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A METHOD FOR DETERMINING EXHUMATION HISTORIES
OF ARC CRUST BASED UPON ANALYSIS OF DETRITAL
CLOSURE AGE DISTRIBUTIONS
Oscar M. Lovera and Marty Grove
Department of Earth and Space Sciences and Institute of Geophysics and Planetary
Physics, University of California, Los Angeles, California 90095-1567
David L. Kimbrough and Patrick L. Abbott
Department of Geological Sciences, San Diego State University
San Diego, CA 92182-1020
Submitted to Journal of Geophysical Research
1
Arc magmatism, denudation, and ensuing forearc accumulation of detritus are inexorably linked
convergent margin phenomena. We have developed a model that simulates these processes to determine
exhumation histories of nascent crust through the analysis of detrital closure age distributions measured from
forearc strata.
In formulating the approach, we have regarded the deeply denuded Peninsular Ranges
batholith and associated forearc strata as representative products of this tectonic environment and have
employed results from them to scale spatial and temporal parameters in our calculations. Detrital closure
ages output by heat flow models simulating coupled intrusion and erosion are sampled in a manner
statistically compatible with observation. Systematic comparison of measured and synthetic closure age
distributions to arrive at best-fit solutions is facilitated by application of the Kolmogorov-Smirnov statistic.
Provided that denudation outlasts intrusion, we find that the method is highly sensitive to the rate of
exhumation and relatively indifferent to the history of intrusion and the initial time of denudation once
sufficient erosion has occurred. Therefore, so long as forearc strata are representative of material removed
from the denuding batholith, the method has vast potential to decipher the evolution of juvenile arc crust.
1. Introduction
Because denudation and generation of abundant clastic debris are direct expressions of the relaxation of
thermal and mechanical energy perturbations inherent within newly-formed arc crust, forearc deposits provide
a vital record of batholith evolution [Dickinson, 1970; Hamilton, 1979]. Mineral thermochronometers
preserved within the eroded material present considerable opportunity for constraining batholith denudation.
The benefit of examining forearc sandstones stems not only from the sequential record of past erosion surfaces
that they are uniquely suited to provide [e.g., Linn et al., 1992] but also the potential for highly representative
sampling that results from fluvial transport. Unfortunately, use of closure age data from detritus to decipher
the exhumation history of the basement source regions [e.g., Copeland and Harrison, 1990] presents a larger
array of challenges than those faced by provenance studies [Gehrels and Dickinson, 1995] or basin history
analysis [Gleadow et al., 1983]. Specifically, the provenance of the material examined must clearly be
established as the source region of interest. Furthermore, it must be possible to predict how detrital closure
age distributions relate to denudation of basement rocks whose evolution has been potentially quite
complicated. In this regard, diffusive loss of radiogenic daughter isotopes during post-deposition subsidence
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must be negligible. Finally, interpretation of the significance of detrital closure age distributions results
requires well-established depositional age relationships in the material examined.
Restricting our attention to forearc strata helps to mitigate against these potential difficulties. For
example, because material constituting these rocks is typically largely derived from juvenile arc crust
[Dickinson, 1982; Marsaglia and Ingersoll, 1992] and/or reset by pervasive magmatism [Barton et al., 1988],
our ability to predict the closure age distributions as a function of syn- and post-batholithic denudation history
is enhanced. Furthermore, genetic links between basin and source region required to deduce exhumation
histories are most readily established in forearc strata that onlap the batholith. Without such a context, the
analysis we describe below is of somewhat diminished value.
Our primary goal in this paper is to describe and illustrate with a specific application how the general
method we have developed may be used to analyze detrital closure age distributions from forearc settings to
determine exhumation histories of immature arc crust. Starting from heat flow calculations that simulate
batholith emplacement and erosion, we calculate detrital closure age distributions for specified
thermochronometers as a function of erosion surface age . Best-fit solutions to the denudation history are then
approached using the Kolmogorov-Smirnov statistic to compare model closure age distributions with those
determined from forearc strata of known deposition age. In formulating the model we have been heavily
influenced by relationships exhibited by the Peninsular Ranges batholith (PRB) along southwestern North
America (Figure 1). Results of our analysis of the PRB allow us to conclude that exhumation histories of
magmatic arcs should be decipherable from detrital closure age distributions, provided that sand supplied to
the forearc is representative of material removed from the batholith.
2. A Case Study: The Northern Peninsular Ranges Batholith
A variety of factors identify the northern PRB as a useful setting for illustrating the nature of data we seek
to interpret. Relatively deep paleodepths exposed within the northern PRB [Todd et al., 1988; Ague and
Brimhall, 1988], assure us that denudation has played an important role in its evolution. Age and stratigraphic
relationships of forearc deposits preserved along the western flank of the PRB are well established. Forearc
strata deposited atop PRB basement in southern California and northern Baja California are
Cenomanian(?)-Turonian through Campanian-Maastrichtian(?) and formed as west-directed alluvial fans and
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fluvial systems that fed basinal submarine fans across a narrow shelf [Nilsen and Abbott, 1981; Bottjer and
Link, 1984].
Age-Depth Relationships of Exposed PRB Basement
Most of the 800 km PRB was intruded 120-90 Ma [Silver and Chappell, 1988; Walawender et al., 1990;
Figure 1]. In its northern extent, the density of intrusion is ~85-90% [Barton et al., 1988] with progressively
deeper structural levels exposed towards the east [Figure 1a; Gastil, 1979]. As shown, shallow, greenschist
facies metavolcanic and hypabyssal wallrocks crop out along the western margin [Todd et al., 1988].
Steeply-dipping, lower amphibolite facies metasedimentary screens metamorphosed at 6-11 km depths are
exposed in the west-central PRB while upper amphibolite facies rocks recording 10-20 km depths occur farther
east [Ague and Brimhall, 1988; Todd et al., 1988; Grove, 1994].
Correlation of K-Ar ages with inferred depth of erosion rather than intrusion identifies denudation as the
primary factor in controlling Ar closure in biotite and K-feldspar (Figure 1). For example, biotite cooling
ages partially overlap 125-100 Ma crystallization ages in the west but post-date emplacement of eastern
plutons by 10-20 Ma [Krumenacher et al., 1975; Silver and Chappell, 1988; Walawender et al., 1990; Grove,
1994; Goodwin and Renne, 1991]. Apatite fission track results also indicate eastward decrease in cooling age
from > 90 Ma to ~50 Ma [Dokka, 1984; George and Dokka, 1992; George and Dokka, 1994; Schmidt et al.,
1998]. Considered together, the above constraints indicate that most of the eastern PRB resided at < 2-3 km
depths throughout the Tertiary and that the western PRB had attained equivalent levels much earlier (i.e.,
during the early late Cretaceous). Stability of the PRB during the early Tertiary is further indicated by
preservation of Paleocene paleosols [Peterson and Abbott, 1979], as well as Eocene erosional surfaces and
fluvial systems that extended from Mainland Mexico across the PRB to the coast [Minch, 1979; Abbott and
Smith, 1989].
