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UBRARY
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Universit

 

 

This is to certify that the
thesis entitled

A NUMERICAL MODEL OF DIFFUSION LIMITED
DISSOLUTION FROM DEEP ATLANTIC CARBONATE
SEDIMENT

presented by

KIRSTEN V. WRIGHT

has been accepted towards fulfillment
of the requirements for the

Master of Science degree in Geological Sciences

 

 

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MSUlsmAflhmActiaVEquaIOpponuMymm

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c:/ClRC/DateDue.p65-p.15

 

A NUMERICAL MODEL OF DIFFUSION LIMITED
DISSOLUTION FROM DEEP ATLANTIC CARBONATE SEDIMENT

By
Kirsten V Wright

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
For the degree of

MASTER OF SCIENCE
Geological Sciences

2003

ABSTRACT

A NUMERICAL MODEL OF DIFFUSION LIMITED
DISSOLUTION FROM DEEP ATLANTIC CARBONATE SEDIMENT

By
Kirsten V Wright

Though hiatuses occur across the Atlantic throughout its history,
mechanisms explaining time periods of missing sediment record are not clear.
Atlantic seafloor below the GOD is overlain by water undersaturated with respect
to CaCOa, and dissolution of carbonate from the sediment would be limited by
diffusion of ions toward the sediment water interface. The flux of Ca2+ depends
on the concentration gradient and diffusion coefficient. The concentration
gradient can be estimated from DSDP measurements, but the diffusion
coefficient is approximated by an empirical relationship, which depends on
porosity. Porosity data allow fitting of a function dependent on depth. Based on
these relationships, a one dimensional finite difference model was developed. It
seems robust with respect to nearly all of the parameters, but appears to be most
sensitive to porosity. Investigation of reaction limited dissolution at the sediment
water interface was also performed. The removal of carbonate from the
sediment column was minimal. For the 10,000year time step, the reduction in
thickness was on the order of microns, and was around 1% for the entire IOOMa.

This is not enough to create a noticeable hiatus.

TABLE OF CONTENTS

THE MODEL RELATIONSHIPS
THE NUMERICAL MODEL
PARAMETER ESTIMATION
Diffusion Coefficrent
Porosnty
Pelagic Clay
SEDIMENT-WATER INTERFACE MODEL

14

.20

26
3O

.41
.41
.43

47

.48

50

56

.58

72

LIST OF TABLES

TABLE 4.1.. .....22
Sample caIcuIation of effect of advection due to reduction in porosity.
TABLE6...1 ..........30

Hypothetical sediment columns developed for modeI Simulations
TABLE 6. 2. .34
Calculated depths of bounding surfaces for 50 layers initially 10m thick.
TABLE 6.3... ..35

Calculated change in thickness for 50 layers initially mm thick. Values
are m for a 10,000 yr time step. Total reduction in thickness over 100Ma
is given in the rightmost column in mm.

TABLE 6.4.... ...36
Calculated depths of bounding surfaces for 50 layers initially 1m thick.
TABLE 6.5... ..37

Calculated change In thickness for. 50 Iayers initially 1m thick. Values are
m for a 10,000 yr time step. Total reduction In thickness over 100Ma is
given in the rightmost column in mm.

TABLE 6.6... ..38
Calculated depths of bounding surfaces for 50 layers initially 0. mm thick.
TABLE 6.7... ..39

Calculated change in thickness for 50 layers initially 0.01m thick. VaIues
are nm for a 10,000 yr time step. Total reduction in thickness over 100Ma
is given in the rightmost column in mm.

TABLE 7.1.... .....42
Statistics for analysis of senSItIVIty of bounding surface depth to variation
in D...

TABLE 7.2... .....44

Depth of selected bounding. surfaces from models including activity
coefficient for shallow and for deep sediment, y for 36m In 10‘0579 and y for
1076m is 10""582

TABLE 7.3... .. ...47
Variation in model output from extreme values of porosity Values are for
a single cell initially bounded by 24m and 29m.

TABLE 9.1.... ..54
Dissolution from the top layer of the three simulated sediment columns.

TABLEi.1.. . 58
DSDP sites used for accumulation rates

TABLE ii. 1.. ..66
InterstitiaI pore water measurements from DSDP for site 603. Predicted
Ca2+ concentration from equation 4. 2 in which the constants were fitted
from minimizing the sum of the residual squared values.

TABLE Iii. 1.. 6..8-69
Porosity Measurements of Deep AtIantic Carbonate Sediment from D.SDP

LIST OF FIGURES

FIGURE 1.1.... ..1
Accumulation Rates for 35 DSDP site on Atlantic oceanic crust under at
least 4000m of water. Rates are calculated from SYNATLAN database
(Wolf-Welling et al 1997), which has depths for 0.5Ma increments.

FIGURE 1 ....2 .. .....2
Frequency of accumulatIon rates for 35 DSDP site in the Atlantic on

oceanic crust In under at least 4000m of water. Mode Is 0 m per 0. 5Ma
with 888 out of 3622 values.

FIGURE 1 ....3 ..3
Sediment accumulatIon for all SYNATLAN sites with dating between 18
and 20Ma. Thickness Is the total sediment between 18 and 20Ma.
Indicated hiatuses are locations with zero thickness for the entire period.

FIGURE 1 4. .. ...4
Sediment accumulatIon for site 513. Temporal resolution is 0. 5Il/Ia and
accumulation Is shown as meters per 0. 5Ma increment.

FIGURE 1 5. ..5
SYNATLAN sites selected as carbonate sediment on oceanic crust under
at least 4000m of water. Solid circles indicate that at least on hiatus was
found at the site, and open circles are locations where no hiatus was

measured.
FIGURE2...1 .. ...............8
Setup of one dImensIonal diffusion model. x= depth, q- flux.
Form of concentration with depth: C(x) = Cm - (Cmg, -e"‘"‘)
Form of concentration gradient with depth: %= k “we "
FIGURE2.4... . ..11
Form of the diffusion coefficIent In sediment pore water with
deptth,= D

1--1n(pz)

vi

-X

Form of porosity with depth: p(x) = pmin + pmge oek'

FIGURE3.1.. .. 14

The setup of matrix final
The MATLAB code
The model variables

FIGURE3....4 .. 17
Location of the bounding surfaces and cells In the model

FIGURE4...1 .. . ..20
Comparison of alkalinity to Ca2+ concentratIon a? pore water of carbonate
sediments from DSDP.

FIGURE 4.2... .. ..24
Measurements of salinity for DSDP sites In the deep Atlantic basin

FIGURE5.1.. .. ..26

Measurements of pore water Ca2+ concentrations in mmol/l. for site 603.
The solid line rerresents the fitted function:
2

Ca 2* (x) = 24.2 - 2.42 . film")

FIGURE 5.2.. ..28
Measurements of porosity for DSDP sites in the deep Atlantic basin. The

solid line represents the fitted function: p(x) = 58.5 + 16.5 - e367"

FIGURE 6.1 ...................................................................................................... 31
Depth of bounding surfaces for layers initially 10 m thick to 500m depth
through 100 million years.

FIGURE 6. 2. .31
Change' In thickness of layers initially 10 In thick to 500m depth through
100 million years. Each calculated value Is the change In thickness In
microns for a 100,000 year period.

FIGURE 6.3... ....32
Depth of bounding surfaces for layers initially 1m thick to 50m depth
through 100 million years.

vii

FIGURE 6.4... ..32
Change' in thickness of layers initially 1m thick to 50m depth through 100
million years. Each calculated value Is the change in thickness In microns
for a 100,000 year period.

FIGURE 6.5... ..33
Depth of bounding surfaces for layers initially 0. 01m thick to 0. 5m depth
through 100 million years.

FIGURE 6.6... .33
Change in thickness of layers initially 0. 01 in thick to 0. 5m depth through
100 million years. Each calculated value Is the change In thickness In

microns for a 100,000 year period.

FIGURE 7.1. . ........41
Example dIstnbutIon of D; introduced into the model for sensItIVIty
analysis.

FIGURE 7.2... .. ...42
Distribution of depth of bounding surface 3 resulting from variation in D; In
the model.

FIGURE 7.3... .. ....43

Standard deviation of depth of bounding surfaces for 500 realIzatIons
incorporating variation in 0..

FIGURE 7. 4. 45
Depth of bounding surfaces for layers initially 10. in thick to 500m depth
through 100 million years with activity coefficient from 36m.

FIGURE 7.5... ..45
Depth of bounding surfaces for layers initially 10 m thick to 500m depth
through 100 million years with activity coefficient from 1076m.

FIGURE 7.6... .46
Change In thickness of layers initially 10 in thick to 500m depth through
100 million years with activity coefficient from 38m. Each calculated
value is the change in thickness in microns for a 100,000 year period.

FIGURE 7.7... ..46
Change In thickness of layers initially .10 m thick to 500m depth through
100 million years with activity coefficient from 1076m. Each calculated
value is the change in thickness in microns for a 100,000 year period.

FIGURE 7. 8. .. . ..47
Distribution of measured porosity values used to estimate the constants In
the function of porosity with depth.

viii

FIGURE 7. 9... 4.9
Depth of bounding surfaces for layers initially 10 m thick to 500m depth
through 100 million years with pelagic clay accumulation rate of
0.03mml1000yr.

FIGURE 7.10... .4.9
Change In thickness of layers initially 10 m thick to 500m depth through
100 million years with pelagic clay accumulation rate of
0.03mml1000yr. Each calculated value is the change in thickness in
microns for a 100,000 year period.

FIGURE 8.1.... ..50
Modifications .to the model code for kinetic dIssqutIon from the sediment-
water interface. Additions are shown In bold.

FIGURE 8.2... ..52
Depth of bounding surfaces for layers initially 1m thick through 10Ma (note
the change In time scale) with reaction limited dissolution from the
sediment-water interface.

FIGURE 8.3... .52
Depth of bounding surfaces for layers initially 1m thick through 10Ma with
reaction limited dissolution from the sediment-water interface assuming
pure carbonate sediment.

FIGURE 8.4... ..53
Depth of bounding surfaces for layers initially 10m thick through 100Ma
with reaction limited dissolution from the sediment-water interface
assuming pure carbonate sediment.

FIGURE I.1.. 59
Map of Atlantic DSDP sites
FIGUREi....2 ..60-64

Depths assigned by SYNATLAN for age at 0. 5Ma increments iébiiéd) and
the corresponding accumulation rate (solid) calculated in m/0. 5Ma. Site
information given on previous page.

FIGURE Iii. 1.. . .......67
Frequency of porosity values for deep Atlantic carbonate sediment.

Introduction

Investigation of deposits under the deep Atlantic shows hiatuses, time
periods of missing sediment. Either erosion or lack of deposition must occur to
generate one of these gaps, but mechanisms that cause them are unclear.
Though erosion and nondeposition can rarely be differentiated in the stratigraphic
record, potential hiatus producing processes can be suggested. One such
mechanism for creating a hiatus is dissolution of calcium carbonate from beneath
the sediment water interface, which would be controlled by pore water diffusion.

Studies conducted for the Deep Sea Drilling Project (DSDP) allow high
resolution dating of sediment cores from many locations in the Atlantic. The
SYNATLAN database contains Atlantic sites that have been dated for 0.5Ma

intervals and was developed by Wolf-Welling et al (1997), appendix 1. Sites

 

chosen from ""8 database Accumulation Rates for Deep Atlantic Sediment

focus on deposits on oceanic

crust in water at least 4000m

.5
O
0

deep to ensure that they are

well below the CCD. Also, the

8

physiographic feature of each

 

Accumulation Rate— m per 0.5Ma

location was considered for

 

eliminating those not in the

 

 

pelagic basin. Age-depth

 

Figure 1.1. Accumulation Rates for 35 DSDP site on
Atlantic oceanic crust under at least 4000m of water.

. Rates are calculated fnom SYNATLAN database (Wolf-
selected sntes were used to Welling et al 1997), which has depths for 0.5Ma
increments.

relationships from the

 

 

 

1

 

Frequency of Accumulation Rates
for Deep Atlantic Sediment

3"- ‘ ' ' fi“
30

25

$20
15

u.

10

500
0

 

l

     
    

m _.__._..L___ ...1 ___L._ .__.__. .-_.L___L_._

 

so 160 1
Accumulation Rata- m per 0.5Ma

O

 

 

Figure 1.2. Frequency of accumulation rates
for 35 DSDP site in the Atlantic on oceanic
crustin underatleast4000mofwater. Mode
isOmper0.5Mawith8880utof3822
values.

 

 

 

calculate accumulation rates
(thickness per unit time) (figure 1.1).
Hiatuses are indicated by values of
zero. Figure 1.2 shows the frequency
of these rates; 888 of the 3622, nearly
1/4, of the values are zero. The

average accumulation rate is 4.5m,

and the mean without the hiatuses is
6.0m. Hiatus duration in the Atlantic

ranges from 0.5Ma to greater than

100Ma (Wolf-Welling 1999, Ehrmann and Thiede 1985).

Physical processes and conditions in the oceans indicate that sediment

should be continuously raining down to the sea floor (T hurrnann 1994).

Carbonate particles settle through the water to the carbonate compensation

depth, though they do not deposit on seafloor that is deeper than the CCD.

Windblown clay particles are laterally continuous across the oceans and typically

deposit at a rate of 1mml1000yr (T hurrnann 1994) to 3mml1000yr (Ehrmann and

Thiede 1985), though much smaller rates will also be evaluated. These rates

result in 1 to 3 meters per Ma producing recognizable thickness of sediment.

