Limnol. Oceanogr., 25(2), 1980, 327-337 @ 1980, by the American Society of Limnology and Occmwgraphy, Inc.

The diffusion coefficients of sulfate, ammonium, and phosphate ions in anoxic marine sediments’

Michael D. Krom and Robert A. Berner Department of Geology and Geophysics, Yale University, New IIavcn, Connecticut 06520

Abstract

The diffusion coefficients of sulfate, ammonium, and phosphate ions were determined directly in the laboratory by placing two samples of homogenized, anoxic mud from Long Island Sound in contact with one another across a planar interface. After 141 h concentration profiles were dctcrmined and from them, values of effective diffusion coefficients (which incorporntc the effects of adsorption) were calculated. Correction of these values for adsorp- tion, using independently determined linear adsorption constants for the same sediments, gave the following values (X lo-” cm2. s- r, 20°C errors 22~): D,(SO,), 5.Ok1.2; D,(NII,), 9.8k2.0; U,(POJ, 3.6kl.l. These values agree well with values calculated for the same scd- iments from estimates of formation factors plus data for diffusion coefficients at infinite di- lution.

In many studies over the past several years mathematical models have been applied to the microbial diagenesis of or- ganic matter in recent sediments. Such diagenetic models have been developed and used to describe and predict the con- centration profiles of dissolved sulfate, ammonium, and phosphate in the pore waters of anoxic sediments (e.g. Berner 1974; Lasaga and Holland 1976; Vander- borght et al. 1977; Murray ct al. 1978; Filipek and Owen unpubl.), to estimate the nutrient flux into the overlying water (Suess 1976; Aller 1977; Toth and Ler- man 1977), and to describe the clemcntal composition of the organic matter undergoing decomposition (Sholkovitz 1973; Hartmann ct al. 1973; Berner 1977). In these models the process of molecular diffusion plays a prominent role in describing the transport of dis- solved substances, especially below the zone of bioturbation, Molecular diffusion is assumed to follow Fick’s Laws and is expressed in terms of the whole sediment diffusion coefficient, D,, which includes within it the effects of tortuosity but not those of adsorption (Berner 1976, 1980).

Despite the importance of diffusion in diagenetic models, there have been very few measm-ements of values of D,s in an-

’ This rcscarch was supported by funds from Na- tional Science Foundation grants OCE77/03473 and OCE79/06919.

oxic pore waters. Shishkina (1972) deter- mined the diffusion coefficient of chlo- ride for several anoxic sediments by juxtaposing sediment cores, a technique similar to that used here. We know of only three direct determinations of the diffusion cocfficicnt of sulfate in marine sediments (Li and Gregory 1974; Gold- haber et al. 1977; Jargenscn 1979) and none at all of the diffusion coefficients of ammonium or phosphate in such sedi- ments. Roscnfeld (in press) has made some preliminary measurements of the diffusion coefficient of NH,+ using a cell similar to ours but with kaolinite, rather than natural mud as the sediment matrix. We have determined values of D,s for s~zl-

t‘atc, ammonium, and phosphate from di- rect measurements of interstitial diffu- sion in samples of anoxic mud collected from Long Island Sound. To correct for retardation due to adsorption we use the results of a series of independent adsorp- tion experiments on anoxic sediments from the same locations for ammonium (Rosenfeld 1979) and phosphate (Krom and Berner in press). We hope that this study will not only provide useful data for calculating rates of diffusion during diagenesis, but also to illustrate how dif- fusion coefficients can be directly cleter- mined in sediments by using natural con- centration gradients. Our procedure provides a direct answer for a given sed- imcnt and avoids problems associated

327

328 Krom und Berner

12.5

-Lid

_ Upper Cell

_ Lower Cell

7.5cm

Fig. 1. Vertical cross section of’cylindrical acryl- ic plastic cells used in dctcrinining D,?‘.

with changes in ionic interactions creat- ed by more indirect techniques.

We thank R. Vaisnys for help with the statistical techniques. We also thank M. Reed for help in collecting samples. We had helpful discussions with J. K. Coch- ran, W. C. Graustein, G. R. Holdren, Jr., E. L. Sjoherg, and J. T. Westrich at var- ious stages during the work. The com- ments of R. McDuff were most uscflzl.

