
along the Mojave section of the San Andreas
fault has been relatively constant over this
time period. The slip rate along the Mojave
section of the San Andreas fault, determined
in this study, agrees well with previous slip
rate calculations for the Quaternary.
Keywords: San Andreas fault, offset alluvial
fans, cosmogenic isotopes, slip rate, Little
Rock Creek.
INTRODUCTION
The rate at which displacement has occurred
through time, especially during the Quaternary,
is fundamental to the understanding of the
general behavior of the San Andreas fault and
its role in the deformation of the wider Pacific–
North American plate boundary zone. The slip
rate is also a principal parameter in evaluating
the fault’s seismic hazard.
The San Andreas fault (Fig. 1) is one of the
most active transform faults in the world. Paleogeographic reconstructions and paleoseismic
research have been conducted along various
parts of the San Andreas fault for the past several
decades (Hill and Dibblee, 1953; Crowell, 1952,
1954, 1962; Powell, 1981, 1993; Ehlig, 1981,
1982; Sieh, 1984; Weldon and Sieh, 1985; Matti
et al., 1985; Frizzell et al., 1986; Barrows et al.,
1985; Niemi and Hall, 1992; Fumal et al., 2002).
Great discrepancies have developed over the timing and amount of total offset along the southern
San Andreas fault, which range between 150 and
270 km (e.g., Matti et al., 1985; Matti and Morton,
1993). Most researchers agree that motion along
the modern San Andreas fault initiated ca. 5 Ma
and resulted in ~150 km of total offset.
Paleoseismic methods such as lichenometrybased dating (Bull, 1996), dating of precariously
balanced rocks (Brune, 1996; Bell et al., 1998),
and the most common method of trenching (e.g.,
Fumal et al., 2002) enable detection of paleoseismic events and calculation of recurrence intervals between surface-rupturing seismic events.
Determining lateral slip rates, however, is much
more difficult (e.g., Weldon et al., 2002). Present
slip rates can be determined by geodetic methods
(e.g., Bennett et al., 1996). However, the determination of slip rates along strike-slip faults over
longer time periods requires the identification
and correlation of displaced geomorphic features
on both sides of the fault (Sieh and Jahns, 1984;
Weldon and Sieh, 1985).
Slip rates along the southern San Andreas
fault, including the Mojave section between
Cajon Creek in the southeast and Three Points
in the northwest (Fig. 1), have been estimated in
several studies (Sieh and Jahns, 1984; Weldon
and Sieh, 1985; Barrows et al., 1985; Powell and
Weldon, 1992) (Table 1). In general, slip rates
along the Mojave section of the San Andreas
fault over the last 5 m.y. have been established
GSA Bulletin; May/June 2005; v. 117; no. 5/6; p. 795–807; doi: 10.1130/B25590.1; 8 figures; 5 tables.
For permission to copy, contact [email protected]
© 2005 Geological Society of America
795
MATMON et al.
Figure 1. Study area. There are three main drainage systems in the area. Little Rock Creek is the biggest with a drainage basin of ~200 km2.
SAF—San Andreas fault (red thick line), LRC—Little Rock Creek, PC—Pallett Creek, BRC—Big Rock Creek (with associated drainages
in color). Thick dashed line—base of mountain front of the San Gabriel Mountains. Notice that Little Rock Creek exits the mountain front
close to the San Andreas fault, thus depositing coarse material north of the fault. Pallett Creek, on the other hand, exits the mountain front
~3 km south of the San Andreas fault. Studied fans are marked in red shapes that approximate the shape of the fans. Hexagons—bedrock
sample locations. Circles—boulder and sediment sample locations. Bright pink areas—outcrops of hornblende, gabbro, and other mafic
rocks. Geology after Jennings and Strand (1969), Barrows et al. (1985), and Dibblee (2002a, 2002b). Inset: Map showing major faults in
southern California and location of study area along the San Andreas fault. Thick line—San Andreas fault. WC—Wallace Creek, TP—
Three Points, LR—Little Rock Creek area, CC—Cajon Creek.
TABLE 1. SLIP RATES ALONG THE SAN ANDREAS FAULT
796
Location
Slip rate
(mm yr–1)
Measured feature
Time span
(yr)
Reference
Mission Creek
Biskra Palms
Biskra Palms
Southern San Andreas
Cajon Pass
Wrightwood
Wallace Creek
Wallace Creek
San Jacinto
Indio Hills
Little Rock
Little Rock
Pallett Creek
Pallett Creek
Three Points
4±2
23–35
23.3 ± 3.5
26 ± 2
24.5 ± 3.5
20–40
33.9 ± 2.9
35.8 ± 5.4
10
2–4
≥16–19
~38
9
35.6 ± 6.7
46–60
Offset paleochannel
Offset fans, age by soil profiles
Offset fans, cosmogenic isotopes
Global Positioning System
Offset terrace risers
900
Late Quaternary
Late Quaternary
Recent
14,400
1600
3700
13,250
Fumal et al. (2002)
Keller et al. (1982)
Van der Woerd et al. (2001)
Bennett et al. (1996)
Weldon and Sieh (1985)
Weldon et al. (2002)
Sieh and Jahns (1984)
Sieh and Jahns (1984)
Sharp (1981)
Sieh and Williams (1990)
Schwartz and Weldon (1986)
Schwartz and Weldon (1986)
Sieh (1984)
Salyards et al. (1992)
Rust (1982, 1986)
Offset channels
Offset channels
Alignment arrays, man-made features
Offset stream
Offset stream
Missing slip in nonbrittle deformation
Paleomagnetic measurements
300
1200
3510
1100
750–1000
Geological Society of America Bulletin, May/June 2005
57.1 ± 2.65
4.41 ± 0.37
12.8 ± 1.05
19.2 ± 1.54
3.41 ± 0.39
31.7 ± 2.17
23.1 ± 1.12
30.9 ± 2.10
11.9 ± 0.65
18.7 ± 0.92
14.7 ± 0.85
16.50 ± 0.55
9.60 ± 0.55
7.40 ± 0.55
5.18 ± 0.55
1.75 ± 0.25
Note: LRC—Little Rock Creek.
†
Measured concentrations were normalized using scaling factors from Lal (1991) for nucleonic production and Granger and Smith (2000) for muogenic production.
‡
Burial sediment samples (0.25–0.85 mm fraction). Sample LRDP-1 was collected from a trench, 160 cm below surface. Samples LROF-26 and LROF-5 were collected from natural
stream gaps, 30–60 m below fan surfaces. Unmarked samples are boulder samples.