Rifting associated with initiation of San Andreas transform and concomitant formation of the Salton
Trough/Gulf of California left an unknown portion of the medial Cretaceous batholith behind in mainland
Mexico [Silver and Chappell, 1988]. Additional Late Cenozoic slip (<50 km) along dextral strike-slip faults
oriented obliquely to the axis of the batholith have moderately disrupted N-S litholithic and isotopic trends.
Moreover, footwall rocks of Late Miocene-Pliocene detachment faults situated along the eastern margin of the
PRB have experienced locally significant denudation [Axen and Fletcher, 1998]. Late Cenozoic deformation
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in the PRB forearc region was dramatic.
With the exception of thick forearc sequences on Vizcaino
Peninsula/Cedros island [Smith and Busby, 1993], only materials onlapping the batholith survived post-Middle
Miocene borderland extension and dextral shear [Howell and Vedder, 1981; Crouch and Suppe, 1993].
Late Cretaceous denudation mechanisms proposed to explain the depth and closure age patterns exhibited
by the northern PRB include westward tilting [Butler et al., 1991], W-directed thrusting [Engle and
Schultejann, 1984; Todd et al., 1988; Goodwin and Renne 1991; Grove, 1994], E-directed extensional faulting
[Erskine and Wenk, 1985; Gastil et al., 1992; Thompson and Girty, 1994; George and Dokka, 1994].
Additional Tertiary denudation has been explained by O’Connor and Chase [1989] as resulting from
forestalled relaxation of a flexurally suppressed root underlying the PRB that was triggered by change in
tectonic environment from convergent margin to transform boundary. While our method can easily be
adapted to simulate each of these processes, such a treatment is beyond the scope of this paper. To maintain
focus upon the methodology involved in applying our approach, we consider only the most basic model
(tilting) that is capable of approximating the observed geologic relationships.
Sampling, Depositional Ages, and Detrital K-feldspar 40Ar/39Ar Closure Ages
In this study, we focus upon forearc strata sampled in the northern Santa Ana Mountains, southeast of
Los Angeles, and in the La Jolla area of San Diego (Figures 1, 2). Upper Cretaceous marine sedimentary
rocks in the San Diego area are assigned to the Rosario Group and include mudstone and sandstone of the
Point Loma Formation overlain by sandstone and conglomerate of the Cabrillo Formation [Figure 2a; Kennedy
and Moore, 1971; Nilsen and Abbott, 1981]. Coccolith flora identified in both formations have been assigned
by Bukry and Kennedy [1969] and Bukry [1994] to the late Campanian/early Maastrichtian. Similarly Sliter
[1968] reported late Campanian/early Maastrichtian foraminifera from mudstones within the lower Point Loma
Formation. Bannon et al. [1989] subsequently identified a reverse chron within the Point Loma mudstones as
32R (see Harland et al., 1982 time scale) and concluded that it represented the base of the Maastrichtian.
Continuing development of the magnetic polarity time scale however, has revealed two additional reverse
chrons in the middle-late Campanian [Gradstein et al., 1994]. Based upon ongoing paleontologic analysis
[W.P. Elder, personal communication, 1996], it appears probable that it is one of the middle-late Campanian
reverse chrons that has been detected in the Point Loma Formation and not 32R. Consequently, both the Point
Loma and Cabrillo Formations appear Campanian with depositional ages ranging between 77-72 Ma (Table 1).
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The geology of the northern Santa Ana Mountains has been mapped and described by Schoellhamer et al.
[1981] while depositional environments and fossil assemblages are documented in Bottjer et al. [1982].
Excellent exposures of the Upper Cretaceous strata occur in the Silverado Canyon area (Figure 2b). There,
unfossiliferous, terrestrial conglomerates and sandstone of the Trabuco Formation depositionally overlie the
volcanic edifice of the PRB (Figure 2a). These are in turn overlain by fossiliferous, marine fan-delta
conglomerates and sandstones of Turonian age [Popenoe, 1937, 1942] that constitute the Baker Canyon
Member of the Ladd Formation. Fining upward within the Ladd Formation produced the deep marine, latest
Turonian to Campanian Holz Shale Member. Conglomerate-dominated, submarine canyon fill was deposited
within the Holz Shale as the Mustang Spring lens (Figure 2b) in the Campanian [Almgren, 1982; Saul, 1982].
Shelf sandstone of the Williams Formation was deposited in late Campanian time and represents the youngest
Upper Cretaceous sedimentary rocks present in the area (Figure 2b). Based upon the Gradstein et al. (1994)
time scale, combined magnetostratigraphy [Fry et al., 1985] and faunal constraints summarized in Table 1
indicate that Late Cretaceous sedimentation in the Silverado Canyon area occurred between about 95 to 72 Ma.
Sandstone samples were obtained from the Point Loma (La Jolla Bay and Bird Rock) and Cabrillo
(Tourmaline Beach) Formations west of San Diego (Figure 2a) and from the Trabuco, Baker Canyon, Mustang
Spring, and Williams samples within the northern Santa Ana Mountains (Figure 2b; see Table 1 for localities).
Single-grain, total fusion, 40Ar/39Ar ages determined for 30-70 individual K-feldspar grains separated from
each of the seven samples are displayed in Figure 2c-i. Analytical details and tabulated 40Ar/39Ar results for
these samples may be obtained from http:\\oro.ess.ucla.edu\PRB_Ksed.html. Also shown in Figure 2c-i are
estimated depositional ages (Table 1). As indicated in Table 1, our ability to constrain depositional ages
varies significantly. Uncertainty of about 2-3 m.y. applies to most estimates. The best known depositional
age is that of the Baker Canyon sample (Table 1) while the largest uncertainty exists for sandstone obtained
from the unfossiliferous Trabuco Formation. The age of the latter is constrained only by those of the
overlying Baker Canyon Member (with which it is continuous) and underlying Santiago Peak Volcanics.
Comparison of the youngest 40Ar/39Ar bulk closure ages determined for each of the samples with their
respective depositional ages reveals close overlap when uncertainties are taken into account (Figure 2c-i).