Despite theoretically continuous deposition, erosion mechanisms are

limited. A major change in ocean water composition to chemically erode

sediment should result in a hiatus that is spatially continuous. There is no time

period in the Atlantic record that shows basin-wide hiatus. The thickness of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hiatus
o 0
Thickness
o 0.4 - 15.4
o 15.4- 30.4
0 30.4. 45.5
C 45.5- 00.5
. 00.5. 75.5

 

 

 

Figure 1.3. Sediment accumulation for all SYNATLAN sites with dating between 18 and
20Ma. Thickness is the total sediment between 18 and 20Ma. Indicated hiatuses are

locationswithzerothiclumforttmentire period.

 

 

 

 

sediment for 18 to 20Ma is shown in figure 1.3, and the accumulation rates

compiled for all sites (figure 1.1) show no time period without accumulated

sediment. Also, each site shows variation in accumulation rate through time.

Sediment for site 513 is shown in figure 1.4. The resolution of dating is 0.5Ma,

so accumulation is meters per 0.5Ma
increment, which varies from zero to
greater than 35. This pattern is apparent
throughout the Atlantic (figure i.2,
appendix I), and the periods of hiatus
and sediment presence do not coincide
across the sites (figure 1.1).

Deep ocean currents could cause
mechanical erosion, but flow is slow with

regard to physically moving sediment

(Ehrmann and Thiede 1985). Also,
currents could not explain why hiatuses

happen throughout the Atlantic. Even

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.4. Sediment accumulation for site
513. Temporal resolution is 0.5Ma and
accumulation is shown as meters per
0.5Ma increment.

 

though flow patterns may vary, hiatuses from currents should be confined to

portions of the seafloor. The DSDP and SYNATLAN sites span the Atlantic

(figure i.1, appendix 1) and values of zero accumulation occur at nearly all of the

SYNATLAN sites (Wolf-Welling et al 1997). The selected deep ocean sites

which have at least one hiatus (figure 1.5) are spread throughout the Atlantic

(except for areas without data).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4000mofwater. Solidcirclesindicatematatleastonehiatusmsfomuatthesite,andopen

circlesarelocationswlnrenohiatuswasnnasured.

 

Figure1.5. SYNATLAN sitesselectedascerbonatesedimentonoceaniccrustunderatleast

 

 

 

The incompleteness of the sediment record has been studied by many
researchers. Garrels and Mackenzie (1971) looked at the mass-age distribution
of global sediment and attributed the decrease in sediment with age to higher
probability of erosion with increasing time. This is more appropriate for the
terrestrial sediment which dominated their study. Veizer and Jansen (1985)
studied oceanic sediment and attributed the reduction in sediment with age to
subduction of oceanic crust, but this does not explain lack of sediment on
existing ocean floor. Sadler and Strauss (1990) observe that accumulation rate
decreases with longer time period of measurement. They attribute this to
unsteady deposition, but do not address zero accumulation. Moore et al (1978)
investigated the frequency of hiatuses through time in the ocean basins, and
assert that variation is due to changes in boundary conditions of the basins.
Proposing that rate of supply relative to the rate of removal determines
accumulation, they refer to the ‘corrosiveness’ of the bottom water. This is the
potential of the water to chemically erode carbonate and depends on advection
and the chemical nature of the solution. They do acknowledge the presence of
clay residue, but assume active dissolution of the sediment takes place.

The potential mechanism of sediment removal by dissolution can be
evaluated by considering the system dynamics. Below the CCD. bottom water is
undersaturated with respect to calcium carbonate, but the sediment surface
should be covered by pelagic clay, preventing dissolution directly from the
sediment-water interface. Below this interface, ions from breakdown of CaCOa

have to travel through the pore water away from grain surfaces. Saturation

would be reached before significant removal of sediment, then further dissolution
would be limited by diffusion toward the undersaturated overlying water. To
explore this, a numerical model was created to calculate how much sediment

could be dissolved in a reasonable time scale.

The Model Relationships

To simulate dissolution from carbonate sediment of the deep Atlantic, a
one-dimensional model was developed. Conceptually, the carbonate particles at
depth should equilibrate with the pore water creating a saturated solution.

Because deep Atlantic bottom water is

 

AAAAAMAAAMAAMAA
AAAAAMAAAMAAMAA

W AAA/\AMA AAAAAMAA ‘ X1=o
sedinerl q1

cel1

undersaturated with respect to CaCOa, Ca2+
will diffuse from the sediment toward the
sediment-water interface. Shown later, the
.x; rate that carbonate could dissolve in open
water is much faster than Ca2+ can diffuse

out of the sediment, so diffusion should be

H

"3 the limiting mechanism. Though other

processes such as mineralization of organic
col 3

matter may influence this system, the simple

 

 

X4

 

 

 

 

_ _ diffusion of ions from CaCOa will be
Figure 2.1. Setup of one dimensional

diffusionmodel. x=depth,q=flux.

 

 

examined. Adding other features would

 

confuse the importance of this particular process.

One consequence of conceptual model is that dissolution is greatest near
the sediment-water interface. The result is that this mechanism could only create
a hiatus at the sediment surface. To generate a hiatus within the column,

deposition would have to resume and bury the eroded sediment.

Depth is represented as x, with zero as the sediment-water interface and
positive values below that. Each cell is delineated as the space between
arbitrarily defined depths (figure 2.1). Using Fick's first law

 

 

 

6C q =flux— mass/area‘time

2.1 (FD-5x- D=diffusion coefficient-arealtime

C =concentration- mass/volume

x =depth- length
the flux at each depth is calculated.

C trado

Then, the change in mass for each cell om" n
can be calculated according to mass (35 \ cg

 

balance: \

 

2.2 AmoIeS(ce”..) = 4...: - (1.. \

 

 

Depth
1:“,

Assuming that no other solid phase

 

contributes to the calculated flux, the

 

 

change in mass represents the change in

 

amount of calcium carbonate in the

 

 

 

 

 

sediment of that cell.

 

 

 

 

 

The concentration with depth is F59”? 22- Fm“ 0‘ cement“Won with
estimated using the form (Adler et al C(x) = Cm -(Cmnge '94“)
2000): C... =maximum concentration- masuvolume

Cm =minimum concentration- mass/volume
2.3 C(x) .__ Cm —(C ~e""'") Cum. =Cw-Cw. mass/volume

range kc
Using CM and Cm,n allows the calculated concentration to be constrained

-concentiation constant— 1Ilength

within a measured range (figure 2.2). Here, Cm,n represents the
concentration in the water at the sediment-water interface, and Cm represents

the steady state concentration approached at depth. The concentration constant,

9

kc, controls how quickly the concentration reaches Cm with increasing depth.

The derivative of this form of C(x) is :

 

 

 

 

 

24 % =' kc . Cmnge . e’kc-x
dc,“ and yields reasonable values. For instance,
/ as x -) oo, 73; -) zero, this Simulates diffusmn
/ reaching equilibrium at depth. Also, as x 9

 

6C
zero, Ex—does not go to 00, as some

 

Depth
“N

 

functions do.

 

The second term in Fick’s first law is

 

 

the diffusion coefficient. The diffusion

 

 

 

 

 

 

coefficients for particular ions in infinitely

Figure 2.3. Form of concentration
gradient with depth: dilute solutions, D°. have been well

6C — k C "v"
— - c' range '9 documented. Temperature has a significant

 

 

 

effect on diffusion because it determines how quickly ions move; colder

temperatures result in slower movement, reflected in a smaller coefficient

(BOUdreaU 1997): D°=infinite dilution diffusion coefficient
mass/time .
2.5 D" = (mo +ml -T)-10“"cm2 sec'l m°=linear regression W1

m1=linear regression constant 2
. . . _ T =temperature in °C
The diffus10n coefficient in sediment pore

water, D., needs to account for the volume of water and the tortuosity. Since the
ions travel within the solution and the volume is no longer 100% solution, porosity

can be used to adjust D°. Highly tortuous sediment leads to difficulty for ions to

10

diffuse due to the longer paths of travel; tortuosity being the actual length of the

sinuous diffusion path divided by the straight line distance between its ends. This

also reduces diffusion and the coefficient. A diffusion coefficient modified for

sediment is (Drever 1982):

2.6 D" -
D, = 2 p
T

 

The problem is that obtaining an independent
value for tortuosity is unfeasible. Measuring it
is impractical, and its expected variation is
large even at short distances. Fortunately,
Adler et al (2000) formulated an empirical
relationship for D. sediment as a function of

porosity in oceanic carbonate sediment:

2.7 D, =__D_0__2_
l-ln(p )

This makes porosity necessary to calculate the
sediment diffusion coefficient.

The form of the porosity function (Adler
et al 2001 ):

-X

2.8 ,
p(x)=pin'n +prange .ek

D.=diffusion coefficient in sediment
mass/time

‘r =tortuosity

p =porosity

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.4. Form of the diffusion
coefficient in sediment pore water

withdepth:
D

3

2L
1-In(p’)

 

 

=maximum porosity
=minimum porosity

prmrpnin
porosity constant- length

is similar to the concentration function, but is altered because porosity becomes

less with depth. Therefore, pm represents the porosity nearest the sediment-

water interface, and pm... represents the final porosity approached at depth.

11

Returning to Fick’s First Law, and applying it to sediment gives:

BC
2.9 q, = D, .6: q.=flux through solution in wdiment
mass/area‘time
Substituting equation 2.7 yields:

D" .6C(x)
1—1n(p(x)’) ax

 

2.10 q: (x) :-

Expanding the function using equations 2.4 and 2.8 provides:

q: (x) = D 2 . kc . Cmnge . e‘kc"

l-ln [plum +prange .ek’]

 

2.11

 

Using this equation, the flux from calcium

Porosity

/[ carbonate at each depth can be

/ gl determined allowing calculation of the
n.

 

 

Pnin

 

/ change in thickness of Sediment layers.

 

/ Bounding surfaces, arbitrary layer

 

 

g / boundaries, are set at the beginning of the
3 1 model. The top surface is initially zero,

 

 

I the sediment-water interface, but it

 

 

deepens due to pelagic clay deposition.

 

 

 

 

I For the layers, the flux through each

 

 

surface is used to find the change in

 

 

Figure 2.5- Form of porosity with depth: mass. The change in mass is translated

p(x) = pm + pm s"; into change in thickness and the new

 

 

 

12

depth of each surface is calculated. Since only the carbonate is dissolving, the
minimum thickness of each layer is controlled by the initial percent carbonate of
the sediment. The depth of the surfaces tracked through time shows the
reduction of the layers. These relationships and equations were then translated

into numerical code used in MATLAB.

13

The Numerical Model

The initial, time=0, depths of the bounding surfaces are defined in vector b
which is entered in line 3 of the model code. Line 4 defines this vector as
lastdep. At each time step, Iastdep is used as the depths of the bounding
surfaces from the previous time step. Lines 1 and 2, are comments that do not
affect the calculations; this is shown by the % which precedes the text. Line 5
initiates the calculation of the minimum thickness for each layer using an average
percent carbonate for the sediment column, see appendix N for details.

Before the flux can be found, several constants need to be defined. In line
7 the pm, pm and kp, are defined for the porosity function, equation 2.8; the
numerical values will be discussed later. The numbers for the concentration
gradient function, equation 2.4, are defined in line 11. 0" is set forth in line 15.

The model constructs a matrix called final, which records the depth of
every surface at all time steps (figure 3.1). Each column of the matrix represents
the depths of the bounding surfaces at a particular time step. From left to right
across the matrix, indexed by y, proceeds from time=0 to time=final. Each row of

Time — the matrix represents a single bounding

 

 

 

D .

e x0,t0 t1 t2 ty surface through time. Down the rows of the

r xl : ; ; matrix, indexed by n, moves down the

h x2 : : ‘L sediment column. For example, the location of
l x" ,, —-) x" , ty n=3 and y=8 represents the depth of the third

 

 

bounding surface from the sediment-water
Figure 3.1. The setup of matrix
final

 

 

interface after seven time steps. The first

 

14

 

1%00rehmb,avectoroforiginaldefihs
A %b isavectorofdepthsin ooeaniccarbonate sediment
' load coreiOcm
. lastdep=b;
‘ cpercent%this performs the minimum thickness calculation for b
:‘ %porosity parameters, p(x)=Pmin+(Pmax-Pmin)e"(-dlkp)
Pmax=0.750;Pmin=0.585;Prange=Pmax-Pmin;kp=36.4;
=' %units: none, none, none, m
1| %Concentration parameters, dCIdx=k"(Cmax—Cmin)e"(kd)
1 1 Cmax=24.2;Cmin=1.78;Crange=Cmax-Cmin;kc=2.75*10"-3;
1 A %units' mollm“3, mollm‘3, mollm‘3, 11m
1 .
1 . %Diffusion coefficient in dilute solution
1 Do=1.701*10"2;%units: m“2l10000yr
1 2
1 %finalwill beamatrixofdepthsofthelayers, eachcolumn representsatimestep
1:- final(:,1)=b;
1 = n=|ength (b);
2i

21 %iy counts time steps, each time step is 10000 yr

A for iy =1:10000

2 ' %initlal first depth, then add 3mml1000yr (0.0003ml100yr) for burial by clay
2 fina|(1.iy+1)=b(1)+0-03*(iv);

2 ‘ for is =1 :n
3' x=lastdep(ia);
2 %flux calculates the amount of flux upward as motlrnZ‘100yr