6.31 ± 0.63
4.81 ± 0.46
5.13 ± 0.49
26.8 ± 1.24
2.31 ± 0.20
9.57 ± 0.77
6.88 ± 0.57
5.50 ± 0.47
5.32 ± 0.67
1.78 ± 0.20
6.00 ± 0.45
5.80 ± 0.67
17.0 ± 1.16
11.6 ± 0.56
5.65 ± 0.42
16.5 ± 1.12
5.99 ± 0.40
6.36 ± 0.35
5.49 ± 0.32
5.43 ± 0.40
10.2 ± 0.50
7.86 ± 0.45
6.44 ± 0.40
1.12 ± 0.05
1.15 ± 0.04
1.52 ± 0.06
1.83 ± 0.06
1.45 ± 0.07
1.76 ± 0.06
1.06 ± 0.04
2.09 ± 0.07
2.93 ± 0.09
1.28 ± 0.15
2.83 ± 0.09
2.14 ± 0.07
1.65 ± 0.06
4.04 ± 0.14
0.35 ± 0.02
2.03 ± 0.06
1.74 ± 0.05
1.95 ± 0.06
1.34 ± 0.06
3.99 ± 0.12
4.70 ± 0.18
4.79 ± 0.15
0.49 ± 0.02
12.0 ± 0.74
2.09 ± 0.10
2.14 ± 0.07
2.83 ± 0.12
3.41 ± 0.11
2.70 ± 0.12
3.28 ± 0.11
1.98 ± 0.08
3.91 ± 0.14
5.46 ± 0.17
2.40 ± 0.29
5.27 ± 0.17
3.99 ± 0.13
3.08 ± 0.11
7.53 ± 0.26
0.64 ± 0.04
3.80 ± 0.12
3.50 ± 0.11
3.63 ± 0.12
2.50 ± 0.12
8.50 ± 0.26
8.78 ± 0.33
8.94 ± 0.28
0.92 ± 0.04
0407066/3818927
0407065/3818927
0408008/3818486
0408290/3818327
0408774/3818135
0410747/3817155
0410262/3817394
0410002/3817529
0410940/3817469
0412785/3816208
0412693/3816342
0412541/3816379
0412306/3816548
0412361/3816411
0411850/3816723
0413965/3815702
0414160/3815632
0414408/3815409
0414474/3815603
0420382/3812510
0420472/3812625
0420700/3812567
0420410/3812660
0.68 ± 0.25
0
0
1
1
1
2
2
2
2
3
3
3
3
3
3
4
4
4
4
5
5
5
5
LROF-22
LROF-23
LROF-15
LROF-16
LROF-17
LROF-11
LROF-12
LROF-13
LROF-14
LROF-6
LROF-7
LROF-8
LROF-9
LROF-10
LROF-26‡
LROF-1
LROF-2
LROF-3
LROF-5‡
LROF-19
LROF-20
LROF-21
LRDP-1‡
TABLE 2. BOULDER AND BURIAL SAMPLES
942
942
982
980
983
1028
1043
1050
1032
1096
1090
1089
1089
1078
1036
1088
1098
1094
1060
1178
1181
1178
1178
Location (UTM)
(NAD 27)
Sample name Fan no.
Distance from
piercing point at LRC
(km)
Measured 26Al
Normalized 10Be
Normalized 26Al
Elevation
Measured 10Be
(105 atoms g–1 quartz) (105 atoms g–1 quartz) (105 atoms g–1 quartz)† (105 atoms g–1 quartz)†
(masl)
26
Al/10Be
5.61 ± 0.39
OFFSET FANS ALONG THE SAN ANDREAS FAULT
to be relatively constant at 3.5 cm yr–1 (Powell
and Weldon, 1992). The existing slip rate estimates for the late Pleistocene and Holocene are
based on several dating techniques, of which 14C
is the most common. Slip rate calculations along
the southern San Andreas fault range between
0.16 and 6.0 cm yr–1 (Table 1). However, most
estimates range between 2.5 and 4.0 cm yr–1.
Early Pleistocene and Pliocene offset rates of 3–
4 cm yr–1 have been calculated along the Mojave
section of the San Andreas fault by reconstructing the magnetostratigraphy of the Phelan Peak
Formation (Weldon et al., 1993). In spite of the
number of studies done along the southern San
Andreas fault, Quaternary offset measurements
and calculated slip rates, especially for the
middle and early Pleistocene, along the Mojave
section are not well constrained.
In the present study we measured the concentration of 10Be, and in some samples 26Al, in
boulders and fine-grained sediments collected
from fan surfaces offset as much as 16.5 km
from Little Rock Creek (Fig. 1) and calculated
the ages of these fans. We calculated slip rates
over the past 0.4 m.y. along the Mojave section
of the San Andreas fault using the calculated
ages and the estimated offsets of the fans. Our
results agree with previous slip rate calculations and suggest that the San Andreas slip rate
has been relatively constant during this time
and that the San Andreas fault has been accommodating a constant percentage of the motion
between the North American and Pacific plates
during the past 0.4 m.y.
The ages of tectonically offset surfaces have
been established using cosmogenic nuclide analysis (Bierman et al., 1995; Siame et al., 1997;
Brown et al., 1998; Zehfuss et al., 2001; Van der
Woerd et al., 1998, 2000, 2002). Concentrations
of cosmogenic nuclides are interpreted using
models dependent on a variety of assumptions
(Bierman, 1994; Gosse and Phillips, 2001).
Using assumed rates of nuclide production, the
exposure age of a surface can be estimated from
the abundance of cosmogenic isotopes preserved
in the surface material (Lal, 1988). In spite of the
complexities and the uncertainties associated
with cosmogenic age dating, this method permits
estimation of ages of surfaces.
SITE DESCRIPTION
A series of alluvial fan remnants are aligned
along the San Andreas fault at distances ranging from 0.7 to 16.5 km from the present mouth
of Little Rock Creek (Fig. 1; Table 2). Incising
streams and roadcuts expose deep cross sections
through the fans. These exposures show that the
fan deposits are bedded and that coarse boulder
units alternate with sandy layers. The fans are
Geological Society of America Bulletin, May/June 2005
797
MATMON et al.
composed of rounded to subrounded boulders
(up to 1 m) embedded in grus (the physical
weathering products of the boulders) and sandy
matrix. The boulders mostly consist of granite,
quartz diorite, granodiorite, and gneiss. Other
lithologies such as gabbro, amphibolite, and
hornblende also occur in lesser amounts. All
of these lithologies outcrop along the slopes of
the Little Rock Creek drainage basin (Barrows
et al., 1985). The alluvial structure of the sediments and the rounded boulders indicate that the
fan material was deposited by alluvial activity
and that deposition did not occur as a result of
mass-wasting events from nearby slopes.
In this study, we examined six locations where
such remnants of alluvial material are preserved
(Fig. 1). These fan remnants are numbered from
0 to 5 with increasing distance from Little Rock
Creek. Fans 0–2 are relatively small and are
dissected. However, in fans 0 and 1, which are
separated by an elevation difference of ~40 m,
the original upper fan surface is preserved in
some locations. The location and morphology
of fan 2 suggest that its surface has been modified by drainage systems that were active after
it was offset from the Little Rock Creek outlet.
Therefore, cosmogenic nuclide concentrations
measured in boulders collected from fan 2 were
not interpreted as exposure ages that represent
the fan’s age. Fans 3–5 are relatively large and
have flat and broad upper surfaces, providing
conditions favorable for dating them.
At present, the fans are not located near
any alluvial source capable of supplying such
coarse-grained alluvial deposits. Barrows et al.
(1985) and Dibblee (1967) suggested that these
alluvial sediments were deposited in a fan at the
mouth of Little Rock Creek, the largest drainage
system in the area, and then transported from its
location of original deposition by the right-lateral slip along the San Andreas fault. This suggestion is supported by the consistent lithologic
assemblage found in the fans with respect to the
rocks exposed in the Little Rock Creek basin.
