A Method For Determining Exhumation Histories of Arc Crust Based upon Analysis of Detrital Closure Ages Distritubion
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, Sand Diego State University
San Diego, CA 91182-1020
JGR 1999, V104, No12, pages 29419-29438
 
Manuscript (PDF file)
Tables
Figures: 
 
Abstract: 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 representatives of material removed from the denuding batholith, the method has vast potential to decipher the evolution of juvenile arc crust. 
 
 
   Fig.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localities (b) Projection of available U-Pb zircon [Silver and Chappell, 1988; Walawender et al., 1990; and Kimbrough, unpublished.] and K-Ar biotite and K-feldspar ages [Krummenacher et al., 1975; Grove, 1994, Grove,unpublished] into X-X' in (a).   Fig.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.
 Fig. 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. Fig. 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.
 Fig. 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). Fig. 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 AgeD = 87, 85, 83, 81, and 79 Ma.  All data normalized to 100.
 Fig. 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.  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. Fig. 8: Model II results.  Figure 7 caption contains explanation of (a)-(h).
 Fig. 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. Fig. 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.
 Fig. 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. Fig. 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.

Tables

Table 1: Depositional Age Constraints (Northern Santa Ana Mountains)

Sample Name
Stratigraphic Unit
Sample Location
Latitude/ Longitude
Magnetostratigraphy
(Chron)1
Time Scale
Position
Estimated Age
(Ma)
  Tourmaline Beach  
Cabrillo
Formation
N3248'26"
W11715'49"
32N
upper
Campanian
73+4-2
  Bird Rock  
Upper 
Point Loma Fm.
N3248'50"
W11716'22"
32R2
upper
Campanian
74+3-1
  La Jolla Bay  
Lower 
Point Loma Fm.
N3251'07"
W11715'38"
33N
mid
Campanian
76+3-1
  Williams  
Williams
Formation
N3345'26"
W11739'21"
C33N/C32R2
mid
Campanian
75+1-3
  Mustang Springs  
Mustang Spring
Member
N3345'32"
W11738'33"
C33R
lower
Campanian
80+3-4
  Baker Canyon  
Baker Canyon
Member
N3344'51"
W11738'29"
C34N
Turonian
90+1-1
  Trabuco  
Trabuco
Formation
N3344'51"
W11738'17"
C34N
Cenomanian-
Turonian (?)
92+10-2
  1. Based on Gradstein et al. [1994]


Table 2: Diffusion Parameters Used in Model

Mineral 
Decay
Scheme
E
[kcal/mol] 
1Log Do/r2
[1/s]
 2Tmin
[C] 
3Tmax
[C] 
4TC
[C]
Reference
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]
1.  r = 300 mm (biotite), 80 mm (hornblende), 50 mm (monazite)
2  Temperature corresponding to 0.5% loss over 15 m.y.
3  Temperature corresponding to 99.5% loss over 15 m.y.
4.  Bulk closure temperature corresponding to 10C/m.y. monotonic cooling


Table 3: Intrusions 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.


Table 4: Denudation Models

Model
 
Timing
(Ma)
Mean
Denudation Rate1
(km/m.y.)
Mean Cumulative
Denudation2
(km)
Cumulative
Rotation
(degrees)
D1
105-65
0.50
20
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
1 Mean rate corresponds to a horizontal position of 75 km
2.  Mean denudation corresponds to a horizontal position of 75 km


Table 5: Summary of Model Results

Run
Intrusive History1
Denudation
History2
Tourmaline Beach
Dt          log 
(Ma)    PROBmax
Bird
Rock
Dt          log 
(Ma)   PROBmax
La Jolla
Bay
Dt          log 
(Ma) PROBmax
Williams
Dt          log 
(Ma)  PROBmax
Mustang
Springs
Dt          log 
(Ma)  PROBmax
Baker
Canyon
Dt          log 
(Ma)    PROBmax
Trabuco
Dt         log 
(Ma) 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. Dti = AgeSi - AgeDmax,i (see text for details).