Sediment Compaction Rates and Subsidence in Deltaic Plains: Numerical Constraints and Stratigraphic Influences T

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Basin Research (2007) 19, 19–31, doi: 10.1111/j.1365-2117.2006.00310.x Sediment compaction rates and subsidence in deltaic plains: numerical constraints and stratigraphic influences T. A. Meckel,1 U. S. Ten Brink and S. J. Williams United States Geological Survey,Woods Hole, MA, USA

ABSTRACT Natural sediment compaction in deltaic plains in£uences subsidence rates and the evolution of deltaic morphology.Determining compaction rates requires detailed knowledge of subsurface geotechnical properties and depositional history,neither ofwhich is often readilyavailable.Toovercome this lackof knowledge, we numerically forward model the incremental sedimentation and compaction of stochastically generated stratigraphies with geotechnical properties typical of modern depositional environments in the Mississippi River delta plain. Using a Monte Carlo approach, the range of probable compaction rates for stratigraphies with compacted thicknesses o150m and accumulation times o20 kyr. varies, but maximum values rarely exceed a few mmyr 1.The fastest compacting stratigraphies are composed primarily of peat and bar sand, whereas the slowest compacting stratigraphies are composed of prodelta mud and natural levee deposits.These results suggest that compaction rates can signi¢cantly in£uence vertical and lateral stratigraphic trends during deltaic evolution.

INTRODUCTION same compacted thickness and time of accumulation.This approach allows us to derive the expected bounds of pre- Determining compaction rates in modern sedimentary sent compaction rates for a stratigraphy in the absence of environments is di⁄cult.There are fewdirect observations detailed boring information, to draw some conclusions re- and monitoring e¡orts are expensive and time consuming. garding characteristic behaviour and dependencies of the Further complications result from our incomplete knowl- compaction process in general, and to gain insight into edge of the speci¢c depositional events resulting in the the stratigraphic characteristics that in£uence the present present stratigraphy.Two sedimentary columns with simi- rates of compaction. To these ends we: (1) present a rela- lar compacted thickness and total time of accumulation tively simple stochastic method for generating synthetic, can have di¡erent accumulation histories (sedimentation uncompacted one-dimensional (1D) stratigraphic col- rates and facies deposited) and are therefore likely to have umns; (2) use Monte Carlo simulations incorporating that di¡erent present compaction rates.With many borings (as method in conjunction with existing compaction routines in theMississippi delta plain),the thickness of a sedimen- to constrain the range of anticipated present compaction tary unit and the approximate age of accumulation are rates for speci¢c compacted thicknesses and accumulation often available on a regional scale. However, the detailed times and (3) summarize the stratigraphic characteristics sedimentation rate and composition of individual layers of those model stratigraphies which result in relatively fast at any speci¢c location vary locally and are typically not and slow compaction rates. well known. This local variability restricts the lateral dis- We have modelled the shallow compaction that occurs tance that calculated site-speci¢c compaction rates can in the upper tens of meters (maximum 150 m) over time be extrapolated. The limited applicability of site-speci¢c periods of thousands of years (maximum 20 kyr), typical calculations argues for the development of a less speci¢c, of Mississippi Delta deposits during the late Pleistocene but more broadly applicable method to constrain the pos- and Holocene. We initially focus on an arbitrarily chosen sible range of compaction rates. subset of those stratigraphies (100^110 m compacted Here, we present a stochastic approach that investigates thickness that accumulated in 10^11kyr). We describe the diverse depositional scenarios (variable layer thicknesses, range of cumulative subsidence and present compaction sedimentation rates and composition) that result in the rates for those stratigraphies, and investigate stratigraphic characteristics that result in fast and slow compaction Correspondence:T.A. Meckel, United States Geological Survey, rates. The present compaction rates for the entire range Woods Hole, MA, USA. E-mail: [email protected] 1 Present address: Bureau of Economic Geology, John A. and of modelled stratigraphies (10^150 m that accumulated in Katherine G. Jackson School of Geosciences, The University of 1^20 kyr) are then summarized.We conclude with a com- Texas at Austin,TX, USA. parison of our modelled rates with other observations of