This assemblage contains lithologies such as
gabbro, amphibolites, and hornblende derived
from the basement complex (Barrows et al.,
1985) (Fig. 1). However, Barrows et al. (1985)
considered many of the coarse-grained alluvial
outcrops, north of the San Andreas fault, to be
remnants of the same fan with the same age. On
the other hand, Crowell (1974) and Weldon et
al. (1993) showed that the alluvial sediments
deposited onto the Mojave Desert floor by Little
Rock Creek are time-transgressive and therefore
increase in age with increasing distance from
the mouth of Little Rock Creek. Weldon (1986)
demonstrated this hypothesis for deposits older
than 0.7 Ma. In this study we test this hypothesis
for units younger than 0.4 Ma.
798
OFFSET DETERMINATION
Offset of fans by the San Andreas fault is
determined by measuring the distance between
the northwesternmost point of each fan and a
piercing point within Little Rock Creek. We
assume that the northwesternmost point of each
fan was the closest to the active stream at the
time of deposition. Piercing point determination within Little Rock Creek is uncertain and
depends on understanding the historical development of the Little Rock Creek outlet. Because
the outlet of Little Rock Creek is not offset as
much as its fan remnants, it is obvious that periodically the offset river is rerouted back to its
general northward flow only to be offset again.
Thus, while the fan remnants are offset by the
San Andreas fault away from Little Rock Creek
in one direction (to the east-southeast) at a rate
determined by the motion along the San Andreas
fault, the outlet of Little Rock Creek has been
oscillating periodically to the east-southeast and
back to the west-northwest. Presently, the Little
Rock Creek outlet is incised in a gap that is offset
from the mouth of the river by ~2 km along the
San Andreas fault (Fig. 2). By considering the
present topographic setting around the Little
Rock Creek outlet (Fig. 2), the amplitude of outlet shift is at least 2 km. The distribution of fan
material associated with Little Rock Creek (Barrows et al., 1985; Dibblee, 1967) (Fig. 2) suggests that in the past Little Rock Creek drained
straight across the San Andreas fault.
It is important, when estimating the amount
of offset of the dated surfaces (especially the
closer and younger ones), to determine the
position of the Little Rock Creek outlet. It is
reasonable to assume that the initial incision of
the gap, which constrained Little Rock Creek
to this particular outlet, occurred when a ridge
(Gap Hill) initially blocked the river’s outlet due
to slip along the San Andreas fault. Until that
time, we assume that Little Rock Creek drained
across the San Andreas fault into the Mojave
Desert in the same general direction of the river
south of its exit from the San Gabriel Mountains
(Fig. 2). The older and more distant fans (fans
3–5, which are displaced more than 2 km) were
displaced to the southeast beyond the reach of
Little Rock Creek, so it did not incise into them.
The younger and closer fans (fans 0–1) were
deposited after Little Rock Creek incised into
Gap Hill. Therefore, Little Rock Creek continued to incise into the fans because it was offset
together with the fans.
To determine the piercing point for the older
fans, we extrapolate the general trend of Little
Rock Creek south of its exit from the San Gabriel
Mountains to the San Andreas fault (Fig. 2).
The crossing point is located in the middle of
the antecedent outlet of the river, which is now
blocked by Gap Hill (Fig. 2). The width of the
antecedent outlet (1.1 km) determines the uncertainty in the offset distance (±0.55 km). As Gap
Hill was offset to the east by the fault, the outlet
of Little Rock Creek, which was constrained to
the gap east of Gap Hill, shifted as well, and the
route of Little Rock Creek was first diverted to
the eastern bank of the antecedent outlet. Later,
as displacement continued, Little Rock Creek
incised along the San Andreas fault to form the
river section that connects the antecedent outlet
with the present one. The piercing point for the
younger fans is determined by extrapolating the
eastern bank of the antecedent outlet to the San
Andreas fault. However, deposition of the fans
may have occurred before the river reached
the eastern bank, thus increasing the amount
of measured offset. In contrast, recent erosion
of the northwestern edge of the fans could have
erased the original fan perimeter, thus decreasing the amount of measured offset. We use the
width of Little Rock Creek along the trace of
the San Andreas fault (0.5 km) to determine the
uncertainty in the amount of slip of the younger
and closer fans (±0.25 km). Using these piercing points we measure slip distances that range
from 0.7 ± 0.25 to 16.5 ± 0.55 km along the San
Andreas fault (Table 2). Although the uncertainty in offset of fans 0 and 1 is only 250 m, it
amounts to 37% and 14% of the offset of these
fans, respectively. The uncertainty of 0.55 km in
the offset of fans 3–5 amounts to only 3%–8%.
CONCEPTS AND METHODS
Any sand grain, clast, or boulder of alluvial
origin presently located on an abandoned fan
surface or buried within a fan in the study area
originated in Little Rock Creek after it was
detached from its bedrock source. It was deposited in the fan after being transported downslope
and downstream by colluvial and alluvial processes. After deposition and while the fan was
displaced by the San Andreas fault, boulders at
the surface were eroded and the surface of the
fan might have been lowered due to erosion.
On relatively young fans, the ages of boulders
exposed at the surface most likely represent the
age of the fan when boulder erosion rate and
inheritance can be accounted for. As the fans
mature and are displaced farther away from
their source, cosmogenic nuclide concentration
might reach a saturation value in some boulders
(Fig. 3). Eventually the boulders at the original
fan surface are eroded completely, and new
boulders are exposed due to lowering of the fan
surface. Thus, their cosmogenic model age does
not represent the age of the fan. As we discuss
below, a better representation of the age of older
Geological Society of America Bulletin, May/June 2005
OFFSET FANS ALONG THE SAN ANDREAS FAULT
Figure 2. (A) Oblique air photo of the Little
Rock Creek outlet. Little Rock Creek is
offset ~2 km along the San Andreas fault
and is incised into a gap southeast of Gap
Hill. Bright gray areas indicate Little Rock
Creek sediments deposited on hills north
and northwest of the present route of Little
Rock Creek. (B) Map of the Little Rock
Creek outlet area (UTM, NAD 27) and
an enlarged oblique photo of the piercing
points area. Shaded areas—bedrock. The
piercing point for fans 0–1 (point A) was
determined by extrapolating the eastern
bank of Little Rock Creek, which is incised
into bedrock, to the San Andreas fault. The
width of Little Rock Creek along the trace of
the San Andreas fault (0.5 km) determines
the uncertainty in the amount of slip of the
younger and closer fans (±0.25 km). The
piercing point for fans 2–5 (point B) was
determined by extrapolating the general
trend of Little Rock Creek south of its exit
from the San Gabriel Mountains to the San
Andreas fault. The crossing point is located
in the middle of the antecedent outlet of the
river now blocked by Gap Hill. The width
of the antecedent outlet (1.1 km) determines
minimum offset of fans 2–5 (±0.55 km).
700,000
ε=0
600,000
ε=10
N (atoms /g quartz)
N(0)=196*103
ε=17.5
500,000
400,000
ε=17.5
N(0)=0
300,000
ε=20
200,000
ε=30
ε=40
ε=50
100,000
0
0
50,000
100,000
150,000
t (years )
200,000
250,000
Figure 3. Cosmogenic nuclide saturation
curves. As erosion rate increases, the saturation value decreases. Saturation value reflects
the balance between production, decay, and
erosion. All erosion rates are indicated
in mm k.y.–1. At erosion rates between 10
and 20 mm k.y.–1, exposure age dating cannot be reliable beyond 50–60 ka. Curves are
calculated for 10Be production rate of 10.3
atoms g–1 yr–1 (the average production rate
of the Little Rock Creek fans). Boulder ages
in this study were calculated considering an
erosion rate of 17.5 mm k.y.–1 (thick lines).