Such a relationship has been invoked to require locally rapid denudation of the source region [e.g., Copeland
and Harrison, 1990]. However, closure ages that are up to 4 m.y. younger than the estimated depositional age
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are clearly problematic for the Baker Canyon sample (Figure 2h). Such a relationship indicates either
overestimation of the depositional age, 40Ar loss during burial, or unrecognized analytical difficulties.
Similarly, the Trabuco sample (Figure 2i) is incompatible with a depositional age in excess of 92 Ma.
An important feature of the closure age distributions is that the majority of results yielded by the
intermediate-aged samples (Williams, La Jolla Bay, and Mustang Spring; Figure 2b-c) are > 8 m.y. older than
their depositional age. Conversely, a significant proportion of the ages determined for both the oldest (Baker
Canyon and Trabuco) and youngest (Toumaline Beach and Bird Rock) samples predate the depositional age by
< 5 m.y. Qualitatively this implies more rapid denudation during the Cenomanian-Turonian (ca. 95-90 Ma)
and Late Campanian (ca. 75-72 Ma) than in the intervening Coniacian-Santonian-early Campanian. Finally,
the paucity of > 100 Ma closure ages in all samples indicates that shallow-level intrusions of the western PRB
which yield K-Ar biotite and U-Pb zircon ages of ~105-120 Ma [Krummenacher et al., 1975; Silver and
Chappell, 1988] contributed insignificant quantities of sand to the strata we have studied.
3. Model Description
Intrusion and denudation operate individually or in concert in our model. We calculate thermal histories
for arc detritus using a 2-D finite-difference algorithm to solve the diffusion equation. Boundary conditions
include zero lateral-flux, constant surface temperature (25°C), and a constant basal heat flux (Figure 3). Heat
conduction is described in a simple manner by maintaining thermal diffusivity at a constant value (10 -6
m2/sec), neglecting radioactive internal heating, and fixing the basal heat flux at an appropriate value to
maintain a 30C/km thermal gradient in the absence of intrusion or denudation. Based upon a
thermobarometric survey of the PRB Rothstein and Manning[1994], proposed a 50C/km geotherm from 0-7
km depth, decreasing to 17C/km between depths of 7-15 km, and to 10C/km between 15-30 km. While our
use of a 30C/km ambient geotherm appears to underestimate temperatures at the shallow levels (<7 km), the
effective near surface gradient is higher than that expected from the ambient geotherm due to pervasive pluton
emplacement in our models. Because we continue calculations 25-30 m.y. after final intrusion, we consider
our use of a initial linear 30C/km ambient geotherm as reasonable since the higher near-surface value of
Rothstein and Manning [1994] likely reflects significant heat input from intrusion [Hanson and Barton, 1989].
Thermal Effects of Batholith Emplacement
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We use a straightforward approach to simulate batholith formation that permits description of relatively
complex intrusion geometries [e.g., Hanson and Barton, 1989]. Random distributions of circular, 2-D plutons
are instantaneously emplaced in successive time frames (Figure 4; Table 3). Thermal effects of intrusion are
simulated by setting the temperature of grid points contained within pluton boundaries to magmatic values at
the time step corresponding to emplacement. The constant emplacement temperature assigned to a given
pluton is a value between 850-1000C. Spatial characteristics of the pluton distributions are allowed to vary
randomly between imposed limits that are specific to particular model runs (Table 3). However, the following
guidelines apply to all models: centers of plutons are restricted to positions further than 20 km from lateral
boundaries and at least 15 km above the base of the grid while tops of plutons are required to be at least 2 km
below the surface at the time of emplacement (Figure 3). Superposition of intrusions is allowed within a
given time frame (Figure 4) while partial obliteration of the older intrusions occurs in successive intervals
(Figure 5). Although the extraordinary amount of host rock deformation and/or assimilation implied by
intrusion of this volume of magma is not explicitly considered in the model (i.e., mass is not conserved),
batholith emplacement in nature presents space problems that are no less daunting [Buddington, 1959].
To illustrate the effect of intrusion history upon detrital closure age distributions, two distinct
emplacement sequences are investigated (Figure 5; Table 3). While the cumulative intrusion density produced
in the both sequences (Figure 5a,b) is comparable to that observed in many Cordilleran batholiths [~ 15% host
rocks remain; Barton et al., 1988], only I2 adequately describes age-distance relationships observed in for the
PRB (Figure 5c). The composite nature of Figure 5b is intended to simulate emplacement of voluminous
tonalite-trondjemhite-granodiorite magmas into the eastern region at 98-92 Ma [Kimbrough and Gastil, 1997].
Denudation, Erosion, and Deposition
Denudation is simulated by sweeping the position of the earth’s surface in the model through the grid in
successive time steps. This is accomplished by setting the temperature of all grid points situated at or above
the defined surface to a constant value (25C). The time (AgeD) at which material at a given grid point is
“eroded” is defined as that in which the 25C surface passes beneath it (Figure 3). We consider all material
bounded by surfaces ± 0.5 m.y. from the corresponding to AgeD to be deposited at this time. This ensures that
the amount of sediment eroded at a given lateral position is proportional to the denudation rate at that location
and time AgeD. While definition of the 25°C surface can be quite general, we simulate only linear denudation
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(i.e., tilting of a planar surface) in the present paper. In each simulation, the axis of rotation is fixed at the
upper left corner of the grid and the movement of the surface towards grid points is clockwise so that samples
in the right-hand portion of the grid experience the greatest denudation (Figure 3; cf. Figure 1). Although a
constant rate of rotation is applied in early models (Table 4), we later introduce variable denudation in the
discussion to demonstrate the ability of the model to fit measured data. In each simulation we initiate
denudation at 105 Ma. This time corresponds to the midpoint of each of the intrusion sequences (Table 4).
Note that because the time of initial denudation is arbitrary fixed, the magnitude of denudation required to fit
measured results is necessarily a relative quantity. However, provided that sufficient exhumation has taken
place, our estimates of denudation rates do not depend strongly upon when we initiate erosion.
Calculation of Detrital Closure Age Distributions
Each run of the model calculates temperature-time (T-t) histories for all points within the upper 30 km of
the grid. From this set of T-t paths, bulk closure ages are computed using experimentally determined
Arrhenius parameters (Table 2). In most of our calculations, we apply average bulk diffusion properties
determined for K-feldspar [Lovera et al., 1997] and assumed a single diffusion domain. Since only bulk
properties are relevant in our model, the approach adopted here is appropriate for interpreting total fusion
measurements from K-feldspar and can be easily adapted to other mineral thermochronometers (Table 2).