r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd 19 No claim to original US government works T. A . M e c k e l et al. subsidence rates from dated peat horizons and suggest (a) how compaction rates may broadly in£uence vertical and Determine a target uncompacted thickness and accumulation time for depositional column, implying a target average sedimentation lateral stratigraphic evolution in deltaic plains. rate (tASR) - Thickness randomly assigned in range 10-200 m Natural compaction (consolidation, autocompaction) - Time randomly assigned in range 1-20 k.y. here refers to the reduction in sediment volume (increase - tASR (mm/yr) = Thickness *1000/Time in bulk density) as a result of pore collapse (mechanical (b) grain reorganization) and £uid expulsion due to the gravi- Define two-parameter gamma distribution for sedimentation rates α tational load of overlying sediment (overburden). We do - Randomly assign in range 1-10 See equation (1) - β = tASR/α not incorporate chemical or biological processes (dissolu- (c) tion, cementation and decay) that may a¡ect compaction. While cumulative thickness < target thickness, build stratigraphy The term ‘compaction rate’ hereafter refers to the rate of - Assign: layer thickness randomly from exponential distribution, vertical elevation change of the uppermost stratigraphic layer sedimentation rate randomly from Gamma distribution, layer facies randomly from list of 5 facies used surface with respect to the base of the compacting column - Calculate cumulative uncompacted thickness and time (assumed static) due to compaction integrated over the (d) stratigraphic column. Evaluate actual average sedimentation rate (aASR) - If |tASR - aASR| < 0.1(tASR), continue - Else, rebuild stratigraphy (e) MODELLED FACIES DATA Pass depositional column to compaction routine Geotechnical parameters used here to describe the physi- - Incrementaly build and compact depositional column - Calculate rate of elevation change of uppermost surface cal properties of consolidating sediments are compressi- due to compaction of existing column at each time step bility (b); Athy,1930), initial porosity (F0), bulk density (r) (f) and the constants c1andc2 relating permeability to porosity Final present compacted stratigraphic thickness (Bryant et al., 1975; Mello et al., 1994). Present rate of elevation change due to compaction We are primarily concerned with compaction processes in the coastal plain of southern Louisiana, and have con- Fig. 1. Flow chart illustrating basic computational procedure for ducted our investigation using data from that environ- generating an uncompacted depositional column and incrementally building and compacting that column to arrive at a ment. For facies comprising the modern Louisiana ¢nal compacted thickness and compaction rate. Details of each coastal plain, the most relevant geotechnical data are from step (a^f) provided in text. Characteristics of the stratigraphies Kuecher et al. (1993) and Kuecher (1994).The ¢ve modern resulting from this method are in Appendix A. facies sampled (locations in Kuecher, 1994) are peat, bar sand, natural levee, bay mud and prodelta mud.The geo- pacted stratigraphies appear in Appendix A. We make no technical parameters for these facies that were used in our assumptions regarding relationships among facies, de- modelling e¡ort are presented in Table1.These values are positional layer thickness and sedimentation rate. Input similar to those presented by Mello et al. (1994; theirTable variables that were randomly chosen from predetermined 1), and Kooi & de Vries (1998; their Table1). Bulk density, distributions to assemble a stratigraphic model are (1) the porosity and permeability change in response to loading depositional thickness for each layer, (2) the sedimentation and are updated throughout the calculations. rate for each layer (implying a certain amount of time for depositing the layer) and (3) the facies assigned to each layer. Our premise is that, by modelling an exhaustive NUMERICAL METHODS range of possible stratigraphies, any observed stratigraphy A £ow chart illustrating our generalized methodology for composed of similar facies will have a present compaction creating a synthetic uncompacted stratigraphy and deter- rate somewhere on our model distributions. mining the present compaction rate is provided in Fig. 1. Initially, a target uncompacted thickness and target Details of each step (a^f) are described below. Speci¢c time of accumulation for a depositional column are chosen characteristics of the stochastically generated uncom- (Fig. 1a), implying a target average sedimentation rate (tASR). Then the depositional column is built from the Table 1. Geotechnical parameter values by facies (see Kuecher, base upward by stacking uncompacted layers of random 1994) thickness, deposition rate and facies, and the process is stopped once the target thickness is exceeded. If the actual 1 3 Facies c1 c2 F0 b (Pa ) r (kg m ) average sedimentation rate (aASR) of the ¢nal uncompacted depositional column is close to tASR, the column Peat 20.0 8.0 0.88 1.0E 06 1.12E103 is passed to the compaction routine for incremental sedi- Bar sand 14.0 4.0 0.57 1.0E 07 1.88E103 mentation and compaction analysis. If, on the other hand, Natural levee 20.0 6.0 0.42 5.0E 07 1.78E103 Bay mud 22.0 8.0 0.61 4.0E 06 1.40E103 the ¢nal layer assignment is quite thick or the sedimenta- Prodelta 22.0 7.0 0.78 1.0E 06 1.22E103 tion rate so low that the time for that layer is quite long, the ¢nal uncompacted column will have di¡erent tASR and See text for explanation of symbols. aASR, and the column in rejected. The criterion that we

20 r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 Compaction and subsidence in deltaic plains apply (|tASR^aASR| o0.1(tASR)) in order to retain a col- deposition of a suite of facies is commonly cited in delta umn for further analysis allows most columns generated to systems (Roberts, 1997; Amorosi et al., 2005), no statistics be retained. This criterion is needed to ensure that the are provided. We note that other ‘cyclic’ systems such as same number of uncompacted stratigraphies (1000) is Pennsylvanian cyclothems and carbonate platforms do generated for each ASR and time of accumulation mod- not have facies frequencies that are statistically distin- elled. guishable from stochastic models (Wilkinson et al., 2003). Sedimentation rates for each layer were randomly se- However, stratigraphies with cyclicity are possible within lected from two-parameter (a and b)gamma(G)probabil- our methodology, though only by coincidence. Nondepo- ity density function f (x): (See inset of Fig. A1 for example sitional events (no thickness in some time interval) are ef- plots) fectively modelled as extremely low sedimentation rates. Erosional episodes resulting in sediment removal are not 1 modelled. f ðxÞ¼ xa1 ex=b ð1Þ baGðaÞ Once a stratigraphy representing an internally consistent (aASRtASR) uncompacted depositional column such that the distribution average (ab) is equal to tASR for has been generated (Fig. 1d), it is used as input for incre- the chosen target uncompactedthickness andtarget accu- mental sedimentation and compaction modelling (Fig. mulation time parameters of each stratigraphic model 1e). For this, we use the calculations of Kooi (1997). The (Fig.1b). Initially, a is chosen from a uniform random dis- application of these calculations to subsidence problems tribution between1and10, with b then equal to tASR/a. G in the Netherlands has been demonstrated by Kooi et al. distributions avoid the undesired outcome of frequently (1998), Kooi & de Vries (1998) and Kooi (2000), so we only assigning extremely low sedimentation rates when using brie£y explain the method here.Their approach is similar an exponential probability density function.The values of to other 1-D compaction- £uid £ow models with no basal a and b are constant within a single stratigraphic model, £ow (Pizzuto & Schwendt, 1997 and references therein). but vary between stratigraphies, allowing for di¡erent Important assumptions included in this treatment are: shapes of the G distribution, even for stratigraphies with (1)saturated sediments,(2) £uid £ow is1-D in the upward the same ASR (tASR). A more constrained method would direction and (3) conservation of mass. Kooi & de Vries have a characteristic and well-de¢ned distribution of sedi- (1998) use the fundamental concepts of Darcy £ow law, a mentation rates for each facies. Data do not exist at this constitutive relationship between porosity (F) and e¡ec- time to allow a distribution for the rates of sedimentation tive stress (se¡): [F 5 Foexp( bse¡)], where b refers to for each facies used in this analysis to be determined. Athy’s (1930) usage and Fo is the initial porosity fromTable Thus, our more generalized approach is taken. 1, and Terzaghi’s (1943) principle of e¡ective stress Individual layer thicknesses were determined by ran- (se¡ 5 s^p£), where s is total stress and p£ is £uid pres- dom selection from an exponential probability density sure. The relationship of permeability (k)withF is mod- lx 1 ðc1þFc2Þ function f (x): f (x) 5 le ,wherel is the distribution elled as k ¼ kr10 ,wherekr is a reference 2 average (Fig. 1c). Exponential distributions are common permeability (1m here), and c1 and c2 are from Table 1. For in stochastic models of sedimentation (Dacey,1979; Wilk- other constants in the calculations (e.g. £uid density,visc- inson etal., 2003). Initially,the average bed thickness of the osity and compressibility) we follow Kooi & de Vries (1998). distribution (l 1) used for all stratigraphic models is de- Each depositional layer is divided into a number of ele- ¢ned to be that which is observed in a 64m boring in mentsthat islinearlyproportionaltoitstime ofaccumula- south-central Louisiana (P-1-90, see Roberts et al. (1994) tion such that the displacement rate of the uppermost for location and description). Roberts et al. (1994) refer to surface was calculated every 100 years throughout sedi- 13soil classi¢cation units in the64m recovered,providing mentation and compaction. At the completion of accumu- an average bed thickness of 4.9m and l 5 0.20. As this is an lation of each stratigraphy, the ¢nal (present) rate of average compacted thickness for the current state of com- vertical displacement of the uppermost surface due to in- paction for this stratigraphy (the distributions used in our tegrated compaction throughout the column was deter- method assign uncompacted thickness to a layer), we use the mined, as well as the ¢nal (present) compacted thickness value of 4.9 only as a starting point. In order to assess the (Fig.1f). in£uence of average depositional bed thickness on distri- In order to consider a wide range of stratigraphic thick- butions of present compaction rates, we repeated our nesses and accumulation times, the parameter space of method varying only the average bed thickness used in de- uncompacted thickness (10^200 m) and accumulation ¢ning the exponential distribution of possible layer thick- time (1^20 kyr) was divided into 361 bins (19 19), each nesses. spanning10 m in thickness and1kyr in duration. Each bin Geotechnical properties for each layer were determined was populated with 1000 stochastically generated uncom- by randomly selecting one of the ¢ve model facies for each pacted stratigraphies (361000 total stratigraphies). This layer (Table1). Each facies can appear 0 to n times in the ensured that each bin in the 10^150m thickness range of same stratigraphic model, with n representing the (uncon- interest contained 41000 compacted stratigraphies. Strati- strained) number of layers for that stratigraphy. No cycli- graphies with uncompacted depositional thickness city has been imposed on the models. Although cyclic 4200 m were not modelled.There may be some stratigra- r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 21 T. A . M e c k e l et al. phies that we did not model with uncompacted deposi- same stratigraphy (Fig. 3d; correlation coe⁄cient 5 0.28). tional thickness 4200 m that could compact to our range Present compaction rates cannot be inferred from of interest (10^150 m), but they are rare and thus do not current magnitudes of subsidence. Current magnitudes contribute substantially to our statistical compaction rate of subsidence cannot be inferred from present compaction distributions. rates.