The saturation value, at an erosion rate of
17.5 mm k.y.–1, increases with the increase of
the cosmogenic nuclide inheritance. Because
the cosmogenic nuclide inheritance value in
each boulder is not known, we use a range of
values determined by the analysis of boulders
at the mouth of the presently active stream.
We determine the most probable age using
Monte Carlo simulations (see Fig. 6). Inheritance values are given in atoms g–1 quartz.
Geological Society of America Bulletin, May/June 2005
799
MATMON et al.
surfaces can be achieved from measuring the
concentration of two cosmogenic nuclides in
material that is assumed to have been shielded
from cosmic rays since its deposition in the fan.
Modeling the Age of the Closer and
Younger Fans
We assume that boulders lying on the surface of fans 0 and 1 have been exposed since
deposition on the fan. The cosmogenic nuclide
concentration measured in any boulder located
on these fan surfaces results from two exposure
periods: (1) prior to deposition on the fan, during transport within the Little Rock Creek drainage basin, and (2) during transport along the San
Andreas fault. According to Brown et al. (1998),
exposure ages of the boulders, and by inference
the fan ages, can be modeled using
N=
P ⎛
− ( ρεΛ
1− e
ρεΛ−1 ⎝
−1
) ⎞ + N 0 e − λt , (1)
( )
⎠
+λ t
where N is the measured concentration of the
cosmogenic nuclide in atoms g–1 quartz, P is the
total surface production rate of the cosmogenic
nuclide in atoms g–1 quartz yr–1, ρ is the density
of the boulder (2.7 g cm–3), ε is the erosion rate of
the boulder in cm yr–1, Λ is the attenuation depth
of neutrons (165 g –2), t is the age of the boulder
in years, N(0) is the inherited cosmogenic nuclide
concentration in atoms g–1 quartz at the time of
deposition on the fan, and λ is the cosmogenic
nuclide decay constant (10Be—4.62 × 10−7 yr–1;
26
Al—9.90 × 10−7 yr–1). Production rate was not
scaled for magnetic intensity variations (Dunai,
2001) and boulder shape and size (Masarik
and Wieler, 2003). The first term in equation 1
expresses the accumulation, decay, and removal
by erosion of atoms during exposure on the fan.
The second term expresses the decay of inherited
atoms that accumulated prior to the deposition
on the fan. Thus, to date the fan, it is essential
to determine the boulder’s cosmogenic nuclide
inheritance at the time of deposition on the fan
and the rate at which the boulder is eroding and
losing its cosmogenically dosed material.
To estimate the inherited concentrations of
cosmogenic 10Be and 26Al in the samples, we
sampled sediment at two locations near the
present mouth of Little Rock Creek (n = 17)
(Fig. 1). At each location, we sampled five boulders (LRBD-1 [A–E], LRBD-2 [A–E]), at least
30 cm in diameter, of different lithologies, and
alluvial sediment (LRSD-1, LRSD-2), which
was sieved and divided into four size fractions: 0.25–0.85, 0.85–2, 2–10, and >10 mm
(Table 3). We assume that the sediment at the
outlet of the present river was transported at
average rates representative of Little Rock
Creek. We are aware that Holocene transport
800
TABLE 3. SEDIMENT SAMPLES FROM ACTIVE CHANNEL
Sample name
LRSD-1 (250–850)†
LRSD-1 (850–2000)
LRSD-1 (2000–10,000)
LRSD-2 (250–850)†
LRSD-2 (850–2000)
LRSD-2 (2000–10,000)
LRSD-2 (>10,000)
LRBD-1A†
LRBD-1B
LRBD-1C
LRBD-1D
LRBD-1E
LRBD-2A‡
LRBD-2B
LRBD-2C
LRBD-2D
LRBD-2E
Sample type
Measured 10Be
Measured 26Al
(105 atoms g–1 quartz) (105 atoms g–1 quartz)
Sediment
Sediment
Sediment
Sediment
Sediment
Sediment
Sediment
Boulder—granite
Boulder—granite
Boulder—granodiorite
Boulder—gneiss
Boulder—quartz diorite
Boulder—granodiorite
Boulder—granite
Boulder—granodiorite
Boulder—gneiss
Boulder—quartz diorite
0.66 ± 0.05
0.66 ± 0.03
0.48 ± 0.03
0.58 ± 0.03
0.63 ± 0.08
0.40 ± 0.03
0.35 ± 0.04
0.55 ± 0.03
1.77 ± 0.06
0.60 ± 0.03
1.06 ± 0.05
0.09 ± 0.03
1.96 ± 0.09
0.09 ± 0.02
0.29 ± 0.03
0.72 ± 0.04
1.13 ± 0.05
26
Al/10Be
3.87 ± 0.36
5.80 ± 0.70
2.33 ± 0.29
4.22 ± 0.55
3.32 ± 0.42
5.56 ± 0.77
12.4 ± 1.1
6.31 ± 0.63
1.37 ± 0.29
4.69 ± 0.49
4.74 ± 1.09
6.55 ± 0.78
†
All LRSD-1 and LRBD-1 samples were collected within 20 m of central coordinate 0406411/3814466 and
elevation 1012 masl (UTM, North American Datum 27).
‡
All LRSD-2 and LRBD-2 samples were collected within 20 m of central coordinate 0405618/3817833 and
elevation 939 masl (UTM, North American Datum 27).
rates have probably been different from those
in the Pleistocene. Therefore, the entire range
of measured inherited values was used in the
calculation of the fans’ ages.
Saturation of cosmogenic nuclide concentration occurs when production on one hand and
decay and erosion on the other are balanced and
is reached more quickly as erosion rate increases
(Fig. 3). The erosion rate of the boulder limits
the time over which cosmogenic concentration
can be modeled as an exposure age. Thus, the
cosmogenic nuclide concentration cannot indicate exposure ages of boulders older than the
saturation period. For example, at a boulder erosion rate of 20 mm k.y.–1, given the uncertainties of 10%–15% associated with cosmogenic
exposure age dating, 50 k.y. old boulders will
have a cosmogenic nuclide concentration that is
essentially time-independent.
In order to estimate boulder erosion rate, we
sampled granitic outcrops on nearby hills (n = 8;
Fig. 1; Table 4). We assume that bedrock outcrops
have been eroding long enough and that they
have reached the nuclide concentration saturation
value. This approach has been used in previous
studies (e.g., Zehfuss et al., 2001) and has proved
to reliably constrain boulder erosion rates. The
granitic outcrops that were sampled are located
1–2 km north of the San Andreas fault. The hills
rise 30–60 m above the adjacent plain and are
disconnected from the drainage systems originating in the San Gabriel Mountains. Thus, they are
subject to similar erosion processes operating on
the fans and to similar climatic conditions and
topographic setting as the boulders on the fan surfaces. The outcrops are generally formed in areas
where the granite is more resistant. The outcrops
rise 30–100 cm above their surrounding surface.
Thus, their geometry is similar to boulders that
rise above the fan surfaces.