Experimental methods ?‘heorg--The method used to deter-

mine diffllsion coefficients rests on two basic assumptions. The first is that dif- fusion occurs solely in the pore water and the value of the diffusion coefficient for a given dissolved species is relatively in- sensitive to changes in its concentration. In other words, -during di ffbsion in the experiments, D, is a constant and inde- p&dent of l.>oth space and time. The sec- ond assumption is that retardation of dif- fusion due to adsorption can be expressed in terms of simple linear equilibrium ad- sorption. With thcsc assumptions, the ba- sic diffusion equation (Crank 1956; Duursma and Hoede 1967; Berner 1980) is

ac __- = at (1)

where C = concentration in the pore water, D, = difflzsion coefficient, K = di- mensionless linear adsorption constant equal to the ratio between the conccntra- tion of adsorbed and dissolved forms of the species under study (K is a function of sediment porosity), x = distance, and t = time.

The procedure used to study difftlsion in the laboratory consists of the juxtapo- sition across a planar interface of two cy- lindrical natural sediment samples, pre- viously mixed to ensure a homogeneous initial concentration in each (Fig. 1). If the interface is adopted as the origin, we thus have a one-dimensional diffllsion problem and the initial conditions are t = 0: x > 0, C = C,; x < 0, C = C,. After diffusion has proceeded the boundary conditions are t > 0: x + 03, C + C,; x -+ -co, C -+ C ,. Diffusion is allowed to proceed over a short enough period that concentrations at the fiu ends of the sam- ples, at +5 and -5 cm (Figs. 24), closely approximate the asymptotic values at in- finity. (For the times used here, errors re- sulting from this assllmption are <2%, well within the range of measurement error.)

Solution of Eq. 1 for these initial and boundary conditions yields

c = c2 + !h(C[ - C,) erfc [xl(41J,‘t) ‘I21

where (2)

D,’ = D,l(l + K). (3)

Substitution of measured values of C as a fLlnction of x and t thus allows detcr- min&ion of D,‘, and from independent measures of K the value of D, is thereby calculated.

General procedure-Sediment was collected by gravity coring from two lo- cations in Long Island Sound: Sachem Head Harbor (Sachem) and the FOAM site (exact locations given elsewhere: Krom and Berner in press). These sedi- ments consist of gray-to-black, organic (-2% org C), anoxic, clayey muds; the FOAM sediment contains sand-sized &CO3 shell fragments (l&15% CaCOs

Diffusion in anoxic sediments

14

Cone C, ImM 1

f 12

8

6 1

a

D;(q)=5.0+1.2 x1o’6

(cm*/sJ

-Distance + cm

Fig. 2. Concentration profile of interstitial dissolved sulfate in diffusion cells after 141 h. Initial con- centrations denoted C, and Cz. Three curves represent best fit (middle curve) plus those of 2 SD from best fit. Inset shows theoretical curve from which best-fit value of D,’ and standard errors were estimated (see text).

by wt). Porosities are 6 = 0.64 for FOAM and 6 = 0.79 for Sachem.

The sediments were taken back in plastic core liners (6.4~cm diam) to the laboratory in New Haven where the dif- fusion experiments began within 4 h of collection. The cores were first sectioned into 40-cm lengths and placed in a N2- filled glove bag (which was evacuated twice and refilled with N2 gas each time it was reopened). The end centimeter of each section was discarded. The remain- ing sediment was extruded and then ho- mogenized by stirring it vigorously for

about 3 min in a bowl with a wooden spatula.

Next we packed the bottom section of a plastic cell (5 cm long) with homoge- nized mud from Sachem (50-90 cm, con- taining low sulfate and high ammonium and phosphate concentrations) taking care to ensure that the cell was entirely full. The upper cell was screwed into place with a circle of Whatman No. 1 fil- ter paper between the cells. The top sec- tion was packed full of mud from the FOAM site (545 cm, containing high sulfate and low ammonium and phos-

330

c

Cone w I I mM

t

4

2

Cl

1 LI

Krom and Berner

- cm + Fig. 3. As Fig. 2, but for dissolved ammonium.

phatc concentrations). The lid was then screwed tightly in place. These two jux- taposed 5-cm cells constituted the exper- imental setup for measuring diffusion (.yee pig. 1). Additional subsamples of each mud were taken for determination of water content and of the concentration of dissolved constituents. Portions of the remaining mud were packed into two separate plastic cells, one filled with FOAM mud, the other with Suchem mud, an d each cell sealed. These samples were used to estimate any significant pro- duction or consumption of the dissolved species during the diffusion experiments.

