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A Cyclostratigraphic Analysis of the Eocene-Oligocene Boundary GSSP, Massignano, Italy
Rachel Brown Senior Integrative Exercise
March 10, 2006
Submitted in partial fulfillment of the requirements for a Bachelor of Arts degree from Carleton College, Northfield, Minnesota
Table of Contents
Abstract
Introduction……………………………………………………………………………...1
Background………………………………………………………………………………3
Milankovitch Cycles
Geologic Setting………………………………………………………………………….5
Field and Laboratory Methods…………………………………………………………6
Sample Collection
Calcium Carbonate and Magnetic Susceptibility
Stable Isotopes
Spectral Analysis
Results…………………………………………………………………………………...12
Calcium Carbonate, Magnetic Susceptibility and Stable Isotope Data
Spectral Analysis
Discussion……………………………………………………………………………….22
Magnetic Susceptibility
Calcium Carbonate and Stable Isotopes
Stable Isotopes and Orbital Cycle Strength
Correlation with the Astronomical Time Scale
Impacts, Comet Showers and Climate Cycles
Conclusions……………………………………………………………………………...35
Acknowledgements……………………………………………………………………..35
References Cited………………………………………………………………………...37
Appendix 1………………………………………………………………………………41
Appendix 2………………………………………………………………………………48
A Cyclostratigraphic Analysis of the Eocene-Oligocene Boundary GSSP, Massignano, Italy
Rachel Brown
Carleton College Senior Integrative Exercise
March 10, 2006
Advisors: Mary Savina, Carleton College
David Bice, Pennsylvania State University Alessandro Montanari, Osservatorio Geologico di Coldigioco
Abstract High-resolution spectral analyses of four climate proxies from Massignano, Italy (Eocene-Oligocene Boundary GSSP) indicate that the deposition of the upper portion (meter levels 15-23) of the rhythmically bedded sedimentary sequence was eccentricity forced. An inverse relationship exists between the magnetic susceptibility record and the co-varied calcium carbonate and stable isotope records. This is indicative of a climate model in which limestones represent dry/cold periods while marly limestones represent warm/wet periods. Through pattern matching constrained by three radiometrically dated volcanic ashes, an astronomical correlation is achieved between Laskar’s eccentricity curve and low-frequency variations in magnetic susceptibility and calcium carbonate data. This correlation yields a refined date for the Eocene-Oligocene boundary of 33.9 ± 0.01 Ma as well as precise ages for the three volcanic ash layers (34.32 ± 0.01 Ma, 34.55 ± 0.01 Ma, 35.13 ± 0.01 Ma), all of which fall within the reported errors of the original radioisotopic ash dates. Orbital forcing is less evident in the lower portion of the Massignano section (meter levels 0-15), which contains evidence of three impact events and a 2.2 My comet shower. It is likely that climate alterations caused by these extraterrestrial events obscure the longer-term Milankovitch climate cycles. Keywords: Milankovitch theory, Eocene, Oligocene, pelagic, impact phenomena, climate, stable isotopes, magnetic susceptibility, calcium carbonate
1
Introduction
The Milankovitch cycles of eccentricity (123 and 95 ky), obliquity (41 ky) and
precession (19 and 23 ky) affect global climate by altering the distribution of sunlight at
different latitudes (Milankovitch, 1941). Like other climatic variations, these cyclical
patterns may in turn, influence the rate and type of sedimentary deposition. Therefore,
pelagic sedimentary rocks can potentially provide a stratigraphic record of paleoclimate,
documenting changes in temperature as well as precipitation. Within the past two
decades, the relationship between lithology and cyclical orbital variations has been
increasingly explored through the technique of spectral analysis (e.g. Hilgen, 1991;
Hilgen et al., 1999; Shackelton et al., 2000; Cleaveland et al., 2002; Mader et al., 2004),
confirming orbital forcing as the fundamental cause of ice ages in the Quaternary, and
even as far back as the Miocene (Hays et al., 1976).
Ice sheets are important in understanding paleoclimate, particularly in the Late
Eocene, a period characterized by accelerated global cooling coincident with the
appearance of Antarctic polar ice sheets (Fig. 1) (Prothero, 1994; Zachos et al., 1994).
This long-term climate cooling trend is reflected by both an increase in marine oxygen
isotope values (Mackensen and Ehrmann, 1992; Zachos et al., 1994) and the occurrence
of significant biotic turnovers (Berggren and Prothero, 1992). The cooling trend,
however, is further complicated by the occurrence of multiple bolide impact events
(Glass and Koerbel, 1999) related to an extensive Late Eocene comet shower (Farley et
al., 1998), which may also have influenced global climate (Vonhof, et al., 2000;
Bodiselitsch et al., 2004).
0.5
11.
52
2.5
32 32.5 33 33.5 34 34.5 35 35.5 36
00.
51
1.5
22.
53
3.5
01
23
45
0 10 20 30 40 50 60 70
Miocene Oligocene Eocene PaleocenePlio.
Plt.
Age
(Ma)
18O
(‰)
Smal
l-ep
hem
eral
Ice-
shee
tsapp
ear
Late
Pale
ocen
eTh
erm
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axim
um
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ciat
ion
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ocen
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imum
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xpan
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t exp
ansi
on
13C
(‰)
01
23
-1C
limat
icE
vent
s18
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)13
C(‰
)
Oi-
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atio
n
Figu
re 1
. Glo
bal d
eep-
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on a
nd o
xyge
n is
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cord
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pel
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200
1).
2
3
The pelagic sediments of the Umbria-Marche basin, Italy, deposited during the
period of Eocene-Oligocene cooling, provide insight into the manner in which local
sedimentation and regional climate patterns were affected by both ice sheet development
and impact events. The 23m sequence of limestone and marly limestone exposed at the
Massignano Quarry (GSSP for the Eocene-Oligocene boundary), located in the
easternmost part of the basin (Fig. 2), is ideal for cyclostratigraphic analysis, as it is both
continuous and undisturbed (Cotillion, 1995). Furthermore, the sequence contains three
radiometrically dated volcanic ashes, which provide time constraints for the section,
thereby allowing for correlation of the stratigraphic climate record with mathematically
predicted orbital variations (e.g. Laskar, 2004) and determination of precise astronomical
ages for stratigraphic horizons. In this study, I analyze four different high-resolution
climate proxies in the Massignano section, including calcium carbonate content, magnetic
susceptibility, and oxygen and carbon stable isotope composition, in order to provide
insight on orbital forcing on the Eocene-Oligocene climate system and astrochronology
during this important time period.
Background
Milankovitch Cycles
Milankovitch cycles, first discovered by Serbian climatologist and astrophysicist
Milutin Milankovitch (1941), describe the variation in the earth’s orbit about the sun. The
three cycles, including precession, obliquity and eccentricity, involve the earth’s axial
wobble, its angle of tilt, and its variation in orbital shape. While Milankovitch
hypothesized a connection between these orbital cycles and climate variation, it was Hays
Rome
Naples
Milan
Figure 2. Location map of the Massignano section, Marche region, Italy. Landsat image in the upper right courtesy of the Global Land Cover Facility.
N
0 100km
43.5 N
13.6 E
4
0 6km
5
et al. (1976) who provided the data and analysis that led to the first real test of the
hypothesis. Ultimately, the three Milankovitch cycles control climate by altering the
distribution of sunlight at different latitudes. The precessional cycle (19 and 23 ky) alters
the angle of insolation on the Earth’s surface, such that the North or South Hemisphere
will experience a year of extreme seasons while the other will experience a milder
summer and winter. The obliquity cycle (41 ky), which incorporates the Earth’s
fluctuation in tilt angle from 22 to 24°, also alters the angle of insolation on the Earth’s
surface. A low tilt angle is synonymous with low seasonality, just as a higher tilt angle
corresponds with higher seasonality. A unique characteristic of the obliquity cycle is that
it simultaneously has the same effect on both the Northern and Southern Hemispheres.
