- Email: [email protected]
On sedimentation rates and porosity
Marine Geology, 35 (1980)M11--M16 Mll © Elsevier Scientific Publishing Company, Amsterdam - - Printed in The Netherlands
Letter Section ON SEDIMENTATION RATES AND POROSITY*
E. W I L L I A M
BEHRENS
Geophysics Laboratory, Marine Science Institute, The University of Texas at Austin, Galveston, Texas 77550 (U.S.A.) (Received August 15, 1979; revised and accepted January 7, 1980)
ABSTRACT
Behrens, E.W., 1980. On sedimentation rates and porosity. Mar. Geol., 35: M l l - - M 1 6 . Apparent sedimentation rate differences between core samples m a y be simply artifacts of porosity differences (a real example is provided). To avoid this problem, vertical thickness per unit time sedimentation rates (e.g. cm/1000 years) should be calculated on a uniform porosity basis. The relationships between porosity and mineral density, water density, bulk density, water contents, and salinity are reviewed; and simple, working equations for determining the necessary parameters are given as well as a choice of equally simple equations for reconstructing a core to a constant, reference porosity.
INTRODUCTION
General Sedimentation rates from cores are usually determined by dividing the distance between t w o radiometrically or paleontologically dated horizons by the difference between their ages. As such, the core interval represents minerals and water in an u n k n o w n ratio. The water c o n t e n t decreases through time due to com pa c t i on, so a core of sediment deposited at a constant rate would show continuously increasing rates towards the present. With such apparent but false variations within a core, comparisons between cores would, obviously, have considerable uncertainty.
Example Data from two cores are given as an example o f the confusion or misconceptions which can occur by using data of this sort. Core IG27-2 was taken in the Orca Basin on the lower continental slope (3320 m water depth) o f the Gulf o f Mexico, and Core IG27-4 was taken in 1790 m o f water on *University of Texas at Austin Marine Science Institute Contribution No. 373, Galveston Geophysics Laboratory.
M12
the open slope adjacent to Orca Basin. Four radiocarbon ages from carbonate material, the depths of the samples, and the apparent rates of sedimentation are shown in Table I. These data would suggest that the basin received sediment at a rate of at least twice that of the open slope; TABLE
I
Sedimentation rates from core depths and radiocarbon ages Depth I (cm)
Age (B.P.)
Sedimentation t rate (cm/1000 yr)
Depth 2 (cm)
Sedimentation 2 rate (cm/1000 yr)
Core IG27-2 (basin core) 0
present
0 61.3
485
7,910
570
10,320
745
17,380
12.9 101.8
53.3
11.37 129.2
24.8
11.32 209.1
Core IG27-4 (slope core) 0
present
0 13.0
155
11.25
11,920
134.1
1Based on original observations. 2Recalculated to a constant porosity of 50%. o IOO
me
IG27- 4
200
o•
3OO 4OO
.Z i
° ' ~ " ' " ~ IG27- 2
70()
900
•
I000 110030
I
40
°1
50
I
60
I
70
L
80
90
WATER CONTENTBY WEIGHT(%) Fig. 1. Weight percents of water in two lower slope cores from the Gulf of Mexico. Water content = weight of saline water/weight of wet sediment.
M13
and that a tremendous increase in sedimentation rate t o o k place within the basin during the Holocene. Fig. 1 shows profiles of weight percent water in each core. Interstitial water salinity in Core 4 was constant at 35 ppt, b u t in Core 2 it decreased from a b o u t 236 p p t at the core top to 112 p p t at the core base. Using the water contents and salinities (latter to estimate densities), the cores were mathematically reconstructed to a constant 50% porosity and the sedimentation rates were recalculated (Table I). The results show that the differences between the basin and the surrounding slope essentially disappear except for a slight increase in the 7900 B.P. to present part of the basin core (2). Actually if a graded bed originally from 234 to 290 cm in Core 2 is considered an instantaneously deposited turbidite, this apparent increase becomes a slight decrease (to 11.0 c m / 1 0 0 0 yr). METHODS AND DISCUSSION To avoid gross distortion of real sedimentation rates (as in the case just illustrated) core thicknesses or depths can be converted to a reference condition of uniform porosity in the following manner. Considering a section of core as a cylinder with volume (V) = ~r2h where r is the radius and h the thickness, a change in volume would be related to a change in thickness by ( V o - - V n ) / V o = 1 - - ( ~ r 2 h n ) / ( ~ r 2 h o ) = 1 - - h n / h o where subscripts o and n indicate the original and the reference conditions respectively. If this change is brought about simply by removal or addition of water, the mineral volumes before and after the change must be equal, i.e., (1 - - P o ) V o = (1 - - P n ) V n where Po and Pn equal average observed porosity and reference porosity respectively (expressed as fractions). Substituting and solving for the new thickness gives: hn = ho[(1 - - P o ) / ( 1 - - P n ) ]
(la)
Hamilton (1976) derived the same equation (solving for ho) to remove the effects of consolidation and reconstruct cores to their original thickness (that with the porosity of surficial sediments) from a similar relationship given by Tschebotarioff (1951) using void ratios instead of porosities. Since Po would c o m m o n l y be determined by averaging porosities at the top (Pl) and b o t t o m (P2) of a section of core, Po = (P1 + P2)/2 and hn = h o [ 2 -- (P, + P 2 ) ] / 2 ( 1 - - P n )
(lb)
Using 50% for a reference porosity (Pn = 0.5) provides the simplest form of this equation: hn = h o [ 2 -- (P~ +P2)]
(lc)
An individual core can then be reconstructed on a constant porosity basis by calculating h n s for core segments between samples with porosity determinations. In the case illustrated, the segments were generally 20 or 40 cm.