Thus, these separate cells served as “jar” experiments (see Goldhaber ct al. 1977).

All cells of mud were left in the glove bag under a slow stream of N, gas for -6 days at room temperature, 20”+-2°C. All the mud from each of the two separate cells (jar experiment) was then packed into 250-ml Lourdes plastic centrifuge tubes fitted with gastight alrrminum caps which were in turn covered with Para- film to prevent contact between sample and aluminum. The mud from the diffu- sion cell was subsampled into prc- weighed plastic centrifuge tubes, four subsamples from the upper and four from

Diffusion in anoxic sediments 331

600

Cone

b I M

t 5oc

$P,= 1.25 f 0.4 x 1o’6 [cm2/s)

6 S

t 4

2

-cm +5

Fig. 4. As Fig. 2, but for dissolved phosphate.

the lower chamber of the cell. Centrifuge tubes were reweighed in the glove bag and from this the mass of mud and the fraction of the total sample in each tube were determined.

The tubes containing the mud samples were then centrifllged at 3,000 rpm for 2 min to separate the interstitial waters, re- turned to the glove bag, and the super- natant water sucked into clean, new plas- tic syringes. Each syringe was removed from the glove bag and the water filtered through 0.4-pm Millipore filters. The first

1.0 ml was discarded, the next l-2 ml col- lected for ammonium and sulfate detcrmi- nations, and the next two 0.5-ml portions for phosphate. If at this stage any water remained, it was added to the l-2 ml al- ready taken for sulfate and ammonium.

At all stages of the procedure WC took great care to ensure that there was no contact of the samples with air, because the measured concentration of dissolved phosphate in anoxic pore waters is lower if the water is allowed to come into con- tact with air at any stage before or during

332 Krom and Berner

filtration (Loder et al. 1978). We have found (Krom and Berner in press) that the adsorption of phosphate by anoxic ma- rine sediment is greatly increased when the system is aerobic, probably due to the adsorption of phosphate on iron oxyhy- droxides. During a preliminary experi- ment to determine D,?’ for phosphate we could see that some oxygen contamina- tion of the mud within one of the cells had occurred: a thin layer of mud (<2 mm) at one end of the cell had gone brown. The effect of this contamination was to decrease the initial phosphate concentration near that end of the cell to about half, and although the form of the diffusion profile was similar to that pre- sented here, the D,’ value was three times larger. This higher value was in- compatible with that predicted from rel- ative mobilities plus measured values of Kp and 0,’ for sulfate.

Analytical methods-All filtered water samples were stored at 4°C until deter- minations could be performed, within 24 h for ammonium and within 48 h for phosphate. We use the term phosphate (PO,) for those phosphorus species which are reactive to the molybdate-blue re- agents of Murphy and Riley (1962). This may include not only the orthophosphate anions (mainly HPOd2- and H,PO,-), but also unknown amounts of other organic an d inorganic phosphorus compounds. No preserving agents were added. Sam- ples for sulfate analysis were placed in 25-ml conical flasks, weighed (as a mea- sure of volume), and the reagents HCl and EDTA added. The flasks were sealed with Parafilm and stored at 4°C for up to 10 days before analysis.

The method used for ammonium de- termination was developed by Krom (1980). It is a variation of the Berthelot reaction in which sodium salicylate is used instead of phenol because it is less toxic and sodium di-isocyanurate instead of sodium hypochlorite because it is more stable. The analytical precision (2~) estimated from replicate 2-mM standards (n = 5) is 0.028 mM (+‘1.4%). Phosphate was determined by an adaptation of the molybdate-blue method of Murphy and

Riley (1962) in which the reagent con- centrations and the sample volumes were adjusted to give the same phosphate : re- agent ratio as in the original method. The analytical precision (95% confidence lim- its) estimated from replicate standards was 22% (n = 10) for phosphate at the level of 600 PM and t1.7% (n = 10) for phosphate at the level of 240 PM.

Sulfate was determined by the method of Howarth (1978). This method was cho- sen because it is fairly simple to use and because only 1 ml is required, compared to the 5 ml required for the standard gravimetric method (Strickland and Par- sons 1969). It should however be noted that we obtained an analytical precision as estimated by replicate determinations of Copenhagen seawater (n = 11) of 24.4% (95% confidence limit) at the level of 29 mM, compared to an analytical pre- cision of 20.2% claimed by Howarth (1978). In addition, after extensive pre- liminary work we found this method to be unsuitable for samples with a sulfate concentration of ~2 mM because there was an undetermined blank problem at these low values.