2 =- e"3|uX(iiJI)=(DO"|<<="Cm"98"exr>(-|<C"x))l(1-|09((F’min+F’fiinge‘WeXi>(-x/kp))"2));
I .
31 96the dissolution can then be calculated: flux out—flux in=dissolution
A %firsttenncalculatesthedissolutionforthatlayer
' %thesecondterm converts n10llrr12‘10"5yrto ml10"5yrwldensity, gfw&porosity

. for ib =1 :n-1
‘ P=Pmin+Prange*exp(—lastdep(ib+1)lkp);
'3‘ dissolve(ib)=(flwr(ib+1)-flux(ib))l((2.7'10‘4)*(1-P));
3 end
:- Wigeinfliicknesisshorterthandepthvector
' for ic =1 :n-1
' I newthick=lastdep(ic+1)—lastdep(ic)+dissolve(ic);
41 if newthick<minthick(ic)
4 A final(ic+1,iy+1)=final(ic,iy+1)+minthick(ic);
. ' else
- - final(ic+1,iy+1)=final(ic,iy+1)+newthick;
4 ‘ end
. 3‘ a“
4 lastdep=final(:,iy+1);
. ;. er“

 

 

 

Figure 3.2. The MATLAB code

 

15

 

 

b = vector of initial depths of bounding surfaces
defined by modeler

lastdep = vector of depths of bounding surfaces from the previous time step
reset with each time step

final = yxn matrix of depths of bounding surfaces’at every time step
model output

y = number of time steps
defined by modeler

iy = matrix index of time step
proceeds from time 1 to y during the model

n = number of bounding surfaces
defined by vector b

ia = vector index of bounding surfaces for calculating flux
proceeds from depth 1 to 11 during each time step

flux = vector of flux values at bounding surfaces for current time step
recalculated in each time step

ib = vector index of cells for calculating amount dissolved

proceeds from cell 1 to n-1 during each time step

dissolve= vector of thickness removed from each cell for current time step
recalculated in each time step

ic = vector index of cells for calculating thickness
proceeds from cell 1 to n-1 during each time step
newthlck = thickness of current cell for current time step

recalculated for each cell within every time step

 

 

 

Figure 3.3. The model variables

 

column of matrix final contains the initial depths, making the second column the

results after the first time step.

 

In line 18, the first column of matrix final is formed from vector b, which

consists of the initial depths of the bounding surfaces. The variable n, line 19, is

defined as the number of bounding surfaces, or the number of values in b. The

size of each time step is controlled by the units from the constants. D" is

calculated in m2l10‘yr; therefore, the time step is ten thousand years. The

number of time steps is set in line 22; this model goes to 10° years.

16

 

 

 

 

 

 

 

 

 

 

 

 

 

The first row of matrix final is defined in line
surface 1
cell 1 24. It starts with the initial value of the top depth
“ma“ 2 from vector b. A deposition rate of 3mml1000yr is
cell 2
surface 3 added to this (Ehrmann 1985). Since the time step
cell 3 m
is 10‘ years and length is meters, 3 -10‘2
surface 4 10,000 yr
cell 4
surface 5 is used. Every time step uses the initial value, b(1),
09" 5 then adds the deposition rate multiplied by the
surface 6 ,
number of the time step.
Figure 34, Location of the Lines 25 through 29 create a vector of flux
bounding surfaces and cells
in the "Net values at the bounding surfaces within each time

 

 

step. First, line 25 establishes the steps down the sediment column; for each
value of is, from 1 to n, the calculation in lines 26 through 28 will be performed.
To compute the flux for each surface, the depth of that surface from the previous
time step is used, line 26. Depth, x, is taken from vector lastdep which contains
the depths of all the bounding surfaces from the preceding time step. Then in
line 28, x is used to calculate the flux for that surface by applying equation 2.11.
The end statement in line 29 forces the model back to line 25 and through the
flux calculation until all surfaces are finished for that time step.

Beginning with line 34, the computations transition to using cells instead of
bounding surfaces. Index ib counts from cell 1, bounded by surface 1 and 2,
(figure 3.4) until cell n-1, which is bounded by surface n at the bottom. In line 36,

the flux out of the cell is subtracted from the flux into the cell, giving the change in

17

moles, equation 2.2. The change in moles of CaCOa is then converted to change

in thickness utilizing gram formula weight and density:

 

 

mole 2.7 - 106 g 2.7 ~10“

mole .lOOg . m3 _ (ACaC03m/10‘yr)
m2 - 104 yr

This change in thickness would be appropriate if the sediment was solid
carbonate, but porosity needs to be accounted for. This is done by dividing by
the percent sediment. For example, if 1 mm of solid is removed, but the sediment

has 75% porosity, then:
1mm -—1— - 4mm
3-2 0.25

4 mm of sediment was actually eliminated. This is the reason for the final term,
(1-p), in line 36.

Now that the thickness removed is known, the new depths of the bounding
surfaces can be determined. Each cell’s new thickness is calCulated by using its
previous thickness and adding the change in thickness:

3.3 NewThiclmess = Pr eviousThickness + AThr'clmess

3.4 NewThr‘clmess = (Pr eviousBottom — Pr eviousT op) + AThiclmess

This is accomplished in line 40. Note that Athickness will be negative, resulting
in reduction of the cell. Lines 41 and 42 ensure that a cell cannot dissolve more
carbonate than it contains. If the computed thickness is less than the non-
carbonate thickness, the model assigns the depth as the surface above plus the
minimum thickness calculated from the percent carbonate. Otherwise, the model
assigns the new depth by adding the cell’s thickness to the surface at the top of

the cell. For example, in cell 3 at time 1, ic=3 and iy=1. The bottom of the cell,

18

Iastdep(4), and the top of the cell, lastdep(3), from the previous time step are
used as the previous thickness. The previous thickness plus the change in
thickness for cell 3, dissolve(3), equals the cell thickness after the first time step.
Looking at line 44, the bounding surface at the top of cell 3 for the current time
step is found in matrix final, row 3, column 2, or final(ic, iy+1). By adding the
thickness of the cell, the depth of the bottom bounding surface is found and
placed in matrix final, row 4, column 2. The end statement in line 46 sends the
model back to line 39 to calculate the next deeper cell. Note that the depth of
surface 1 is defined earlier by using pelagic accumulation rate in line 24, allowing
the first row value, final(1,2), to be known.

Once all of the bounding surfaces for the current time step are calculated,
the vector lastdep is redefined before the next time step. The current time step
filled column iy+1 of matrix final; line 47 traces that column to reset the values of
lastdep. The final end statement sends the model to line 22 to compute the next

time step.

19

Assumptions

To create a model that focuses on simple diffusion, certain assumptions
must be made. The system must be in a state that makes diffusion the primary
transport mechanism. Limitations on the transport of the sediment and pore
water are necessary. Plus, the influence of other ions in the system needs to be
negligible. Particular characteristics are also necessary to generalize from the
Ca” ion and its measurements. Finally, the mineralogy and lateral variation of
the sediment needs to be consistent.

Equilibrium of the calcium carbonate with the pore water must occur if
dissolution is not limited by the rate of surface reaction. Then, the overlying
water needs to have a lower concentration of Ca” for it to diffuse toward the
sediment-water interface. The gradient of lower Caz” toward the overlying water

is shown by DSDP measurements (figure 5.1) which will be discussed with the

 

parameter estimation.

RolationahipofCa" ConcontratlontoAlkalliity The lower

100

 

concentration of Ca2+

in the sediment pore

10

 

 

solution seems to be

 

calclun- rnmolIL

o balanced by alkalinity

 

 

1 . . to account for

0.1 1 10 100
alkalinity- inmollL

 

equilibrium with respect

 

 

Figure 4.1. Comparison of alkalinity to calcium concentration in to ca'Cium carbonate-
porewaterofcerbonate sedimentsfrom DSDP.

 

 

Comparison of

 

20

alkalinity to Ca2+ concentration (figure 4.1) suggests an inverse relationship; as
one of these ions increases, the other ion decreases. The correlation does not
appear strong, but the measurements come from several locations and various
depths. Plus, the dynamics of inorganic carbon are complex, and may interfere
with the Caa-alkalinity relationship.

For molecular diffusion to be the primary means of transport, advection
must be negligible. This is justifiable for deep Atlantic sediment because the
lateral variation in hydraulic head is minute relative to its value. The lack of
advection results in a lack of mechanical dispersion, leaving diffusion as the main
transport mechanism. Since molecular diffusion is the primary transport process,
the assumption in Fick’s law of Gaussian distribution is probably not critically
violated. Brownian motion of diffusing molecules in solution will result in a
normal distribution. If advection was present, it would increase dissolution and
introduce mechanical dispersion. Also, the rate of transport due to advection is
much greater than diffusion, and the CaCOa would probably not reach
equilibrium with the pore water.

As the sediment is buried by pelagic clay, the porosity is reduced. The
change in pore space results in expulsion of water, leading to slight advection of
pore solution toward the sediment-water interface. A sample calculation of the
amount of Ca2+ carried by this mechanism examines the importance of it relative
to molecular diffusion. A cell at the sediment-water interface initially 0.01m thick
was chosen because it is located where the porosity gradient us high. Plus, clay

deposition in one time step (10,000yr) will deepen the cell 0.03m, more than its

21

 

 

 

 

 

 

 

 

 

original thickness. This setting lnitiall Finafl
Porosity 0.75 0.7499600

should show the greatest Fl'hickness- m 0.01 0.0099999
, Pore Volume- m3 0.0075 0.0074995
influence Of pore water Change in water volume- m3 3 4.77E-07
. Calcium concentration- mollm 0.125

movement. Calculations (table Ca2+ removed by advection- mol 5.96E-08I
Ca” removed by diffusion- moi 6.94E-04

 

 

 

 

4.1) show that the Calcium
Table 4.1. Sample calculation of effect of

advection due to reduction in porosity.

 

 

removed by advection is four

 

orders of magnitude less than Ca2+ removed by molecular diffusion.

Dispersion of sediment and water due to bioturbation is ignored in the
model, too. In a study of deep-sea carbonate sediment, Kier (1984) investigated
anomalous isotope dates, showing that bioturbation could explain the problem by

mixing older sediment with more recent deposits. She used a bioturbation

2 2

;this converts to 0.2 :4

coefficient of 200 cm

 

 

. This is three orders of
y ,

magnitude smaller than the diffusion coefficient for Ca” in sediment, which is

m2

04

 

greater than 100 near the sediment-water interface. Like advection,

y
bioturbation would increase dissolution by exposing sediment particles to the
overlying undersaturated water.

To estimate the Ca” concentration gradient, a function of concentration
with depth was formulated. This presumes that the concentration is at steady
state and is not a function of time. Steady state condition is shown by the shape
of concentration with depth (figure 5.1). If non-steady state conditions were

present, the shape of the curve would be altered from uniform decrease in Ca2+

22

toward the sediment-water interface. For example, if microbes were altering the
pore water chemistry to enhance dissolution or cause precipitation of Ca”, the
concentration would suddenly change at the range of depths where the microbes
existed. Also, a spike in concentration at depth could indicate a non-uniform
source of Ca2+ or lack of transport through the pore water.

The numerical values in the concentration function and its derivative were
estimated using measurements of deep Atlantic sediment pore water from DSDP
sites. For the gradient to be accurate, the measured Ca” needs to be
proportional to the Ca2+ free in solution and any measurement error should be
regular across samples. The actual value of concentration could be inaccurate
by a consistent amount, and still produce an acceptable derivative. Graphically,
this is equivalent to shifting the location of a curve, but not altering its shape; the
change in concentration with depth will remain unaltered. The likeliest causes of
measurement error are the change in pressure as the sediment is brought to the
surface and the extraction of pore water from the core (World Data Center for
Marine Geology 8 Geophysics 2000). The same conditions are experienced by
all of the samples, so measurements should be consistent relative to each other.
For the effective concentration to be relatively consistent, speciation of Ca"+
needs to be uniform with depth. The activity coefficient should not vary greatly
with depth because the pore water at various depths is fairly similar, see
sensitivity analysis.

Focusing on the concentration of Caz" also presumes that the electrical

potential gradient caused by other ions does not significantly contribute to the

23

 

 

 

 

 

 

 

difiusion of Caz“. ‘Diffusion in most pore
Sdirity from DSU’
waters in sufficiently like diffusion in dilute
. . 0 20 40 a) 30

solution that we can normally ignore the 0 1
complications arising from the .

200
multicomponent interactions” (Boudreau ,

400
1997). Boudreau supports this E ‘
proclamation by deriving equations for the a 6m 0" °.

1: .° '

correction factor to the diffusion coefficient a!) . '0
and showing that it is insignificant. The 1000 . ';
exception is when the main electrolytes 12m .

 

 

 

 

 

 

(Cl’ and Na’) are involved, they need to . , ,
Figure 4.2. Measurements of salinity for

be considered. Salinity measurements DSDP 3"“ i" "'9 “”9 “antic ”935"-

 

 

 

from deep Atlantic sediment pore water show the trend of the main electrolytes
(figure 4.2). The values are rather consistent with depth and do not show an
obvious trend (The data that deviate from the trend are almost exclusively from
one site).

Moles of Ca” removed are equated to the moles of CaCOa dissolved from
a cell. This assumes that there is no other contributor of 0a“ to the pore water.
Though clay minerals may interact with Ca”, they are not included. Sorption,
which incorporates absorption into the clay structure and adsorption to the
surface, should be at equilibrium. The time step of the model, 10‘yr, is much
longer than the rate of cation exchange. Measurement of this rate in terrestrial

clay sediment shows a half life of 2 to 3 seconds (Langmuir 1997). This disparity

24

is eleven orders of magnitude, so even though the mineral assemblage could be
different for pelagic clay, cation exchange should be in equilibrium in 10,000yr.
This leaves carbonate as the supplier of Ca2+.