Finally, the distance between the Earth and sun is altered by the eccentricity cycle (95
and 123 ky). The Earth’s orbit is not consistent in its shape, but fluctuates between a
more circular ellipse to a more elongated shape. Depending on the shape of the orbit, the
Earth will be closer or further from the sun. Alone, the eccentricity cycle has little impact
on insolation, but it is still climatically important, as it controls the amplitude of the
precessional cycle. All three of these orbital variations appear to have major effects on
climatological factors, altering surface temperature, seasonal duration and intensity, and
atmospheric and oceanic circulation.
Geologic Setting
The Massignano Section, which became the GSSP for the Eocene-Oligocene
Boundary in 1993 (Premoli Silva and Jenkins, 1993), is an ideal location for a
cyclostratigraphic study. The 23-meter thick outcrop consists of alternating pale green-
6
and pink- colored pelagic limestones and marly limestones (Fig. 3). As the type section of
the Eocene-Oligocene boundary, it has been the subject of a number of detailed studies
integrating litho-, bio-, magneto-, and chemostratigraphy (see Premoli Silva et al., 1988,
Montanari and Koerbel, 2000, Jovane at el., 2004, and references therein). Three
radiometrically dated volcanic ashes are contained within the section at meter levels 7.2,
12.7 and 14.7, providing independent age constraints necessary for compelling
astronomical dating. In addition, the section contains several other biotite-rich volcano-
sedimentary layers as well as impactoclastic layers marked by Ir anomalies and shocked
quartz grains (Bodiselitsch et al., 2004).
Field and Laboratory Methods
Sample Collection
The Massignano section was logged, following the work of Coccioni et al. (1988)
and sampled at a five-centimeter resolution between meters 0.5 and 23 (Fig. 3). Because
the Massignano Quarry is now an interactive science park, the meter levels are marked
with plaques, which we utilized during the measuring and sampling process. Limestone
samples were primarily collected using a Bosch PbH 200 RE masonry drill with a size 12
bit, which allowed for greater sampling precision, while marly limestone layers were
collected as hand samples. Each sample weighed a minimum of 20 grams. Upon return to
the laboratory, the samples were dried and those that were not already powdered were
crushed using a brass mortar and pestle and coarse sieved to remove possible root
material and then sieved to two millimeters to ensure homogeneity.
0
2
3
4
5
6
7
1
8
10
11
12
13
14
15
9
16
18
19
20
21
22
23
17
EO
CE
NE
OL
IGO
CE
NE
(1)
LEGEND
obstructed section
limestone
marly limestone
biotite-rich layer
shocked quartz
dated volcanic ash layer
REFERENCES
(1) Premoli Silva & Jenkins, 1993.
Figure 3. Lithostratigraphy of Massignano, Eocene-Oligocene boundary GSSP.
reddish interval
m
7
8
Calcium Carbonate and Magnetic Susceptibility
Both the calcium carbonate and magnetic susceptibility analyses were completed
on all 450 samples at the Osservatorio Geologico di Coldigioco. Calcium carbonate
content was measured using a Dietrich-Fruling water calcimeter with ±2% precision.
Samples of 300.0 to 320.0 mg were reacted in excess 10% HCl for two minutes.
Atmospheric temperature and barometric pressure were recorded along with sample mass
and the volume of water displaced by the carbon dioxide for the calculation of percent
calcium carbonate. Carrara marble served as the standard of pure CaCO3, as it
consistently attains calcium carbonate values of ~100%, and was run after every twenty
samples to ensure proper calibration of the calcimeter. Every twentieth sample was also
repeated for the same purpose.
Mass specific magnetic susceptibility measurements were carried out on a
Bartington MS2 and a Bartington MS2B dual frequency sensor on low frequency
(0.465kHz) and x0.1 sensitivity. Samples were measured at a constant volume and their
masses were noted. Air measurements were made between samples to correct for
thermally induced drift.
Stable Isotopes
Oxygen and carbon stable isotopic compositions were obtained from bulk rock
carbonate at five-centimeter intervals in two smaller portions of the Massignano section:
meter levels 5.25-7.1 and 15-20 (Fig. 3). The first of these intervals was selected because
it is known to contain an impactoclastic layer, while the second contains the Eocene-
Oligocene boundary at meter level 19. The use of bulk carbonates in stable isotope
analysis is convenient, as it requires very little sample material and allows for the rapid
9
analysis of numerous samples. However, one concern with this method is that, because
the bulk samples represent a mixture of carbonates from different sources, the δ18O of
seawater will not be accurately represented (Stoll and Schrag, 2000). While this concern
is valid, comparisons of single species foraminiferal δ18O records with those of bulk
carbonates show that bulk carbonates do in fact accurately represent changes in both sea
surface temperature and the δ18O of seawater when environmental changes are universal,
affecting species throughout the water column (Shackelton et al., 1993; Schrag et al.,
1995). Another potential problem with using bulk carbonates is that weathering and
diagenesis may alter the original carbon and oxygen isotopic compositions (Banner and
Hanson, 1990). At Massignano, there are few indications of weathering. The quarry cut is
relatively fresh and well maintained, as the quarry is now part of an interactive science
park. Furthermore, Odin et al. (1988) found no evidence of carbonate recrystallization at
Massignano, though SEM analysis has revealed that foraminifers from the section contain
secondary, blocky calcite (Vonhof et al., 1998). As long as sediments in the same section
experience recrystallization at the same rate through time, they will contain about the
same amount of secondary calcite. If this is the case, the mean δ18O values may be shifted
in either direction, but the important primary variations are preserved (Stoll and Schrag,
2000).
Stable isotope analyses were carried out at Pennsylvania State University. About
50µg of each sample was transferred into copper boats and set into a drying oven
overnight to remove excess H2O. Analysis was performed by reacting samples with
phosphoric acid for 20 minutes at a constant reaction temperature of 90°C on a
Commonbath Fairbanks Autocarbonate Device coupled to a Finnigan MAT 252 Isotope
10
Ratio mass spectrometer. Each sample run consisted of thirty-eight samples and nine
standards, including both the carbonate standard NBS-19 and the internal University
standard, Biogeochem. The isotope data are reported in per mil deviations from the
international PDB carbonate standard, to which the data have been calibrated with NBS-
19.
Spectral Analysis
Spectral analyses of the four proxy datasets were conducted in Matlab 5.2, using
algorithms modified from Muller and MacDonald (2000). While the sample interval
through the section was 5 cm, a linear interpolation was applied to provide a regular
interval where the ash deposits were removed, thereby improving Fast Fourier Transform
(FFT) results. The FFT procedure distinguishes the frequencies and relative powers of
cycles appearing in the raw data by comparing the data set to various sine and cosine
functions. To determine the statistical significance of the spectral peaks, 1000 sets of
random numbers, which were the same size as the proxy data sets, were generated in
Matlab. A curve was then plotted two standard deviations above the spectral powers of
the frequencies found in the data. Peaks rising above this curve can be attributed to
cyclicity with 95% certainty. Prominent, statistically significant peaks related by ratios
that fit the expected range of ratios between Milankovitch cycles are assumed to
represent precession, obliquity, and eccentricity, making it possible to correlate meter
level to age through the calculation of an average sedimentation rate. For the Massignano
section, an average sedimentation rate of 10.6 m/My was calculated, which is consistent
with the possible range of sedimentation rates (4.2 m/My to 37.8 m/My) calculated from
the independently dated volcanic ashes found at meter levels 7.2, 12.7, and 14.7
11
(Montanari et al., 1988). The 23-meter section, therefore, spans a time period of 2.39 My,
with an average time interval of 4.7 ky between sediments as sampled every 5 cm.