Red ts Profiles of dissolved sulfate, ammoni-

um, and phosphate concentrations after 141 h compared with the initial ones in the diffusion cells are shown in Figs. 2- 4. To obtain the best estimate for D,‘, us- ing Eq. 2, we drew a series of theoretical curves (C vs. x) for possible values of D,’ for each species. For this purpose we used the values measured for the sample closest to the end wall of the cell at the end of the diffusion experiment for C, and C2. These are within the range of val- ues given in Table 1 for the initial con- centrations in subsamples of the homog- enized sediment. Next we measured the distance, in the C direction, from the midpoint of each data bar to each theo- retical curve. Graphs of the sum-of- squares of this distance (expressed by the symbol S) vs. D,’ is plotted (as insets) in Figs, 2-4. The best estimate for D,’ is the minimum value on the curve. By this method the value of D,’ at m standard

Diffusion in anoxic sediments 333

deviations from the mean (assuming a normal error distribution) is read from each inset curve by using the correspond- ing value of S at m given by

s=s,i, 1++ [ 1 -

where m = number of standard devia- tions, and n = number of data points used. Best estimates (X lo-” cm2’s-l) plus errors representing 2 SD are (T = 2OOC): D,‘(SO,) = 5.Ok1.2; D,‘(NH,) = 4.OkO.8; D,‘(PO,) = 1.3kO.4.

These values include the effects of ad- sorption (if any), which a true sediment diffusion coefficient should not (Berner 1980). To obtain values of the true dif- fusion coefficient, D,, we must correct for adsorption using Eq. 3:

D, = (1 + K)D,‘. (4) In order to do this we have determined

values of K, the linear adsorption con- stant, from sediments of the FOAM and Sachem sites. Rosenfeld (1979) by means of laboratory adsorption-desorption ex- periments has demonstrated rapidly re- versible equilibrium adsorption of NH,+ in these sediments; his resulting values are K(NH,) = 1.6 (FOAM) and K(NH4) = 1.3 (Sachem). For our purposes the av- erage value for FOAM and Sachem sed- iments K(NHd) = 1.45 is used. Similar studies that we made under strictly an- oxic conditions (Krom and Berner in press) yield the result (FOAM site only) I((P0,) = 1.8+0.5. The value of K for sul- fate is assumed equal to zero; this is rea- sonable for marine sediments where sul- fate adsorption is negligible (Li and Gregory 1974). Insertion of the above K values into Eq. 4 yields values (X lo-”

2.s-1) of (T = 20°C): D,(SO,) = ;&I.2; D,(NH,) = 9.8k2.0; D,(PO,) = 3.6_+‘1.1. Here th e error range represents 2 SD. It does not include errors associ- ated with the estimate for K.

Results of the jar experiments indicate that bacterial sulfate reduction and phos- phate and ammonium production during the diffusion experiment must have been small and much lower than changes tak-

Table 1. Concentration changes due to sulfate reduction and phosphate and ammonium produc- tion in jar experiments (141 h; T = 20°C).

Sediment Dissolved

species

Initial Final concn concn

mmol per liter AC(%)

FOAM SO.?- 13.7 12.9 -6 Sachem sod+ 4.0 4.6 +15

FOAM NHd+ 1.26 1.43 +13 Sachem NH.,+ 5.14 4.89 -5

FOAM Pod”- 0.189 0.190 +l Sachem PO,= 0.612 0.633 +3

ing place as a result of diffusion (Table 1).

Discussion Our value for the diffusion coefficient

of sulfate D,(SO,) is in good agreement with previous measurements on fine- grained marine sediments, both in Long Island Sound and elsewhere (Table 2). The values of JGrgensen (1979) and Li and Gregory (1974) are for tracer diffu- sion of 35S04, the others are for bulk counter-diffusion of SOd2- and HC03-. The agreement indicates that interionic electrical effects during diffusion of sul- fate in marine pore waters are negligible compared to errors of measurement in these studies. Interionic effects on dif- fusion in sediments have been discussed by Ben-Yaakov (1972) and Lasaga (1979).