Finally, using a one dimensional model assumes that the sediment is
laterally uniform. The processes influencing sediment deposition across the
pelagic realm within an ocean are comparatively uniform relative to coastal or
terrestrial depositional environments . Acknowledging that the sediment on the
Atlantic crust should be fairly consistent allows conclusions to be drawn from the
model. Recognizing the potential variation in sediment limits the generalizations

made to other locations.

25

Parameter Estimation

The foundation of calculating transport by diffusion is Fick’s first law,
equation 2.1, which requires estimation of a diffusion coefficient and the
concentration gradient. The concentration gradient can be determined by using
the derivative of a concentration function if an analytical solution is possible.
However, determining the diffusion coefficient for an ion in pore water solution is
more complex. Departure from standard temperature conditions needs to be
considered as well as the complications resulting from the surrounding sediment.
Tortuosity affects the rate of diffusion and is nearly impossible to characterize.

This makes an analytical solution impossible, demanding a more empirical

 

approach.

Calcium- mmolIL

Measurements of pore water 0 10 20 30

 

chemistry in deep Atlantic sediment are

 

 

 

2m -
available from the Deep Sea Drilling

400
Project (World Data Center for Marine B 000

 

Geology 8. Geophysics 2000). The Ca” g 300

 

. D
D LAM»
D

ion is used instead of alkalinity because of 1000 .

 

a?

the complex relationships involved in the 120°

.

 

 

R2=0.89

 

thermodynamics of inorganic carbon. “00

 

 

. . . 2. F' ure5.1.Measurementsofporewater
Unlike alkalinity, moles of Ca can be CE» concentrations in mm for site 303,

. The solid line represents the fitted function:
equated to moles of CaCOa dissolved, Ca 2+ (x) = 24.2 422421410027»: )

 

 

see assumptions. Of the sites that are on

oceanic crust, pore water Ca2+ is available for 29 locations, appendix ll. Site 603

26

 

lies under 4633 meters of water and has the most measurements available, so its
values were used for calibrating the concentration function, equation 2.3. Shown

in figure 5.1, the resulting equation is:

C x =C - C ~e”‘"‘ C... =24.2 moi/m3
( ) m ( range ) Cm =1.78 mms
Cm =22.4 mollm"1
" =2.75*10 '
5.1 C(x) = 24.2% — (22.4_n1_031_ . e-0.0027Sm -x) kc m
m m

The constants were found simultaneously by minimizing the squared residual
values. The R 2 is 0.89, and the larger departures from the estimated values
occur below 500m, which is the deepest modeled depth. The derivative,
equation 2.4, is then:

5-2 23:; = 0.00275m’I - 22.4-m—01--e’°'°°275'"_"’

m3

Determination of the diffusion coefficient for Ca” in the sediment pore
water, D... begins with the coefficient in pure water, D°. Here, all diffusion
coefficients refer to Ca” since no other ions are used. The values of rn0 and mi,

equation 2.6, are from linear regression for infinite dilution (Boudreau 1997, p.

115x
D" = (ma + m1 'T)-10‘6cm2 sec’l mo=3.60
m1=0.179
T =10°C
5-3 13° = (3.60 + 0.179 .10).10 J cm2 sec"

2
D" = 5.39-10‘6 3"—
SOC

m
1 0,000 yr

D" =170

 

27

Though temperature may vary down the sediment column, a single temperature

is used. Variation by several degrees leads to less change in D. than will be

introduced for sensitivity analysis of 0.. This D° is appropriate for open water

and needs to be adjusted for sediment effects. The only additional information

necessary for the empirical relation of equation 2.7 is porosity.

Adler et al (2001) used a function, equation 2.8, for porosity with depth in

Pacific carbonate sediment, which was formulated by Rabouille and Gaillard

(1991). The form of this relationship retains many of the physical characteristics

of porosity. The exponential component controls the overall shape of the curve,

which shows a regular reduction with depth. The magnitude of the porosity

 

Porosity
40 60 80 100

 

 

 

 

 

 

 

 

 

R2=0.31

 

 

 

 

 

 

Figure 5.2. Measurements of porosity for DSDP
sites in the deep Atlantic basin. The solid line
reprewnts the fitted function:

-x

p(x) = 58.5 + 16.5 . e35“

 

 

 

28

constant, kp, determines how
quickly porosity reaches its
minimum value. Pm, and Pm...
constrain the curve between
particular porosity values.
Physically, PM represents the
initial porosity at deposition, and
Pm... is the porosity after
compaction has reached its

greatest influence. The magnitude

of kp shows how much burial is
required to compact the sediment.

The numerical values of the

constants were found using porosity measurements from deep Atlantic sediment,

(figure 5.2 and appendix Ill):

“1

p(x) = pmin + prange .ek' =0750

print
9min
pm, =0.165
kp =36.4m

'X

5.4 p(x) =0.535+0.165.e56-4~

The DSDP measurements are based on density and water content, and they
include nine sites and 197 values for carbonate sediment in the deep Atlantic
basin. All of these were used to find the constants for equation 5.4 by
simultaneously minimizing the squared residual values. The R2 value is 0.31,
which is much less than the R2 for concentration. Some of the scatter can be
attributed to using several sites, and the variation is evaluated in the sensitivity

analysis.

29

Results

Calculations were performed on three hypothetical sediment packages.

Each started with layers of uniform thickness beginning at zero depth (table 6.1).

 

This allowed investigation of sediment removal at s of ’ 30mm of

. . Layersn Th Column
depth, while providing detail for the upper portion of met Mars.

 

 

 

 

 

 

 

 

50 10 500
the sediment column. Uniform thickness within 50 1 50
50 0.01 0.5
each simulation allowed comparison of the amount Tare 6,1, Hypothetical
sediment columns developed
dissolved from shallow and deep sediment. for nnodal simulations.

 

 

Due to the pelagic clay deposition, the top surface was 300 meters deep
at the end of all three simulations. The final depth of the deep column (table 6.2)
was 797.52, showing a reduction of 2.48m from 500m of sediment over the
100Ma period. As seen in figure 6.1, the depth of the surfaces becomes greater
through the simulation, but reduction in thickness is imperceptible on the graph.
The change in thickness for several time steps is given in table 6.3, note that
units are microns. The carbonate removal is greatest near the sediment-water
interface and deteriorates with depth (figure 6.2 and table 6.3); this is controlled
by the concentration gradient. The total reduction in thickness of each layer is
shown in millimeters and follows the same trend. Over the 100Ma period
2476mm of sediment was dissolved from the 500m column. This matches the
2.48m from table 6.2.

The calculations for the intermediate column are shown in tables 6.4 and
6.5, and figures 6.3 and 6.4. The elimination of sediment is still greatest near the

sediment-water interface, with the top layer reduced by 15mm over 100Ma. The

30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Layer Depth Figure 6.1. Depth of
- bounding surfaces for
for Sediment to 500m Depth layers inmany 10m Wok
0 g . , . to 500m depth through
:5 100 million years.
800 . . 1 1 1 . 1 e ‘57:?
010 20 30 4o 50 60 70 80 90100
Time in Ma
Change in Layer Thickness for 5:90"? 626313199, “i'fi any
- lckness ayers in
Sediment *0 500m Depth 10 m thick to 500m depth
I . , . j through 100 million years.
Each calculated value is
the change in thickness in
microns for a 100,000 year
period.
E
:L
J:
8 -
it
;E -40
j.
.E '
8:50
5
.r: ‘50 ’
0

ii
0

 

 

 

l l J 1 l l

-80 . a.
010 20 3040 5 60 70 80 90100

 

Time in Ma

 

 

 

 

31

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Layer Depth mes. w offor
' l SU 30%
for Sediment to 50m Depth | 3910 any m m to
o . 50m depth through 100
~ million years.
E
e
0
o
010 2050405060“; 8050100
Time in Ma
Change in Layer Thickness Figure 6.4. Change in

Change in Thickness pm

for Sediment to 50m Depth

 

00 a
010

l

J

 

 

l

20 3040 5060708090100

Time in Ma

 

thickness of layers
initially 1m thick to 50m
depth through 100
million years. Each
calculated value is the
change in thickness in
microns for a 100,000

yearpenod.

 

 

 

32

 

 

 

 

 

 

 

 

 

 

 

 

 

Layer Depth 531:: 6.5. Dfepth off
. ing su aces or
for Sediment to 50 cm Depth layers initiany 0.01m
0 r . thick to 0.5m depth
through 100 million
years.
50 ~
100 - \
at.
8
o 200 ~ 4
250 ~ \ .
300 » \
3500 10 20 30 40 50 60 70 80 90 100
Time in Ma
Change in Layer Thickness Esme 6-66ft‘ihange in
- ickness ayers
for Sediment to 50 cm Depth initial” (mm thick to
0 —. - 0.5m depth through
100 million years.
Each mlculated value
-0.02 is the change in
thickness in microns
g fora 100,000 year
I '0-04 ' period.
00
8
5 -0.06 r
0
:E
I— -0.08 »
.E
8
c -o.10
(B
.C
O -o.12
'0-14 .____J..__ .4 l L l L l

 

 

 

 

 

 

0102030405060708090100
TrmeinMa

 

 

33

 

 

 

 

 

Initial Depm(m)Loepthato.1Maloepthar1Mal Depthat10MdDepthat 100M

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 0.30 3.00 30.00 300.
10.00 10.30 12.99 39.95 309.86
20.00 20.30 22.99 49.92 319.75
30.00 30.30 32.98 59.89 329.64
40.00 40.30 42.98 69.87 - 339.55
50.00 50.30 52.98 79.85 349.46
60.00 60.30 62.98 89.83 359.38
70.00 70.30 72.98 99.82 369.30
80.00 80.30 82.97 109.81 379.2
90.00 90.30 92.97 119.80 389.16

100.00 100.30 102.97 129.78 399.09
110.00 110.30 112.97 139.77 409.03
120.00 120.30 122.97 149.77 418.96I
130.00 130.30 132.97 159.76 428.
140.00 140.30 142.97 169.75 438.
150.00 150.30 152.97 179.74 448.7
160.00 160.30 162.97 189.73 458.7
170.00 170.30 172.96 199.72 468.
180.00 180.30 182.96 209.72 478.62
190. 00 190.30 192.96 219.71 488.57
200. 00 200.30 202.96 229.70 498.52
210. 00 210.30 212.96 239.69 508.47
220.00 220.30 222.96 249.69 518.43
230.00 230.30 232.96 259.68 528.38
240.00 240.30 242.96 269.68 538.341
250. 00 250 30 252.96 279.67 548.29
260.00 260.30 262.96 289.66 558.2
270. 00 270. 30 272.96 299.68 568.27!
280.00 280.30 282.96 309.65 578.17
290.00 290.30 292.96 319.65 588.13
300. 00 300.30 302.96 329.64 598.09
310. 00 310. 30 312.96 339.64 608.06‘
320.00 320.30 322.96 349.63 618.02
330.00 330. 30 332.95 359.63 627.99
340.00 340. 30 342.95 369.62 637.95I
350.00 350.30 352.95 379.62 647.92
360. 00 360. 30 362.95 389.61 657.89
370. 00 370.30 372.95 399.61 667.86]
380. 00 380.30 382.95 409.60 677.83l
390.00 390. 30 392.95 419.60 687.80
400.00 400.30 402.95 429.60 697.77
410.00 410.30 412.95 439.59 707.74:
420.00 420.29 422.95 449.59 717.72
430.00 430.29 432.95 459.58 727.69
440. 00 440.29 442.95 469.58 737.661
450. 00 450.29 452.95 479.58 747.641
460. 00 460.29 462.95 489.57 757.61
470. 00 470.29 472.95 499.57 767.5
480.00 480.29 482.95 509.57 777.57]
490. 00 490.29 492.95 519.56 787.551
500.00 500.29 502.95 529.56 797.52

 

 

34

 

 