Erosion rates were calculated accounting for
production of cosmogenic nuclides by nucleons
and muons using
N=
Pfu
P− u
P− u
Pn
, (2)
+
+
+
ρεΛ−1 + λ ρεL1−1 + λ ρεL−21 + λ ρεL−31 + λ
where N is the measured concentration of the
cosmogenic nuclide in atoms g–1 quartz, Pn,
P-µ, Pfµ are the production rates of cosmogenic
nuclides in atoms g–1 quartz yr–1, from nucleons,
negative muons, and fast muons, respectively, ρ
is the density of the eroding rock in g cm–3, ε is
the erosion rate of the rock in cm yr–1, Λ is the
attenuation depth of nucleons in g cm–2, L1, L2
and, L3 are the attenuation depths of negative
and fast muons in g cm–2, and λ is the cosmogenic nuclide decay constant in yr–1. Production
by nucleons was scaled for altitude and latitude
using Lal (1991). Scaling factors for production
by muons and muon attenuation lengths were
taken from Granger and Smith (2000).
We sampled two boulders from fan 0 (LROF22 and LROF-23) and three boulders from fan
1 (LROF-15, LROF-16. LROF-17). All the
boulders where raised at least 50 cm above
their surrounding surface. All the boulders
were rounded and were either fresh or slightly
weathered at the surface with no evidence
of spalling. Sample thickness did not exceed
5 cm. Accounting for production by secondary neutrons and muons (with scaling factors
as mentioned above), we used a high-latitude
Geological Society of America Bulletin, May/June 2005
‡
†
5.5 ± 0.32
18.31 ± 0.86
34.14 ± 1.61
Datum: NAD 27.
Normalized using scaling factors from Lal (1991) for nucleonic production and Granger and Smith (2000) for muogenic production.
§
Erosion rates calculated using a high latitude, sea level total production rate of 5.31 10Be atoms g–1 quartz, of which 2.6% are caused by muons (Granger and Smith, 2000).
#
Bedrock surface samples.
††
Bedrock pinnacle samples.
18.0 ± 2.3
27.6 ± 3.6
41.6 ± 5.4
39.5 ± 5.1
17.2 ± 2.2
87 ± 11
124 ± 16
93 ± 12
160 ± 21
1.21 ± 0.04
0.80 ± 0.04
0.80 ± 0.03
3.32 ± 0.10
0.59 ± 0.02
0.42 ± 0.02
0.55 ± 0.02
0.33 ± 0.02
2.41 ± 0.08
1.42 ± 0.06
1.84 ± 0.06
6.20 ± 0.2
1.35 ± 0.05
0.96 ± 0.04
1.27 ± 0.05
0.74 ± 0.04
1092
929
1206
1283
1278
1285
1278
1273
0415257/3816730
0405811/3820747
0419114/3814778
0424299/3812856
0425081/3812825
0424962/3812847
0424781/3812939
0424563/3813047
LRWH-1#
LRCF-1#
LRPL-1#
LRHR-1††
LRHR-2††
LRHR-3††
LRHR-4††
LRHR-5††
Elevation
(m)
Location
(UTM)†
Sample name
TABLE 4. EROSION RATE SAMPLES
Measured 26Al
Normalized 10Be
Normalized 26Al
(105 atoms g–1 quartz) (105 atoms g–1 quartz)‡ (105 atoms g–1 quartz) ‡
Measured 10Be
(105 atoms g–1 quartz)
26
Al/10Be
10
Be erosion rate
(mm k.y.–1)§
26
Al erosion rate
(mm k.y.–1)§
OFFSET FANS ALONG THE SAN ANDREAS FAULT
sea-level total production rate of 5.31 atoms g–1
quartz for 10Be for the exposure age calculations
(Schaller et al., 2001). We assume that production by muons at high latitude and sea level
is 2.6% of the total production (Granger and
Smith, 2000). We used a Monte Carlo approach
to calculate the median and most likely age of
each sampled boulder and for the mean age of
each fan surface. All boulder samples were processed following Bierman and Caffee (2001),
and isotopic ratios were measured at the Lawrence Livermore National Laboratory.
Modeling the Age of the Older Fans
Boulders on fans older than 105 yr probably
have not been exposed since deposition in the
fan and have, most likely, reached a saturation
concentration of cosmogenic isotopes. Furthermore, surface processes on the older fans cannot
be ignored. Exhumation of the fan surface, soil
production and stripping, and modification of
the original fan’s topography have influenced the
exposure history of the boulders on the surface.
Straightforward dating of boulders, even if they
are eroding at a rate of only several mm k.y.–1,
cannot yield realistic fan ages (Fig. 3). 10Be concentrations that were measured in the boulder
samples collected from the surfaces of fans 3–5
(Table 2) were not used to date these fans.
We dated the older fans using the burial
dating method (Bierman et al., 1999; Granger
and Smith, 2000; Granger and Muzikar, 2001).
Assuming a known initial 26Al/10Be in samples
that have been shielded from cosmic rays since
deposition, we can estimate the age of the
sample by measuring its present 26Al/10Be. By
solving equation 3 we estimate the burial period
(Granger et al., 1997):
(
N(
N
26
10
) =⎛ N (
⎜
Be) ⎝ N (
Al
⎛
)
)
Al ⎞ − t ⎜⎜⎝ τ (
⎟0e
10
Be ⎠
26
1
26
Al
−
) τ(
1 ⎞
⎟
Be ⎟⎠
10
)
, (3)
where N(26Al) and N(10Be) are the measured concentrations in atoms g–1 quartz of 26Al and 10Be,
⎛N
⎜
⎝N
(
(
26
10
)
)
Al ⎞
⎟ 0,
Be ⎠
is the initial ratio, τ(26Al) and τ(10Be) are the mean
lives in years of 26Al (1.02 × 106 ± 0.04) and 10Be
(2.18 × 106 ± 0.09), and t is the burial period in
years. High-latitude and sea-level production
rate and scaling factors are similar to those used
for the age calculations of the younger fans.
The burial dating method cannot be applied to
the young fans since the shift of the 26Al/10Be
ratio is too small to be detected. Sand samples
were collected from the base of slopes adjacent
to natural stream gaps in fan 3 (LROF-26) and
fan 4 (LROF-5). The sand was collected from
the alluvial material beneath the colluvium on
the slope. Sample LRDP-1 was collected from
the bottom of a pit dug into the upper surface of
fan 5. The samples from the bases of the slopes
in fans 3 and 4 were deposited during the time
the fan was constructed at the mouth of Little
Rock Creek. Since then they have been buried
by 30–60 m of fan material, and only recently
they have been exposed by the active drainage
system. We assume that their burial signal has
not been significantly modified by this recent
exposure. We did not account for production of
cosmogenic isotopes at depth by muons. Therefore, burial ages are minimum ages. We estimate
that production at depth by muons will affect the
calculated ages of fan 4 (sample LROF-26) and
fan 3 (sample LROF-5) by only a few percent
and the calculated age of fan 5 (sample LRDP-1)
by >20% (Granger and Muzikar, 2001). Sediment sample preparation followed the same procedure as boulder sample preparation.
RESULTS
Inheritance Values
The measured 10Be concentrations in boulders (n = 10) sampled from the present riverbed
of Little Rock Creek range between 0.09 ± 0.02
× 105 and 1.96 ± 0.09 × 105 atoms g–1 quartz
(Fig. 4; Table 3). When the production rate of
the sampling site is used, these abundances
could imply a near-surface residence time
within the Little Rock Creek drainage basin that
ranges between 0.9 ± 0.2 and 20.0 ± 2.2 k.y.