Stratigraphic influences on present RESULTS compaction rates Present compaction rates and subsidence Here, we investigate the characteristics of the subset of magnitudes stratigraphies with relatively high and low present compaction rates (4P90 and oP10, respectively; Fig. 2). By Here, we present the characteristic compaction behaviour analysing a large number of stratigraphies with similar of a subset of the stratigraphies we modelled: those strati- compacted thicknesses and accumulation time graphies with ¢nal compacted thicknesses between 100 (N 51087), we have allowed stratigraphies to naturally sort and 110m and with accumulation times between 10 and themselves into subsets with similar present compaction 11 kyr (N 51087). The variability of present compaction rates (natural sorting).This is an advantage of Monte Carlo rates that results from a wider range of present thicknesses simulations for informal sensitivity analyses. (10^200 m) and accumulation times (1^20 kyr) are presented farther below. Layer thickness The modelled present compaction rates of this subset vary over three orders of magnitude (10 1^102 mmyr1; We did not impose any order or cyclicity in layer thickness Fig. 2), but the central 80% of the results are between 0.69 in our stochastic method for generating uncompacted de- 1 and 2.2mmyr (i.e. fairly low).We hereafter use P10 to re- positional columns, so model stratigraphies will rarely fer to the 10% rate (0.69 mm yr 1) from the cumulative show such trends. Thus, our methodology does not allow distribution function (CDF) and P90 for the 90% rate us to make any statements regarding relationships between (2.2 mm yr 1). trends in uncompacted layer thickness and present com- The cumulative magnitudes of compaction (subsi- paction rate. dence) of the subset (Fig. 3a and b) alsovary over two orders However, it is possible that the thickness of the most re- of magnitude (o100^102 m; Fig. 3c). However, 90% of cently assigned layer correlates with the present compac- modelled total subsidence magnitudes are o20 m, and tion rate by dominating the signal. That is, assigning 80% are o7m.The presentcompaction rate does notcor- thicker units (which have a constant facies and sedimenta- relate strongly with the magnitude of subsidence for the tion rate) towards the present may allow individual layers

Present compaction rate (mm/yr) 10−1 100 101 102 1

0.9

P90 = 2.2 mm/yr 160 0.8 N = 1087 140 0.7 120 0.6 Fig. 2. Cumulative probability 100 distribution function (CDF) for 0.5 present compaction rates for 80 stratigraphies with compacted 0.4 thickness100^110 m and accumulation

Cumulative probability Cumulative time10^11kyrThe rate corresponding

60 # of stratigraphies 0.3 to the nth percentile is the rate below P10 = 0.69 mm/yr which n% of the modelled values 0.2 40 occur.The central 80% of modelled values occur between the10th and 90th 0.1 20 percentiles (P10, P90 labelled). Colours correspond to subsets shown in Figs 3a 0 0 and 5. Inset frequency distribution 0 2 4 (histogram) shows same rates from Present compaction rate (mm/yr) which CDF was constructed.

22 r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 Compaction and subsidence in deltaic plains

(a) P90 200 N=1087 Total stratigraphies 180

160

140

120

Initial depositional thickness (m) 100 100 101 102 103 104 105 106 107 108 109 110 Final compacted thickness (m)

(b) 150 (c) 1 N=1087 Total stratigraphies 0.8 100 0.6

0.4 50 0.2 Cumulative probability Cumulative Number of occurrences

0 0 − 0 10 20 30 40 10 1 100 101 102 Cumulative subsidence (m) Cumulative subsidence (m)

Fig. 3. Data for cumulative (d) compaction (subsidence). (a) Initial 103 depositional thickness vs. ¢nal N=1087 Total stratigraphies compacted thickness. Di¡erent 2 colours represent di¡erent subsets 10 of the cumulative probability distribution function (CDF) in 101 Fig. 2. (b) Frequency distribution of subsidence magnitudes used to 100 create CDF in (c). (d) Present compaction rates do not correlate