Table 6.2.
Calculated
depths of
bounding
surfaces for
50 layers
initially 10m
thick.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Change in Thickness in for an Interval of Reduction
10,000” for 50, 10m Thiclkm Layers of Sediment for 100Ma 1018:0212; mugged
Layer 1 -76.50 -75.64 57.80 -29.44 -5.30 136.08 10m “1101‘. values are
-52.45 -51.% 47.50 -23.66 -5.17 117.02 in“ for a 10.000 yr
-38.38 -38.08 -35.34 -1 9.67 -5. 103. time step. Total
{-23.70 -23.57 -22.35 44.76 4.78 87.37 over 100Ma is given in
6' 49.68 -1 9.59 —18.73 -13.21 4.65 81.81 the rightmost column
7 -16.83 -16.76 -16.15 -12.03 4.5 77.33 in mm,
5 -14.75 -14.71 -14.25 -11.11 4.41 73.60
-1 3.20 -1 3.1 7 42.82 -10.38 4.29 70.43
10 42.02 —12.00 -11.73 -9.78 4.17 67.67
11| -11.10 -11.08 -10.87 -9.28 4.05 65.21
12 -1 0.37 -1 0.36 -10.18 -8.86 4.951 63.00
1 -9.78 -9.76 -9.62 -8.50 -3.85 60.95
141 -9.28 -9.27 -9.15 -8.18 -3.75 59.05
15 -8.86 -8.85 -8.75 -7.89 -3. 57.29
16I -8.50 -8.49 -8.40 -7.63 -3.55 55.60
17 -8.18 -8.17 -8.09 -7.38 -3.45 54.01
15 -7.89 -7.88 -7.81 -7.15 ~3. 52.47
19— -7.62 -7.62 -7.55 -6.94 -3.27 51.01
20 -7.38 -7.37 -7.31 -6.74 -3.18 49.591
21[ -7.15 -7.15 -7.09 -6.54 -3.10 48.22
22[ -6.94 -6.93 -6.88 -6.36 -3.01 46.89
25 -6.74 -6.73 -6.68 -6. 18 -2.93 45.61
24[ -6.54 -6.54 -6.49 -6.01 -2.85 44.3
25 -6.36 -6.35 -6.30 -5.84 -2.78 43.1
26' -6.18 -6.17 -6.13 -5.68 -2.70 41.95
27 -6.01 -6.00 -5.96 -5.53 -2.63‘ 40.85
25 -5.84 -5.84 -5.79 -5.38 -2.56 39.75
-5.68 -5.68 -5.63 -5.23 -2.49 38.66I
30 -5.52 -5.52 -5.48 -5.09 -2.42 37.62
31 -5.37 -5.37 -5.33 4.95 -2.36' 36.61
32 -5.23 -5.22 -5.18 4.81 -2.29 35.61
35 -5.08 -5.08 -5.04 4.68 -2.23 34.
34{ 4.95 4.94 4.91 4.56 -2.17 33.71
35 4.81 4.81 4.77 4.43 -2.11 32.80
4.68 4.68 4.64 4.31 -2. 31.91
37 4.55 4.55 4.52 4.20 -2.00 31.
4.43 4.43 4.39 4.08 -1 .95 30.21
35 4.31 4.31 4.27 -3.97 -1 .89 29.39
45 4.19 4.19 4.16 -3.86 -1. 28.60
41I 4.08 4.08 4.05 -3.76 -1.79 27.82
421 -3.97 -3.96 -3.94 -3.66 -1 .75 27.07
4r -3.86 -3.86 -3.83 -3.56 -1.70 26.341
44[ -3.76 -3.75 -3.73 -3.46 -1 .6 25.62
45 —3.65 -3.65 -3.62 -3.37 -1 .61 24.
46V -3.55 355 353 -3.28 -1. 24.25l
4 -3.46 -3.46 -3.43 -3.19 -1.5 23.60 Reduction for
-3.36 -3.36 -3.34 -3.10 -1. 22.95 Entire Column |
45 -3.27 -3.27 -3.25 -3.02 -1.44[ 22.34] [2476 mm 1
Sd -3.18 -3.18 -3.16 -2.93 -1 .45 21.74] *

 

35

 

 

 

lnitialDeptho(m03 Depthat0.1Ma Depthat1Ma Depthat10Ma Depthat100M5

 

 

 

 

 

 

 

 

Table 6.4.
Calculated
depths of
bounding
surfaces for
50 layers
initially 1m
thick.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0. 30 3. 00 30. 00 300. 011
1.00 1.30 4.00 30. 99 300. 96|
2.00 2.30 5.00 31.99 301 .97|
3.00 3.30 6.00 32.98 302.96l
4.00 4.30 7.00 33.98 303.94]
5.00 5.30 8.00 34.97 304.93]
6.00 6.30 9.00 35.97 305.91
7.00 7.30 9.99 36.96 306.
8.00 8.30 10.99 37.96 307.89
9.00 9.30 11.99 38.95 308.87
10.00 10.30 12.99 39.95 309.86
11.00 11.30 13.99 40.95 310.85
12.00 12.30 14.99 41.94 311.
13.00 13.30 15.99 42.94 312.62
14.00 14.30 16.99 43.94 313.811
15.00 15.30 17.99 44.93 314.
16.00 16.30 18.99 45.93 315.79
17.00 17.30 19. 99 46.92 316.78
18.00 16.30 20. 99 47.92 317.77
19.00 19.30 21. 99 48.92 318.75
20.00 20.30 22. 99 49.91 319.3)
21.00 21.30 23. 99 50.91 320.731
22.00 22.30 24.99 51.91 321.72
23 00 23.30 25. 99 52.91 322.71
24.00 24.30 26.99 53.90 323.70
25 00 25.30 27. 99 54.90 324.69
26 00 26.30 28.98 55.90 325.66
27 00 27.30 29.96 56.69 326.87
26.00 28.30 30. 96 57.69 327.
29.00 29.30 31 98 56.89 326.65
30. 00 30. 30 32.96 59. 89 329.
31.00 31.30 33.98 60. 88 330.63
32.00 32.30 34.98 61.88 331.62
33.00 33.30 35.98 62.86 332.61
34.00 34.30 36.98 63.86 333.60
35.00 35.30 37. 98 64.88 334.59
36. 00 36.30 38. 96 65.67 335.561
37.00 37.30 39. 98 66.67 336.57
36.00 36.30 40. 98 67.87 337.
39.00 39.30 41. 96 68.67 336$
40.00 40. 30 42.98 69.66 339.
41.00 41.30 43.98 70.66 340.53
42.00 42.30 44.96 71.88 341.
43.00 43.30 45.98 72.86 342.52
44.00 44.30 46.96 73.86 343.51
45.00 45.30 47. 96 74.65 344.50
46.00 46.30 48. 98 75.85 345.49
47.00 47.30 49.98 76. 65 346.48
48.00 48. 30 50. 98 77.85 347.47
49. 00 49.30 51. 98 78. 85 348.46
50.00 50.30 52.98 79.85 349.46

 

 

 

 

36

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Change in Thickness in pm for an Interval of Reduction for
10,000yrfor50, 1m ThickLayersofSediment 100Ma
initial 0.1Mal 1M4 10M5 100Ma in mm
Layer 1! -9.94 -9.81 -8.63 -3.36 054 15.05
r947 -9.35 -8.25 -3.27 -0.53 14.741
L -9.04 -8.92 -7.90 -3.19 -0.53 14.4
4[ -8.63 -8.52 -7.57 -3.11 -0.53 14.19
SI -8.25 -8.15 -7.26 -3.03 -0.53 13.
6F -7.89 -7.80 -6.96 -2.96 -0.53 13.68
7 -7.56 -7.48 -6.69 -2.89 -0.53 13.4
8 -7.25 -7.17 -6.43 -2.82 -0.53' 13.22.
T -6.96 -6.88 -6.19 -2.76 -0.53 13.01
1V -6.68 -6.61 -5.96 -2.70 -0.5 12.8
11[ -6.43 -6.36 -5.74 -2.64 -0.52 12.60
12[ -6.18 -6.12 -5.54 -2.58 -0.52 12.42
13! -5.95 -5.89 -5.34 -2.52 -0.5 12.23
14F -5.74 -5.68 -5.16 -2.47 -0.52 12.05]
15 -5.53 -5.48 4.99 -2.42 -0.52 11.89
16' -5.34 -5.29 4.82 -2.37 -0.52 11.73
17 -5.16 -5.11 4.67 -2.32 -0.51 11.57
18 4.98 4.94 4.52 -2.28 -0.51 11.42
1 4.82 4.78 4.38 -2.23 -0.51 11.28
2 4.66 4.62 4.24 -2.19 -0.51 11.13
21 4.52 4.48 4.12 —2.15 -0.51 11.01
4.38 4.34 4.00 -2.11 -0.51 10.87
2 4.24 4.21 -3.88 -2.07 -0.51 10.7
24L 4.11 4.08 -3.77 -2.04 -0.51 10.6
25[ -3.99 -3.96 -3.66 -2.00 -0.50 10.51
28 -3.88 -3.85 -3.56 -1.97 -0.50 10.40
27 -3.77 -3.74 -3.47 -1.93 -0.50 10.2
28 -3.66 -3.63 -3.38 -1.90 -0.50 10.1
2Q -3.56 -3.53 -3.29 -1.87 -0.50 10.08
SCI -3.46 -3.44 -3.20 -1.84 —0.50 9.98
31F -3.37 -3.35 -3.12 -1.81 -0.50 989'
32[ -3.29 -3.26 -3.05 -1 .79 -0.50 9.79
33 -3.20 -3.18 -2.97 -1.76 -0.49. 9.70
34{ -3.12 -3.10 -2.90 -1.73 -0.49 9.61
35 -3.04 -3.02 -2.83 -1.71 -0.4 9.53
38 -2.97 -2.95 -2.77 -1.68 -0.49 9.44)
37 -2.90 -2.88 -2.71 -1.66 0491 9.36]
38 -2.83 -2.81 -2.65 -1.64 045 9.25
39 -2.77 -2.75 -2.59 -1.61 049 9.21]
40 -2.70 -2.69 -2.53 -1.59 -0.48[ 9.15
41 -2.64 -2.63 -2.48 -1.57 -0.48 9.06'
42[ -2.59 -2.57 -2.43 -1.55 -0.48‘ 9.00
45 -2.53 -2.51 -2.38 -1.53 -0.48 8.92
44F -2.48 -2.46 -2.33 -1.51 -0.48 8.86]
45F -2.42 -2.41 -2.28 -1.49 0.48 8.75
-2.38 -2.36 -2.24 -1 .47 -0.4d 8.73]
4 -2.33 -2.31 -2.20 -1.46 -0.48' 8.
-2.28 -2.27 -2.16 -1.44 -0.47 8.61
4? -2.24 -2.23 -2.12 -1.42 -0.47 8.54|
5d -2.19 -2.18 -2.08 -1.41 -0.4 8.49

 

 

37

 

Table 6.5.
Calculated change
in thickness for 50
layers initially 1m
thick. Values are
pm for a 10,000 yr
time step. Total
reduction in
thickness over
100Ma is given in
the rightmost
column in mm.

 

 

 

Reduction for I
Entire Column
[544.16 mm I

 

 

 

Initial Depth (mflDepth at 0.1Maloepth at 1Mal Depth at 10M5Depth at 100M

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.00 0.30 3.00 30.00 300.
0.01 0.31 3.01 30.01 300.01
0.02 0.32 3.02 30.02 300.02
0.03 0.33 3.03 30.03 300.03
0.04 0.34 3.04 30.04 . 300.041
0.05 0.35 3.05 30.05 300.05
0.06 0.36 3.06 30.06 300.06
0.07 0.37 3.07 30.07 300.07
0.08 0.38 3.08 30.08 300.09
0.09 0.39 3.09 30.09 300.09
0.10 0.40 3.10 30.10 300.1
0.11 0.41 3.11 30.11 300.11
0.12 0.42 3.12 30.12 300.12
0.13 0.43 3.13 30.13 300.1
0.14 0.44 3.14 30.14 300.141
0.15 0.45 3.15 30.15 300.15
0.16 0.46 3.16 30.16 300.16
0.17 0.47 3.17 30.17 300.17
0.18 0.48 3.18 30.18 300.18
0.19 0.49 3.19 30.19 300.19
0.20 0.50 3.20 30.20 300.20
0.21 0.51 3. 21 30 21 300.21
0. 22 0.52 3. 22 30. 22 300.22
0. 23 0.53 3. 23 30. 23 300.23
0.24 0.54 3.24 30.24 300.24;
0.25 0.55 3. 25 30. 25 300.25
0. 28 0.56 3. 26 30. 26 300.26
0.27 0.57 3. 27 30. 27 300.2
0.28 0.58 3.28 30.28 300.2
0.29 0.59 3. 29 30.29 300.2
0 30 0.60 3. 30 30. 30 300.30
0. 31 0.61 3. 31 30. 31 300.31
0.32 0.62 3.32 30.32 300.32
0.33 0.83 3.33 30.33 300.32
0.34 0.64 3.34 30.34 300.33
0.35 0.65 3.35 30.35 300. 341
0. 36 0.66 3. 36 30.36 300. 35]
0. 37 0.67 3. 37 30. 37 300

0 38 0.68 3. 38 30 38 300.37
0.39 0.69 3. 39 30. 39 300.38
0. 40 0.70 3. 40 30. 40 300.3
0. 41 0.71 3. 41 30 41 300.
0.42 0.72 3.42 30.42 300.41
0.43 0.73 3.43 30.43 300.42
0.44 0.74 3. 44 30.44 300.4
0.45 0.75 3. 45 30. 45 300.44;
0.46 0.76 3. 46 30.46 300.4
0.47 0 77 3. 47 30. 47 300.46
0. 48 0. 78 3. 48 30. 48 300.47
0. 49 0.79 3. 49 30. 49 300.
0.50 0.80 3.50 30.50 300.4

 

 

38

 

Table 6.6.
Calculated
depths of
bounding
surfaces for
50 layers
mmmw
0.01m thick

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

in Thiclmessinpmformlntervalof Reduction

10,000yr for 50, 10cm Thick Layers of Sediment for 100Ma
initiai 0.1Ma1 1Ma1 10Ma] 100qu in mm
Layer1 -O.1028 0.1014 0.0890 0.0341 0.00541 0.15
0.1027 0.1013 -0.0889 0.0341 0.00541 0.15