The lowest values (LRBD-1E, LRBD-2B) in
this range suggest the possibility of boulders
derived recently from nearby bedrock outcrops
by mass-wasting events that exposed previously
shielded rock. The higher 10Be concentrations,
which were measured in the other boulders,
accumulated during a longer exposure period as
these boulders were transported downstream.
The concentration of 26Al was measured in
five of the ten sampled boulders. The 26Al/10Be
ratio in these boulders ranges between 6.6 ± 0.8
and 4.2 ± 0.6. Three of these boulders have a
ratio of ~6, indicating no significant burial.
These boulders had a long and a relatively
continuous surface exposure within the Little
Rock Creek drainage system. The boulders that
yielded a 26Al/10Be ratio significantly lower than
6 (LRBD-1A, LRBD-2C) suggest that, after initial exposure, they were buried for 400–615 k.y.
within the terraces in the upper part of Little
Rock Creek. This long burial period might have
occurred in middle Pleistocene terraces, still
Geological Society of America Bulletin, May/June 2005
801
MATMON et al.
250,000
10
Be atoms/g quartz
Boulders
Fine sediment
200,000
150,000
100,000
50,000
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Samples
10
Figure 4. Inheritance values. Dark bars (1–10)—measured Be concentrations in boulders at the mouth of the active streambed of Little
Rock Creek. Light bars (11–17)—measured 10Be concentrations in fine sediment at the mouth of the active streambed of Little Rock Creek.
Inherited values of 10Be in boulders range between 9 × 103 and 196 × 103 atoms g–1 quartz, with an average of 82 × 103 atoms g–1 quartz.
Fine sediment inherited values are more uniform with an average of 55 × 103 atoms g–1 quartz, indicating a more typical residence time in
the Little Rock Creek drainage system.
widespread along the slopes of Little Rock
Creek (Barrows et al., 1985; Dibblee, 1967).
In contrast to the boulder samples, 10Be concentrations values in the sediments are relatively
uniform. Sediment samples (n = 7) yielded 10Be
concentrations that range between 0.35 ± 0.04
× 105 and 0.66 ± 0.06 × 105 atoms g–1 quartz
with an average of 0.54 ± 0.04 × 105 atoms g–1
quartz (Fig. 4; Table 3). These values indicate
that fine-grained sediments in Little Rock Creek
have a more characteristic residence time than
boulders. 26Al concentration was measured in
one sediment sample, LRSD-1 (0.25–0.85 mm).
A 26Al/10Be ratio of 5.8 ± 0.7 in this sample suggests that fine-grained sediment delivered to the
mouth of Little Rock Creek either was never
buried or was exposed long enough to erase any
past burial signal.
Erosion Rates
Erosion rates were determined from eight
bedrock samples. Three samples were collected
from flat bedrock surfaces. 10Be concentrations
from these three samples range between 1.4 ±
0.06 × 105 and 2.4 ± 0.08 × 105 atoms g–1 quartz
(Table 4). Assuming steady-state erosion of
bedrock, and considering production by nucleons and muons, these concentrations imply
average erosion rates that range between 27.6 ±
3.6 and 41.6 ± 5.4 mm k.y.–1.
Five bedrock samples were collected from
the top of small pinnacles that imitate the
802
geometry of boulders. 10Be concentrations from
these samples range between 0.74 ± 0.04 × 105
and 6.2 ± 0.2 × 105 atoms g–1 quartz. Assuming
steady-state erosion of bedrock, these concentrations imply average erosion rates that range
between 17.2 ± 2.2 and 160 ± 21 mm k.y.–1.
The large range of erosion rates can be a
result of a combination of several factors that
affect the rock to different degrees. Resistance
to weathering of various lithologies, range fires
that cause spalling (Bierman and Gillespie,
1991), and soil-stripping events are among
the processes and factors that can cause a large
range in erosion rates in bedrock in this area.
It is reasonable to assume that only the most
resistant bedrock pinnacles that will not be
affected by fires and other erosional processes
will become boulders in the future. Similarly,
the boulders in the fans consist of bedrock
fragments that were composed from the
most resistant lithologies and that were least
affected by erosion and weathering processes.
Therefore, we assume that they have been
eroding slower than the average erosion rate in
the area. Thus, we prefer the lowest model erosion rate calculated from the bedrock samples.
We used the value of 17.5 ± 2.2 mm k.y.–1 (the
average of the 10Be and 26Al model erosion
rates for sample LRHR-1, Table 4) for calculating the exposure age of boulders on fans 0
and 1. At this erosion rate, only boulders that
are younger than ca. 60 ka can be reliably
dated (Fig. 3).
Fan Ages
Boulder samples from six fan surfaces (n =
20, including four samples from fan 2, which
was not dated) and fine-grained buried samples
(n = 3) were collected (Table 2). Boulders from
fans 1, 2, 3, and 4 exhibit a large range of 10Be
concentrations (Fig. 5). 10Be concentrations,
normalized to a sea-level and high-latitude
production rate, increase from fan 0 to fan 1.
This trend does not continue from fan 1 to more
distant fans. Best-fitting curves through the
entire data set (Fig. 5) and through the maximum normalized 10Be concentrations in each
fan indicate that 10Be concentrations reach the
saturation value and therefore do not reflect the
ages of fans 2–5.
Only measurements from boulders collected
from fans 0 and 1 can be interpreted in terms
of exposure age dating (Fig. 6). 10Be concentrations in boulders from fan 0 range between 2.09
± 0.10 × 105 and 2.14 ± 0.07 × 105 atoms g–1
quartz (Table 2). 10Be concentrations in boulders
from fan 1 range between 2.70 ± 0.12 × 105 and
3.41 ± 0.11 × 105 atoms g–1 quartz (Table 2). The
26
Al/10Be ratio in these samples range between
5.4 ± 0.4 and 5.6 ± 0.4.
The large range of 10Be concentrations in
boulders in the active drainage systems (Fig. 4)
indicate that there is no typical inherited value
and therefore prevents the use of a single value
to calculate the age of the sampled boulders. In
order to calculate these ages we performed a
Geological Society of America Bulletin, May/June 2005
OFFSET FANS ALONG THE SAN ANDREAS FAULT
5
-1
Be (10 atoms g quartz)
6
4
Normalized
10
5
Fan 5
3
Fan 0
2
Fan 4
Fan 1
1
Fan 3
Fan 2
0
0
5
10
15
20
Distance (km)
Figure 5. Scaled 10Be concentrations (to sea-level high-latitude production) in boulders
exposed at the surface of the offset fans. The scatter in the 10Be concentrations on each fan
could be due to several factors such as different amounts of inherited cosmogenic nuclides
or different boulder erosion rates. However, the average normalized concentrations reach a
saturation value beyond fan 2. Therefore, fans 2–5 cannot be dated by measuring 10Be concentrations in exposed boulders. Lower curve is a log fit through the entire data set. Upper
curve is a log fit through the maximum values from each fan. In both cases, fans 2–5 lie
along the nearly flat part of the curve, suggesting cosmogenic nuclide saturation and timeindependent nuclide concentration.
series of 30,000 Monte Carlo simulations for
each boulder. In each simulation, a random set
of values was chosen, one from the measured
10
Be concentrations and the other from the range
of inherited values, and equation 1 was solved
using an erosion rate of 17.5 mm k.y.–1. The only
constraint on the calculation was that the value of
N – N(0)eλt could not be negative. A median age
was calculated from all the valid simulations for
each boulder (Fig. 6). The average age of fan 0 is
16 ± 5 (1σ) ka and of fan 1 is 29 ± 7 (1σ) ka.