M14 Porosities m a y be computed from bulk density or water loss measurements. From the relationships: Bulk density (B) = total weight (W t)/total volume (V t), W t = solid weight (Ws) + liquid weight (Wl), V t = solid volume (V s) + liquid volume (V I), and liquid and solid densities (Pl and Ps respectively) equal the appropriate weight/volume ratios:
porosity
(P) = V1/V t = (B -- Ps)/(Pl
--
Ps) = (Ps --
B)/(Ps
--
Pl)
(2)
Using the definition: weight percent liquid (wl) = W I / W t (i.e., w 1 + w s = 1): P = WlPs/(WlP s +
WsPl)
(3)
Using an alternative definition of water content (w*) advocated by Inderbitzen (1974) and others: w * = W I / W s (i.e., based on dry weight), P = W*Ps/(p I +
W*Ps)
(4)
The liquids referred to are interstitial waters at their in-situ salinities. Water contents (relative to either total wet weight or to dry weight) based on pure water (e.g., loss by evaporation) can be converted to saline water c o n t e n t simply by dividing by (1 -- S) where S is salinity expressed as a decimal percent (normal sea water S = 0.035). Salinity m a y be determined with a refractometer (Behrens, 1965) on a drop or two of interstitial water squeezed or centrifuged from a small core sample. Then only densities are required to determine porosity from bulk density or water loss measurements. Mineral density (Ps) may be determined precisely by p y c n o m e t r y or other methods given in mineralogy texts (e.g., Muller, 1967; Hurlbut, 1971). Variations in observed mineral densities in several marine environments are discussed by Hamilton (1970 and 1974). Although distinct differences may occur between sedimentary provinces and from bed to bed within a core, within sections of core several tens of cm thick they may tend toward sufficiently uniform values to justify using a constant, c o m m o n density such as 2.65 g/cm 3 (quartz). Sedimentation rate errors that might result from using a single mineral density will be very nearly the same as errors in the density estimate. For example, an error of 0.07 g/cm 3 (the difference between quartz and calcite) would lead to a sedimentation rate error of about 2.5%. Liquid densities (P l) for sea water or sodium chloride solutions can be determined from salinity from standard references (e.g., Weast, 1974). Sodium chloride and sea water values differ by less than 0.5% and would lead to sedimentation rate differences of the same magnitude. The goal of these computations could also be accomplished by conversion of vertical thickness sedimentation rates to mass sedimentation rates.
M15
Although this measure is more useful in some types of investigations (e.g., Swift and Wenkam, 1978), it is often less desirable because the expression mass per unit area per unit time is conceptually and operationally more complex. Different reference porosities may be chosen to reflect different concepts of reconstruction. For example, a low porosity would reconstruct thicknesses to a simulated, deeply buried, compacted condition, and high values might be used to reconstruct to initial conditions. A reference porosity of 50% has the advantage of requiring a slightly simpler calculation. Furthermore, 50% may roughly approximate many natural sediments below the uppermost few meters and thus permit semi-quantitative comparisons with published rates based on unspecified porosities (e.g., Diester-Haass, 1976). CONCLUSIONS
Sedimentation rates calculated from core depths without adjusting to a constant porosity can lead to major misconceptions concerning relative rates of sedimentary processes. Conversion to any reference porosity may be done with eqs. la or lb or to 50% porosity with eqn l c . Porosity can be calculated from eqs. 2, 3, or 4 which require knowledge of mineral density, water density or salinity, and bulk density or water content. Adequate porosities can c o m m o n l y be obtained from only one measurement (bulk density or water content) and reasonable estimates of other, necessary data. ACKNOWLEDGEMENTS
I thank Drs. E.L. Hamilton and S.K. Addy for their reviews and constructive criticisms of the manuscript.