Present compaction rate (mm/yr) − strongly with the magnitude of 10 1 −1 0 1 2 subsidence (correlation 10 10 10 10 coe⁄cient5 0.28). Cumulative subsidence (m)

to potentially exert a dominant in£uence (fast or slow) on (4.9m).The CDFs from these results are presented in Fig. present compaction rate. Having rapidly changing thick- 4, and indicate that present compaction rates are not very ness (and consequently facies and sedimentation rate) to- sensitive to changes in average uncompacted layer thick- wards the present may prevent any single facies from ness used to construct the stratigraphies (P90 rates vary by dominating the present compaction rate. We compared o0.5 mm yr 1). themostrecentlayerthicknessassignmentswithpresent compaction rates. No relationship was identi¢ed, indicat- Sedimentation rates ing that present compaction rates cannot be attributed to recently assigned layer thickness in the uncompacted de- Layer sedimentation rates were chosen randomly, and are positional column. independent of the position in the depositional column. To further investigate the in£uence of layer thickness, Thus, we do not expect trends in recent sedimentation we repeated the procedure used to generate the modelled rates to exist other than by coincidence. However, through CDF in Fig. 2 changing only one parameter: the average natural sorting, the fastest compacting stratigraphies may layer thickness used to de¢ne the exponential distribution have similar patterns of sedimentation rates (e.g. rapid re- from which uncompacted layer thicknesses were chosen. cent sedimentation). For the stratigraphies of interest, the We repeated the process twice using values for average most recently assigned layer sedimentation rate does not layer thickness of 2.5 and 7.5 m.These values represent ap- correlate strongly with present compaction rate (correla- proximately 0.5, and 1.5 times that used to generate Fig. 2 tion coe⁄cient5 0.10). r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 23 T. A . M e c k e l et al.

1 More complex is the relationship among present compaction rates, the time or depth interval during which more 0.9 compactable facies were deposited, and the subsequent 0.8 loading history. For example, the in£uence that compactable facies deposited thousands ofyears ago have on present 0.7 compaction rates may (or may not)be negligible, depending 0.6 on their burial history.Toinvestigate this, we computed the running averages of the proportion of each facies through- 0.5 out deposition, both with respect to cumulative strati- 0.4 5 Facies, Avg. Thick = 4.9m graphic time and uncompacted depositional thickness. 5 Facies, Avg. Thick = 7.5m For the running averages, the time window width was Cumulative probability 0.3 5 Facies, Avg. Thick = 2.5m 100% bar sand, Avg. Thick = 4.9m 100 years, or 20% of the average deposition time per layer 0.2 100% prodelta, Avg. Thick = 4.9m (given average layer thickness is 5 m and ASRs are 100% peat, Avg. Thick = 4.9m 10 mm yr 1). For the thickness window width, the win- 0.1 100% natural levee, Avg. Thick = 4.9m 100% bay mud, Avg. Thick = 4.9m dow size is 5 m (average layer thickness). Other window 0 0 1 widths were tried, but the parameters above provided the 10 10 most e⁄cient trade o¡ between resolution and computa- Compaction rate (mm/yr) tion time. Allwindow and step combinations showed simi- Fig. 4. Cumulative probability distribution functions (CDF) for lar gross patterns. Owing to extremely long computational a variety of model parameters indicated in the key.Each curve times, the P10^P90 stratigraphies (N 5 869) were not ana- represents 41000 stratigraphies with compacted thickness lysed in this manner. between100 and110 m that accumulated in10^11kyrVarying Figure6suggests thatthe proportion of peat in the un- average bed thickness used to de¢ne the exponential compacted depositional column in£uences the present uncompacted bed thickness distribution by 50% does not have a dramatic in£uence on present compaction rates.The compaction rate, which is expected (Bloom, 1964; Berry & range of present compaction rates for stratigraphies consisting of Poskitt, 1972; Kuecher et al., 1993; Roberts et al., 1994; Piz- 100% of each of the ¢ve-model facies used from the Louisiana zuto & Schwendt, 1997; Long et al., 2006). The slowest coastal plain are shown for reference. compacting stratigraphies (left side of Fig.6) have low proportions of peat throughout, decreasing towards the present, and high proportions of prodelta mud. The fastest Facies proportions compacting stratigraphies (right side of Fig. 6) have peat Stratigraphic heterogeneity in£uences compaction rates. as the highest proportion of window thickness, followed It seems intuitive that the fastest compacting stratigraphy by bar sand, throughout the total accumulation time and might be composed of 100% peat (the most compactable uncompacted stratigraphic thickness. material), but our data do not con¢rm this. Figure 4 shows The proportion of peat that accumulated in an uncom- that the range of compaction rates for entirely homoge- pacted stratigraphic section is useful for estimating the nous stratigraphies is generally slower than the heteroge- present compaction rate (Fig. 6), but it is clearly not diag- neous stratigraphies, except for stratigraphies composed nostic given the weak correlation noted previously for the of 100% bar sand, which have the widest range and most total proportion of each individual facies with present extreme compaction rates. The low density of peat does compaction rate (Fig. 5; upper left). not allow columns of100% peat to compact as fast as those that include some proportion of other facies. Facies order For stratigraphies with present compaction rates 4P90 and oP10 we determined the proportion of each facies in High compaction rates are likely to result from loading a the uncompacted (depositional) column and compared those compactable material with a high-density material with values with present compaction rates (Fig. 5). Some quali- high porosity and permeability.A natural example of such tative observations are notable: high proportions of de- a scenario is the loading of peat occurring at relatively posited peat favour current compaction rates 4P10; high shallow depth intervals (before it is mostly compacted; proportions of natural levee favour present compaction the determination of that depth is the subject of ongoing rates oP90; high proportions of bay mud favour a current research) with bar sand. Indeed, the fastest ¢ve compacting rate in the P10^P90 range. However, correlation coe⁄cients stratigraphies (compaction rates 4P99 on Fig. 2) show just are generally quite low for an individual facies, with peat such a behaviour for their most recent history.This sug- being the highest at 0.25. Some stratigraphies with low gests that the repeated sedimentation of peat and sand proportions of peat have present compaction rates 4P90, would tend to generate high compaction rates. That con- and the converse is also true (Fig. 5, upper left). Further- cept is validated in the model data by the high peat and more, these results are not easily applied; given observa- sand content throughout the stratigraphies with present tions of an existing stratigraphy of interest, it is unlikely compaction rates 4P90 (Fig. 6; right side).There is no cor- that one would know what the facies proportion of the un- relation between the most recently assigned facies and the compacted thickness would have been. present compaction rate.