Ages of fans 3–5 were calculated considering the concentration of 10Be and 26Al in depth
samples. Although the burial ages are based on
a single sample from each fan, each sample
contains at least 105 individual quartz grains,
which average the burial and exposure history
of the sediment in the fan. 10Be measured concentrations in depth samples collected from fans
3–5 range between 0.64 ± 0.04 × 105 and 2.50
± 0.12 × 105 atoms g–1 quartz. 26Al measured
concentrations in these samples range between
3.4 ± 0.4 × 105 and 12.8 ± 1.1 × 105 atoms
g–1 quartz. 26Al/10Be ratios in the depth samples
range between 5.3 ± 0.7 and 4.8 ± 0.5 (Fig. 7;
Table 2). By solving equation 2 we obtain ages
of 227 ± 242 ka for fan 3, 281 ± 181 ka for fan
4, and 413 ± 185 ka for fan 5.
DISCUSSION
Calculated fan ages show a trend that clearly
indicates increasing ages with increasing
distance of the fans from Little Rock Creek
(Fig. 8A). This is consistent with a simple linear
regression that suggests an average slip rate of
3.7 ± 1 (1σ) cm yr–1 over the past 413 k.y. A
similar average slip rate of 4.2 ± 0.9 cm yr–1 is
calculated arithmetically from the individual
slip rates of each fan. However, the large uncertainties in the calculated fan ages exclude these
calculated slip rates as unique and most likely
solutions. In order to estimate a more probable
slip rate that accounts for the large age and offset
uncertainties, we performed a χ2 test (Fig. 8A).
The results of the test suggest a most likely slip
rate of 3 ± 1 (1σ) cm yr–1 for the past 413 k.y.
along the Mojave section of the San Andreas
fault (Figs. 8A and 8B).
Generally, most of the published slip rate
estimates along the San Andreas fault, north
of Cajon Pass, from periods as short as the late
Holocene to long-term geologic time spans,
suggest a slip rate of 3.5 ± 1 cm yr–1. Estimates
of the amount of displacement of pre-Cenozoic
rock units range between 210 and 315 km
(Barrows et al., 1985). However, more recent
Figure 6. Results of the Monte Carlo simulations for samples collected from boulders
on fans 0 and 1. We performed a series of
30,000 simulations for each boulder. In each
simulation, a random pair of values was
chosen: one from the measured 10Be concentrations and the other from the range of
inherited values. Age calculations were done
using an erosion rate of 17.5 mm k.y.–1. The
only constraint applied was that the value
of N–N(0)e–λt could not be negative. The
median age (marked with a black vertical
line) was calculated from all the valid simulations for each boulder. The average age of
fan 0 is 16 ± 5 ka, and of fan 1, 29 ± 7 ka.
studies present evidence for total displacement
along the southern San Andreas fault in general,
and the Mojave section in particular, that range
between 150 and 185 km for the last 5 m.y.
(Powell and Weldon, 1992; Dillon and Ehlig,
1993; Matti and Morton, 1993; Weldon et al.,
1993; Powell, 1993). If all the slip has occurred
along the modern San Andreas fault north of the
San Gabriel Mountains during the past 5 m.y.
as suggested by Crowell (1982), the slip rate
ranges between 3.0 and 3.7 cm yr–1 (Fig. 8C).
Several estimates of late Pleistocene and
Holocene slip rates along and close to the
Mojave segment were calculated (Table 1). In
Geological Society of America Bulletin, May/June 2005
803
MATMON et al.
Figure 7. Exposure-burial, two-isotope diagram based on sea-level high-latitude 10Be
production rate of 5.31 atoms g–1 yr–1. Numbers across top are millions of years of total
exposure. Bold numbers down right side are
millions of years of total burial. Samples
that have a simple history of exposure and
steady erosion fall within the shaded area.
All the samples from the Little Rock Creek
fans have low 26Al/10Be ratios and fall below
the shaded area. The low 26Al/10Be ratios
indicate total periods of burial that range
between ~227 k.y. (LROF-26) and 413 k.y.
(LRDP-1). Error bars are 1σ. In samples
LROF-26 and LRDP-1, x-axis error bars
are smaller than symbol.
Figure 8. Slip rates along the Mojave section
of the San Andreas fault. (A) An average slip
rate of 4.2 ± 1.0 cm yr–1 is calculated from the
slip rates of each individual fan (thick dotted
line). A simple linear regression through the
mean age values suggests an average slip
rate of 3.7 ± 1.0 cm yr–1 for the past 413 k.y.
(thick striped line). The similarity between
the slip rate determined from the χ2 test
(thick double-dotted line; see Fig. 8B) and
the slip rate determined from the linear
regression implies that in spite of the large
uncertainties associated with the burial age
dating, the mean values, which show a clear
trend of increasing with increasing distance
from the mouth of Little Rock Creek, are
significant. (B) A most probable slip rate of
3.0 ± 1.0 cm yr–1 was determined from the
calculated ages of the Little Rock Creek fans
using a χ2 test (thick double-dotted line).
The χ2 test was done by selecting regression
slopes ranging from 0 to 6 cm yr–1 with 0.1
increments. At each slope, fans were attributed random ages (from their calculated age
range), and the sum of deviations from the
slope was calculated. Ten thousand scenarios
were performed for each slope, and the
average deviation was calculated. The most
probable slip rate is expressed by the slope
that yielded the lowest average deviation. (C)
Comparison of the slip rate results from this
study with previous results. There is a good
agreement between the average slip rate for
the past 413 k.y. calculated in this study and
previous results. However, individual slip
rates calculated from the ages of fans 0 and
1 are higher than expected and in some cases
higher than the total slip rate between the
North American and Pacific plates.
804
Geological Society of America Bulletin, May/June 2005
OFFSET FANS ALONG THE SAN ANDREAS FAULT
the Wallace Creek area, Sieh and Jahns (1984)
calculated slip rates of 3.4 ± 0.3 cm yr–1 for the
past 3.7 k.y. and 3.6 ± 0.5 cm yr–1 for the past
13.3 k.y. A rate of 2.5 ± 0.4 cm yr–1 for the past
14.4 k.y. was calculated in the Cajon Creek area
(Weldon and Sieh, 1985). This lower rate was
measured south of the split between the San
Andreas fault and the San Jacinto fault, which
accommodates ~1.0 cm yr–1 of slip. Based on
a study spanning the region from Little Rock
Creek to Cajon Creek, Weldon et al. (1993) proposed a slip rate of 3.6 ± 0.8 cm yr–1. A similar
rate of 3.6 ± 0.7 cm yr–1 was obtained at Pallett
Creek by Salyards et al. (1992) for the past several hundred years.
Using various geodetic techniques, several
measurements of recent slip rates along the San
Andreas fault are proposed. Savage (1990) suggested a rate of ~3.0 cm yr–1. A similar rate, 3.0
± 0.6 cm yr–1, was calculated by Eberhart-Phillips et al. (1990) in the Tejon Pass area. Spacebased geodetic measurements suggest a rate of
2.7 ± 0.3 cm yr–1 (Sauber et al., 1989).