REFERENCES Behrens, E.W., 1965. Use of the Goldberg refractometer as a salinometer for biological and geological field work. J. Mar. Res., 23: 165--171. Diester-Haass, L., 1976. Quaternary accumulation rates of biogenous and terrigenous components on the East Atlantic continental slope off N W Africa. Mar. Geol., 21: 1--24. Hamilton, E.L., 1970. Sound velocity and related properties of marine sediments, North Pacific. J. Geophys. Res., 75: 4423--4446. Hamilton, E.L., 1974. Prediction of deep s e a s e d i m e n t properties: state of the art. In: A.L. Inderbitzen (Editor), Deep Sea Sediments. Plenum Press, New York, N.Y., pp. 1--43. Hamilton, E.L., 1976. Variations of density and porosity with depth in deep sea sediments. J. Sediment. Petrol., 46: 280--300. Hurlbut, C.S. Jr., 1971. Dana's Manual of Mineralogy. Wiley, New York, N.Y., 18th ed., pp. 134--135. Inderhitzen, A.L. (Editor), 1974. Deep Sea Sediments. Plenum Press, New York, N.Y., p. 483.
M16 Muller, L.D., 1967. Density Determination. In: J. Zussman (Editor), Physical Methods in Determinative Miners]ogy. Academic Press, New York, N.Y., pp. 459--466. Swift, S.A. and Wenkam, C., 1978. Holocene accumulation rates of calcite in the Panama Basin. Mar. Geol., 27: 67--77. Tschebotarioff, G.P., 1951. Soil Mechanics, Foundations, and Earth Structures. McGrawHill, New York, N.Y., 655 pp. Weast, R.C. (Editor), 1974. Handbook of Chemistry and Physics. CRC Press, Cleveland, Ohio, 54th ed., Section D, pp. 219 and 222.
Letter Section ON SEDIMENTATION RATES AND POROSITY*
E. W I L L I A M
BEHRENS
Geophysics Laboratory, Marine Science Institute, The University of Texas at Austin, Galveston, Texas 77550 (U.S.A.) (Received August 15, 1979; revised and accepted January 7, 1980)
ABSTRACT
Behrens, E.W., 1980. On sedimentation rates and porosity. Mar. Geol., 35: M l l - - M 1 6 . Apparent sedimentation rate differences between core samples m a y be simply artifacts of porosity differences (a real example is provided). To avoid this problem, vertical thickness per unit time sedimentation rates (e.g. cm/1000 years) should be calculated on a uniform porosity basis. The relationships between porosity and mineral density, water density, bulk density, water contents, and salinity are reviewed; and simple, working equations for determining the necessary parameters are given as well as a choice of equally simple equations for reconstructing a core to a constant, reference porosity.
INTRODUCTION
General Sedimentation rates from cores are usually determined by dividing the distance between t w o radiometrically or paleontologically dated horizons by the difference between their ages. As such, the core interval represents minerals and water in an u n k n o w n ratio. The water c o n t e n t decreases through time due to com pa c t i on, so a core of sediment deposited at a constant rate would show continuously increasing rates towards the present. With such apparent but false variations within a core, comparisons between cores would, obviously, have considerable uncertainty.
Example Data from two cores are given as an example o f the confusion or misconceptions which can occur by using data of this sort. Core IG27-2 was taken in the Orca Basin on the lower continental slope (3320 m water depth) o f the Gulf o f Mexico, and Core IG27-4 was taken in 1790 m o f water on *University of Texas at Austin Marine Science Institute Contribution No. 373, Galveston Geophysics Laboratory.
M12
the open slope adjacent to Orca Basin. Four radiocarbon ages from carbonate material, the depths of the samples, and the apparent rates of sedimentation are shown in Table I. These data would suggest that the basin received sediment at a rate of at least twice that of the open slope; TABLE
I
Sedimentation rates from core depths and radiocarbon ages Depth I (cm)
Age (B.P.)