3 0.1027 0.1013 0.0889 0.0341 0.00541 ‘ 0.16
41 -0.1026 0.1012 0.0889 0.0341 0.00541 0.15
f 0.1026 0.1012 0.0888 0.0341 0.00541 0.15
6' 0.1025 0.1011 -0.0888 0.0341 0.00541 0.15
7 0.1025 0.1011 0.0887 0.0340 0.00541 0.16
a 0.1024 0.1010 0.0887 0.0340 0.00541 0.15
9F 0.1024 0.1010 0.0887 0.0340 0.00541 0.15
10 0.1023 0.1009 -0.0886 0.0340 0.00541 0.15
11 0.1023 0.1009 -0.0886 0.0340 0.00541 0.15
12 0.1022 0.1008 0.0885 0.0340 0.00541 0.16
1 0.1021 0.1008 0.0885 0.0340 0.00541 0.15
141101021 0.1007 -0.0885 0.0340 0.00541 0.15
1L01020 0.1007 0.0884 0.0340 0.00541 0.15
161 0.1020 0.1006 0.0884 0.0340 0.00541 0.15
17 0.1019 -0.1006 0.0883 0.0340 0.00541 0.16
1 0.1019 0.1005 0.0883 0.0339 0.00541 0.15
19101018 0.1005 0.0882 0.0339 0.00541 0.15
2f 0.1018 0.1004 -0.0882 0.0339 0.00541 0.15
211 0.1017 0.1004 -0.0882 0.0339 0.00541 0.15
2101017 0.1003 0.0881 0.0339 0.00541 0.16
231 0.1016 0.1003 0.0881 0.0339 0.00541 0.15
24L-0.1016 0.1002 0.0880 0.0339 0.00541 0.15
251 0.1015 0.1002 0.0880 0.0339 0.00541 0.1
26V0.1015 0.1001 0.0880 0.0339 0.00541 0.15
27 0.1014 0.1001 0.0879 0.0339 0.00541 0.15
2L01014 0.1000 -0.0879 0.0339 0.00541 0.16
2? 0.1013 0.1000 0.0878 0.0338 0.00541 0.15
3d 0.1013 0.0999 0.0878 0.0338 0.00541 0.15
31b01012 0.0999 -0.0878 0.0338 0.00541 0.15
32F 0.1012 0.0998 0.0877 0.0338 0.00541 0.15
331 0.1011 0.0998 -0.0877 0.0338 0.00541 0.15
341 0.1011 0.0997 0.0876 0.0338 0.00541 0.15
35f0.1010 0.0997 0.0876 0.0338 0.00541 0.16
0.1010 —0.0996 0.0876 0.0338 0.00541 0.15

3 0.1009 0.0996 -0.0875 0.0338 0.00541 0.15
0.1009 0.0995 -0.0875 0.0338 0.00541 0.15
39 0.1008 0.0995 -0.0874 0.0338 0.00541 0.15
41f 0.1008 0.0994 0.0874 0.0337 0.00541 0.15
411 0.1007 0.0994 -0.0874 0.0337 0.00541 0.15
421 0.1007 0.0994 0.0873 0.0337 0.00541 0.15
«£01006 0.0993 0.0873 0.0337 0.00541 0.15
44F0.1006 0.0993 —0.0872 0.0337 0.00541 0.16
451 0.1005 0.0992 0.0872 0.0337 0.00541 0.15
$01005 0.0992 0.0872 0.0337 0.00541 0.15
41 0.1004 0.0991 0.0871 0.0337 0.00541 0.15
0.1004 0.0991 0.0871 0.0337 0.0054L 0.15
491 0.1003 0.0990 0.0870 0.0337 0.00541 0.15
511 0.1003 0.0990 0.0870 0.0337 0.00541 0.15

 

 

39

 

 

Table 6.7.
Calculated change
in thicknees for 50
layers initially 0.01m
thick. Values are
run for a 10.000 yr
time step. Total
reduction in
thickness over
100Ma is given in
the rightmost column
in mm.

 

 

Reduction for
Entire Column
I7.58 mm

 

 

 

 

total reduction of the 50m column was 544mm (table 6.5) or 0.54m (table 6.4).
The surfaces shown in figure 6.3 deepen through the simulation; this appears
more pronounced than for the 500m column, but is identical because the pelagic
accumulation rate was the same. Clay deposition dominates this sediment
column; the thickness of the layers is barely perceptible on the depth scale that
accommodates the final column.

A detailed examination of the top 0.5m of sediment was achieved with the
shallow column. The removal of sediment is still greatest near the sediment-
water interface, but the change in thickness is similar for all of the layers at each
time step. The top layer was reduced by 0.15mm, and the column decreased in
total thickness by 7.6mm for 100Ma. Relative to the increase in depth from clay
deposition, the layers of this column are indiscemible (figure 6.5). Also,
individual surfaces in figure 6.6 cannot be seen at the scale necessary for the
change of thickness. The sediment removal for each time step is much less near
the end of the simulation because clay deposition has moved them relatively far

from the sediment-water interface.

40

Sensitivity Analysis
Diffusion Coefficient

Since the diffusion coefficient through sediment cannot be directly
measured, it is the most difficult variable in the model to approximate. Sensitivity
of depth of bounding surfaces to D. was investigated. Arbitrary variation was
introduced into the model within the calculation for flux at each surface. Within
each time step and at every bounding surface, Ds was calculated then a
component was added or subtracted to achieve different D$ values before the

flux calculation. This created a different 0,, for each layer that also changed for

 

each time step. The values for the surfaces

 

Frequency Distribution of D,
300’ for Depth=20m 1 represent differences in the sediment likely
250 at deposition, and the changes with time
g 3:: correspond to alteration expected during
1% 100 1 early diagenesis. The model was run 500

50

 

0 times to achieve enough results to evaluate
60 70 80 90 100110120130 _ . _ _
0.— n12I10000yr the variation of the Input relative to the

 

 

Figure 7.1. Example distribution of D; varlatlon °f the °“tp“t-
introduced into the model for sensitivity _
analysis. Slnce no measurements of D. are

 

 

 

available, a normal distribution was arbitrarily chosen with enough standard
deviation to establish a range of D8 values wide enough to compare to the model
output. For example, the distribution of D. introduced for surface 3 is shown in
figure 7.1. Its mean is 96.34m2/10,000yr, which is very close to the calculated

value of D. at 20m, 96.07. The standard deviation is about 10% of D3, which

41

 

Frequency

120

80 *
60
40
20

 
  
    
  

0
20.2982 20.2988 20.2994

1Ma

 

22.985 22.9875 22.990

120
100
80 -
60 .
40
20;
0
49.912

110Ma

49.918 49.924

12° ‘100Ma
100

80'
60
40
20 -

0
319.735

319.750
Depth— meters

319.765

 

 

Figure 7.2. Distribution of depth of
bounding surface 3 resulting from

variation in D; in the model.

 

 

gives a range of 62.7 to 125.5. The
resulting variation in depth is shown in
figure 7.2 and table 7.1. Note that the
mean for each time matches the depth for
surface 3 in table 6.2.

The standard deviation of each
layer’s depth is shown in figure 7.3. Each
line represents the standard deviation of the
bounding surfaces at a particular time step;
four times are listed on the graph. The
depth of surface one is based on pelagic
clay deposition and does not incorporate
diffusion, so its standard deviation is zero
for all time steps. For the other surfaces,
the standard deviation increases through
time. Since the average values of depth

and D; for each layer are different,

 

 

Table 7.1. Statisties for analysis of sensitivity
of bounding surface depth to variation in Us.

 

 

 

42

evaluation of them for all . .1

 

 

 

 

 

 

 

 

 

 

 

Standard Deviation of Layer Depth
layers together is not
appropriate. Bounding 6 1— a? ‘ V — 130$]
' 'i . —— 1 M
surface 3will beanalyzed .6 51 1| , . _ 1111:
because it is the first g 4 ” J
._ 1 ‘
surface surrounded by g 3 5; ~
2 ‘2 *
diffusion influenced g 2 1:!
8 .5
surfaces. ‘0 1 .. a _
Since the values for 17 ““7— . . ‘7".— __{"_—.“’“T‘“
; 0 5 1 1 2 2 3 3 4 4 5
D. and bounding surface 1 3000609 Surface Number

 

 

 

 

 

 

 

 

depth are different by "ear” Figure 7.3. Standard deviation of depth of bounding
surfaces for 500 realizations incorporating variation in D3.

 

an order of magnitude,

 

 

direct comparison of the standard deviation may not be the best assessment.
The coefficient of variation is based on the standard deviation but is normalized
by the mean. Regardless of which is evaluated, the variation in depth is at least
four orders of magnitude less than the variation in D. (table 7.1). This indicates
that this model of dissolution is not very sensitive to the diffusion coefficient
through sediment.
Activity

The difference in speciation of Ca2 at shallow sediment depth versus in
deep sediment can be assessed by looking at the activity coefficient for the pore
water solutions. All of the available ions at site 603 were used. The shallowest

depth where several ions were measured was 36.75m and the deepest was

43

1076.15. Using PHREEQC to evaluate the solutions gave activity coefficients for
Ca” of 10""579 at 36m and 10°532 at 1076m. These were inserted into the model

by multiplying the concentration, equation 2.3, by the coefficient:

7.1 C(x) = 7 (Cum -(Crange 14(1)) 'Y =activity coefficient

The resulting gradient equation is:

7.2

The model was modified at line 28 where the concentration gradient is calculated
within the flux equation, and results were found with 36m and 1076m coefficients.
Graphically the difference between the shallow and deep models is
imperceptible, and the depth of bounding surfaces is identical except at very high

resolution. The change in layer thickness (figures 7.4 and 7.5) is less than for
the original model. This is expected because the activity of Ca2+ is less than its

concentration. It was not included in the original model because measurements

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

for many of the ions

Surface Initial Depth at 1Ma Depth at 100Ma
number Depth(m) yfor36m yfor1076m yfor 36m yfor1076m ,
1 0 2.970 2.970 299.970 299.970 '" the 9°” water
5 40 42.969 42.969 339.952 339.952 ,
10 90 92.969 92.969 389.935 389.934 were "0t 3V3"ab'91
15 140 142.969 142.969 439.921 439.920 , ,
20 190 192.969 192.969 489.908 489.908 and the aCtIVItY
25 240 242.969 242.969 539.898 539.897 .
30 290 292.968 292.968 589.889 589.888 coeffiment W00“
35 340 342.968 342.968 639.881 639.880
40 390 392.968 392.968 689.874 689.873 have introduced
45 440 442.968 442.968 739.867 739.867
50 490 492.968 492.968 789.862 789.861 unwarranted error.
Table7.2. Depthofselected bounding surfacesfnom models
including activity coefficient for shallow sediment and for deep
sediment, y for 36m is 10*"579 and y for 1076m is 10415”.

 

 

 

Figure 7.4. Depth of
bounding surfaces for

layers initially 10 m

thick to 500m depth
through 100 million
years with activity
coefficient from 36m.

 

 

 

Figure 7.5. Depth of
bounding surfaces for
layers initially 10 m
thick to 500m depth

through 100 million

1078m.

years with activity
coefficient from

 

 

 

 

with Activity Coefficient from 36m

Layer Depth for Sediment to 500m Depth

 

 

 

 

 

0 10 20 30 40 50 60 70 80 90 100

Time in Ma

 

 

Layer Depth for Sediment to 500m Depth
with Activity Coefficient from 1076m

 

 

 

 

 

40 50 60 70 80 90 100
TimeinMa

010 20 30

 

 

45

 

Change in Layer Thickness for Sediment to
500m Depth with Activity Coefficient from 36m

   

._ ' \ I 1 1
1 \~ ‘ ‘4
‘\‘ \

 

 

 

 

Figure 7.6. Change in
thickness of layers
initially 10 m thick to
500m depth through
100 million years with
activity coefficient
from 36m. Each
calculated value is the

 

 

 

 

 

 

('11
.
.

-10-',

-15

 

Change in Thickness- pm

-20 '

 

 

J l l 1 L l I L 1

5
0102 30405060708090100
TimeinMa

 

 

 

g change in thickness in
, microns for a 100,000
a + year period.
-10 - ~
5
O
E
l.-
.E -15 > 1
0
U)
C
2
o -20-
' 01020 30405060708090100
Time in Ma
Change in Layer Thickness for Sediment to Elects 7-76fclnan99 in
' ' ' ' I ness ayers
500m Depth Wlth ActiVIty Coeffi6lent from 1076m inmaw 10 m thick to
500m depth through
100 million years with
activity coefficient

from 1076m. Each
calculated value is the
change in thickness in
microns for a 100,000
year period.

 

 

 

46

 

 

Porosity

Physical mechanisms indicate that porosity should consistently decrease
with depth, but measurements show irregularities (figure 5.2). Some of this can
be attributed to variation in the sediment at deposition. The highest porosity
measurement was 88.07% at a depth of 24.42m, and the lowest porosity
measurement near the same depth (0 to
50m) was 50.20% at 28.66m. To investigate

the error that could be caused by this, the

 

 

 

 

 

 

 

 

 

 

reduction in thickness was calculated using a
Table 7.3. Variation in modeloutput
{gluexahrewf'ore 23$:ng hypothetical cell with bounding surfaces at
bounded by 24m and 29m.
24m and 29m.
Three porosity values were
6° 1 ' ' 7 . .
50 1 used in separate calculations: the
3 40 -5 minimum, the p(x) prediction, and the
C
0
g- 30 ” maximum (table 7.3). The changes in
20 «~
“ 10 thickness for the first 10,000yr
o , , , , , . , , increment vary considerably relative to
45 50 55 60 65 70 75 80
each other, but all of them are small
Poroslty
Figure 7.8. ”minim of red .I relative to the 5m thickness of the cell.
values used to estimate the constants in the , _
function of porosity with depth, The total reduction of the cell during

 

 

 

100Ma also varies, but even for the maximum porosity, the removal is less than
one meter. The differences calculated here may be more than the actual

changes caused by the error in porosity with depth because a systematic error

47

was introduced. The actual variation of porosity seems normally distributed and
is shown in figure 7.8.
Pelagic Clay

The sensitivity of the model to pelagic clay accumulation was investigated
by using a rate two orders of magnitude smaller than the original rate. In the
original model, the depth of the layers after 100Ma was dominated by clay
thickness, so a faster rate was not explored, but less clay may allow more
sediment removal. The small rate was equivalent to 30 microns per 1000 years
and resulted in a depth of 3m instead of 300m after 100Ma. Through time, the
change in thickness did not become less as dramatically as in the original model
because the layers were not moved as far from the sediment-water interface.
The total reduction of each layer was about one millimeter from 10cm, which still

does not make a measurable removal.