24 r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 Compaction and subsidence in deltaic plains

Peat Bar Sand 100 100

10 10 (mm/yr) 1 1 Present compaction rate 0 20 40 60 80 100 0 20406080100 Proportion (%) of facies in each uncompacted stratigraphy Proportion (%) of facies in each uncompacted stratigraphy

Natural Levee Prodelta 100 100

10 10 (mm/yr)

1 1 Present compaction rate

0 20406080100 0 20406080100 Proportion (%) of facies in each uncompacted stratigraphy Proportion (%) of facies in each uncompacted stratigraphy

Bay Mud P90 10

0 20406080100 Proportion (%) of facies in each uncompacted stratigraphy Fig. 5. Di¡erent proportions of each of the ¢ve-model facies in the uncompacted stratigraphies comparedwith the present compaction rate for that stratigraphy.The same1087 stratigraphies (see Fig. 2; each represented by a single point) are represented in each plot. Di¡erent coloured points represent the stratigraphies comprising the three di¡erent subsets of the cumulative probability distribution functions in Fig. 2.There is a very inconsistent correlation between the proportion of a single facies in the uncompacted column and the present compaction rate.

Faster compaction rates are favoured by high proportion, P90 values increase with increased thickness (Fig. 8a). tions of compactable facies (i.e. peat) that are loaded with For a given thickness, P90 values decrease with time of ac- high density,permeable materials such as bar sand. Slower cumulation. P10 rates show similar behaviour to P90 rates compaction rates are favoured by low proportions of com- (Fig.8b).The reader can use Fig.8 to estimate the P10^P90 pactable material deposited combined with high propor- range of probable compaction rates for any combination of tions of facies that make good hydrologic seals (in our compacted thickness and time of accumulation that we case, prodelta mud). modelled.

Average net accumulation rates (NARs) DISCUSSION The average NAR is the compacted thickness divided by the time of accumulation. Here, we consider distributions To summarize, the distributions of present compaction of present compaction rates for a range of NAR and times rates of all our modelled stratigraphies are strongly in£u- of accumulation, ofwhich the stratigraphies previously fo- enced by the average NAR. Distributions of modelled cused on are only a subset. The model data for stratigra- compaction rates shift towards higher values with in- phies that compacted to 10^150m and that accumulated creased NAR, as expected. Focusing on a speci¢c group in 1^20 kyr indicate that higher NAR rates shift CDFs of of stratigraphies of interest (e.g. 100^110 m in 10^11kyr), present compaction rates to higher values (Fig.7).We arbi- the present compaction rate is further in£uenced by the trarily consider P90 and P10 rates to be the maximum and proportion and combinations of speci¢c facies in the un- minimum (respectively) probable compaction rate for each compacted depositional column (notably peat, bar sand, CDF in Fig. 7.For each CDF in Fig. 7, P90 and P10 rates are and prodelta mud). Position on extreme portions of a plottedwith their corresponding thickness and time of ac- CDF(e.g.4P90 or oP10) can be related to general litholo- cumulation in Fig. 8a and b. For a given time of accumula- gic composition. The conclusions of the stratigraphic r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 25 T. A . M e c k e l et al.

Peat ProDelta Natural Levee Bay Mud Sand Bar

P90 Stratigraphies 0 0 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100 100 Depth (m) in uncompacted depositional column Depth (m) in uncompacted depositional column 0 5 10 15 20 25 30 35 40 45 0 10 20 30 40 50 60 Proportion (%) of window thickness Proportion (%) of window thickness

0 0 1000 1000 2000 2000 3000 3000 4000 4000 5000 5000 6000 6000 7000 7000 Time (yrs) before present Time (yrs) before present 8000 8000 9000 9000 10000 10000 0 5 10 15 20 25 30 35 40 45 0 102030405060 Proportion (%) of window thickness Proportion (%) of window thickness Fig. 6. Running averages of the proportion (%) the ¢ve di¡erent model facies throughout deposition. Each curve is an average of the fastest or slowest compacting stratigraphies (N 5109). Left: stratigraphies with present compaction rates oP10. Right: stratigraphies with present compaction rates 4P90.Top row: percent of each facies within the moving average window (see text) with respect to uncompacted depositional thickness. Second row: same as top row,but the vertical axis represents time before present. Slow compacting stratigraphies have low proportions of peat and high proportions of prodelta mud throughout.The fastest compacting stratigraphies are composed predominantly of peat with lesser amounts of bar sand throughout. in£uences for the subset of stratigraphies investigated Present compaction rates should not be speculated likely hold for other compacted thicknesses and times of upon knowing only the facies of sur¢cial deposits. Model- accumulation, but have not been veri¢ed. ling data indicate that low density, highly compactable

Average net accumulation rate = < 5 mm/yr 5 - 20 mm/yr > 20 mm/yr 1

0.8

0.6 Fig. 7. Cumulative probability distribution 0.4 functions (CDFs) of present compaction rates 0.2 for a wide range of compacted thicknesses and

Cumulative probability times of accumulation. Di¡erent colours 0 represent stratigraphies with di¡erent average −2 −1 0 1 10 10 10 10 net accumulation rates [net accumulation Present compaction rate (mm/yr) rates (NAR) in Fig. 8].

26 r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 Compaction and subsidence in deltaic plains

(a) 150 6 7 5 4 2 mm/yr 7 3 mm/yr

20 mm/yr NAR 100 5

90 rate 4 P

5 mm/yr NAR 3

Compacted thickness (m) 50

1 mm/yr 2

5,000 10,000 15,000 20,000 Total accumulation time (yrs)

(b) 150 0.75 mm/yr

1.25

1.25 mm/yr

1 mm/yr 20 mm/yr NAR 1 Fig. 8. P90 (a) and P10 (b) present 100 compaction rates from the cumulative probability distribution 0.5 mm/yr functions (CDFs) in Fig. 7 plotted 0.75 with their corresponding thickness 10 rate P and accumulation time.This ¢gure 5 mm/yr NAR canbeusedtodeterminetheP10^ 0.25 mm/yr 50 0.5 P90 range of probable present Compacted thickness (m) compaction rates for any shallow stratigraphy with known compacted thickness and time of accumulation. 0.25 Dashed red lines represent constant net accumulation rates (NAR) of 5 1 and 20 mmyr . Black curves 0 contour constant compaction rates 0 5,000 10,000 15,000 20,000 (labelled). Total accumulation time (yrs) deposits such as peat at the surface can be associated with tional computational expense. Our modelled samples a wide range of compaction rates, which re£ect the deeper adequately represent the full range of variability in the geology.High density, permeable sediments such as sand, model procedure, and the present compaction rate for at the surface (typically considered relatively stable) can be any model stratigraphy would fall somewhere on our associated with high compaction rates, especially if they CDF for the corresponding present thickness and time overlie thick peat deposits. of accumulation.