Further analysis incorporated a sliding window technique, in which FFT’s are
performed on a specified portion or “window” of the data that shifts incrementally
through the time series. The sliding window technique is useful because it allows us to
see the stratigraphic changes in spectral power, which are the result of likely variations in
environmental conditions and sediment accumulation rates during the 2.39 My of
deposition. By looking at the continuity of peaks through time, we can establish whether
they represent long term cyclicity or whether they are the result of random variations and
climatic noise (Muller and MacDonald, 2000). However, this technique is somewhat
subjective, as the choice of window size will affect which cycles appear important, with
high frequency cycles standing out in smaller windows and low frequency cycles
appearing only in larger windows. This problem can be overcome by using a variety of
window sizes for the analysis and noting which frequencies are present, at least in part, in
multiple windows. Frequencies that are both continuous over time and observed in a
range of window sizes are considered to reflect actual cyclic trends in the data, while
frequencies that are resolved sporadically and discontinuously are attributed to noise
within the climate system (Cleaveland, 2001). Finally, prior to the sliding window
analysis, a broad band-pass filter was employed to smooth the raw magnetic
susceptibility and δ13C data so as to remove long-period, low frequency contributions that
may be swamping the higher-frequency signals. Spectral peaks with periods greater than
~800 ky are not significant in the Massignano section because the whole section studied
spans 2.39 My.
12
Astronomical dating was similarly accomplished through the use of broad
bandpass filtering. Variations in the raw carbonate and magnetic susceptibility data
between 140 and 85 ky were isolated so as to emphasize the variance in the eccentricity
band. This smoother data was then used for correlation with the Laskar et al. (2004)
theoretical eccentricity curve.
Results
Calcium Carbonate, Magnetic Susceptibility and Stable Isotope Data
The calcium carbonate contents of the limestones and marly limestones of the
Massignano section range in value from 47.4% to 96.09%, with an average of 76.86%
(Fig. 4, see Appendix 1 for the complete data table). A persistent trend in the data is not
apparent across the section. This is not, however, true for the magnetic susceptibility
data, which fluctuates between 1.42 and 122.93 (SI Units), averaging 4.72 SI, and
exhibits an upward trend of decreasing variability with an absence of the very high values
associated with ashes (Fig. 4). Both proxy curves correspond well with lithology, as the
limestone beds primarily exhibit higher calcium carbonate values and lower magnetic
susceptibility values. Furthermore, magnetic susceptibility spikes are located in
stratigraphic layers known to contain ash deposits. The two data sets are inversely
related, such that calcium carbonate highs correspond with magnetic susceptibility lows.
The oxygen and carbon isotopic data are also listed in Appendix 1 and illustrated
in Figure 5. For meters 15-20, the δ18O values range from –0.729‰ to –1.51‰
(averaging -1.05‰), and are characterized by a slightly decreasing trend. For meters 5.35
to 7.10, the values vary between –0.843‰ and –1.43‰ (averaging -1.16‰) and also
meter level(m)
2
3
4
5
6
7
1
8
10
11
12
13
14
15
9
16
18
19
20
21
22
17
EO
CE
NE
OL
IGO
CE
NE
40 50 60 70 80 90 100Magnetic Susceptibility (SI) % Calcium Carbonate
Figure 4. Magnetic susceptibility and percent calcium carbonate results for Massignano. Ashes have been removed from the magnetic susceptibility record to accentuate variabil-ity. Note the primarily inverse relationship between the two proxy records.
1 2 3 4 5 6 7 8 9 10
3020
13
0.9 1.3
δ18O[‰PDB]
δ13C[‰PDB]1.7
-0.6-1.0-1.4
2.1
20
15
10
5
0
5.35
5.75
6.15
6.55
6.95
-0.6-1.0-1.4 -1.2 -0.8
1.55 1.65 1.75 1.85
-0.6-1.0-1.4 -1.2 -0.8-1.6
1.2 1.4 1.6 1.81.00.8
15
16
17
18
19
20
Figure 5. Oxygen and carbon stable isotope results for the Massignano section. On the left is a composite of both the data from this study and that of Bodiselitsch et al. (2004). The insets contain data from this study. Note the scale changes.
-0.4
2.5
δ18O
δ18O
δ13C
δ13C
14
15
exhibit a decreasing trend upward through time. In the upper section (meters 15-20), a
marked increase is seen in the δ13C record, with a significant jump at about meter level
17.5. The values range from 0.837‰ to 1.60‰ (with an average of 1.28‰), while in
meters 5.35 to 7.10, the δ13C values fluctuate between 1.53‰ and 1.83‰ (averaging
1.7‰). In the upper section in particular, the δ18O and δ13C records appear to co-vary,
with δ18O highs corresponding with δ13C highs and similarly lows with lows. This
relationship is less clear in the lower section.
By combining the isotope data from this study with that of Bodiselitsch et al.
(2004), we can see a decreasing trend in the δ13C data through the majority of the section
followed by an increasing trend from about meter level 17 to the top (Fig. 5). Trends in
the δ18O data are less pronounced, but there appears to be a general decrease in values
from meter level 3 to 8, followed by an increase and a subsequent decrease from about
meter level 15 to 21.
Spectral Analysis
Spectral analysis results of calcium carbonate and magnetic susceptibility data
using a linear sedimentation rate of 10.6 m/My across the entire Massignano section are
shown in Figure 6. The plots are quite noisy, particularly the calcium carbonate, and
while orbital peaks are present, they do not emerge significantly above the noise level.
Prominent spectral power peaks for the %CaCO3 occur at 315, 60, 41, 30, and 24 ky and
for MS at 254, 116, 43, and 24 ky, all of which rise above the 95% confidence interval.
Knowledge of the comet shower and multiple volcanic ashes in the lower and
central portion of the section prompted a split analysis of the outcrop. The results of the
spectral analysis of the four proxies for the split section are shown in Figures 7 and 8.
0 0.01 0.02 0.03 0.04 0.05 0.060
10
20
30
40
50
60
frequency
Whole Section MS
116
95
6943
5126
24
21
254
348
414
201
38 3119 17
0 0.01 0.02 0.03 0.04 0.05 0.060
5
10
15
20
25
frequency
Whole Section CaCO3
315
441
130 96
77
60
66
41
50
3338
30
24
236
2721 20
19 18
17
44
Figure 6. Spectral analysis results for %CaCO3 and MS for the entire Massignano section
using a sedimentation rate of 10.6 m/My and 10-700 ky bandpass to remove long-period, low frequency contributions. The green line is the 95% confidence line. While orbital peaks are present, other peaks appear more pronounced.
16
0 0.01 0.02 0.03 0.04 0.05 0.060
5
10
15
20
25
30
frequency
% Calcium Carbonate for meters 15-23
97
77
127
3742
5530
23 20 1818
1926
3349
228
0 0.01 0.02 0.03 0.04 0.05 0.060
5
10
15
20
25
30
35
frequency
Magnetic Susceptibility for meters 15-23
125
95
6155 36
42 24
27 1719
236
spec
tral
pow
er (
cycl
es/k
yr)
spec
tral
pow
er (
cycl
es/k
yr)
Figure 7. Spectral analysis results for all four proxies in the upper portion of the Massig-nano section. These plots are considerably less noisy than those for the whole section. Common elements in the four plots include a peak or peak cluster at 36-43 ky, and pronounced peaks at 95 or 97 ky, as well as at 23-25 ky. Both the eccentricity and preces-sion peaks consistently clear the 95% confidence line (in green), however the obliquity peak does not.