Sampling of detrital closure ages is performed using random deviates with a uniform probability
distribution and the transformation method described by Press et. al [1988, p. 200-203]. The probability that
a closure age corresponding to a given horizontal position along the erosion surface will be sampled is
proportional to the denudation rate at that location at time AgeD. Since sample points do not generally coincide
with grid points, closure ages are computed by interpolation. To avoid possible complications arising at
lateral boundaries, we only sampled horizontal positions between 25-125 km (Figure 3).
Comparison of Model Results with Measured Age Distributions
A crucial element for our method is an appropriate protocol for evaluating the similarity of measured and
model distributions. We have applied the Kolmogorov-Smirnov (K-S) statistic [Press et al., 1986, p.475], a
generally accepted test to compare populations. Because the parameter produced by the K-S statistic (D) is
defined as the maximum value of the absolute difference between two cumulative distribution functions, it is
most sensitive to the overall character of cumulative distributions and relatively insensitive to outlying data.
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A major benefit of the K-S statistic is that the numerical significance of D, defined as PROB, can be
assessed for the null hypothesis (i.e., data sets from the same distribution). Values of PROB near unity
indicate that two distributions are similar while values approaching zero point to significantly different
distributions. To evaluate the sensitivity of PROB in our application, we sampled detrital closure ages
corresponding to a single AgeD value in different ways and applied the K-S test. This exercise entailed
systematically comparing one hundred cumulative distribution functions (each defined by 32 randomly
selected detrital closure ages) with a distribution function represented by a larger sampling based upon 1000
detrital closure ages from the same result. We found that the resulting log(PROB) values varied -1.6 to 0 with
a mean value of ~-0.4 and conclude that the sensitivity of the K-S test in terms of log(PROB) units is ~1 for
cumulative distribution functions calculated from small samples.
Our approach for comparing measured detrital age distributions with those produced by the model is
summarized in Figure 6. In this example, we compare measured closure ages from the Mustang Spring
sample with those produced by a representative run of the model. To determine the model age distribution
that best matches the measured distribution, we obtain synthetic distributions corresponding to different values
of AgeD and apply the K-S test to determine which of the distributions represents the maximum value of PROB
(PROBmax; Figure 6a). We refer to the AgeD value corresponding to PROBmax as AgeDmax and define the
difference between the stratigraphic age (Table 1) and Age Dmax as t. Model results for AgeD values within ±4
m.y. of AgeDmax are compared with the measured Mustang Spring detrital age distribution in Figure 6 b-f.
The model distribution corresponding to AgeDmax is shown in Figure 6d. AgeD distributions ±2 m.y. from
AgeDmax yield log(PROB) values of about -3 and can just be resolved from the measured distribution (Figure
6c, 6e). Alternatively, AgeD distributions ±4 m.y. from AgeDmax yield much lower PROB values (< -7) and are
easily distinguished from the measured data (Figure 6b, 6f). The asymmetry in PROB about AgeDmax results
from the definition of the K-S statistic and the nature of the distribution functions. However, the rate at which
PROB drops off on either side of AgeDmax is strongly influenced by the denudation rate.
4. Results
To illustrate how K-feldspar detrital closure age distributions are affected by intrusion and denudation
history, we ran the program for different combinations of intrusion (Table 3) and denudation (Table 4). The
specific permutations employed in the first six models are outlined in Table 5. In order to illustrate how
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intrusion and denudation interact to affect our results, we examine results from models I (Figure 7) and II
(Figure 8) in detail. We then vary key model parameters (Figure 9; Table 5) and conclude by examining how
the time of initial exhumation and the retentivity of the mineral thermochronometer influence closure age
distributions.
Denudation without Intrusion
Important effects observed in all our simulations are clearly demonstrated in Model I which involves
tilting in the absence of intrusion. The distribution of K-feldspar K-Ar closure ages throughout the grid
(Figure 7a) reflects the interplay between temperature change produced by denudation, accumulation of
radiogenic 40Ar (40Ar*) in K-feldspar, and 40Ar* from K-feldspar by diffusion. Initially, protolith ages (= 120
Ma) occur at 0-4 km depths while closure ages between 120-105 Ma are horizontally distributed between 4-7
km (Figure 7a). Inspection of Table 2 indicates that K-feldspar effectively retains all 40Ar* below ~150°C or
~4 km (Table 2). Similar analysis indicates that K-feldspar loses virtually all of its 40Ar* at temperatures
>250°C (>7 km) during this period (Table 2). The onset of denudation at 105 Ma allows samples initially
deeper than ~ 7 km to begin closing with respect to Ar diffusion as they approach the surface. The faster the
denudation, the less time is required for a sample at a given depth to close with respect to 40Ar* loss. After
denudation ceases at 65 Ma, age contours rapidly achieve a steady-state configuration (Figure 7a).
Detrital closure age distributions (Figure 7c-h) relate directly to corresponding surface age profiles
(Figure 7b). Note that the 100 Ma surface formed 5 m.y. after the onset of tilting in Model I exposes only
rocks from the upper <5 km (< 200°C) of the crust. These rocks are characterized by K-feldspars that are
effectively closed with respect to Ar diffusion and preserve protolith ages. By 95 Ma, continued denudation
has begun to expose partially outgassed K-feldspars (i.e. those originating from below 4 km; Figure 7a). By
90 Ma, most K-feldspars exposed at the surface were open to Ar loss prior to 105 Ma (Figure 7b). Despite
this, shallow levels sampled from the left portion of the grid still yield protolith ages. This results in bimodal
detrital closure age distributions (Figure 7c-h). The skewed character of the younger age maxima is a direct
consequence of the proportionality between the amount of material eroded and the denudation rate which
increases from left to right across the grid. With continued denudation the percentage of results contributing
to the younger age maxima grows at the expense of samples recording protolith ages while the interval
between AgeD and the lower age maxima K-feldspar bulk closure ages recorded systematically decreases.
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Overlapping Intrusion and Denudation
The uniformly varying age trends observed in Model I are disrupted when intrusion overlaps denudation
(Model II, Figure 8). A prominent effect of magmatic heating is that significantly fewer grid positions
preserve protolith ages, particularly below 2 km depth (compare Figures 7a and 8a). The distribution of
apparent ages at shallow positions within the grid directly reflects the sequence of intrusion at depths less than
~ 7 km (see Figures 4; 5a). In contrast, the distribution of closure ages at greater depths is insensitive to
intrusion and closely resembles Figure 7a. The latter is true because tilting outlasts intrusion by 30 m.y.