As an additional check on the validity of the measurements, we have calculated values of true diffusion coefficients, D,, for ammonium and phosphate. We as- sumed that all three ions (sulfate, am- monium, and phosphate) are retarded equally by sediment tortuosity and that the ratio of diffusivity in seawater to that at infinite dilution is the same for all three ions; these assumptions, within our errors of measurement, are valid (Turk 1976; Li and Gregory 1974; McDuff and Ellis 1979; Lasaga 1979). Under these conditions

D”( SO,) DsWJ

= D’WL) = D”(PO-1) = s6Ft Ds(S0.J Ds WJ

(5) where Do = diffusion coefficient in water

334 Krom and Berner

Table 2. Measured values of D,&SO,) for fine-grained marine sediments (T = 20%).

Locality Porosity JUSO,)

cb 10-R crn2.s-1 Reference

Long Island Sound (FOAIM site) Limfjorden, Demnark Deep Pacific (red clay) Long Island Sound (FOAM + Sachem)

0.64 4.0* 1.4 0.80 5.1” 0.71 5.OkO.2 0.72t 5.Ok 1.4

Goldhaber et al. 1977 Jergenscn 1979 Li and Gregory 1974 This study

Errors given arc 2 SD except for that of Li and Gregory which represents mainly counting statistics for the ‘% technique used.

* Corrected for tempcratlire. t Mean porosity of’ FOAM and Snchem sediments.

at infinite dilution, and F’ = constant (a modified formation factor-see helow). D,(NHJ and D,(POJ are then calculated by rearranging Eq. 5 to

D”(NH,) D,s(NK) = 4F/ (6)

an d

D”( PO,) DsW4) = 4F’ * (7)

Values of c/Z’ were obtained in two ways. First we calclllated 4bI;’ using Eq. 5, from the value of D”( SO,) f’or 20°C (in- terpolated from the data of Li and Greg- ory 1974) and the measured value for D,(SO J of this paper. The result is cl,F ’ = 1.9. In the other method the Archie relation (Munheim 1970) is used:

F = $4 (8)

where 4 = sediment porosity, and F= t&nation factor (ratio of electrical con- ductivity of pore fluid alone to conductiv- ity of bulk sediment containing the pore fluid). The parameter F’ (in terms of tor- tuosity and porosity) is approximately re- lated to F by the relation (Li and Gregory 1974)

F’ _ %WI; (9) 73,

where qw = viscosity of pure water, and 7lS\V = viscosity of seawater. At 20°C q,,,/ rlw = 1.08. Using this value and the mean value of cb for the FOAM and Sachem sediments ($ = 0.72), we obtain, from Eq. 8 and 9, cl,F’ = 1.5. When we consid- er the crudeness of the Archie relation, this is in surprisingly good agreement

with that calculated above from sulfate dif’fusion coefficients and serves as an in- ternal check between the two calculation methods. We will use the value based on s&ate diffusion coefficients, , +F’ = 1.9.

The value of D,(PO,J that we have giv- en here is actually a composite repre- senting the diffusivities mainly of HPOJ2- and II,PO,- ( as ion pairs). Therefore we estimated the value of D”(P0,) from the data presented by Li and Gregory (1974) for D” of HPOd2- and H,PO,- using the relative distribution of these two species (as ion pairs) in seawater at pI1 = 7.0 (Kester and Pytkowicz 1967). For 20°C we obtain the approximate value D”(P0,) = 7.0+0.5x10-” crn2*s-l. From the data of Li and Gregory we also obtain the value (at 2OOC) DO(NH,) = 1.7~10~~ cm2. s-l. From these values and +F’ = 1.9, derived above, using Eq. 6 and 7, we fi- nally obtain D,(NII,) = 9.3x lo-” cm2* s-l and D,(PO,) = 3.7~ lo-” cm2* s-l. In view of all the possible errors involved, we consider these results for D, to be in good agreement with our measured values. Thus, both independent measurements of D,(SO,) and independent calculations ol’ D,(NH,) and D,(PO.J serve to confirm the reslllts reported here and provide evi- dence that the 3ssumptions involved in the experimental procedures and in the calculations arc essentially valid.

Dissolved phosphate is easily affected by contamination of the sample by air (Lodcr et al. 1978), because iron oxyhy- droxidcs are formed by oxidation and strongly adsorb phosphate ions. We be- lieve that the close agreement between the measured and the calculated values

Diffusion in anoxic sediments 335

of D&PO,) provide evidence that no sig- nificant oxidation of the sediment had taken place despite the extensive manip- ulations in our experimental procedure.