0 0.01 0.02 0.03 0.04 0.050
10
20
30
40
50
60
frequency
δ13C for meters 15-20
95
122
25213750
6575
176
0 0.01 0.02 0.03 0.04 0.05 0.060
2
4
6
8
10
12
14
frequency
δ18O for meters 15-20
23
19
31
3943
48
55
68
97
265
147
spec
tral
pow
er (
cycl
es/k
yr)
spec
tral
pow
er (
cycl
es/k
yr)
17
frequency
δ13C for meters 0-15
0 0.01 0.02 0.03 0.04 0.05 0.060
5
10
15
20
25
30
35
frequency
% Calcium Carbonate for meters 0.5-15348
58
735
6789158
110
4440
33 2724
222420 17
183036
245
0 0.01 0.02 0.03 0.04 0.05 0.060
10
20
30
40
50
60
70
frequency
Magnetic Susceptibility for meters 0.5-15
114
276
9269 51 44
3836 26 24
22 20 1731
80
spec
tral
pow
er (
cycl
es/k
yr)
spec
tral
pow
er (
cycl
es/k
yr)
spec
tral
pow
er (
cycl
es/k
yr)
spec
tral
pow
er (
cycl
es/k
yr)
Figure 8. Spectral analysis results for all four proxies in the lower portion of the Massig-nano section. Data from Bodiselitsch et al. (2004) was combined with data from this study to produce the carbon and oxygen stable isotope plots. Like the spectral plots for the entire section, these plots exhibit a significant amount of noise.
0 0.01 0.02 0.03 0.04 0.05 0.060
5
10
15
20
25
30
35
40
45
50
389
245
150
123 86 72 565046 39 31 20 18232527
frequency
δ18O for meters 0-15
0 0.01 0.02 0.03 0.04 0.05 0.060
2
4
6
8
10
12
14
77
368
144
245
86
99
58 50
47
64 4238
34 2831 26
2322
20
18
18
19
The plots for the upper portion (meters 15-23) are considerably less noisy. Common
elements to all four proxies include a peak or cluster of peaks at 36-43 ky, and
pronounced peaks at 95 or 97, as well as at 23-25 ky (note that spectral peaks with
periods greater than 250 ky are not considered significant, as the section under scrutiny
spans just 755 ky). Although neither rise above the 95% confidence interval, a peak at 55
ky is prominent in three of the records, as is a peak at 30 or 31 ky, which, according to
Mix et al. (1995) may be caused by nonlinear coupling of eccentricity and obliquity. The
δ18O plot is notable, as the peaks at 23 and 19 ky are of much greater significance than in
the other three plots. The spectral plots for the lower portion are reminiscent of the whole
section plots, exhibiting an elevated level of noise (Fig. 8). The most prominent peaks in
the magnetic susceptibility and CaCO3 data that are possibly orbital in origin are at 44
and 24 ky. A peak at 58 ky seen in the CaCO3 data is not echoed in the magnetic
susceptibility record. In the δ13C record peaks at 245 and 150 ky are the only to rise
above the 95% confidence interval, though peaks at 123, 86 and 56 ky all seem to stand
out from the rest. Finally, in the δ18O record, prominent peaks at 144, 77, 22 and 18 ky
appear significant.
In comparing results from sliding window analyses using both medium and small
window sizes on the upper section, it is apparent that long term cyclic variations are most
prevalent in the CaCO3, MS and δ13C data. While all four proxies exhibit coherent
spectral peaks in the medium-sized windows (200-400 ky) (Fig. 9), continuous low
frequency ~95-118 ky peaks are also evident in the CaCO3, MS and δ13C data in the
smaller windows (100-226 ky) (Fig. 10). Furthermore, faintly continuous peaks are also
visible at about 38-42 ky and 23-26 ky. The peaks within the δ18O data appear primarily
Age
(M
a)
10
9
8
7
6
5
4
3
2
1
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/k.y.)
Spec
tral
pow
er
Age
(M
a)
10
15
5
20
00.01 0.02 0.03 0.04 0.05 0.06
Frequency (cycles/k.y.)
Spec
tral
pow
er
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/k.y.)
Spec
tral
pow
er
Age
(M
a)
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
Spec
tral
pow
er
00.01 0.02 0.03 0.04 0.05 0.06
Frequency (cycles/k.y.)
0
Age
(M
a)
CaCO3 for meters 15-23
376 kyr windowMS for meters 15-23
400 kyr window with 10-200 kyr bandpass
13C for meters 15-20200 kyr window with 10-200 kyr bandpass
18O for meters 15-20210 kyr window
Figure 9. Results from the medium-sized sliding window spectral analyses, which are used to reveal changes in the spectral power of different frequencies over time. A medium window size is between two fifths to one half of the time scale in question, in this case ~750 ky for the upper two plots and ~470 ky in the lower. Spectral power scales are displayed to the right of each graph. The y-axis represents ages (Ma) of the sliding window midpoints.
30
25
20
15
10
5
0
34.15
34.1
34.05
34
33.95
33.9
33.85
34.15
34.1
34.05
34.2
34.25
34.15
34.1
34.05
34.2
34.25
34.15
34.1
34.05
34
33.95
33.9
33.85
20
85
105
103
135
81
91
115
87
127
59
58
118
124
44
38
38
285
346113
346
105
24
23
2319
16
97
98
103
95
220 90
Age
(M
a)9
8
7
6
5
4
3
2
1
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/k.y.)
Spec
tral
pow
er
Age
(M
a) 10
12
4
16
00.01 0.02 0.03 0.04 0.05 0.06
Frequency (cycles/k.y.)
Spec
tral
pow
er
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/k.y.)
Spec
tral
pow
er
Age
(M
a)
Spec
tral
pow
er
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/k.y.)
0
Age
(M
a)
CaCO3 for meters 15-23
226 kyr windowMS for meters 15-23
226 kyr window
13C for meters 15-20100 kyr window with 10-200 kyr bandpass
18O for meters 15-20100 kyr window
Figure 10. Results from the small-sized sliding window spectral analyses, which are used to reveal changes in the spectral power of different frequencies over time. Small-sized windows range between one third to one sixth of the time scale in ques-tion. Spectral power scales are displayed to the right of each graph. Relatively continuous low frequency ~95-118 ky peaks are evident in the CaCO
3, MS and δ13C
data.
34.15
34.1
34.05
34.2
34.25
34.15
34.1
34.05
34
33.95
33.9
33.85
33.8
34.2
34.25
14
8
6
2
34.15
34.1
34.05
33.95
33.9
33.85
33.8
34.2
34.25
34
10
12
4
16
0
14
8
6
2
18
20
34.3
34
10
12
4
0
8
6
2
34.15
34.1
34.05
34.2
34.25
34.3
34
21
118
86
147 81
95
110
147
110
156
93
97
57
45 39
5440
46
25
25
22
19
25
21
17
15
90135
93
99
110
128
84
101
22
discontinuous in the smaller window. Despite this, because three of the proxy records
display coherent spectral peaks in multiple window sizes, it is reasonable to assert that
the cyclicity apparent from the initial spectral analyses is not a result of random
depositional variations, but of repeated climatic or depositional cycles.
Discussion
Magnetic Susceptibility
All materials are susceptible to magnetization when subjected to a magnetic field.
The magnetic susceptibility measurement compares the strength of this acquired
magnetism to that of a temporarily induced magnetic field. The magnitude of magnetic
susceptibility (MS) in a sample will thus reflect the concentration of magnetizeable
materials, including ferrimagnetics, such as iron-bearing minerals, as well as less
susceptible paramagnetics, such as clay minerals and biotite (Ellwood et al., 2000).
Pelagic limestone and marl sequences are generally characterized by low magnetic
susceptibility values, as they contain calcite and/or quartz, which, as diamagnetic
minerals, acquire negative MS in low frequency fields. These diamagnetic minerals serve
to dilute the overall magnetic susceptibility signal, though a small amount of
paramagnetic material is generally enough to outweigh the diamagnetic presence (Richter
et al., 1997).
Variability within the magnetic susceptibility record of a particular rock sequence
can have numerous causes. For one, hematite records a much lower MS value than
magnetite, so a change in MS could be illustrating a change in mineralogy. While the
Massignano section does exhibit packages of reddish-tinted sediments, possibly
23
indicative of elevated hematite content, these sections do not correspond with relatively
lower MS values. In fact, the reddish interval from about meter level 2 to 5 exhibits MS
values that are elevated in comparison with the rest of the sequence (Fig. 4). Because
iron-bearing minerals in pelagic sediments are primarily sourced from terrigenous
sediments, magnetic susceptibility variations are also thought to reflect variations in
weathering and erosion caused by sea level fluctuation or alterations in wet/dry climate
cycling (Ellwood et al., 2000). Changes in sea level affect the supply of detrital material
to the marine environment, as drops in base level associated with regressive periods
enhance continental erosion (Crick et al., 1997). The variability in the magnetic
susceptibility signal of the Massignano section could be linked to either climatically
controlled continental erosion, or conversely, to variations in biogenic carbonate
production, which would dilute an otherwise constant sediment supply.