Features of surface age profiles that are clearly related to individual plutons (Figure 8b) persist at 95 Ma but
are largely obliterated by 90 Ma (i.e., 5 m.y. after final intrusion). Although the distribution of detrital
cooling ages exhibited by the earliest erosional debris produced by model II is distinct from model I for older
sediments, the results converge to those produced by pure denudation, becoming indistinguishable by AgeD =
85 Ma (compare Figures 7f-h with Figures 8f-h).
Systematic Analysis of Intrusion and Denudation Effects
Inspection of Figure 9 and Table 5 clearly indicate that for the case in which exhumation outlasts
intrusion, denudation rate is the dominant control in determining bulk closure age distributions from
K-feldspar. All models characterized by a mean denudation rate of 0.5 km/m.y. (Models I, II, III) predict
similar depositional ages for each of the samples examined (compare Age Dmax values in Figure 9b, 9c, and 9d).
For these runs, only the oldest sample (Trabuco = 92 Ma.) is markedly sensitive to the intrusion history (Figure
9h). Values of t produced by each of the models are generally ± 5 m.y. with all runs yielding identical
results by 76 Ma. (Figure 9i). In contrast, reducing the denudation rate by a factor of two produces
discernable differences in detrital closure age distributions for contrasting sequences of intrusion. Moreover,
all predicted ages are shifted 10-20 m.y. to younger values (Figure 9e-g).
Varying the Time of Initial Denudation
The detrital closure age systematics depends strongly upon the rate at which samples originally open to
Ar diffusion approach the surface. Consequently, the time of initial denudation has a relatively small impact
upon the model results depicted in Figure 9 provided that a significant proportion of the grid has been denuded
by > 7 km prior to the time that the first sample is deposited. As previously discussed, K-feldspar effectively
retains no Ar below this depth assuming an ambient geotherm of 30C/km (Table 2). To examine the effect
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of starting denudation earlier, we began eroding material in Model I at 115 Ma rather than 105 Ma. We found
that t values for Trabuco and Baker Canyon decrease by only 1 m.y. (relative to Model I) while those of the
younger samples remain unaffected. This is expected since the mean denudation occurring between 105 and
92 Ma is 6.5 km. In contrast, starting denudation later than 105 Ma has a somewhat greater effect because an
insufficient amount of denudation (mean value of 4 km) occurs prior to Trabuco deposition. More erosion is
required before the model results match the measured age distributions. As a result t values for the Trabuco
and Baker Canyon samples increase by 3 and 2 m.y. respectively while those of the younger samples increase
by 1. Although slower denudation is more sensitive to the time of initial denudation, this is counteracted by
pervasive intrusion. In summary, while our approach is highly sensitive to the exhumation rate, it is only able
to place lower bounds upon the amount denudation that has taken place. However, use of more retentive
thermochronometers than K-feldspar would provide additional constraint upon the magnitude of exhumation.
Effect of Daughter Product Retentivity
Closure age contour plots calculated for apatite ((U-Th)-He); biotite, K-feldspar, and hornblende (K-Ar);
and monazite (Th-Pb) in Figure 10 illustrate the effect of varying the retentivity of the thermochronometer
used in the analysis (Table 2). In this example, the intrusion and denudation histories applied are those of
model II. Low retentivity phases like apatite are most sensitive to denudation history and are essentially
unaffected by intrusion history (Fig. 10a). In contrast, the most retentive phase, monazite, faithfully records
the intrusion history at shallow to middle crustal levels and is affected by the denudation only at deeper levels
(Fig. 10e).
5. Discussion
The interpretive framework just described has the potential to decipher unroofing histories from
thermochronometers shed from denuding batholiths. A major advantage of sampling forearc sandstones over
more conventional analysis of basement exposures resides in the potentially highly representative sampling of
past (i.e. eroded) basement surfaces preserved by these materials. However, the effort required for obtaining
statistically meaningful sampling of sedimentary materials dictates that focus be placed upon a single mineral
thermochronometer. We advocate the use of apatite, K-feldspar, or biotite in detrital closure age studies
depending upon the following considerations. Highly unretentive mineral thermochronometers such as
(U-Th)-He in apatite record denudation effects to the greatest extent possible (Figure 8a) and hence represent
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the obvious choice for study of shallowly denuded systems. Balanced against this however, is the
susceptibility of apatite to thermal overprinting during sedimentary burial [Gleadow et al., 1983].
In examining more deeply eroded terranes, the most favorable prospect for success is offered by
moderately retentive biotite and K-feldspar (Figure 8b-c). The resistance of K-feldspar to chemical
weathering during erosion, transport, and burial combined with its modal dominance in granitoids, and
comparative ease of analysis using total fusion 40Ar/39Ar laser techniques make it a highly appropriate phase
for study. Moreover, alkali feldspar is sufficiently retentive that it experiences only minor 40Ar* loss during
modest burial [Mahon et al., in review]. Despite these advantages, we acknowledge that plutonic K-feldspar
may be difficult to separate from albite, particularly in first cycle volcano-plutonic detritus whereas biotite may
prove easy to extract. Moreover alkali feldspar populations may be dominated by volumetrically insignificant
bodies such as granitic pegmatite. In relatively calcic magmatic arcs, biotite may provide a better sampling of
the main phase granitoid intrusions. Finally, while relatively modest sampling (N ~ 32) of model distributions
appears sufficient to adequately describe their fundamental characteristics (see panels (c)-(h) in Figure 5-7),
the number of detrital closure age results required to adequately define natural distributions is less certain. To
constrain parameters such as variability in protolith age, the timing and relative volume of intrusion, as well as
the general characteristics of the denudation history, a larger sampling may be necessary.
While we emphasize erosion in our model, the effect of faulting may also need to be considered.
Because the tectonic environment within arcs ranges from extensional, to strike-slip, to compressive
[Hamilton, 1979], the relationship between faulting, erosion, and sedimentation may be complex [Ingersoll
and Busby, 1995]. Nevertheless, it is relatively easy to modify the heat conduction model in our approach to
simulate effects produced by faulting and topography [e.g., Quidelleur et al., 1997]. Thus complications such
as intra-arc extension [Busby-Spera, 1988] which conserve shallow rocks while exposing the middle crust can
be adequately dealt with if necessary.
Modeling Denudation Histories of Magmatic Arcs
As an exercise to demonstrate the potential of our approach to reveal temporal variation in the denudation
histories of batholiths, we further model the detrital closure age distributions from the PRB. Before
continuing, we acknowledge that the three models which use the faster, constant denudation history (D1)
reproduce the closure age distributions of the PRB forearc samples reasonably well taking uncertainties into
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account (Figure 9h). In models I-III, only t values for the Baker Canyon and Williams samples (Table 5) are
larger than their estimated uncertainties (Table 1). Nevertheless, refinement of the constant denudation
models is easily accomplished when warranted by more precise depositional age data. In such instances, the
sign of t provides a guide to improve the fitting of the measured distributions. Specifically, positive values
require faster denudation and vice versa. Applying this criterion, all that is required is to vary the denudation
rate between the times of deposition of successive units to minimize t for each of the samples. Because
earlier history affects that latter on, we first match results from the oldest sample and then proceed to younger
strata.