Number of realizations Relaxing model constraints Some concern was devoted to verifying that the number of model realizations (41000 per stratigraphy)is su⁄cient to Present compaction rates vary minimally but consistently characterize the full range of possible present compaction as a result of changes in the average bed thickness used to rates. The CDF distributions do not vary signi¢cantly construct uncompacted stratigraphies (Fig. 4). Using a when the number of realizations increases 10-fold. The smaller average thickness results in negligibly higher pre- improvement to the CDF shape does not justify the addi- sent compaction rates; a larger average thickness results in r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 27 T. A . M e c k e l et al. negligibly smaller present compaction rates.The variabil- sands of years). Figure 9 compares our predicted compac- 1 ity is o0.5 mm yr for P90 values. tion rates with subsidence rates determined from buried We recognize that facies are not likely to have single peat samples. Kulp (2000) provides subsidence rates for parameter values, as in Table1. Ideally, rather than having radiometrically dated (14C) peat horizons in southern single values for each parameter for each facies, each facies Louisiana corrected for calendar age and paleo-sea level would have a known (observed) distribution of values for changes. each parameter from which values would be selected in a We chose a subset of samples with ages o1kyrandbur- Monte Carlo approach. Rather than using a range ofvalues ial depths o3m (N 5 68; locations mapped in Meckel that is currently less justi¢able (not yet observed) for facies et al., 2006) which minimize potential correction errors, of the Mississippi Delta plain, we chose to use actual va- presumably re£ect only recent subsidence, and are the lues measured from the ¢eld samples.While this is a lim- most appropriate for comparing with our model results itation of the model, it does not invalidate the results. because the amount of overburden has been minimized. Using a range of parameter values could change the shape Using the subsample stratigraphic thickness, an estimate of distributions in Figs 2 and 4. However, solutions would of the total accumulation time, and Fig. 8, the radiometric still likely fall in the range illustrated in Fig. 7, although subsidence rate can be compared with expected model that cannot be con¢rmed without generating a completely compaction rates (Fig.9; see Meckel et al., 2006 for details). new set of model results. Subsidence rates determined from radiometrically da- Were facies to have distributions of parameter values, ted peat samples in the Louisiana coastal plain are gener- distributions may overlap.With overlapping distributions, ally within the expected range (P10^P90) of modelled the term ‘facies’ as used in this modelling would cease to compaction rates for the stratigraphy underlying the sam- have discernible meaning. As one goal of this research ple. This is reasonable because both methods are essen- was to assess the in£uence of di¡erent facies on subsidence tially measuring subsidence at very long time scales and compaction rates, itwas necessary to have distinct and (sediment accumulation and compaction over thousands limited geotechnical properties for each facies. of years). The fact that some radiometric subsidence rates are higher than the expected distribution of modelled Modelled compaction rates and observed compaction rates suggests that processes other than shal- subsidence rates low compaction (Penland & Ramsey, 1990; Morton et al., 2005; Dokka, 2006) likely contribute to subsidence at those Our e¡orts to model compaction rates stemmed from the locations (Meckel et al., 2006). Regionally and over geolo- lack of available direct observations. However, we can com- gic time scales, compaction seems to reasonably explain pare our modelled rates to subsidence rates from other subsidence rates from many radiometric data, and com- typesofobservationsoversimilartimescales(i.e.thou- paction is therefore likely to in£uence lateral and vertical stratigraphic patterns.

8 Compaction and stratigraphic evolution 7 We have discussed how lithologic composition (facies) in- 6 £uences compaction rates. It is tempting to speculate on how our modelled compaction rates might, in turn, in£u- 5 ence the geologic evolution of deltas (i.e. delta prograda- 4 tion, crevasse splay events, delta lobe switching, stratigraphic trends) such as the Mississippi River delta

Rate (mm/yr) 3 (Coleman et al., 1998).We will assume that the stratigraphic characteristics of the fastest and slowest compacting stra- 2 tigraphies identi¢ed for the small subset of stratigraphies 1 also apply to the wider range of thicknesses and times of accumulation modelled. 0 0 10 20 30 40 50 60 70 Stratigraphies composed of high proportions of prodel- Holocene thickness underlying sample (m) ta mud (e.g. Fig. 4, 100% prodelta mud curve) or a combination of prodelta mud and natural levee (e.g. Fig. 6, left 14 Fig. 9. Comparison of subsidence rates determined from 68 C side) result in some of the lowest modelled compaction samples (red points) with the expected P10^P90 range of rates.These stratigraphies should facilitate delta lobe pro- compaction rates (blue lines) for the thickness of Holocene gradation,as sedimentation rates can easily exceed the ex- sediments underlying the 14C samples. Approximately half of the 14C rates are within the expected modelled range of rates for pected compaction rates.This concept is supported by the shallow compaction. Di¡erences between 14C rates and modelled observation of the dramatic seaward protrusion of the compaction distributions indicate processes in addition to modern ‘birdfoot’ delta of the Mississippi River. Our re- Holocene compaction are likely to contribute to subsidence for at sults predict slow compaction rates for stratigraphies typi- least half of the sites (Meckel et al., 2006). cal of the natural levees in the lower reaches of the

28 r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 Compaction and subsidence in deltaic plains