Calcium Carbonate and Stable Isotopes
Both alone and in conjunction with magnetic susceptibility, the calcium carbonate
content of pelagic sediments has also been broadly used as a proxy for paleoclimate.
Calcium carbonate highs are thought to represent periods of increased carbonate
production, decreased carbonate dissolution, or periods in which a steady supply of
carbonate is periodically less diluted by fluxes in terrigenous input (Einsele and Ricken,
1991). Generally the calcium carbonate content and magnetic susceptibility records of
unconsolidated marine carbonates are inversely related, as is seen throughout the majority
of the Massignano section (Fig. 4). MS is essentially a function of the amount of iron-
bearing minerals deposited compared with the total amount of deposited material. Any
increase, then, in CaCO3 will proportionally decrease the magnetic susceptibility value of
24
a particular sedimentary layer, such that MS lows correspond to CaCO3 highs. This
relationship implies that to some extent, MS increases at the expense of CaCO3 and vice
versa, which is consistent with Einsele and Ricken’s (1991) proposed dilution cycle.
A dilution cycle of this sort is inextricably linked to the oscillations of wet/dry climate
cycles, as wet periods are associated with increased fluvial transport of detrital material
and dry periods are marked by enhanced wind erosion. While the amount of terrigenous
input may not change across these wet/dry periods, presumably the type of detrital matter
is altered, as is the distribution. Continental erosion, along with ocean circulation, is also
linked to productivity, as variations in these parameters will affect the nutrient supply.
Finally, dissolution cycles are linked to sea level change. Greater saturation
concentrations of CO32- are found under conditions of higher pressure, meaning that
carbonate dissolution is enhanced at greater depths (Rühlemann, 1999). The degree of
carbonate dissolution will therefore be reduced during periods of regression and
increased during transgression.
Greater insight into which interpretation of calcium carbonate highs might best fit
the upper portion of the Massignano section can be found by comparing the calcium
carbonate content with the stable isotope data. At Massignano, there is a generally
persistent covariance in the CaCO3, δ13C and δ18O records, which implies that the
fluctuation in these parameters might be linked to a common paleoenvironmental cause
(Fig. 11). High carbonate accumulation corresponds with high planktonic productivity,
evidenced by heightened δ13C values resulting from the preferential fractionation of
oceanic 12C by marine photosynthesizers (Bickert, 2000). High carbonate accumulation is
0234567 18101112131415 916181920212223 17
EOCENEOLIGOCENE(1
)
5060
7080
903
57
9M
agne
tic S
usce
ptib
ility
(SI
)%
Cal
cium
Car
bona
te-1
.4-1
.0-0
.60.
91.
31.
72.
1δ18
O [
‰PD
B]
δ13C
[‰
PDB
]-0
.21
Figu
re 1
1. L
ithos
trat
igra
phy,
mag
netic
sus
cept
ibili
ty, c
arbo
nate
, and
δ18
O a
nd δ
13C
rec
ords
of
the
Mas
sign
ano
sect
ion.
The
lege
nd f
rom
Fi
gure
3 s
till a
pplie
s. T
he b
lack
das
hed
lines
hig
hlig
ht th
e ge
nera
lly c
onsi
sten
t pos
itive
rel
atio
nshi
p be
twee
n C
aCO
3,δ
13C
andδ18
O.
25
26
simultaneously matched with increased δ18O values, implying high salinity conditions or
cold water temperatures at the time of limestone deposition. Salinity conditions are
elevated when the rate of sea water evaporation exceeds that of precipitation, and their
correspondence with highs in δ18O results from the preferential transfer of lighter 16O to
the atmosphere during evaporation (Faure, 1977). Similarly, ocean waters are enriched in
18O during cool, glacial periods, as lighter 16O is sequestered in developing ice sheets
(Ruddiman, 2000). Following Mader et al. (2004), I interpret the correspondence of
stable isotope highs with calcium carbonate highs as an indication that Eocene-Oligocene
Mediterranean limestone formation occurred during dry, cold periods marked by higher
productivity. Increased ice volume with the appearance of small ephemeral ice sheets in
the late Eocene caused a sea level drop and a corresponding slight increase in continental
erosion, providing the nutrients necessary for high planktonic productivity. Also, an
increase in deep water formation tied to ice sheet expansion is balanced by increased
upwelling in other parts of the oceans. These upwelling waters are similarly nutrient-rich,
thus leading to high productivity. In light of the inverse relationship between CaCO3 and
magnetic susceptibility, it is reasonable to imagine that marly layers were deposited
during relatively wet (and possibly warm) periods with a greater fluvial influx of detrital
matter. It is important to note however, that while ice sheet development is a global
phenomenon, productivity changes in a site like the Mediterranean probably occurred on
a more local scale. Cold periods, therefore, may not be equated with high productivity at
other latitudes.
27
Stable Isotopes and Orbital Cycle Strength
The spectral power of the orbital cycles of eccentricity, obliquity, and precession
varies significantly from proxy to proxy. Most notably, the δ18O spectral plot for meter
levels 15-20 exhibits pronounced high-frequency precessional peaks, which dwarf the
other possible orbital signals and are the only peaks that rise above the 95% confidence
interval. This is in stark contrast with the δ13C spectral plot for the same interval, in
which the low-frequency eccentricity cycle greatly exceeds the 95% confidence level
(Fig. 7). One possible explanation for this phenomenon lies in the response times of the
environmental cycles to which the proxies are tied. δ13C is linked to the global carbon
cycle, which, with many reservoirs, including sediments and rocks as well as the
atmosphere, ocean and vegetation, has a slow response time (relative to the hydrologic
cycle). The long-period eccentricity cycle, then, may be the only orbital cycle long
enough to overcome this dampening to significantly impact global carbon cycling. In
contrast, the hydrologic cycle, tied to δ18O, is characterized by much faster response
times, partly because of the large (relative to carbon) fluxes of water through the different
parts of the system. The shorter, precessional cycles are perhaps amplified by the
hydrologic cycle’s rapid response time. For instance, it is believed that the African
monsoon undergoes large changes in tune with the precessional cycle; a shift in the locus
of precipitations and evaporations associated with the monsoon could lead to significant
salinity changes in the proto-Mediterranean.
Correlation with the Astronomical Time Scale
The spectral analysis results from the upper portion of the Massignano section
indicate that the sequence’s rhythmic bedding reflects orbitally paced climate variations.
28
Even though eccentricity weakly affects insolation, the prominent ~95 ky peak common
to all four proxies implies that the late Eocene and early Oligocene climate experienced
eccentricity forcing. Others have similarly found the eccentricity signal to be
disproportionately significant as far back as the Miocene, with strength far greater than its
theoretical contribution to insolation would suggest (e.g. Clemens and Tiedmann, 1997;
van Vugt et al., 2001; Cleaveland et al., 2002). This disproportional relationship of
eccentricity to climate could perhaps be explained by an amplifying mechanism such as
the ice-albedo feedback (Cleaveland et al., 2002). With ice sheets emerging in the
Eocene, it is conceivable that this feedback mechanism would come into play during the
deposition of the Massignano section.