We had to use sediment of different porosity from two locations in Long Is- land Sound in the two halves of the dif- fusion cell in order to get sufficiently dif- ferent initial concentrations of sulfate, ammonium, and phosphate to result in measurable diffusion gradients. In the calculation of $F’ via Archie’s Law, only the average porosity for the two muds from Sachem and FOAM was used. IIow- ever, the porosity differences, as well as other differences in properties such as adsorption constants between these two muds, appear to be unimportant. Diffu- sion profiles of each ion were symmetri- cal between the two halves of the diffri- sion cell (see Figs. 24), indicating that diffusion rate and degrees of adsorption were essentially the same in both sedi- merits.

It has been suggested that ionic inter- action during codiffusion or counter-dif- fusion may appreciably affect the value of the diffusion coefficient of certain ions in seawater (Ben-Yaakov 1972; Lasaga 1979). An assumption implicit in our comparisons between measured and cal- culated D, values is that this cross-cou- pling between ions does not significantly affect D, for sulfate, ammonium, and phosphate in anoxic pore waters. Our re- sults show that this assumption is valid and is in agreement with the conclusions of Goldhabcr et al. (1977) and McDuff and Ellis (1979). Lasaga (1979) has cal- culated the relative importance of this cross-coupling term tar sillfate, ammoni- run, and phosphate in anoxic pore waters and has shown it to bc insignificant for these three species.

Applications to other sediments The results reported here apply strictly

only to sediments of the FOAM and Sachem sites of Long Island Sound at 20°C. To apply our results to other sedi- ments, one must correct for differences in temperature and porosity. Correction for temperature, in the ease of sulfate, can be

done directly by using the data of Gold- haber et al. (1977) or Li and Gregory (1974). For ammonium and phosphate it is necessary to use temperature coeffi- cients for D0 (infinite dilution); Li and Gregory (1974) g ive values and methods of calculation. Their results are well ap- proximated over the range O”-25°C by the empirical expressions D”(SOJ = 10.7 + 0,23(T - 25”), D”(NH4) = 19.8 + 0.40(T - 25’), D”(HPOd2-) = 7.34 + O.l6(T - 25”), and D”(H2P0,-) = 8.46 + 0.19( T - 25”). Do is in units of 1O-6 cm2. s-l and T is in “C. More direct sediment data at lower temperatures are needed to see how well the temperature coefficient of D0 for each ion approximates that for D, in marine sediments. In the case of sul- fate the approximation appears to be good (Li and Gregory 1974).

To correct for porosity differences be- tween our sediments and other marine sediments we assume (for the same tem- perature and salinity) that the following relation is valid:

$FD, = constant. (10)

Here I; is the true formation factor as measured by conductivity techniques. From the value c$F’ = 1.9 and Eq. 9 we can calculate F for this study to be 2.4. Thus, from measurements (or estimates) of the formation factor for a given sedi- ment, values of the diffusion coefficients of sulfate, ammonium, and phosphate can be estimated from Eq. 10 and our values of (b, I’, and D,. Discussions of F detcr- mination via conductivity are summa- rized by Manhcim and Waterman (1974) and McDrrff and Ellis (1979).

The method of determining F by esti- mation, using Archie’s approximation (Eq. S), gives values about 20% too low for the data of this study and also for the measurements of D,(SO,$) made by Gold- habcr et al. (1977) and Jorgensen ( 1979). All these studies have been done with sediment from the top meter or less. The Archie relationship can also be shown to be about 20% too low for shallowly bur- ied deep-sea sediments where (b2F (with- in 10 m of the surface) measured by elec- trical resistivity varies from 1.2 to 1.3

336 Krom and Berner

depending on the sediment type (data of Manheim and Waterman 1974). Accord- ing to the Archie method this product should equal 1.0. At depth, however, the Archie equation is rather inaccurate (McDuff and Gieskes 1976). More infor- mation is needed about shallow marine sediments before we can know whether Archie’s approximation (corrected by 20%) can be generally used in the top meter of the sediment, where much of the diagenetic modeling is done, or whether F must be measured directly on each occasion when a diagenetic model is being used.

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Submitted: 21 May 1979 Accepted: 9 October 1979