Slip rates calculated from the ages of individual fans, although independent of previous
measurements, can be tested by limiting considerations. Several measurements of the total
motion between the North American and the
Pacific plates indicate an average slip rate in
southern California of ~5.0 cm yr–1. Minster
and Jordan (1978) calculated a velocity of 5.6
± 0.3 cm yr–1 for the Pacific plate (RM2), while
the Nuvel 1 model predicts a slip rate of 4.9 ±
0.3 cm yr–1 between these two plates (DeMetz et
al., 1987). Humphreys and Weldon (1994) used
kinematic analysis to calculate a slip rate of
4.8 ± 0.2 cm yr–1 for the Quaternary. Thus, the
maximum slip rate along the San Andreas fault
cannot exceed ~5 cm yr–1, the total relative plate
motion velocity. Furthermore, studies suggest
that the San Andreas fault has been accommodating 70%–80%, but no less than 50%, of the
total motion between the North American and
TABLE 5. SLIP RATES
Fan
Sample
Age
(ka)
Slip rate
(cm yr–1)
0
LROF-22
LROF-23
15.7 ± 5.3
4.36 ± 2.17
1
LROF-15
LROF-16
LROF-17
29.5 ± 7.4
5.94 ± 1.70
3
LROF-26
227.4 ± 242
3.26 ± 3.50
4
LROF-5
281.4 ± 181
3.41 ± 2.23
5
LRDP-1
412.8 ± 185
4.00 ± 1.81
Notes: See text for details concerning age
calculations.
the Pacific plates (e.g., Weldon and Humphreys,
1986; Humphreys and Weldon, 1994).
Using the ages we determined for fans 0, 1, 3,
4, and 5, we calculated the average rate at which
each fan was displaced by the San Andreas fault
(Table 5; Fig. 8C). The most probable age of
fan 0, calculated from the Monte Carlo simulations, yields a slip rate of 4.4 ± 2.2 cm yr–1 over
the past ~16 k.y. This slip rate lies at the upper
boundary of the expected rates along the Mojave
section of the San Andreas fault, and its upper
limit of 5.2 cm yr–1, which is faster than the total
slip rate between the North American and the
Pacific plates, is unreasonable. The most probable age of fan 1 yields an average slip rate of 5.9
± 1.7 cm yr–1. This rate is inconsistent with the
total slip rate between the North American and
the Pacific plates, and is obviously too high.
The inconsistency in slip rates calculated from
the ages of fans 0 and 1 suggests that sampled
boulders from these fans might have contained
lower inherited nuclide concentrations than
expected. It is also possible that the ages calculated for the boulders on fans 0 and 1 are underestimated (and accordingly, slip rate is overestimated) due to the underestimation of boulder
erosion rate. Boulder erosion rate, which was
calculated from granitic bedrock outcrops, averages the erosion rate over ~105 years (the time it
takes to erode the upper 2 m at an erosion rate of
~17.5 mm k.y.–1). This time span represents the
average erosion rate over several climatic cycles.
However, boulders on fans 0 and 1 might have
eroded, on average, at a faster rate due to the wetter conditions during the late Pleistocene.
The age calculated from depth sample LROF26 indicates a slip rate of 3.3 ± 3.5 cm yr–1 over
the past 227 k.y. for fan 3. A slip rate of 3.4 ±
2.2 cm yr–1 over the past 280 k.y. is calculated
from the age of fan 4 (determined from sample
LROF-5), and a slip rate of 4.0 ± 1.8 cm yr–1
over the past 413 k.y. is calculated from the
age of fan 5 (determined from sample LRDP-1,
150-170). Because production at depth by muons
was not accounted for, these ages are minimum
ones and slip rates are maximum rates. Nevertheless, it can be seen that calculated slip rates
from the ages of fans 3–5 are consistent with the
expected rates along the Mojave section of the
San Andreas fault and do not exceed the total
slip rate between the North American and Pacific
plates. The calculated average slip rates for the
past 413 k.y. obtained in this study are consistent
(within 1σ) with these earlier studies.
exposure histories of rocks and surfaces in the
landscape. The large drainage system enables
sediment to be stored for long periods on one
hand while mass wasting on the slopes deliver
previously shielded debris rapidly on the other.
After deposition in the fans, surface processes
such as boulder erosion, fan surface lowering,
and soil development operate, and each boulder
acquires a unique exposure history. Thus, the
complex environment results in large uncertainties in boulder erosion rate and boulder cosmogenic nuclide inheritance. Together with the
large uncertainties associated with exposure and
burial age dating, fan age determinations are,
therefore, accompanied by large uncertainties.
Nevertheless, the results of this study show a
clear trend of increasing fan ages with increasing
distance from Little Rock Creek. The two closest
fans, at distances of 0.7 ± 0.25 and 1.7 ± 0.25 km
from the mouth of Little Rock Creek, were dated
to 16 ± 5 and 29 ± 7 ka using exposure age
dating of exposed boulders. The three farthest
fans, at distances of 7.5 ± 0.55, 9.6 ± 0.55, and
16.5 ± 0.55 km, were dated to 227 ± 242, 281
± 180, and 413 ± 185 ka, respectively, using the
burial age dating method. Based on these ages,
the calculated slip rates vary depending on the
method of calculation. An average slip rate of 4.2
± 1.0 cm yr–1 is calculated from the individual
slip rates of each fan. A linear regression yields
a slip rate of 3.7 ± 1.0 cm yr–1. A most probable
slip rate of 3.0 ± 1.0 cm yr–1 is acquired using a χ2
test. These results are consistent with results from
previous studies. Although the statistical analysis
enables us to quantify the results in terms of ages
and slip rates, it did not eliminate the problems
that arise in using cosmogenic exposure and
burial age dating. For example, slip rates calculated from the ages of fans 0 and 1 are higher
than the total motion between the North American and Pacific plates and point to limitations of
dating surfaces in a complex natural geomorphic
environment.
The present study clearly demonstrates that a
simple interpretation of measured cosmogenic
nuclide concentrations in boulders residing on
fan surfaces is likely to result in misinterpretation of the geologic history of a studied site. For
each individual site, it is critical to understand
field relations, climatic conditions, and surface
processes in order to interpret cosmogenic
nuclide concentrations in a meaningful way.
Future work is needed to learn how to constrain
the relevant parameters in order to reliably
acquire exposure ages from eroding landscapes.
CONCLUSIONS
ACKNOWLEDGMENTS
The Little Rock Creek area is a typical natural environment where surface processes combine in a variety of ways to produce variable
We thank Coyn Criley and John Fitzpatrick for
lab assistance and ICP (inductively coupled plasma)
measurements and Fred Pollitz for statistical analysis.
Geological Society of America Bulletin, May/June 2005
805
MATMON et al.
We thank Kyle Nichols for excellent discussions and
advice. This study was performed under the auspices
of the U.S. Department of Energy by the University of
California, Lawrence Livermore National Laboratory,
contract number W-7405-Eng-48. This project was
funded by a USGS Mendenhall Postdoctoral Research
Fellowship. We thank T. Fumal, W. Thatcher, and
three anonymous reviewers for excellent reviews and
comments.
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