An astronomical correlation between Laskar’s eccentricity curve and
Massignano’s smoothed magnetic susceptibility and calcium carbonate data is achieved
through pattern matching constrained by the dated volcanic ashes at meter levels 7.2, 12.7
and 14.7. Following Cleaveland et al. (2002) eccentricity highs are matched with
magnetic susceptibility highs and calcium carbonate lows. In order to lengthen the span
of time available for pattern matching, I used the smoothed magnetic susceptibility data
from the entire Massignano section (meters 0.5-23), rather than from just the upper eight
meters (meters 15-23) (Fig. 12). Of all four proxies, the magnetic susceptibility data
exhibits the least amount of noise and Milankovitch peaks rise above the 95% confidence
interval in both the whole section and lower section spectral plots (Figs. 6 and 8). In order
to confirm the validity of the match, I similarly matched the smoothed CaCO3 data from
the upper portion of the sequence to Laskar eccentricity and found the two correlations to
be in agreement (Fig. 13). The correlation yields a refined date for the Eocene-Oligocene
33
33.5
34
34.5
35
35.5
36
20
12
10
4
2
6
8
14
16
18
22
meterlevel
Eocene
Oligocene
EccentricityAge (Ma)
85-140 kyrbandpass
filter
SmoothedMagnetic
Susceptibility
Eocene
Oligocene
34.4 ± 0.4
34.6 ± 0.4
35.4 ± 0.4
Figure 12. Correlation between Massignano magnetic susceptibility and Laskar eccen-tricity. The magnetic susceptibility data has been smoothed by a 85-140 ky bandpass filter so as to bring out variability in the data. Pattern matching constrained by the three volcanic ashes yields a date for the Eocene-Oligocene boundary of 33.9 ± 0.1 Ma, somewhat older than the previously determined date of 33.7 ± 0.4 (Montanari et al., 1988).
29
33
33.5
34
34.5
35
35.5
36
20
12
10
4
2
6
8
14
16
18
22
meter level
Eocene
Oligocene
EccentricityAge (Ma)
85-140 kyrbandpass
filter
SmoothedMagnetic
Susceptibility
Eocene
Oligocene
34.4 ± 0.4
34.6 ± 0.4
35.4 ± 0.4
Figure 13. Correlation between Massignano magnetic susceptibility, Massignano calcium carbonate and Laskar eccentricity. Both the magnetic susceptibility data and the CaCO
3 data have been smoothed by a 85-140 ky bandpass filter so as to bring out
variability in the data. The smoothed CaCO3 data confirms the pattern match made with
the smoothed magnetic susceptibility curve.
SmoothedCaCO
3
85-140 kyrbandpass
filter
30
31
boundary of 33.9 ± 0.01 Ma, which is just 0.2 m.y. older than the previously proposed
date of 33.7 ± 0.5 Ma (Montanari et al., 1988). Precise ages of 35.13 ± 0.01 Ma, 34.55 ±
0.01 Ma, and 34.32 ± 0.01 Ma are also obtained for the three radiometrically dated
volcanic ashes at meter levels 7.2, 12.7 and 14.7 respectively. All three precise ages fall
within the error bars of the previous radiometric dates.
Impacts, Comet Showers and Climate Cycles
Spectral analysis results from the lower portion of the Massignano section do not
conclusively reveal orbital forcing as the mechanism for rhythmic deposition. Because
orbital forcing is so clearly prevalent in the upper eight meters of the outcrop, it is
difficult to imagine that orbital pacing had no role in the deposition of the lower portion.
The lower section, however, is unique in that it contains evidence of at least two, possibly
three, extra-terrestrial impacts, including the Popigai and Chesapeake Bay impact events
(Bodiselitsch et al., 2004). Evidence of these events has been reported in numerous other
early late Eocene sedimentary records (e.g. Kaye et al., 1961; Glass et al., 1985; Koerbel
and Glass, 1988). At Massignano, an impactoclastic layer at ~5.6 m is marked by an
iridium anomaly (Montanari et al., 1993), shocked quartz (Clymer et al., 1996;
Langenhorst, 1996), extraterrestrial Ni-rich spinel and altered microkrystites (Pierrard et
al., 1998), and finally a 3He anomaly (Farley et al., 1998). 3He serves as a tracer of fine-
grained interplanetary dust, as extraterrestrial matter is comparatively enriched in the rare
helium isotope (Farley et al., 1998). Impactoclastic layers at meter levels 6.19 and 10.25
are similarly distinguished by 3He anomalies as well as increased iridium (Bodiselitsch et
al., 2004). The 3He anomaly at Massignano is in fact quite broad, spanning from about
meter level 2 to 15, with its maximum value coincident with the Ir anomaly at 5.6m
32
(Farley et al., 1998). Farley et al. (1998) argue that this 3He enhancement is attributable
to an early late Eocene comet shower lasting 2.2 My.
Both individual impact events and comet showers have the potential to affect
global climate. An impact occurring on a continental shelf, such as the one at Chesapeake
Bay, is coupled with the release of methane hydrates, which contribute to the greenhouse
effect and induce global warming. A terrestrial impact, such as the Popigai, on the other
hand, is often linked to global cooling with a corresponding decrease in bio-productivity.
Global cooling could also be attributed to the dust particle loading of the atmosphere
associated with the increased levels of planetary dust inherent to a comet shower.
Evidenced by stable isotope variations, Bodiselitsch et al. (2004) propose that the impact
events observed at Massignano were responsible for cooling and warming trends in the
Eocene-Oligocene climate. It is possible, then, that the climate alterations caused by these
impact events served to obscure the longer-term climate cycling events caused by
Milankovitch cycles.
This finding is surprising because impacts are known to affect the climate on
relatively short timescales (Toon et al., 1997). In order for events such as impacts and
comet showers to disrupt the much longer-term Milankovitch cycles, their climatic
effects must somehow be exaggerated. Indeed, evidence of an exaggerated climatic
disruption is visible in the CaCO3 and MS sliding window plots of the lower Massignano
section (Fig. 14). Beginning at a window midpoint of ~4 m and extending to ~7 m, the
CaCO3 sliding window plot exhibits a curious undulating pattern that can perhaps be tied
to the impact events at meter levels 5.6 and 6.19. This same undulating pattern re-
emerges at window midpoints of ~9 to ~11 m, also possibly tied to the impact event at
met
er le
vel
10
8
6
4
2
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/ky)
Spec
tral
pow
er
0
CaCO3 for meters 0.5-15
477 kyr window
6
5
4
12
14
16
9
8
7
12
11
10
met
er le
vel 25
20
15
10
5
0.01 0.02 0.03 0.04 0.05 0.06Frequency (cycles/ky)
Spec
tral
pow
er
0
MS for meters 0.5-15477 kyr window
30
35
40
6
5
4
9
8
7
12
11
10
3
Figure 14. Results from the sliding window spectral analyses of the lower section. Begin-ning at a window midpoint of ~4 m and extending to ~7 m, the CaCO
3 sliding window
plot exhibits a curious undulating pattern. This same undulating pattern re-emerges at window midpoints of ~9 to ~11 m. The MS sliding window plot also shows undulations, however not in the same distinct bands as are seen in the CaCO
3 plot. Spectral power
scales are displayed to the right of each graph and the y-axis represents meter levels of the sliding window midpoints.
33
34
meter level 10.25. The fact that these disruptions are visible in the plots before the actual
occurrence of the impact events is not necessarily problematic, as the sliding window
plots have somewhat of a smearing effect. Furthermore, the disruption is also probably at
least partially coupled to the ongoing comet shower, evidence for which lies in the 3He
anomaly extending from about meter level 2 to 15. Possible mechanisms for the
exaggeration of the impact related climatic changes include the ice-albedo feedback or
the combined effect of impact related atmospheric alterations with the ongoing dust
particle loading associated with the comet shower. Because the increased atmospheric
dust loading related to the comet shower will alter according to the flux of comets in our
part of the solar system, we might expect a more random variation in dust during the
comet shower.