Mississippi River (where natural levee deposits overly pro- SUMMARY delta muds; as in Fig. 6, left side). Slow local compaction We use stochastic forward models of incremental sedi- rates in these environments likely inhibited the river from mentation and compaction to constrain present compac- avulsing (before arti¢cial levee construction) the notice- tion rates for stratigraphies with speci¢c present ably short distance (o3 km) to the coast at Breton Sound, compacted thickness and time of accumulation, and to LA, or to the west at the Barataria Bay region.The low tidal identify stratigraphic characteristics that in£uence com- range, dominance of river inputs and lack of accommoda- paction rates.The rates and subsidence magnitudes pre- tion space (including slow compaction rates) favour pro- gradation (Galloway & Hobday,1996). sented here are the most comprehensive estimates to date of the contribution of shallow compaction in deltaic envir- Landward of extending delta distributaries such as the onments. Mississippi’s birdfoot, deposition evolves as bays ¢ll with Compaction is a complex nonlinear process; the instan- mud, organic marshes accrete (e.g. peat in our models), taneous result is a combination of many variables, encom- and local distributaries deposit bar sands and natural passing prior and present depositional events. Modelled levees. The high predicted compaction rates of stratigra- compaction rates for stratigraphies characteristic of the phies composed of peat and bar sand (Fig. 6, right side), Holocene of the Mississippi River delta are generally less as might typically be encountered at the margin of a 1 distributary meander belt (Rajchl & Ulicny,2005),may than a few mmyr . Stratigraphic heterogeneity increases Ł compaction rates. Modelled compaction rates do not cor- encourage crevasse splay processes. On a broader scale, relate consistently with cumulative subsidence, recent se- as entire inter-distributary regions accumulate higher dimentation rates, or the thickness and facies of the most proportions of peat, their regional evolution towards recently deposited layer. generally higher predicted compaction rates may even- Of the model stratigraphies that we analysed in detail, tually encourage river avulsion due to resulting gradient the fastest compacting stratigraphies have high propor- advantages, and the formation of a new delta lobe. Prior tions of peat and bar sand throughout, whereas the slowest avulsion studies have focused on substrate erodibility and high aggradation rates (T˛rnqvist, 1994; Aslan et al., compacting stratigraphies have low proportions of peat and high proportions of prodelta mud, followed in abun- 2005). We provide predicted rates of compaction in these dance by natural levee deposits. These proportions refer various environments for consideration in models of to the uncompacted depositional column, before sedi- avulsion. mentation and compaction. Overall, subtle variability in compaction rates of hetero- Modelled compaction rates are similar to many long- geneous deposits (which are expected to be slightly faster, term radiometric subsidence rates in the Louisiana delta on average, than homogeneous deposits; Fig. 4) may in£u- plain, suggesting that compaction can account for much ence the regional evolution of deltaic morphology and stratigraphy over geologic timescales. Our compaction re- of (but not all of) the rate of accommodation space created during the Holocene. Thus, compaction rates may be a sults are consistent with the depositional evolution of del- dominant in£uence of vertical and lateral stratigraphic tas that has been described for decades (Fisk, 1944; trends during Holocene deltaic evolution. Roberts, 1997). We suggest that the generalized vertical stratigraphic trends of a depositional lobe at the 100-m scale may in fact betray underlying stochastic depositional processes at the (sub)meter scale, and their in£uence on ACKNOWLEDGEMENTS compaction rates. Stratigraphic composition in£uences This research was conducted during a USGS Mendenhall compaction rates, and compaction rates may in£uence Research Fellowship held by the lead author.We are grate- long-term stratigraphic evolution. We have demonstrated ful to H. Kooi for generously providing compaction rou- the former, but can only speculate on the latter until it tines. This manuscript bene¢ted from geostatistical can be more fully explored using integrated and dynamic discussions with A. Solow, B. Wilkinson, L. Lake and J. 3D models of sedimentation and compaction. Yet, our re- Jensen. Helpful reviews before submission were provided sults begin to reconcile the heterogeneity that is actually by W.Barnhardt (USGS) and B. Dugan (Rice University). observed at small scales vertically and laterally in deltaic successions with the larger-scale upward stratigraphic trends that have been so successfully applied towards un- APPENDIX A derstanding deltaic evolution, were geotechnical properties drastically di¡erent than what is observed in modern Here, we provide detailed information regarding the char- environments (e.g. extremely compactable prodelta depos- acteristics of the modelled stratigraphies that resulted its, or incompressible peat accumulations), an entirely dif- from our methodology to construct uncompacted strati- ferent ‘typical’ delta-lobe stratigraphy may result. Such graphies.These data are for stratigraphies that have com- concepts may be useful for understanding variability in pacted thicknesses of 100^110 m and that accumulated in stratigraphic evolution of deltas in di¡erent latitudes (e.g. 10^11kyr (N 51087). equatorial vs. arctic), as the geotechnical properties of the The ab pairs that de¢ne the shapes of G distributions various facies may di¡er. used to randomly assign layer sedimentation rates for the r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 29 T. A . M e c k e l et al. modelled stratigraphies appear in Fig. A1. Each point re- thickness range of the stratigraphies of interest. The presents a uniquely shaped distribution, from which on points between the lines ab 510 and 20 represent strati- average 30 random sedimentation rates were chosen for graphies with depositional thicknesses 110 m, which an uncompacted stratigraphy. The high density of the ultimately compacted to between 100 and 110 m. Our re- points around the line ab 5 10 mm yr 1 (Fig. A1) re- striction that |tASR^aASR| o0.1tASR results in very few £ects the high proportion of stratigraphies that accumu- stratigraphies with low a values being used (a 5 1isan lated with that ASR that compacted to within the exponential distribution, which we wanted to avoid). The

10 α x 0.14 α β α β = 20 = 3 = 3.33 x 9 0.12 α β β = 6 = 1.66 =10 α = 9 β = 1.11 0.1 8 Data for all layers N = 32,076 0.08 7 0.06 Probability Fig. A1. a and b values used to de¢ne G 0.04 6 distributions for selecting layer 0.02 sedimentation rates. Each point

) value assigned 5 represents a uniquely shaped G β 0 0 5 10 15 20 25 30 distribution with an average of ab. Layer sedimentationn rate (mm/yr)

Beta ( 4 Di¡erent symbols indicated are for stratigraphies falling on di¡erent portions N = 1087 stratigraphies 3 of the cumulative distribution function of P10-P90 present compaction rates (see Fig. 4).The inset histogram provides examples of 2 >P90 three di¡erent G distributions, and the

102 (a) N = 32, 076 total layers

102

100 100 101 102 103 104 Sedimentation rate (mm/yr) Layer time (yr)

102 (b) Line is 10 mm/yr sedimentation rate 100

N = 32, 076 total layers Fig. A2. Characteristics of each of −2 Layer thickness (m) 10 the uncompacted 32 076 layers used 100 1 2 3 4 10 10 10 10 to construct the1087 stratigraphies Layer time (yr) that compacted to a thickness 400 between100and110mandhadan (c) N = 1087 accumulation time between10 and 300 Total 11kyr (a) Layer sedimentation rate Stratigraphies vs.layertime.(b)Layerthickness 200 vs. layer time. (c) Frequency distribution of the number of 100 stratigraphies with a given number of layers.Thirty depositional layers Number of stratigraphies 0 0 20 40 60 are most characteristic for the Number of layers in a stratigraphy stratigraphies of interest.