48

 

 

2.5 “

3.0 *

3.5

Layer Depth for Sediment
to 50 cm Depth with Pelagic Clay
Deposition Rate of 0.03mml1000yr

 

 

 

 

 

0102030405060708090100

Time in Ma

 

Figure 7.9. mpth of
bounding surfaces for
layers initially 0.01m
thick to 0.5m depth
through 100 million
years with pelagic
clay accumulation
rate of
0.03mmf1000yr.

 

 

 

 

 

Change in Thickness— um

Change in Layer Thickness for Sediment
to 50 cm Depth with Pelagic Clay
Deposition Rate of 0.03mml1000yr

.0 7 i r T Y r i r r F “
I

 

 

 

 

I L _.__L__ ..._.L___

010 203040 50 60 7080 90100

Time in Ma

 

 

l-"igUre 7.10. Change in
thickness of layers
initially 0.01 m thick to
0.5m depth through
100 million years.
with pelagic clay
accumulation rate of
0.03mml1000yr.
Each calculated value
is the change in
thickness in microns
for a 100,000 year
period.

 

 

 

49

 

 

Sediment-water Interface Model

Since the sediment at the sediment-water interface is exposed to open
water, the concentration of Ca” immediately adjacent to the grain surface will be
the same as the overlying water. On ocean floor below the CCD , dissolution will
be controlled by the rate of detachment (surface reaction) of species from the
mineral surface (Drever 1982). This is not included in the primary model
because its purpose is to investigate the potential importance of molecular
diffusion, and additional features may obscure the results. Usually clay
deposition would remove the carbonate sediment from exposure to the overlying
water, but some areas within the pelagic Atlantic may not experience clay

deposition. For instance, a temporally persistent current could keep clay from

 

5 %cpercent %this performs the minimum thickness calculation for b

15 Do=1.701*10"2;%units: m"2/10000yr

16

16a %kinetlc dissolution parameters, rate=kk*(1-om)*nk
16b kk=100;om=0.84;nk=4.5;

16c %units: r=mmollm*2day

16d r=kk*(1-om)*nk;

160 krate=r'10‘-3*365.242’10‘5;%mollm“2*1000Oyr

17 %final will be a matrix of depths of the layers, each column represents a time step

28 flux(ia)=(Do*kc*Crange*exp(-kc"x))l(1-log((Pmin+Prange*exp(-xlkp))"2));
28a Weaseign flux for top of column

28b if lastdep(ia)-=0

28c flux(ia)=krate;

28d end

29 end

30 final(1,iy+1)=b(1);%+0.03*(iy);

 

 

Figure 8.1. Modifications to the model code for kinetic dissolution from the sediment-
water interface. Additions are shown in bold.

 

 

 

50

depositing, even at low velocity. To simulate this, the flux at x=0 is redefined
using the rate equation for dissolution of carbonate sediment due to
undersaturation (Kier 1980):

8.1 rate = lit,t (l - Q)"

The modified model code, figure 8.1, includes the rate equation and its constants
inserted between lines 16 and 17 of the original model. If the saturation state of
the overlying water does not vary with time, the flux from exposed carbonate
sediment at the sediment-water interface is constant. The constants for flux at
the sediment-water interface were taken from the work of Kier (1984), Berelson

et al (1990) and Berelson et al (1994):

8.2 rate = 100(1 -0.s4)‘-’

 

itk =100 mmollmz*day
I 9 =0.84
rate = 0.026 "2mm n ‘45
m a
8 3 mol
- rate = 957-7—7—
m - 10 yr

The rate of dissolution is calculated in line 16d, and is converted to the

model units of £—

2

m .154), in line 16a; this value is used for the duration of the
model. Lines 28b to 28d insert the modified flux if the depth of an interface is
zero. A % was added to line 30 before the addition of 0.03(iy) to remove clay
deposition, and the rest of the model code is unchanged.

The results from an initial column that is 50m deep with layers 1m thick

show an additional hindrance to surface reaction dissolution (figure 8.2).

According to DSDP measurements, carbonate sediment in the Atlantic contains

51

 

Layer Depth for 85% Carbonate Sediment with
Kinetic Dissolution from the Sediment-Water interface

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11

on
at
’ 1

l

 

i

 

1
l
1

\

 

fi
0
it
1
l
l
’1

.11

 

 

 

 

 

.—
t—
t—

 

 

012345678910
TimeinMa

 

 

Figure 8.2 . Depth of
bounding surfaces for

layers initially 1m thick
through 10Ma (note
the change in time
sale) with reaction
limited dissolution from
the sediment-mater
interface.

 

 

 

 

Layer Depth for Pure Carbonate Sediment with
Kinetic Dissolution from the Sed’ment—Water Interface

 

 

 

 

 

Time in Ma

 

 

Figure 8.3 . Depth of
bounding surfaces for
layers initially 1m thick
through 10Ma with
reaction limited
dissolution from the
sediment-water
interface assuming
pure mrbonate
sediment.

 

 

 

 

 

 

Layer Depth for Pure Carbonate Sedinent with
Kinetic Dissolution from the Sed’ment-Water Interface

 

 

 

 

01020304050607080?moo
TimeinMa

500

 

 

 

Figure 8.4 . Depth of bounding surfaces for layers initially
10m thick through 100Ma with reaction limited dissolution
from the sediment-Mar interface assuming pure carbonate
sediment.

 

 

 

an average of 85%
CaCOa. This means that

. 15% of each layer would

remain after all of the
carbonate had dissolved,
preventing the next lower
layer from being exposed
to open water. The
effect of this can be seen
at about 1Ma. The top

layer thins to its

minimum thickness, than
dissolution virtually stops

as the surface reaction

mechanism is no longer active. Note that even nearly pure carbonate sediment

would still leave residual clay at the surface which would remove the carbonate

from the undersaturated water . Changing the sediment to 100% carbonate

allows reaction controlled dissolution to continue and complete removal of layers

(figure 8.3). By designing conditions that allow dissolution due to undersaturation

to persist, 9m of sediment was dissolved in 10Ma. Looking at a 500m column

through 100Ma (figure 8.4), reveals the potential of this mechanism. The first

20m of sediment is removed at 21Ma, and nearly 100m of sediment is eliminated

in 100Ma.

53

Conclusions

In the original model, the reduction in thickness of the individual layers is

very small, even in the top layer. In each column the decrease in thickness of

this layer over 100Ma is approximately 1.5% (table 9.1). The removal from the

entire sediment column for each simulation is nominal relative to its magnitude;

less than one meter was dissolved from 50m of sediment and less than 2% was

removed from any column. Even accounting for percent carbonate in the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Top Layer Whole Column
Initial Final Percent Initial Final Percent
Thickness Thickness Dissolved Thickness Thickness Dissolved
meters meters
10 9.86 1.40 500 497.52 0.50
1 0.985 1.50 50 49.46 1.09
0.01 0.00985 1.50 0.5 0.49 1.52

 

 

 

 

Table 9.1. Dissolution from the top layer of the three simulated
sediment columns.

 

 

sediment, dissolution by
diffusion would not
remove a significant
proportion of the
carbonate from a natural

layer.

Imposing persistent reaction controlled dissolution from the sediment-

water interface created significant sediment removal. However, the necessary

conditions that would allow this restrict the potential locations where it could

happen. Pelagic clay deposition must be eliminated, which is conceivable, but

the sediment also has to be practically pure carbonate. Dissolution controlled by

surface reaction would proceed until the clay residue was continuous across the

sediment surface. The required thickness of clay would depend on the zone of

mixing through the clay of the pore solution and the overlying water (which is

difficult to determine, but usually on the order of a few millimeters (Chapra

1997)). But, if all of the sediment at the top of the sediment column was nearly

54

100% carbonate, notable thickness might be removed before enough clay
accumulated. Most deep Atlantic carbonate sediment is between 85% and 95%
08003 (appendix lll). Using the average accumulation rate of 4.5m per 0.5Ma,
the sediment would have to be 99.78% pure carbonate to leave only 1cm of clay,
which is thicker than the likely mixing length. Even though many measurements
show thinner layers, only a small percentage of clay is required to stop this
process.

Combining diffusion through the sediment with reaction controlled
dissolution from the sediment-water interface might removed enough carbonate
to create a hiatus. Nonetheless, particular conditions would have to be aligned,
so a hiatus by this mechanism would be limited in extent and duration. Perhaps

this is why carbonate persists for millions of years despite undersaturated water.

55

Discussion

Dissolution of deposited carbonate by diffusion through the sediment does
not allow enough removal to create a perceptible hiatus. Other physical
processes need to be invoked to explain their existence. One such mechanism
that could enhance carbonate removal is mineralization of organic carbon. The
rates of decomposition found by researchers (Honjo et al 1982, Berelson et al
1990 and Wenzhofer et al 2001) are similar to the rate surface reaction limited
dissolution (equation 8.3), and carbonate dissolution attributable to breakdown of
organic matter is about half that (Wenzhofer et al 2001). Also, degradation is
restricted to the upper few centimeters of sediment and limited in duration. The
amount of organic carbon which is deposited is very minor relative to CaCOa, and
it would be eliminated before significant carbonate was removed. Plus,
deposition of organic carbon on the ocean floor is primarily restricted to within
30" of the equator and near the continental margins (Jahnke 1996), which limits
the geographical extent of this process.

Bioturbation could expose carbonate to the overlying water, allowing
surface reaction limited dissolution to continue. Removal of carbonate is directly
related its exposed area at the sediment surface and that area is proportional to
the percent carbonate in the sediment (Kier 1984). The clay content is enriched
by dissolution of CaCO3, but fresh carbonate could be introduced by bioturbation.
The mixing zone from bioturbation is approximately 80m (Kier 1984), and

average deep Atlantic carbonate sediment is 85% pure carbonate. It would take

56

only 53.3cm (Bent/15%) of sediment to fill the mixing zone with non-carbonate
sediment.

Another possibility is that the dynamics of alkalinity in the pore solution
allows additional dissolution of CaCOa. To explore the complexity of this system,
extensive characterization of the fluid would be required. Also, change in ocean
chemistry in the past could have created greater dissolution. This could not
explain hiatuses at regional and local scales, nor the variation in duration.
Finally, oceanic conditions could have caused lack of deposition, but different
conditions to effect hiatuses of both local and global extent are difficult to

contrive.

57

Appendix I

Sediment Accumulation Data

DSDP sites that have age-depth relationships in SYNATLAN database at

http:llwww.geomar.del~tw0lfIListADM0dels.html by Wolf-Welling et al (1997). Each

of these sites is on oceanic crust under at least 4000m of water.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Leg] Sitel Latitud31 LonlitudeIWater Depth
11 99 23°41.1420 73°50.9880w 491
11 100 24°41.2680 73°47.9820w 583:3]
11 101 25°11.9280' 74°26.3100w
11 105 34°53.7180N 69°10.3980w 5251
11 106 36°26.0100 69°27.6900w 4500
12 119 45° 1.902010 7°58.4880w 4447
36 3281 49°48.6720'S 36°39.5280w 5095
39 354i 5°53.9520'Nl 44°11.7780w 4045
39 355 15°42.5880'S 30°36.0300'W 4901
39 373931209 35°57.8220'W 4962
40 361 35° 3.97205 15°26.9100‘E 4549
41 370 32°50.2500N 10°46.5600'W 4214
43 382 34°25.0380‘ 56°32.2500w 5526
43 385 37°22.1700 60° 9.4500w 4936
43 386 31°11.2080 64°14.9400'W 4782
431 387 32°19.2000N 67°40.0020w 5117
441 391 28°13.7280N 75°38.7620w 4974

45146 396 22°28.8780'N 43°30.9480w 4450
481 400 47°22.9020'N 9°11.8980'W 4399
50 416 32°50.1780~ 1048me 4191

51 417 25° 6.6300 88° 2.4780'W 54681

5153 4181 25° 2.1000N 68° 34me 5514
71 513 47°34.9920s 24°38.4000w 4373
72 515 26°14.3280'S 36°30.1680w 4250
73 520 25°31.39808 11°11.1420w 4207
75 521 26° 4.42809 10°15.87oow 4125
7 52 26° 6.8400'8 5° mm 4441
73‘ 52 203313209 2°15.0780w 4562
7 52 202905208 3°30.7380'E 47961
74| 527 28° 2.49005 1°45.7980'E 4428
75 530 19°11.2620’S 9°23.1480‘E 4629
73 542 15°31.0200Nl 58°42.7 5016
7 543 15°42.7380'N 58°39.2220W 5633:
80 550 48°30.9120' 13°26.3700'W 4420
931 6031 35°29.6580N1 70° 1.6980W

 

 

Table i.1. DSDP sites
used for accumulation
rates.

 

 

 

58

 

Selected Atlantic DSDP Site Locations

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure i.1 Lowtions of DSDP sites with carbonate sediment on oceanic crust under at least
4000m of water. Site information given on previous page.