Still, while it is exciting to imagine that impacts and comet showers could be
affecting global climate on such a long time scale, questions remain. Milankovitch
forcing is certainly obscured in the CaCO3, δ18O, and δ13C proxy records of the lower
Massignano section, but the magnetic susceptibility record emerges largely unscathed. It
is curious that this particular proxy would be less susceptible to impact-related climatic
overprinting than the other proxies. Perhaps its perseverance can be attributed to the fact
that even during a comet shower sediment influx continues, with planetary dust replacing
the usual fluvial or wind deposited detrital input. Despite lingering questions, it is
reasonable to assert that impact related climatic changes interacted with the continuous
record of longer term Milankovitch cylces in such a way that they were disrupted or
obscured during the deposition of Eocene sediments at Massignano.
35
Conclusions
Spectral analyses of four high-resolution climate proxies indicate that the
deposition of the upper portion (meters 15-23) of the Massignano section was orbitally
controlled. The relationship between these proxies, with stable isotope highs
corresponding to calcium carbonate highs and magnetic susceptibility lows, help to reveal
the paleoclimatic conditions imposed by orbital forcing. Marly limestones are inferred to
represent wet/warm periods while limestones represent dry/cold periods characterized by
enhanced productivity. By means of pattern matching, the presumed eccentricity signal in
the Massignano magnetic susceptibility and calcium carbonate data is correlated to
Laskar’s theoretical eccentricity curve to provide astronomical ages for the entire section.
This correlation yields a refined date for the Eocene-Oligocene boundary of 33.9 ± 0.01
Ma.
Unlike the upper portion of the Massignano section, the rhythmic alterations in
the lower portion (meters 0-15) cannot conclusively be attributed to orbital forcing. This
portion of the outcrop, however, contains three possible impact events and a 3He
anomaly indicative of a comet shower 2.2 My in duration. Climate alterations caused by
these extraterrestrial events were most likely exaggerated such that Milankovitch forcing
was overprinted and obscured.
Acknowledgements
I am first and foremost thankful to my three advisors and would like to thank
Mary Savina (Carleton College) for her constant support, her wise advising, and for her
helpful comments on this paper; Sandro Montanari (Osservatorio Geologico do
36
Coldigioco) for introducing me to this project, allowing me to stay on in Coldigioco for a
few extra days, and guiding my field work; and thirdly, Dave Bice (Penn State) for
patiently advising me throughout this project, fixing problematic Matlab files, answering
many questions, commenting on drafts, and also for igniting my enthusiasm for geology.
I can honestly say I wouldn’t be a Geology major if it weren’t for Dave. I am also
thankful to a number of others, including: Laura Cleaveland (Brown) for answering many
questions about Milankovitch cycles and being a fantastic role model; Nick Swanson-
Hysell for help with completing magnetic susceptibility measurements; Kelsey Dyck,
Maggie Doheny-Skubic, Lee Finley-Blasi, Jenny Heathcote and Kendra Murray for their
help with both field and lab work, and for fun and crazy times in Italy; Michael Arthur
(Penn State) for allowing me to use his mass spec; Denny Walizer (Penn State) for being
a mass spec wizard; Katja Meyer (Penn State) and Burt Thomas (Penn State) for sharing
their home with me and showing me the ropes at Penn State; Cam Davidson (Carleton
College) for help with figures and formatting; Bereket Haileab (Carleton College) for
keeping me on my toes; my fellow geology majors for late night music and Tavern
breakfasts; my parents for love, support, encouragement and a Carleton education; and
finally the Carleton College Duncan Stewart Fellowship for funding this research.
37
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Appendix 2
Following are the Matlab 5.2 programs used for spectral analysis of the four climate proxies. Algorithms are modified from Muller and MacDonald (2000). Spectral plots in terms of meter
% This analyzes the data from MAS and shows cycles in terms of meter level clear; load lowCO.dat; % input data file h=lowCO(:,3); % name the data vector h m=lowCO(:,2); % name the meter vector m % subtract the mean then plot h=h-mean(h); figure (1); plot(m,h); title ('Carbon'); zoom on; % calculate FFT and Power after padding npt=2^14; H=fft(h,npt); P=H.*conj(H); % calculate frequency array Nyquist=0.5/(m(2)-m(1)); f=linspace(0,Nyquist,npt/2); % normalize to unit mean power P=P/mean(P(1:npt/2)); % plot fmax=.05; num=round(npt/2*fmax/Nyquist); figure (2); plot(f(1:num),P(1:num)); axis([0 0.05 0 20]); XLABEL('frequency') YLABEL('spectral power (cycles/cm)') title ('Carbon'); mark1x
Spectral plots in terms of time
% This analyzes the data from MAS, and shows cycles in terms of time clear; load MAS2.dat; %input data file h=MAS2(:,3); % name the data vector h m=MAS2(:,2); % name the meter vector m %subtract the mean then plot h=h-mean(h);
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figure (1); plot(m,h); zoom on; %interpolation to evenly spaced meter levels a=linspace(min(m),max(m),2*length(m)); h=interp1(m,h,a); t=35810-(a*95/101); % conversion to time in kyr assuming that meter level 0 is % 35810 kyr and using an inverse sed rate of 41kyr/46cm % bandpass filter to remove noise
% first define the range of frequencies to keep, between f1 and f2 f1=1/1000; % denominator is the period f2=1/10; % denominator is the period n=length(t); ft=fft(h); Nyquist=abs(0.5/(t(1)-t(2))); fre=linspace(0,2*Nyquist,n)'; [m,k1]=min(abs(fre-f1)); [m,k2]=min(abs(fre-f2)); k3=n-k2+2; k4=n-k1+2; % zero all but the desired band ft(1:k1)=zeros(k1,1); ft(k2:k3)=zeros(k3-k2+1,1); ft(k4:n)=zeros(k1-1,1); % take inverse FFT; remove the imaginary part hnew=real(ifft(ft)); figure (2); plot(a,hnew); zoom on;
% calculate FFT and Power after padding npt=2^14; H=fft(hnew,npt); P=H.*conj(H); % calculate frequency array % Nyquist=0.5/(m(2)-m(1)); f=linspace(0,Nyquist,npt/2); % normalize to unit mean power P=P/mean(P(1:npt/2)); % plot fmax=.06; num=round(npt/2*fmax/Nyquist); figure (3); plot(f(1:num),P(1:num)); XLABEL('frequency') YLABEL('spectral power (cycles/kyr)') title ('MS whole section'); mark1x
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Sliding window without bandpass % this routine loads the data, and then performs a fft with a sliding window clear; load upCO.dat; t=upCO(:,2); h=upCO(:,3); figure(1) plot(t,h); % interpolation to evenly spaced ages a=t; h_interp=h;
t=35810-(a*95/101); % conversion to time in kyr assuming that meter level 0 is % 35810 kyr and using an inverse sed rate of 41kyr/46cm % define size of sliding window and the offset fract=.5; %window as a fraction of the whole dataset wdw=floor(length(a)*fract); % size of window shft=15; % fraction of window length by which it is shifted shift=floor(wdw/shft); % amt by which window is shifted last=length(a)-wdw; % position where windowing ends % calculate frequency array Nyquist=abs(0.5/(t(2)-t(1))); npt=2^14; f=linspace(0,Nyquist,npt/2); fmax=.07; num=round(npt/2*fmax/Nyquist); % misc steps before iteration steps=1+floor(last/shift); Power=zeros(num,steps); h_sub=zeros(wdw+1,1); w=0; for i=1:shift:last w=w+1; h_sub=h_interp(i:(i+wdw)); h_sub=h_sub-mean(h_sub); % calculate FFT and Power after padding H=fft(h_sub,npt); P=H.*conj(H); % normalize to unit mean power P=P/mean(P(1:npt/2)); Power(:,w)=P(1:num); freq=f(1:num); age(w)=a(i+round(wdw/2)); end wndow=round((max(t)-min(t))*fract); % size of window in kyr Power=Power'; figure(2) pcolor(freq,age,Power) colorbar shading interp title(['CaCO3 with Sliding Window of ',num2str(wndow),' Kyr'],'FontSize',14) XLABEL('Frequency (cycles/k.y.)','FontSize',14)
