Modeling Cape- and Ridge-Associated Marine Sand 

Deposits: A Focus on the U.S. Atlantic Continental Shelf 

Chapter M of 

Contributions to Industrial-Minerals Research 

Bulletin 2209–M
 

U.S. Department of the Interior 

U.S. Geological Survey 
This page intentionally left blank 
 

Modeling Cape- and Ridge-Associated Marine Sand 

Deposits: A Focus on the U.S. Atlantic Continental Shelf 

By James D. Bliss, S. Jeffress Williams, and Karen S. Bolm 

Chapter M of 

Contributions to Industrial-Minerals Research 

James D. Bliss, Phillip R. Moyle, and Keith R. Long, Editors 

Bulletin 2209–M
 

U.S. Department of the Interior 

U.S. Geological Survey 
U.S. Department of the Interior 

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

Mark D. Myers, Director 

U.S. Geological Survey, Reston, Virginia: 2009 

This report and any updates to it are available online at: 

http://pubs.usgs.gov/bul/b2209-m/ 

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Telephone: 1–888–ASK–USGS 

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and living resources, natural hazards, and the environment: 

World Wide Web: http://www.usgs.gov 

Telephone: 1–888–ASK–USGS 

Suggested citation: 

Bliss, J.D., Williams, S.J., and Bolm, K.S., 2009, Modeling cape- and ridge-associated 

marine sand deposits; a focus on the U.S. Atlantic Continental Shelf: U.S. Geological 

Survey Bulletin 2209–M, 22 p.

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not 

imply endorsement by the U.S. Government. 

Although this report is in the public domain, permission must be secured from the individual copyright 

owners to reproduce any copyrighted materials contained within this report. 

Cataloging-in-Publication data are on file with the Library of Congress (URL http://www.loc.gov/). 

Produced in the Western Region, Menlo Park, California 

Manuscript approved for publication, May 27, 2008 

Text edited by George A. Havach 

Layout and design by Stephen L. Scott 
Contents

Abstract -------------------------------------------------------------------------------------------------------1

Introduction---------------------------------------------------------------------------------------------------1

Acknowledgment---------------------------------------------------------------------------------------------2

Marine-Sand-Deposit Models -----------------------------------------------------------------------------2

Introduction---------------------------------------------------------------------------------------------2

Descriptive Models ------------------------------------------------------------------------------------2

Quantitative Models -----------------------------------------------------------------------------------2

Mineral-Resource Assessment ----------------------------------------------------------------------------3

Introduction---------------------------------------------------------------------------------------------3

Quantitative Models -----------------------------------------------------------------------------------3

Monte Carlo Simulation -------------------------------------------------------------------------------------4

MCS Applications in Mineral-Resource Assessments -------------------------------------------------5

Cape- and Ridge-Associated Marine Sand Deposits ---------------------------------------------------5

Basic Data ----------------------------------------------------------------------------------------------5

Modeling Sand-Deposit Variables -------------------------------------------------------------------6

Introduction---------------------------------------------------------------------------------------6

Area Model ---------------------------------------------------------------------------------------6

Thickness Model---------------------------------------------------------------------------------8

Mean-Grain-Size Model-------------------------------------------------------------------------9

Grain-Sorting Model-----------------------------------------------------------------------------9

Volume Model ---------------------------------------------------------------------------------- 11

Sand-Dominated-Facies Model -------------------------------------------------------------- 12

Spatial-Density Model------------------------------------------------------------------------- 13

Estimating the Number of Undiscovered Deposits----------------------------------------------------- 13

Setting Up the MCS, Using Marine-Sand-Assessment Data ----------------------------------------- 14

Executing the MCS Program ----------------------------------------------------------------------------- 15

Summary ---------------------------------------------------------------------------------------------------- 16

Conclusions------------------------------------------------------------------------------------------------- 16

References Cited------------------------------------------------------------------------------------------- 17

Appendixes

A. An Interim Descriptive Model for Cape- and Ridge-Associated Marine Sand Deposits,

 by S. Jeffress Williams and James D. Bliss---------------------------------------------------- 20