30 r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 Compaction and subsidence in deltaic plains inset frequency distribution (upper right of Fig. A1) pro- ¢ll; implications for wetland loss in Terrebonne and Lafource vides examples of G distributions for three ab pairs where Parishes, Louisiana, PhD Thesis: Louisiana State University, ab 5 10, and also the distribution of all 32 076 layer rates Baton Rouge, 346pp. assigned for all the1087 models. Kuecher, G.J., Chandra, N., Roberts, H.H., Suhayada, J.H., Williams S.J. Penland S.P. Autin W.J. The times of accumulation for each layer are compared , , , & , (1993) Consoli- to that layer’s sedimentation rate in Fig. A2a, and to that dation settlement potential in south Louisiana. In: Coastal Zone’93. Proceedings of the Eighth Symposium on Coastal and Ocean layer’s thickness in Fig. A2b. A single point in these plots Management held in New Orleans, LA, July 19^23, 1993 (Ed. by could correspond to any of the ¢ve facies used in the mod- O.T.Magoon,W.S.Wilson, H. Converse & L.T.Tobin), pp.175^ els. The frequency distribution of the number of layers in 192. each of the1087 stratigraphies is seen in Fig. A2c. Kulp, M.A. (2000) Holocene stratigraphy, history, and subsidence: Mississippi River delta region, north-central Gulf of Mexico, PhDThesis, University of Kentucky, Lexington, REFERENCES 336pp. Long, A.J., Wa l l e r, M.P. & Stupples, P. (2006) Driving me- Amorosi, A., Centineo, M.C., Colalongo, M.L. & Fo ri n i, chanisms of coastal change: peat compaction and the destruc- F. (2005) Millennial-scale depositional cycles from the Holo- tion of late Holocene coastal wetlands. Mar.Geol., 225, 63^84. cene of the Po Plain, Italy. Mar. Geo., 222^223,7^18. Meckel, T. A . , ten Brink, U. & William s, S.J. 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(2005) Rapid subsidence and historical wetland loss in the Bryant,W.R ., Hottman,W. & Trabant, P. (1975) Permeability Mississippi delta plain: likely causes and future implications. of unconsolidated and consolidated marine sediments, Gulf of U.S.G.S. Open-File Report 2005-1216, 116pp. Mexico. Mar. Geotech., 1(1), 1^14. Penland, S. & Ramsey, K.E. (1990) Relative sea-level rise in Coleman, J.M., Roberts, H.H. & Stone, G.W. (1998) Missis- Louisiana and the Gulf of Mexico: 1908^1988. J. Coastal Res., sippi river delta: an Overview. J. Coastal Res., 14(3), 698^716. 6(2), 323^342. Dacey, M.F. (1979) Models of bed formation. Math. Geo., 11, Pizzuto, J.E. & Schwendt, A.E. (1997) Mathematical model- 655^ 668. ling of autocompaction of a Holocene transgressive valley- ¢ll Dokka, R.K. (2006) Modern-day tectonic subsidence in coastal deposit,WolfeGlade, Delaware. Geology, 25(1), 57^60. Louisiana. Geology, 34(4), 281^284. Rajchl, M. & UlicŒnyŁ, D. (2005) Depositional record of an avul- Fisk, H.N. (1944) Geological investigation of the alluvialvalley of sive £uvial system controlled by peat compaction (Neogene, the lower Mississippi River, U.S. Army Corps of Engineers, Most Basin, Czech Republic). Sedimentology, 52,601^625. Mississippi River Commission,Vicksburg, MS, 78pp. Roberts, H.H. (1997) Dynamic changes of the Holocene Missis- Galloway, W.E . & Hobday, D.K. (1996) Terrigenous Clastic De- sippi river delta plain: the delta cycle. J. Coastal Res., 13(3), 605^ positional Systems; Applications to Fossil Fuel and Groundwater 627. Resources, 2nd edn. Springer, 283pp. Roberts, H.H., Bailey, A. & Kuecher, G.J. (1994) Subsidence Kooi, H. (1997) Insu⁄ciency of compaction disequilibrium as in the Mississippi river delta ^ Important in£uences of valley the sole cause of high pore £uid pressures in pre-Cenozoic se- ¢lling by cyclic deposition, primary consolidation phenom- diments. Bas. Res., 9(3), 227^241. ena, and early diagenesis. Trans. ^ Gulf Coast Assoc. Geo. Soc., Kooi, H. (2000) Land subsidence due to compaction in the 44,619^629. coastal area of the Netherlands: role of lateral £uid £ow and Te r z a g h i, K. (1943) Theoretical Soil Mechanics. J. Wiley & Sons, constraints from well-log data. Global Planet. Change, 27,207^ NewYork, NY,510pp. 222. T˛rnqvi st, T. E . (1994) Middle and late Holocene avulsion his- Kooi, H. & de Vries, J.J. (1998) Land subsidence and hydrody- tory of the River Rhine (Rhine-Meuse delta, Netherlands). namic compaction of sedimentary basins. Hydrol. Earth Syst. Geology, 22, 711^714. Sci., 2(2^3), 159^171. Wilkinson, B.H., Merrill, G.K. & Kivett, S.J. (2003) Stratal Kooi, H., Johnston, P., Lambeck, K., Smither, C.& Molen- order in Pennsylvanian cyclothems. Geo. Soc. Am. Bull., 115(9), dijk, R. (1998) Geological causes of recent (100 yr) vertical 1068^1087. land movement in the Netherlands. Tectonophysics, 299, 297^ 316. Kuecher, G.L. (1994) Geologic framework and consolidation Manuscript received 29 May 2006; Manuscript accepted 28 settlement potential of the Lafourche Delta, topstratum valley November 2006

r 2007 The Authors. Journal compilation r 2007 Blackwell Publishing Ltd, Basin Research, 19,19^31 31