Below we describe the reasoning that led us to deduce the variable denudation history (D3) in Table 4.
Of the initial six simulations, model III produces the best agreement with the measured closure age
distributions (Figure 9h). Fortuitous agreement between the model III results and measured values for the
oldest sample (tTrabuco = 0) led us to begin denudation history D3 at the same rate as D1 (0.5 km/m.y.; Table
4) and then increase denudation after deposition of the Trabuco sample to fit the next youngest sample (i.e.,
Baker Canyon). The magnitude of the adjustment to the denudation rate was determined from model III.
Specifically, the net denudation between deposition of the Trabuco and Baker Canyon samples is given by
[AgeD, Trabucomax - AgeD, BakerCyn.max]  D1 = (92 Ma-87 Ma)  0.5 km/m.y. or 2.5 km. Thus, increasing the
denudation rate by a factor of 2.5 (i.e., from 0.5 km/m.y. to 1.25 km/m.y.) at 92 Ma reduces t for Baker
Canyon from 3 to zero (Table 5). Equivalent calculations indicate that shortly after 90 Ma, the denudation
rate should be decreased to 0.15 km/yr to reduce t for the Mustang Spring sample to zero. Likewise
increasing the denudation rate at 79 Ma to 0.45 km/m.y. minimizes t values for the younger samples to 1 m.y.
or less.
It is clear that errors in depositional age and/or the time of initial denudation could appreciably affect
details of the variable denudation model deduced above. For example, the magnitude of the mean denudation
rate between 92-90 Ma (Table 3) is critically dependent upon the depositional ages of the Trabuco and Baker
Canyon samples (Table 1). Because the former is poorly constrained, the rate indicated for this interval
necessarily represents only a crude estimate. Specifically, if the Trabuco sample is older than 92 Ma, the rate
between 92-90 would be diminished while that prior to 92 Ma would necessarily increase. Regardless of this
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uncertainty, strong overlap of depositional age and measured detrital closure ages for the Baker Canyon
sample (Figure 2c-d) necessarily require higher denudation rates to prevail at ca. 90 Ma than at later times.
Model detrital closure age distributions obtained using the D3 denudation history are compared with our
measured values in Figure 11b-d. Just as in the case for D1, the cumulative denudation produced in D3 is
sufficiently high that only the closure age distributions of the older samples are differentially affected when
distinct intrusion histories are imposed (compare Figure 9h with Figure 11e). Note that while t values for
each of the samples are 1 m.y. or less in the case of Model IX, major improvements in PROBmax over values
obtained in the constant denudation models were not realized. Because the lowest PROBmax values are
yielded by the oldest samples, it appears likely that in detail, the I2 intrusion history is inappropriate for the
PRB. For example, inspection of the predicted and measured closure age distributions for the Trabuco sample
in Figure 11g reveals closure age maxima at about 118 and 103 Ma that reflect significant shallow level
intrusion at this time (Figure 5b). These features alone account for the low PROBmax value yielded for this
sample. Similarly, the 92 Ma maxima exhibited for the Baker Canyon sample (Figure 11h) maybe unduly
influenced by pervasive invasion of the eastern batholith at ~ 10-15 km depths by granitoids of this age (Figure
5b). Younger samples are less affected by intrusion and in general yield higher PROBmax values.
Implications for the Exhumation History of the Northern PRB
Our primary goal in this paper has been to present a general method to analyze detrital closure age
distributions from forearc settings. However, in having scaled the dimensions and intrusive history of our
models to values more or less appropriate for the northern PRB (e.g., Figure 1), general statements regarding
the magnitude and timing of denudation are possible. Due to the limited data presented here (Figure 2) and
the simplistic denudation/intrusion model and ambient geothermal structure employed to interpret results, we
caution readers that it may be premature to draw broad tectonic conclusions from the present study.
Bearing these limitations in mind, it is clear that when only the simplest constant denudation models are
considered, the faster (D1) agrees best with both the measured detrital closure age distributions (Figure 9) and
basement K-feldspar total fusion ages (Figure 12c-d) while the slower (D2) produces incompatible results.
Moreover, close correspondence of the youngest measured detrital closure ages and estimated depositional
ages (Figure 2c-I) also seem to require D1 rates. Specifically, the youngest detrital closure ages produced by
D1 models are ~ 3-5 m.y. older than their erosion ages (Figure 7) whereas the time lag produced in D2 models
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is much greater (~ 11 m.y.; Table 4). Because the detrital closure age systematics depends strongly upon the
rate at which samples approach the surface, beginning denudation earlier than 105 Ma does not make the
slower D2 exhumation rates more favorable for the PRB.
The main difficulty with maintaining D1 exhumation rates in the PRB over a 40 m.y. interval is the high
cumulative mean denudation that results (20 km; Table 4). Current paleodepth estimates [Ague and Brimhall,
1988; Todd et al., 1988; Rothstein and Manning, 1994] are more consistent with a mean denudation magnitude
of about 12-16 km. Increasing the ambient geothermal gradient and/or shortening the duration of exhumation
would readily resolves this discrepancy. To a first approximation, increasing the geothermal gradient from 30
to 40C/km would reduce the cumulative mean denudation from 20 to 15 km because a reduction in the
denudation rate from 0.5 km to 0.37 km/m.y would be required to maintain the same fit to the data.
Alternatively, reducing the duration over which D1 rates operate from 40 to 30 Ma achieves the same effect.
The variable denudation model (D3) reduces the cumulative mean denudation (Table 4) while improving
the fit of the measured detrital results (Figure 11; Table 5). Although permitting denudation to vary in this
manner pushes interpretation of our data to reasonable limits given uncertainties in depositional age, we also
emphasize that D3 is quite consistent with independent thermochronologic and geologic evidence gathered
from basement exposures. For example, comparison of Figures 12a and 12b reveals that available K-feldspar
bulk closure ages from the east-central batholith define maxima that correlate with periods of accelerated
denudation that were deduced from the detrital results. More detailed thermochronologic analysis of PRB
basement rocks has indicated rapid cooling at ~100-90 Ma [George and Dokka, 1994; Grove, 1994] with
elevated rates again becoming important at times <80 Ma [Krummenacher et al., 1975; Grove, 1994, Goodwin
and Renne, 1991]. As summarized in Ingersoll and Busby [1995, p.39-42] suturing of a fringing island arc to
the continental margin coupled with development of a more compressive strain regime appear to have
produced a relatively high-standing continental arc by ca. 100 Ma. Moreover, Kimbrough and Gastil [1997]
have estimated that roughly half the intrusive mass of the PRB was emplaced between 98-92 Ma. Thus higher
exhumation rates coincident with the final stages of batholith emplacement appear geologically supported.