Introduction------------------------------------------------------------------------------------------- 20

Brief Description ------------------------------------------------------------------------------------- 20

Regional and Local Geologic Attributes----------------------------------------------------------- 20

Economic Limitations -------------------------------------------------------------------------------- 21

B. Statistical Methods and Diagrams-------------------------------------------------------------------- 22

III
Figures

 1. U.S. Atlantic Continental Shelf, showing location of study area and approximate 

 locations of surveys with deposits either used as data sources or mentioned

 in text----------------------------------------------------------------------------------------------------4

 2. Histogram and normal quantile-quantile plot of area data for 47 of 54 

 cape- and ridge-associated marine sand deposits in survey areas ----------------------------8

 3. Area model of cape- and ridge-associated marine sand deposits --------------------------------8

 4. Histogram and normal quantile-quantile plot of mean-grain-size data for 36 of 54 

 cape- and ridge-associated marine sand deposits in survey areas--------------------------- 10

 5. Mean-grain-size model of cape- and ridge-associated marine sand deposits ---------------- 10

 6. Histogram and normal quantile-quantile plot of grain-sorting data for 24 of 54 

 cape- and ridge-associated marine sand deposits in survey areas--------------------------- 11

 7. Grain-sorting model of cape- and ridge-associated marine sand deposits -------------------- 11

 8. Histogram and normal quantile-quantile plot of volume data for 54 cape- 

 and ridge-associated marine sand deposits in survey areas ---------------------------------- 11

 9. Volume model of cape- and ridge-associated marine sand deposits --------------------------- 12

10. Sand-dominated-facies model of cape- and ridge-associated marine sand deposits -------- 12

11. Schematic flowchart illustrating overall structure of the Monte Carlo simulation

 program------------------------------------------------------------------------------------------------15

12. Plot of cumulative distribution of predicted sand resources in cape- and ridge-

 associated sand deposits in a hypothetical survey area --------------------------------------- 16

13. Same histogram and normal quantile-quantile plot for 47 of 54 cape- and 

 ridge-associated marine sand deposits as in figure 3, with normal-distribution 

 curves and Lilliefors confidence boundary indicated------------------------------------------- 22

Tables

1. Areas of cape- and ridge-associated marine sand deposits on the U.S. Atlantic 

 Continental Shelf considered in this study ---------------------------------------------------------7

2. Phi scale of grain sizes for sedimentary deposits ---------------------------------------------------9

3. Mineral-deposit density (MDD value) of cape- and ridge-associated marine sand 

 deposits in three survey areas--------------------------------------------------------------------- 13

4. Probable number of undiscovered deposits estimated by three assessment-team 

 members for a hypothetical assessment tract--------------------------------------------------- 14

5. Probabilities of numbers of undiscovered deposits estimated for a hypothetical 

 assessment tract ------------------------------------------------------------------------------------ 15

6. Default distribution of undiscovered deposits and probabilities used in a Monte 

 Carlo simulation-------------------------------------------------------------------------------------- 15

IV
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Modeling Cape- and Ridge-Associated Marine 

Sand Deposits: A Focus on the U.S. Atlantic 

Continental Shelf 

By James D. Bliss, S. Jeffress Williams, and Karen S. Bolm 

Abstract 

Cape- and ridge-associated marine sand deposits, which 

accumulate on storm-dominated continental shelves that are 

undergoing Holocene marine transgression, are particularly 

notable in a segment of the U.S. Atlantic Continental Shelf 

that extends southward from the east tip of Long Island, N.Y., 

and eastward from Cape May at the south end of the New 

Jersey shoreline. These sand deposits commonly contain sand 

suitable for shore protection in the form of beach nourishment. Increasing demand for marine sand raises questions 

about both short- and long-term potential supply and the 

sustainability of beach nourishment with the prospects of 

accelerating sea-level rise and increasing storm activity. To 

address these important issues, quantitative assessments of 

the volume of marine sand resources are needed. Currently, 

the U.S. Geological Survey is undertaking these assessments 

through its national Marine Aggregates and Resources Program (URL http://woodshole.er.usgs.gov/project-pages/

aggregates/). 