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YLABEL('Age in Kyr of Window Midpoint','FontSize',14) mark1x
Sliding window with bandpass
% this routine loads the data, and then performs a fft with a sliding time window clear; load MAS1.dat; m=MAS1(:,2); w=MAS1(:,3); figure(1); plot(m,w); t=35810-(m*95/101); % conversion to time in kyr assuming that meter level 0 is % 35810 kyr and using an inverse sed rate of 41kyr/46cm % interpolation to evenly spaced ages a=linspace(min(t),max(t),2*length(t)); h=interp1(t,w,a); % bandpass filter to remove noise % first define the range of frequencies to keep, between f1 and f2 f1=1/1000; % denominator is the period f2=1/10; % denominator is the period n=length(a); ft=fft(h); Nyquist=abs(0.5/(a(1)-a(2))); fre=linspace(0,2*Nyquist,n)'; [m,k1]=min(abs(fre-f1)); [m,k2]=min(abs(fre-f2)); k3=n-k2+2; k4=n-k1+2; % zero all but the desired band ft(1:k1)=zeros(k1,1); ft(k2:k3)=zeros(k3-k2+1,1); ft(k4:n)=zeros(k1-1,1); % take inverse FFT; remove the imaginary part hnew=real(ifft(ft)); figure (2); plot(a,hnew); zoom on; % define size of sliding window and the offset size=100; % window size in kyr wdw=floor(size*length(a)/(max(a)-min(a))); % size of window shft=25; % fraction of window length by which it is shifted shift=floor(wdw/shft); % amt by which window is shifted last=length(a)-wdw; % position where windowing ends % calculate frequency array Nyquist=0.5/abs(a(2)-a(1)); npt=2^14; f=linspace(0,Nyquist,npt/2); fmax=.07;
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num=round(npt/2*fmax/Nyquist); % misc steps before iteration steps=floor(last/shift); Power=zeros(num,steps); h_sub=zeros(wdw+1); w=0; for i=1:shift:last w=w+1; h_sub=hnew(i:(i+wdw)); h_sub=h_sub-mean(h_sub); % calculate FFT and Power after padding H=fft(h_sub,npt)'; P=H.*conj(H); % normalize to unit mean power P=P/mean(P(1:npt/2)); Power(:,w)=P(1:num); freq=f(1:num); age(w)=a(i+round(wdw/2)); end Power=Power'; figure; pcolor(freq,age,Power) colorbar shading interp title([' Window = ',num2str(size),'Kyr'],'FontSize',12) xlabel('Frequency','FontSize',12) ylabel('Age in Kyr of Window Midpoint','FontSize',12) mark1x
95% Confidence Interval
% basic FFT of MAS data % calculates noise too with a Monte Carlo approach clear; load COlow.dat; % the whole data set m=COlow(:,1); % meters c=COlow(:,4); % 18O % interpolation to evenly spaced meters a=linspace(min(m),max(m),2*length(m)); c=interp1(m,c,a); % subtract mean c=c-mean(c); % convert meters to age in kyr t=35810-((1/.0106)*a); % from 10.6m/Myr sed rate % calculate the noise t0=35810-((1/.0106)*m); % from 10.6m/Myr sed rate t2=linspace(min(t0),max(t0),2*length(t0))'; % calculate frequency array Nyquist=0.5/abs(t0(2)-t0(1)); npt=2^12; f=linspace(0,Nyquist,npt/2); fmax=.06;
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num=round(npt/2*fmax/Nyquist); freq=f(1:num); % misc steps before iteration steps=1000; % number of iteration steps Power=zeros(num,steps); % creates an empty array for the spectral power w=0; % a counter for i=1:steps r=rand([(length(t0)) 1]); % generates a string of random numbers with a certain spacing hh=interp1(t0,r,t2); % interpolates between random numbers hh=hh-mean(hh); % subtracts the mean w=w+1; % advances the counter % calculate FFT and Power after padding H=fft(hh,npt)'; % puts the result into a column vector P=H.*conj(H); % gets rid of the imaginary part % normalize to unit mean power P=P/mean(P(1:npt/2)); Power(:,w)=P(1:num)'; % loads the Power column into the larger array end PQ=mean(Power'); % calculates the mean of each column of the transpose of Power PR=std(Power'); % calculates the standard deviation of each column of the transpose of Power PS=PQ+PR; % adds 1 std dev to mean P2S=PQ+PR+PR; % adds 2 standard deviations to the mean % now the data % calculate FFT and Power after padding npt=2^16; H=fft(c,npt); P=H.*conj(H); % calculate frequency array Nyquist=0.5/abs(t(1)-t(2)); f=linspace(0,Nyquist,npt/2); % normalize to unit mean power P=P/mean(P(1:npt/2)); % plot fmax=.06; num=round(npt/2*fmax/Nyquist); figure (1); plot(f(1:num),P(1:num),freq,P2S) title(['18O'],'FontSize',14) XLABEL('frequency') YLABEL('spectral power') mark1x
95% Confidence interval with bandpass
% basic FFT of MAS data % calculates noise too with a Monte Carlo approach clear; load COlow2.dat; % the whole data set m=COlow2(:,1); % meters c=COlow2(:,3); % 13C
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mm=m; % interpolation to evenly spaced meters a=linspace(min(m),max(m),2*length(m)); c=interp1(m,c,a); % subtract mean c=c-mean(c); % convert meters to age in kyr t=35810-((1/.0106)*a); % from 10.6m/Myr sed rate % calculate the noise t0=35810-((1/.0106)*m); % from 10.6m/Myr sed rate t2=linspace(min(t0),max(t0),2*length(t0))'; % calculate frequency array Nyquist=0.5/abs(t2(2)-t2(1)) npt=2^12; f=linspace(0,Nyquist,npt/2); fmax=.06; num=round(npt/2*fmax/Nyquist); freq=f(1:num); % misc steps before iteration steps=1000; %number of iteration steps Power=zeros(num,steps); % creates an empty array for the spectral power w=0; % a counter for i=1:steps r=rand([(length(t0)) 1]); % generates a string of random numbers with a certain spacing hh=interp1(t0,r,t2); % interpolates between random numbers hh=hh-mean(hh); % subtracts the mean w=w+1; % advances the counter % calculate FFT and Power after padding H=fft(hh,npt)'; % puts the result into a column vector P=H.*conj(H); % gets rid of the imaginary part % normalize to unit mean power P=P/mean(P(1:npt/2)); Power(:,w)=P(1:num)'; % loads the Power column into the larger array end PQ=mean(Power'); % calculates the mean of each column of the transpose of Power PR=std(Power'); % calculates the standard deviation of each column of the transpose of Power PS=PQ+PR; % adds 1 std dev to mean P2S=PQ+PR+PR; % adds 2 standard deviations to the mean % now the data % bandpass filter to remove noise because there is a long-period trend to the data % first define the range of frequencies to keep, between f1 and f2 f1=1/500; % 1/longer period f2=1/10; % 1/shorter period n=length(t); fc=fft(c); fre=linspace(0,2*Nyquist,n)'; [m,k1]=min(abs(fre-f1)); [m,k2]=min(abs(fre-f2));
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k3=n-k2+2; k4=n-k1+2; % zero all but the desired band fc(1:k1)=zeros(k1,1); fc(k2:k3)=zeros(k3-k2+1,1); fc(k4:n)=zeros(k1-1,1); % take inverse FFT; remove the imaginary part newc=real(ifft(fc)); % calculate FFT and Power after padding npt=2^16; H=fft(newc,npt); P=H.*conj(H); % calculate frequency array Nyquist=0.5/abs(t(1)-t(2)) f=linspace(0,Nyquist,npt/2); % normalize to unit mean power P=P/mean(P(1:npt/2)); % plot fmax=.06; num=round(npt/2*fmax/Nyquist); figure; plot(f(1:num),P(1:num),freq,P2S) title(['13C'],'FontSize',14) XLABEL('frequency') YLABEL('spectral power') mark1x