We believe waning intrusion and reduced buoyancy of cooling arc crust likely accounts for the decrease
in D3 denudation rates subsequent to 90 Ma (Figure 12a). Accordingly we view delayed rapid exhumation at
80-70 Ma as reflecting a fundamental change in tectonic environment. Modification of the tectonic regime by
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rapid, shallow-inclination subduction [e.g., Coney and Reynolds, 1977] as proposed for other batholiths along
the Cordilleran margin [e.g., Dumitru, 1990] at this time is an obvious factor to consider. Dumitru [1990]
regarded reduction of the ambient geotherm beneath the extinct arc as a fundamental consequence of
low-angle subduction. However, to induce rapid cooling by this mechanism requires that the subducting slab
underlie the arc at relatively shallow depth (~ 30 km). Based upon modern analogy [Smalley and Isacks,
1989], the depth of the subducting slab beneath the arc was probably much deeper (~100 km). Consequently,
rapid cooling by downward heat conduction beginning at ~80 Ma seems unlikely to us. It appears more
plausible that change in the stress regime produced by shallow-inclination subduction triggered exhumation
[e.g., O’Connor and Chase, 1989]. Regardless, it is the combined prominence of Late Cretaceous cooling
postdating intrusion by 10-20 m.y. and comparatively deep denudation (Figure 1) that characterize the PRB
and help distinguish it from adjacent, more shallowly-denuded, medial Cretaceous arcs such as the Sierra
Nevada to the north [Ague and Brimhall, 1988; Barton et al., 1988].
6. Conclusions and Future Research Directions
Results such as those depicted in Figure 9 prompt us to conclude that analysis of detrital closure age
distributions in the manner we advocate is quite promising and potentially capable of yielding
thermochronologic constraints no less valuable than those available from the exposed basement. A major
advantage of relying upon detrital materials to deduce exhumation histories is the statistically favorable
sampling they afford. While our approach is highly sensitive to the exhumation rate, it is only able to place
lower bounds upon the amount denudation that has taken place. However, simultaneous use of multiple
thermochronometers would largely obviate this limitation and strengthen calculated denudation histories. The
major limitation thus is likely to reside in the ability to accurately determine depositional ages. Work in
progress is focused upon automating the method to fully explore the range of equivalent solutions that are
capable of reproducing the measured data. When extended to additional measurements of detrital closure age
distributions elsewhere along the western margin of the PRB [Kimbrough et al., 1996] we anticipate that it will
be possible to refine our approach sufficiently to identify along strike variations in exhumation history that
relate to the nature of the underlying crust and/or other fundamental properties.
Acknowledgments
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T.M. Harrison, R.V. Ingersoll, C.E. Manning, H. Lang, and P. Rummelhart are acknowledged for helpful
reviews of the manuscript. D.R. Rothstein made available unpublished basement K-feldspar and biotite
results from Baja California and was influential in formulating our approach for pluton emplacement. This
work was funded by grants from the DOE and NSF.
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LOVERA ET. AL., DETRITAL CLOSURE AGE ANALYSIS OF FOREARC STRATA
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Figure Captions
Figure 1: (a) Location of northern Peninsular Ranges batholith (PRB). Inset shows distribution of batholith
rocks, pattern of cooling ages [modified after Krummenacher et al., 1975], and erosion depth [modified
after Gastil, 1979] throughout southern and Baja California. NSA (northern Santa Ana mountains) and
LJPL (La Jolla/Point Loma) denote sample localities (b) Projection of available U-Pb zircon [Silver and
Chappell, 1988; Walawender et al., 1990; and Kimbrough, unpublished.] and K-Ar biotite and K-feldspar
ages [Krummenacher et al., 1975; Grove, 1994, Grove,unpublished] into X-X' in (a).
Figure 2: Stratigraphy of PRB forearc strata in (a) San Diego area and (b) northern Santa Ana Mountains.
(c)-(i) Histograms of measured detrital K-feldspar closure age distributions.
Figure 3: Schematic of numerical model illustrating scaling and boundary conditions. Light gray shading
indicates portion of grid where closure ages are calculated. Samples assigned to a given depositional age
(AgeD) are from ±0.5 m.y. region. Bold line represents the final (65 Ma) erosion surface.
Figure 4: Progressive thermal development of the batholith in Model II (Table 5). Net area intruded in each
interval indicated in lower left-hand panel corners. (a)-(f) Isothermal sections prior to the onset of
denudation (115, 113, 111, 109, 107, and 105 Ma); (h-k) Isothermal sections for times characterized by
simultaneous intrusion and denudation (103, 101, 99, 97, and 95 Ma). Active erosion surfaces represented
by bold lines; (l) isothermal distribution at 65 Ma.
Figure 5: Contours of emplacement age for final pluton distributions in (a) I1and (b) I2 (Table 3). (c) Mean
intrusion age of plutonic rocks vs. horizontal distance. Values calculated for I1 and I2 represented by
solid and dashed lines respectively. Superposed symbols represent U-Pb zircon age determined for PRB
plutons (see Figure 1 legend).
Figure 6: Kolmogorov-Smirnov (K-S) statistical comparison of model and measured closure age distributions.
(a) Variation of significance level of K-S statistic (PROB) in comparing model and measured
distributions for Mustang Spring sample. Depositional age and uncertainty for Mustang Spring sample
indicated above. (b)-(f) Comparison of model (light gray) and measured results (black) for Age D = 87,
85, 83, 81, and 79 Ma. All data normalized to 100.
Figure 7: Model I results: (a) Contour plot of final f K-feldspar bulk closure age distribution (10 Ma contour
interval). Surface positions every 5 m.y. after initial denudation represented by labeled black lines.
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Final (65 Ma) surface is bold line; (b) basement surface mineral age profiles at indicated times; (c)-(h)
Histograms of detrital K-feldspar closure ages at indicated times. For each stratigraphic horizon, we
overlay distributions calculated from 32 (black) and 1000 (light gray) random samples. All data
normalized to 100.
Figure 8: Model II results. Figure 7 caption contains explanation of (a)-(h).
Figure 9: (a) Depositional ages and uncertainties for each samples (see Table 1). (b) -(g) Model I-VI results
(see Figure 6 caption). PROBmax values represented by symbols defined in (a) above (see Table 5). (h).
t vs. depositional age models based upon (b)-(g) above.