In this chapter, we present a hypothetical example of a 

quantitative assessment of cape- and ridge-associated marine 

sand deposits in the study area, using proven tools of mineral-resource assessment. Applying these tools requires new 

models that summarize essential data on the quantity and 

quality of these deposits. Two representative types of model 

are descriptive models, which consist of a narrative that 

allows for a consistent recognition of cape- and ridge-associated marine sand deposits, and quantitative models, which 

consist of empirical statistical distributions that describe 

significant deposit characteristics, such as volume and grainsize distribution. Variables of the marine sand deposits considered for quantitative modeling in this study include area, 

thickness, mean grain size, grain sorting, volume, proportion 

of sand-dominated facies, and spatial density, of which spatial density is particularly helpful in estimating the number 

of undiscovered deposits within an assessment area. A Monte 

Carlo simulation that combines the volume of sand-dominated-facies models with estimates of the hypothetical probable number of undiscovered deposits provides a probabilistic 

approach to estimating marine sand resources within parts 

of the U.S. Atlantic Continental Shelf and other comparable 

marine shelves worldwide. 

Introduction 

Research is underway by the U.S. Geological Survey 

(USGS) to find new ways of estimating potential aggregate 

resources in the U.S. offshore Exclusive Economic Zone 

(EEZ). A requirement is that these estimates reflect the degree 

of uncertainty in the analysis. The U.S. EEZ, as defined by 

Presidential declaration in 1983, is a margin extending seaward 

370 km (200 nautical miles) around the United States and its 

territories. Of the known resources in this 12-million-km2 area, 

aggregate, which includes sand, gravel, and combinations 

thereof, is likely to be one of the most important commodities 

in the near term for the United States (Williams, 1992). Marine 

sand and gravel is currently an important source of aggregate 

in Japan, the United Kingdom, the Netherlands, and other 

maritime countries. Currently, most nonpetroleum-resource 

production from the U.S. EEZ has been from marine sand 

deposits. The principle use of marine sand has been for beach 

replenishment, with ~920 million m3 of material extracted 

and used since the 1920s (URL http://psds.wcu.edu/1038.asp, 

accessed Sept. 11, 2007). Currently, demand for additional sand 

to maintain and replenish beaches and other coastal landforms 

is increasing for both natural and manmade features and is 

likely to continue increasing in the near future with mitigation 

of erosion and sea-level rise along heavily developed coasts. A 

method is needed to estimate the marine sand resources available near areas undergoing coastal erosion. To reflect the uncertainty and variation in these estimates, a probabilistic approach 

is required. 

We adopted the approach of Singer (1993), which has been 

used extensively for quantitative mineral-resource assessment 

onshore. Mineral-resource assessment is a highly formalized process, each part of which is explicitly stated. Mineraldeposit types successfully addressed by this approach have 

been predominately of metallic minerals (for example, porphyry copper) but also include several industrial minerals (for 

example, bedded barite). Numerous metallic-mineral-resource 

assessments have been completed in the United States, includModeling Cape- and Ridge-Associated Marine Sand Deposits 1 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ing some for the Nation as a whole (Ludington and others, 

1996; Nation Mineral Resource Assessment Team, 1998) and 

outside, including all of Costa Rica (U.S. Geological Survey, 

1987). Such assessments are now being conducted on a global 

scale (Schulz and Briskey, 2003). Some past activities and proposed modifications of this approach were reported by Singer 

(1993, 2007). 

Mineral-resource models, as defined in detail below, are 

available for many metallic and a few industrial minerals (Cox 

and Singer, 1986; Bliss, 1992). Models for industrial-mineral 

deposits were presented by Orris and Bliss (1991, 1992). Bliss 

and Page (1994) constructed models for onshore sand and 

gravel deposits, and Bliss and others (2003) suggested some 

guidelines for sand and gravel assessment. To assess marine 

sand resources, a new set of models is needed. Several new 

models for cape- and ridge-associated marine sand deposits are 

presented here for the first time. 