Sedimentation t rate (cm/1000 yr)
Depth 2 (cm)
Sedimentation 2 rate (cm/1000 yr)
Core IG27-2 (basin core) 0
present
0 61.3
485
7,910
570
10,320
745
17,380
12.9 101.8
53.3
11.37 129.2
24.8
11.32 209.1
Core IG27-4 (slope core) 0
present
0 13.0
155
11.25
11,920
134.1
1Based on original observations. 2Recalculated to a constant porosity of 50%. o IOO
me
IG27- 4
200
o•
3OO 4OO
.Z i
° ' ~ " ' " ~ IG27- 2
70()
900
•
I000 110030
I
40
°1
50
I
60
I
70
L
80
90
WATER CONTENTBY WEIGHT(%) Fig. 1. Weight percents of water in two lower slope cores from the Gulf of Mexico. Water content = weight of saline water/weight of wet sediment.
M13
and that a tremendous increase in sedimentation rate t o o k place within the basin during the Holocene. Fig. 1 shows profiles of weight percent water in each core. Interstitial water salinity in Core 4 was constant at 35 ppt, b u t in Core 2 it decreased from a b o u t 236 p p t at the core top to 112 p p t at the core base. Using the water contents and salinities (latter to estimate densities), the cores were mathematically reconstructed to a constant 50% porosity and the sedimentation rates were recalculated (Table I). The results show that the differences between the basin and the surrounding slope essentially disappear except for a slight increase in the 7900 B.P. to present part of the basin core (2). Actually if a graded bed originally from 234 to 290 cm in Core 2 is considered an instantaneously deposited turbidite, this apparent increase becomes a slight decrease (to 11.0 c m / 1 0 0 0 yr). METHODS AND DISCUSSION To avoid gross distortion of real sedimentation rates (as in the case just illustrated) core thicknesses or depths can be converted to a reference condition of uniform porosity in the following manner. Considering a section of core as a cylinder with volume (V) = ~r2h where r is the radius and h the thickness, a change in volume would be related to a change in thickness by ( V o - - V n ) / V o = 1 - - ( ~ r 2 h n ) / ( ~ r 2 h o ) = 1 - - h n / h o where subscripts o and n indicate the original and the reference conditions respectively. If this change is brought about simply by removal or addition of water, the mineral volumes before and after the change must be equal, i.e., (1 - - P o ) V o = (1 - - P n ) V n where Po and Pn equal average observed porosity and reference porosity respectively (expressed as fractions). Substituting and solving for the new thickness gives: hn = ho[(1 - - P o ) / ( 1 - - P n ) ]
(la)
Hamilton (1976) derived the same equation (solving for ho) to remove the effects of consolidation and reconstruct cores to their original thickness (that with the porosity of surficial sediments) from a similar relationship given by Tschebotarioff (1951) using void ratios instead of porosities. Since Po would c o m m o n l y be determined by averaging porosities at the top (Pl) and b o t t o m (P2) of a section of core, Po = (P1 + P2)/2 and hn = h o [ 2 -- (P, + P 2 ) ] / 2 ( 1 - - P n )
(lb)
Using 50% for a reference porosity (Pn = 0.5) provides the simplest form of this equation: hn = h o [ 2 -- (P~ +P2)]
(lc)
An individual core can then be reconstructed on a constant porosity basis by calculating h n s for core segments between samples with porosity determinations. In the case illustrated, the segments were generally 20 or 40 cm.