 

59

 

 

Age-Depth Relationships

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

for the sites used from SYNATLAN
0-- ............................ T ............ 0 'W r T
E1001
1.1 ”I“ ........
um’ sit100
- e
”$1899; . m L 1 1
II 20 Ill ill 91 ill 70 w ill till 110
o'.v j—w o .................................... WW
.1
35m 501
8
3119101 5118105
low 4 L lollo . - 1
II 20 III ill 8) ll 20 III 60 80 m
00.2,. W— o 4 '\/'”"'
EM» M1
2
1'1
1‘;er mi ............
. sile119
1mm1w _l 1 1 m r 1 J j 1
ll 5 III 15 20 25 12 II 16 18 20 22 24
age-Ila age-Ma

 

 

Figure i.2 Depths migned by SYNATLAN for age at 0.5Ma increments (dotted) and the
corresponding accumulation rate (dashed) calculated in rnI0.5Ma. Site information given on

previous page.

 

60

 

 

Age-Depth Relationships
for the sites used from SYNATLAN (cont)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0... " ~nvfi
an. 1
,4: .

O.
3“
58328

n 1 r i

o lo 20 30 il

l... 1,. ..5
E . ....................................
£20
1111
U ’sile356
m L 1 l

o 20 ill ill or

lI-__ ..-w
E . .........
1Eillll
.9111».

0 5119361

its . . .

it it to ill in

on ' fl “

5101/

5
9m»

'U '1 .........................................

$36382

m L l

r 2 i a II III

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

01.4-4 -
5001 1
5m“ ..................

1m . . . .
o 20 ill so all roll
0 J1 44
m1 1
sile358
‘” L 1 1 J
20 30 ill to ill
a - 4
till
200 ...................................................
19cm
m 1 l
13 14 15 ii 11 ll
0. - ......
w.
is»
519385
150

I l l 1 I

 

61

 

 

Age-Depth Relationships
for the sites used from SYNATLAN (cont)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.... 1— .... --
E
19’
0
'0
$386
1“ l 1 l l 1
II III 20 ill 40 50 ill
1),, .-. .
E
in»
s
U 538391
1” l 1 1 1 #
13141516111819
lir— r .—
E ..
is
s
0
515400
MI 4 ‘ °
II 20 III ill 0 till
0 ..2 ..
E
a”
s
0
do“?
m L l L I
ll 20 40 ill II m
age-Ma

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 WV- _
am.
“31038? .................
m l L 1

lo 45 to 55 ill 65
o ..... . \
loll»
m ......

sile396

o 2 i i ll Ill
0 .1 -..

W.

98416
1m .

o 20 ill so ill loo
0 .............

1001

”8110418 ,

o to iii an in roll

age-Ma

 

62

 

 

Age-Depth Relationships
for the sites used from SYNATLAN (cont)

 

 

do h—m
depth-m pt

depth-m

é

 

 

§§o§

sag

 

site 513

 

1020304050

 

 

...,
........

 

 

15

 

 

 

 

 

....

 

 

 

70

 

 

 

 

 

 

 

 

 

 

 

 

0y .... ,.
5M1
sle515
1m 1 1
0 20 40
0 m ..
50.
1m ......
sile521
150 ' °
0 10 20
0,, .._..,
100~
sile523 .......
m 1 1 1
0 20 40 60
0... - ..5
2w.
sile527
4w 1 1 1
0 20 40 60
age-Ma

 

63

 

 

 

 

 

 

Age-Depth Relationships
for the sites used from SYNATLAN (cont)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

llw - .. o .
E \9/
501
i m
“1M1
4mm5§o # 1 1 1 “fie“? 1
o 20 it to lo loll 120 o 2 i ll 10
0.... 1 ow
Em»
.4 111 '
9111. """ m.
1: sile54
3 5118550
m 1 1 1 m 1 ..........
II 20 to ill in o 21 ill lo 100
1....- -. are-Ma
E
1‘11“1
0
D
steam
m r l 1
o 21 ill ill ill loll
agelllli

 

 

Appendix II
Calcium Concentration Data

Since mixing of solutions is not linear with respect to saturation, using data
from several sites is not appropriate, so a single site was chosen. 0f the deep
Atlantic sites that are on in the pelagic basin, 29 have pore water Caz“
measurements, see appendix l, and site 603 has markedly more measurements
than any other site. The data came from three holes at the site and were used to
fit the function for Ca” concentration with depth. Minimization of the sum of
squared residuals was used to find the constants for the function (figure 5.1):

.e—kc-X)

2.3 C(x) = 0,,m -(C C111... :2“ moi/m3

C...n =1.78 mollrn3

- e -3 -1
4.1 C(x)=24_2£'_(:_I_(22.4M0’.e-o.0027s.-l.,) kc -2.7510 m
in

mg:

3
in

Then the derivative is:

2.4 ; = kc ' Change ' 64"):
4'2 99— : 0.00275m'I 22.4310; ..3—00027511145
8x m

65

 

 

Interstitial Pore Water Ca” Concentration

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

for DSDP Site 803
[file 1Depth to 0- lFitted Residual
Sample- m mmlL Value Squared
6030 36.75 3.36 3.941 0.32
6030 85.35 6.01 5.481 0.2
6030 90.69 6.56 6.741 0.03
603C 123.85 8.59 8.27 0.10
6030 171.85 9.31 10.241 0.87
603 213.05 12.46 11.741 0.54
6030 219.85 11.21 11.97 0.581
6030 261.85 13.79 13.31 0.231
603 269.15 13. 13.53 0.00
603 318.65 16.17 14.89 1.63'
6030 322.45 15.36 14.99 0.15
6030 354.25 14.85 15.76 0.84
603 368.15 15.69 16.08 0.15
603 454.55 18.22 17.81 0.17
603 594. 21.12 19.85 1.60
603 645.051 18.87 20.43 2.43
603 670.85 20.31 20.69 0.14
603 721.87 25.11 21.15 15.87
603 800.16 20.51 21.75 1.53
6038 902.85 19.45 22.36 8.46
6038 938.05 261 22.53 12.03
6033 989.05 20.7 22.75 4.22
6038 1031.05 16.1 22.92 46.451
6038 1076.15 22.12 23.07 0.90
6038 1178.45 24.62 23.35 1.60
6038 1268.35 25.41 23.55 3.44
8 1298.65 27.22 23.60 13.10

Table ii.1 Interstitial pore water measurements from

DSDP for site 603. Predicted 0a2+ concentration

from equation 4.2 in which the constants were fitted

from minimizing the sum of the residual squared

values.

 

 

 

66

Appendix III
Porosity Data

Porosity measurements from several DSDP sites were used. The sites
were selected to be carbonate sediment in the deep Atlantic basin. Deep Atlantic

basin was ensured by checking

 

the water depth, crust type, and 3° 1’
physiographic feature.
Carbonate content was
checked by looking at the
percent 030%, which needed

 

 

 

 

 

 

 

 

to be at least 50% carbonate. . 50 60 70 80 i 90 l 1 100
Percent Carbonate

The average was 85.0%, and

the distribution is shown in gfiiic-aImFWonMdm smut. “mes for deep

figure iii.1.

The data from all appropriate sites were compiled, and the constants for
the porosity with depth relationship:

'1

'1; =75.0

2.11 p(x)=p.... +p....,.-e 5:: 41115
p,.,,. =18.5
lr. =36.4rn

4-4 p(x) = 58.5 + 16.5 . e347

were found by minimization of the sum of squared residuals (figure 5.2).

67

 

 

Table iii.1. Porosity Measurements of Deep Atlantic Carbonate Sediment from DSDP

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sits] Depth- m] Porosity] Site] Depth- m] Porosity] Site] Depth- m Porosity]
515al 76.05 60.88] 17h 115.56 49.51 116 309.2 541
11 76.16 57.61 355 116.95 62.371 116 312.16 50.81
515a 78.9 61.341 355 117.02 80.031 515b 312.68 66.9]
126 79.65 66.2] 17b 117.06 541 335 318.06 55.83]
116a 82.66 58.61 17b 118.56 50.5 515b 331.23 67.06]
17b 86.86 52.251 176 120.06 53.25 515b 334.73 73.31
51 87 63.211 335 130.95 52.67] 5156 334.7 69 .51
17 88.16 52.861 3341 137.25 581 5156 348.99 69. 781
51 88.3 64.391 140.55 581 5156 356 68. 511
12 88.65 48.251 328 141.32 72.161 116 359. 49 56.61
11661 88.661 54.41 32 142.41 72.731 116 362. 501
515a1 90.181 63.891 18 142.76 56.291 515b 368.27 68.351
1165 90.441 64.5 326 142.6 77.05 5156 379.16 68. 46]
17b 91.16 55.431 328 143.01 73.331 5156 362.62 67. g
335 91.45 61.171 328 1 72.921 515b 395.76 65.42]
51 91.92 62.241 3341 148.55 60.33F 5156 400.62 65.811
176 92.91 521 18 154.86 641 11 410.66 efl
515a 93.1 60.281 12b 157. 45.881 5156 412.3 65.131
116a1 93.44 57.61 12b 157.44 72.25 5156 415.96 62 871
515al 94.19 65.87F 11 159.51 56.21 5156 421.95 70. 781
176 94.56 50.41 18 161.36 55.61 5156 422.84 66.33]
328] 94.77 79.481 116] 162.36 54.21 515b 444.85 64.85
116a1 94. 94 54.5 162.55 63.29F 5156 455. 66.381
17b 95. 76 541 116 166.86 60.41 116 459.18 54.21
51 95.91 62.591 1 168.9 58.671 11 . 462.15 511
328 96.37 77.81 334 168.9 621 515b 464.41 66181
51 97.1 60.1] 334i 184. 631 515b 471.9 66.781
17b 97.26 52.291 515 193.42 70.65 5156 483.341 65.191
126 97. 41 691 328 193.85 68.45 5156 502. 64] 65.14]
51 98.41 60.85 32 193.86 70.281 5156 507. 761 86.631
17b 98.76 51.331 515b 196.7 73.271 515b 516.8 55.77]
5156 99.22 60.83r 200.45 64.29] 5156 528.52 52. 891
515a 100 60.051 515 201.76 72.521 5156 537.5 52. 751
515b 100.1 60.331 5156 203.36 69.191 515b 541.71 51.69]
515a1 101.1 58.131 515b 203. 66.95 5156 555.92 50.65]
17b 103.26 54.291 116 210.91 52.21 5156 564.21 50. 25
51 104.58 59. 711 118 212.21 50.61 515b 574. 49.791
170 104.96 50.67] 116 215.15 5651 5156 579.52 50.11]
515a] 106.06 57.021 3341 219.45 60.831 515b 597.71 49.971
51 106.08 58.241 335 21.45 56.171 5156 599.61 49.521
17b 106.46 53.75 227.45 63.831 515b 612.57 47.921
51 107.58 57.8] 328 239.65 64.45 515b 619.82 41.041
17b 107.96 521 334 241.65 581 515b 628. 07 41.27]
116 109.25 58.41 11 259.36 54.81 116 662 86 58.21
17b 109.46 521 116 264.26 55.2F 116 668.59 44.81
126 110.16 701 355 267.5 57.721 116 684.86 47.41
17b 110.96 52.51 515b 270 70.791 1161 714. 95 50.41
17b 112.71 54.41 5156 283.261 70.871 1

 

 

 

 

 

68

538.3
A

29.
30.
31.7
32.1
32.
33.
33.
34
34.
35.
36.
36.
36.
37.
37
37
38.
38.
39.1

.3
#&
—l

 

69

Appendix IV
MATLAB Codes

The peripheral model codes not in the text are listed here.

 

original=b;
n=length (original);
%m will refer to the last column of depths
m=size(final,2);
for iy=1:m
for ii=1:n-1
thick(il,iy)=final(ii+1,iy)-final(il,iy);
end
end
for iy=1zm-1
chthick(:,iy)=thick(:,iy+1 )-thick(: ,iy);
end

 

 

 

dthick was used to calculate the change in thickness for each layer at every time

step.

 

carbpercent=0.85;
=length(b);
for ib=1zn-1
minthick(ib,1)=(b(ib+1)-b(ib))*(1-O.85);
%min thickness=original thickness*percent noncarbonate
end

 

 

 

cpercent calculated the minimum thickness of a layer based on its original

thickness and clay content. It appears in line 5 and 41 of the original model.

 

16 sigma=0.05*Do;

27a Ds=Dol(1-iog((Pmin+(Prange)*exp(-xlkp))"2));
27b Dsrand=randn‘sigma+Ds;

28 flux(ia)=Dsrand*(kc*Crange*exp(-kc*x));

 

 

 

carbrand was the original model modified to include a random variation in D. for

each layer of sediment.

7O

 

%This will run the model with random distribution of D5 N times

N=500;

for i=1:N
carbrand;
Ma10th(:,i)=finai(:,11);
Ma(:,i)=final(:,101);
Ma10(:,i)=finai(:,1001);
Ma100(:,i)=final(:,10001);

end

for j=1 :51
avMa10th0)=mean(Ma10th0,1:N));
stillla10th0)=std(Ma10th0,1:N));
avMa0)=mean(Ma0,1:N));
stMa0)=std(Ma0,1 :N));
avMa100)=mean(Ma100,1:N));
stMa100)=std(Ma100,1:N));
avMa1000)=mean(Ma1000,1:N));
stMa1000)=std(Ma1000,1 :N));

end

 

 

 

runs executed the carbrand model multiple times and saved results for 0.1Ma,
1Ma, 10Ma and 100Ma. This code also evaluated the mean and standard

deviation of the saved results.

71

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