Acknowledgments 

Development of new tools and construction of new models 

for assessment of marine sand deposits requires scientific 

insight from at least two differ types of expertise. We thank 

Matthew Arsenault (USGS) for providing suggestions from a 

marine-geologic perspective, and Keith Long (USGS) from a 

mineral-resource-assessment and modeling perspective. Jeffrey 

Waters of the U.S. Army Corps of Engineers and Gary Lore of 

the U.S. Minerals Management Service also provided suggestions and additions that have resulted in significant corrections 

and clarifications to the manuscript. 

Marine-Sand-Deposit Models 

Introduction 

Modeling is a fundamental tool of scientific research that 

facilitates interpolation and extrapolation from sparse and 

commonly incomplete data. Many different types of model are 

used, but generally they are simplifications of what are perceived to be complex entities or processes. Model construction 

inevitably results in selecting some data and ignoring others. 

One unavoidable problem is that the uncertainty in model 

construction cannot be overcome (Gorokhovski and Nute, 

1995). Modelers of most geologic systems can view them as 

either simple or complex; however, Ahnert (1996) suggested 

that nature is not necessarily either one or the other. Depending on the assumptions and approach used in the analysis of a 

natural system, the set of models constructed to characterize it 

can be more complex than necessary. Comparison of several 

observations leads to an abstraction in which some attributes 

are considered essential, while others are deliberately ignored. 

This approach, in turn, allows classification criteria to be identified and the natural system under investigation to be classified 

as one of several possible types. These types, however, are only 

abstractions—they are “models of reality” (Ahnert, 1996, p. 

92). One particular problem that plagues all types of model is 

that the more assumptions, the less reliable the model (Ahnert, 

1996, p. 111). A second deception can also arise with the 

assumption that a complex explanation is automatically better 

than a simple one, considering that the complex model may be 

more impressive (Ahnert, 1996). Complex systems, however, 

may not necessarily be adequately described by computer 

simulation using too few models. In both model construction 

and the design of the stochastic programs using a Monte Carlo 

simulation (MCS), the natural system under investigation must 

be adequately portrayed. 

Descriptive Models 

One type of model of specific interest in this study is the 

descriptive model (Singer and Berger, 2007), which is a systematic arrangement of all known information about a presumably unique mineral-deposit type. An important characteristic 

of descriptive models is that they consist of an assemblage of 

data that are empirical or that are found to be genetically interrelated. All shared attributes must be included in the model, 

even in the absence of a clear explanation as to why they are 

present. Descriptive models allow scientists conducting an 

assessment to recognize deposits that belong to a specific type. 

Descriptive models also provide information that can help 

assessment teams recognize local and regional geologic conditions associated with the deposit type. The regional-geologic 

guidelines in the descriptive model help in determining whether 

a specific geologic setting (or tract) is permissive for the occurrence of the deposit type. Specifically, the descriptive model 

gives guidelines allowing recognition of boundaries of areas (or 

tracts) where deposits occur; no deposits of the types addressed 

are expected to be found outside tract boundaries. This determination should be possible by using information contained in the 

descriptive model, even if a deposit of the type under investigation is not currently recognized as present in the assessment 

area. Descriptive models help sort out available data about 

important sites and may reveal the presence of an undiscovered 

deposit that is one of a specific type. These tasks are possible 

only if the descriptive model includes clearly recognizable and 

distinctive regional features. For example, the information in 

descriptive models is intended to allow someone who has never 

seen a marine sand deposit to be able to recognize one readily. 

The identification of marine sand deposits is complicated by 

the fact that many occurrences may be described as sand bearing but lack such characteristics as minimum thickness and 

volume to be considered a potential source of sand. An interim 

descriptive model for cape- and ridge-associated marine sand 

deposits that is suitable for deposit tract recognition and preparation is presented in appendix A. 