M14 Porosities m a y be computed from bulk density or water loss measurements. From the relationships: Bulk density (B) = total weight (W t)/total volume (V t), W t = solid weight (Ws) + liquid weight (Wl), V t = solid volume (V s) + liquid volume (V I), and liquid and solid densities (Pl and Ps respectively) equal the appropriate weight/volume ratios:
porosity
(P) = V1/V t = (B -- Ps)/(Pl
--
Ps) = (Ps --
B)/(Ps
--
Pl)
(2)
Using the definition: weight percent liquid (wl) = W I / W t (i.e., w 1 + w s = 1): P = WlPs/(WlP s +
WsPl)
(3)
Using an alternative definition of water content (w*) advocated by Inderbitzen (1974) and others: w * = W I / W s (i.e., based on dry weight), P = W*Ps/(p I +
W*Ps)
(4)
The liquids referred to are interstitial waters at their in-situ salinities. Water contents (relative to either total wet weight or to dry weight) based on pure water (e.g., loss by evaporation) can be converted to saline water c o n t e n t simply by dividing by (1 -- S) where S is salinity expressed as a decimal percent (normal sea water S = 0.035). Salinity m a y be determined with a refractometer (Behrens, 1965) on a drop or two of interstitial water squeezed or centrifuged from a small core sample. Then only densities are required to determine porosity from bulk density or water loss measurements. Mineral density (Ps) may be determined precisely by p y c n o m e t r y or other methods given in mineralogy texts (e.g., Muller, 1967; Hurlbut, 1971). Variations in observed mineral densities in several marine environments are discussed by Hamilton (1970 and 1974). Although distinct differences may occur between sedimentary provinces and from bed to bed within a core, within sections of core several tens of cm thick they may tend toward sufficiently uniform values to justify using a constant, c o m m o n density such as 2.65 g/cm 3 (quartz). Sedimentation rate errors that might result from using a single mineral density will be very nearly the same as errors in the density estimate. For example, an error of 0.07 g/cm 3 (the difference between quartz and calcite) would lead to a sedimentation rate error of about 2.5%. Liquid densities (P l) for sea water or sodium chloride solutions can be determined from salinity from standard references (e.g., Weast, 1974). Sodium chloride and sea water values differ by less than 0.5% and would lead to sedimentation rate differences of the same magnitude. The goal of these computations could also be accomplished by conversion of vertical thickness sedimentation rates to mass sedimentation rates.
M15
Although this measure is more useful in some types of investigations (e.g., Swift and Wenkam, 1978), it is often less desirable because the expression mass per unit area per unit time is conceptually and operationally more complex. Different reference porosities may be chosen to reflect different concepts of reconstruction. For example, a low porosity would reconstruct thicknesses to a simulated, deeply buried, compacted condition, and high values might be used to reconstruct to initial conditions. A reference porosity of 50% has the advantage of requiring a slightly simpler calculation. Furthermore, 50% may roughly approximate many natural sediments below the uppermost few meters and thus permit semi-quantitative comparisons with published rates based on unspecified porosities (e.g., Diester-Haass, 1976). CONCLUSIONS
Sedimentation rates calculated from core depths without adjusting to a constant porosity can lead to major misconceptions concerning relative rates of sedimentary processes. Conversion to any reference porosity may be done with eqs. la or lb or to 50% porosity with eqn l c . Porosity can be calculated from eqs. 2, 3, or 4 which require knowledge of mineral density, water density or salinity, and bulk density or water content. Adequate porosities can c o m m o n l y be obtained from only one measurement (bulk density or water content) and reasonable estimates of other, necessary data. ACKNOWLEDGEMENTS
I thank Drs. E.L. Hamilton and S.K. Addy for their reviews and constructive criticisms of the manuscript.
REFERENCES Behrens, E.W., 1965. Use of the Goldberg refractometer as a salinometer for biological and geological field work. J. Mar. Res., 23: 165--171. Diester-Haass, L., 1976. Quaternary accumulation rates of biogenous and terrigenous components on the East Atlantic continental slope off N W Africa. Mar. Geol., 21: 1--24. Hamilton, E.L., 1970. Sound velocity and related properties of marine sediments, North Pacific. J. Geophys. Res., 75: 4423--4446. Hamilton, E.L., 1974. Prediction of deep s e a s e d i m e n t properties: state of the art. In: A.L. Inderbitzen (Editor), Deep Sea Sediments. Plenum Press, New York, N.Y., pp. 1--43. Hamilton, E.L., 1976. Variations of density and porosity with depth in deep sea sediments. J. Sediment. Petrol., 46: 280--300. Hurlbut, C.S. Jr., 1971. Dana's Manual of Mineralogy. Wiley, New York, N.Y., 18th ed., pp. 134--135. Inderhitzen, A.L. (Editor), 1974. Deep Sea Sediments. Plenum Press, New York, N.Y., p. 483.
M16 Muller, L.D., 1967. Density Determination. In: J. Zussman (Editor), Physical Methods in Determinative Miners]ogy. Academic Press, New York, N.Y., pp. 459--466. Swift, S.A. and Wenkam, C., 1978. Holocene accumulation rates of calcite in the Panama Basin. Mar. Geol., 27: 67--77. Tschebotarioff, G.P., 1951. Soil Mechanics, Foundations, and Earth Structures. McGrawHill, New York, N.Y., 655 pp. Weast, R.C. (Editor), 1974. Handbook of Chemistry and Physics. CRC Press, Cleveland, Ohio, 54th ed., Section D, pp. 219 and 222.