Figure 10: Effect of radiogenic daughter product retentivity upon Model II results (see Table 2). (a) apatite
((U-Th)-He); (b) K-feldspar, (c) biotite, (d) hornblende (K-Ar); and (e) monazite (Th-Pb) age
distributions. (f) Closure ages variation along final (65 Ma) surface.
Figure 11: Ability of variable rate denudation models to fit measured detrital closure age distributions. (a)
Depositional ages and uncertainties for measured samples. (b)-(d) Model VII-IX results (see Figure 9
caption for explanation; Table 5). (e) Deviation of AgeDmax from estimated stratigraphic ages in models
VII-IX. (f)-(l) Comparison of measured detrital closure age with those of Model IX. All data
normalized to 100.
Figure 12: (a) Mean denudation rate vs. time for indicated models (b) Histogram of bulk closure ages (= total
fusion ages) calculated from 40Ar/39Ar step-heating of K-feldspars from east central PRB (see Figure 1
caption for data sources). (c)-(e) Comparison of predicted surface ages from models I-IX with measured
basement K-feldspar results vs. horizontal distance.
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Table 1 Depositional Age Constraints
Sample Name
Stratigraphic Unit
Tourmaline Beach
Cabrillo
Formation
Sample Location
Latitude/ Longitude
N32°48’26”
W117°15’49”
Magnetostratigraphy
(Chron)1
32N
Time Scale
Position
upper
Campanian
Estimated Age
(Ma)
73+4-2
Bird Rock
Upper Point
Loma Fm.
N32°48’50”
W117°16’22”
32R2
upper
Campanian
74+3-1
La Jolla Bay
Lower Point
Loma Fm.
N32°51’07”
W117°15’38”
33N
mid
Campanian
76+3-1
Williams
Williams
Formation
N33°45’26”
W117°39’21”
C33N/C32R2
mid
Campanian
75+1-3
Mustang Springs
Mustang Spring
Member
N33°45’32”
W117°38’33”
C33R
lower
Campanian
80+3-4
Baker Canyon
Baker Canyon
Member
N33°44’51”
W117°38’29”
C34N
Turonian
90+1-1
Trabuco
Trabuco
Formation
N33°44’51”
W117°38’17”
C34N
CenomanianTuronian (?)
92+10-2
1. Based on Gradstein et al. [1994]
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Table 2 Diffusion Parameters Used in Model
Mineral
Decay
E



.

Log Do/r2

Tmin

Tmax

TC
Reference
Scheme
[kcal/mol]
[1/s]
[°C]
[°C]
[°C]
Apatite
(U-Th)-He
36.3
7.82sphere
8.8
75
74
[Wolf et al., 1997]
K-feldspar
K-Ar
46.5
5.00slab
144
252
248
[Lovera et al., 1997]
Biotite
K-Ar
47.1
1.93cylinder
197
344
329
[Grove and Harrison, 1996]
Hornblende
K-Ar
64.1
2.57sphere
339
525
502
[Harrison, 1981]
Monazite
Th-Pb
43.0
-5.58cylinder
380
753
670
[Smith and Giletti, 1997]
r = 300 m (biotite), 80 m (hornblende), 50 m (monazite)
Temperature corresponding to 0.5% loss over 15 m.y.
Temperature corresponding to 99.5% loss over 15 m.y.
Bulk closure temperature corresponding to 10°C/m.y. monotonic cooling
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Table 3 Intrusion Models
Model
Intrusion
Interval
(Ma)
Pluton
Radius
(km)
Number
of Plutons
(Each 2 m.y.)
Average Intrusion
Density3
(Each 2 m.y.)
I1
115-95
3-7
3-30
21
I2 (west)1
120-105
2-8
6-18
25
I2 (west) 1
105-100
1-4
3-10
4
I2 (east) 2
105-95
2-8
6-21
46
I2 (east) 2
95-90
2-6
4-14
23
1. West denotes horizontal grid positions between 20-75 km
2. East denotes horizontal grid positions between 20-75 km
3. Pluton overlap in successive frames not considered.
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Table 4 Denudation Models
D1
Timing
(Ma)
105-65
Mean
Denudation Rate1
(km/m.y.)
0.50
Mean Cumulative
Denudation2
(km)
20
Cumulative
Rotation
(degrees)
14.9
D2
105-65
0.25
10
7.6
D3
105-92
0.50
6.5
5.0
92-89
1.25
10.3
7.8
89-78
0.15
11.2
8.9
78-65
0.45
17.8
13.5
Model
1. Mean rate corresponds to a horizontal position of 75 km
2. Mean denudation corresponds to a horizontal position of 75 km
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Table 5 Summary of Model Results
Run
Intrusive
History1
Denudation
History2
Tourmaline
Beach
t
(Ma)
log
PROBmax
t
(Ma)
Bird
Rock
La Jolla
Bay
Williams
Mustang
Springs
Baker
Canyon
Trabuco
log
PROBmax
t
(Ma)
log
PROBmax
t
(Ma)
log
PROBmax
t
(Ma)
log
PROBmax
t
(Ma)
log
PROBmax
t
(Ma)
log
PROBmax
I
n/a
D1
-2
-1.0
-3
-3.2
-4
-1.1
-5
-1.2
-2
-1.2
+6
-1.0
+4
-2.9
II
I1
D1
-2
-1.1
-3
-2.8
-4
-2.0
-5
-1.1
-3
-0.5
+5
-1.5
0
-2.7
III
I2
D1
-2
-1.1
-3
-3.2
-4
-3.2
-5
-1.2
-4
-1.4
+3
-1.9
0
-2.9
IV
n/a
D2
+8
-1.5
+8
-1.6
+7
-2.4
+6
-2.0
+9
-2.9
+18
-3.1
16
-4.2
V
I1
D2
+8
-0.6
+6
-0.5
+4
-0.2
+4
-0.6
+7
-1.3
+13
-0.6
7
-3.1
VI
I2
D2
+8
-0.8
+6
-0.8
+3
-1.3
+3
-1.1
+5
-2.1
+11
-2.6
7
-4.6
VII
n/a
D3
+1
-0.4
+1
-0.1
0
-1.5
+1
-0.9
+2
-1.0
+5
-1.1
+2
-3.8
VIII
I1
D3
+1
-0.3
+1
-0.4
0
-2.7
+2
-0.7
+2
-1.8
+1
-1.6
0
-2.7
IX
I2
D3
+1
-0.4
+1
-0.2
0
-2.6
+1
-0.8
0
-1.8
0
-1.8
0
-2.3
1. See Table 3; Figure 5
2. See Table 4
3. ti = AgeSi - AgeDmax,i (see text for details).
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