Quantitative Models 

Construction of quantitative models for marine sand 

deposits suitable for use in coastal construction is limited by 

2 Contributions to Industrial-Minerals Research 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

available data. In this initial effort, we constructed quantitative 

models of cape- and ridge-associated marine sand deposits that 

were grouped together for assessment purposes. One complication is caused by the fact that although the geologic literature 

on marine sand is plentiful, reports that focus on marine sand 

deposits identified as resources suitable for use as aggregate 

or beach replenishment are considerably scarcer. Most reports 

on marine sand deposits are focused on understanding how 

the observed characteristics of these deposits are produced in 

the marine environment, both modern and historical, without 

regard to their economic value. One reason for this focus may 

be the past perception that marine sand resources are unusually 

large and that little additional information about resource size is 

need. One important factor is that considerations of end use and 

extraction requirements commonly make many sand deposits 

unsuitable because of the unacceptable contents of fine sediment, shelly debris, or coarse materials in these deposits. 

Mineral-Resource Assessment 

Introduction 

Simply stated, the mineral-resource-assessment approach 

defined by Singer (1993) consists of three parts: 

1. Delineation of areas, known as permissive tracts, where 

deposits of a given type may be expected to occur, given 

knowledge of the local and regional geology. 

2. Estimation of the amount of minerals by using grade, 

tonnage, or other distributions said to be “models” of the grade, 

tonnage, and so on. For some industrial-mineral-deposit types, 

this estimate may include volume and other special characteristic distributions unique to each deposit type (for example, a 

distribution of mean (phi) units for marine sand deposit types). 

3. Estimation of the number of undiscovered sand deposits 

of a specific type, with due consideration of exploration intensity and associated successes and failures within permissive 

tracts. Use of subjective estimates is the standard approach, for 

which various guidelines were outlined by Singer (2007). One 

guideline is the use of mineral-deposit density (MDD)—the 

number of deposits per unit area where they have been well 

explored. 

All three parts are interconnected, and some may need 

to be repeated and refined as the assessment proceeds. This 

approach is greatly facilitated by a team of experts familiar 

with (1) the deposits being considered, (2) the areas being 

assessed, and (3) assessment methodologies. 

Once the mineral-resource assessment has been completed, 

an MCS is run, as described below. The quantitative models 

described in part 2 are combined with estimates of the probable 

number of undiscovered deposits in part 3 to assess undiscovered mineral resources within the permissive tract. The product 

of the simulation is a probabilistic distribution. All three parts 

of this approach need to use mineral deposits that are consistently defined. Uncertainty and variation in deposit characteristics, such internal features as sand content, and MDD are 

inseparable and are incorporated into the final assessment of 

marine sand resources. 

Before attempting to assess marine sand resources, however, several underlying factors need to be clearly understood. 

First, scale and dimensional properties are always important 

during each part of the assessment. For example, a sand body 

is not a cape- and ridge-associated marine sand deposit as the 

term is used here unless it has a sufficient volume (length, 

width, thickness) to justify extraction. Therefore, assessment 

is ultimately focused on deposits that under the most favorable circumstances are considered suitable for extraction. Such 

deposits normally include both geologic and economic elements in their definition. 

Scale is important in defining two fundamental products of 

a marine-sand assessment—the permissive tract and the criteria 

used for recognition of marine-sand-deposit targets. Some of 

the same geology (as expressed by bathymetry, geophysics, 

side-scan sonar, and sediment-sample characteristics) can be 

used to help define either a permissive tract or a marine sanddeposit target, though in different ways in relation to scale. 

Note that bathymetry includes bottom depth, shape, slope, and 

geomorphology. The types of marine shelf and currently active 

regional processes involved (tide dominated, storm dominated, 

and so on) are important because they help identify the possible 

types of marine sand deposits present. Marine sand deposits 

may be currently forming, or they may be undergoing modification or destruction. Some marine sand deposits may be relict 

features covered by younger sediment. 

The permissive tract, which is needed to meet the requirements of part 1, can encompass as area of hundreds to thousands of square kilometers that is expected to be considerably 

larger than that of a marine sand deposit. All undiscovered 

deposits are dispersed inside the tract boundaries and suggested 

by targets. Marine-sand-deposit targets, which are needed to 

meet the requirements of part 3, are those parts of the permissive tract where marine sand deposits are expected to occur. 

Again, the same type of geology used to define permissive 

tracts may be applicable here, although for marine-sand-deposit 

targets the focus is on those variables with values that suggest the presence of a deposit. This information is then used to 

construct an exploration model. The number and area of targets 

identified is an important guideline in making subjective estimates of the possible number of undiscovered deposits required 

in part 3. 

Several models have been constructed that may help in 

identifying cape- and ridge-associated marine sand deposits 

but are not used directly in an MCS. This information, which 

includes the areas of marine sand deposits on the sea floor, can 

help determine whether a suspected marine-sand-deposit target 

has a comparable area. 

Quantitative Models 

Quantitative models include distribution, relation, and 

spatial models. Distribution models consist of frequency 

distributions of geologic, economic, geometric, and geotechModeling Cape- and Ridge-Associated Marine Sand Deposits 3 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

nical variables for marine sand deposits that are members of 

a population identified by using a descriptive model. Compilation and analysis of the data used in model construction 

may also imply that these data are actually from two deposit 

types, not from one as initially proposed. Clarification and 

improved descriptive models may be one product of the data 

analysis. Most of the models described below are examples 

of distribution models, some of which can be described 

by using a common statistical distribution or may have an 

empirical distribution. 

Models are needed to satisfy the requirements of part 

2 of Singer’s (1993) approach; without these models, an 

MCS cannot be run. Most deposit variables, when correctly 

grouped into deposit types, have either an approximately 

normal or log-normal distribution. Variables considered for 

deposit modeling include area, volume, thickness, median 

grain size (reported in Φ units, as discussed below), grain 

sorting (also reported in Φ units), and the proportion of sanddominated facies (that is, sand content). One data source 

for both modeling and assessment is the USGS usSEABED 

database, a compilation of marine-sea-floor observations of 

all types covering the entire U.S. EEZ (Williams and others, 

2007a). The data for the U.S. Atlantic Continental Shelf are 

particularly useful (Reid and others, 2005), including the 

interpretation by Williams and others (2007b), as well as the 

reports noted in the subsection below entitled “Basic Data.” 

Additional useful references are contained in the report by 

Williams and others (2003). Two of the models include variables that are important for an MCS: volume and sand-dominated facies. The first model gives the distribution of material 

found in cape- and ridge-associated marine sand deposits, 

and the second model gives the proportion of material within 

those deposits that meets the definition of “sand,” or has a 

Φ value of −1 to 4. Other models have been constructed that 

may help assessment teams characterize marine sand deposits 

as a group. For example, the mean-grain-size model for capeand ridge-associated marine sand deposits may be used to 

compare sample data in an assessment area. 

Monte Carlo Simulation 

Mathematical investigations of geologic phenomena 

can be deterministic, probabilistic, or some combination of 

both. Deterministic methods progress in a fixed and predictable manner that may involve equations, and the outcome is 

expected to be known and certain (URL http://www.optimizationpartner.se/index.php, accessed Apr. 24, 2006). For each 

set of initial conditions, there is a constant outcome. Probabilistic methods, in contrast, incorporate random chance, 

and the outcome is not expected to be known but may be 

expressed as a distribution of values. For each set of initial 

conditions, there is a range of possible outcomes. 

The MCS method, simply defined, is “a procedure that 

involves statistical sampling techniques in obtaining a probabilistic approximation to the solution of a mathematical or 

physical problem” (James and James, 1976, p. 256). The output 

is a probability distribution. This type of stochastic program 

is random but also needs to be organized with some direction 

(URL http://www.cs.bham.ac.uk/~wbl/thesis.glossary.html, 

accessed Apr. 24, 2006) when preparing an MCS program. Stochastic programs using MCS are of specific interest here. An 

MCS combines data about marine sand deposits as contained 

in models (for example, volume) with estimates of the probable 

number of undiscovered deposits where iterations are expected 

to reflect one of many states of nature (Bliss and others, 2003). 

The resulting distribution of sand resources is expected to 

represent the full range of possible outcomes within the boundaries set by the quantitative models used and estimates of the 

probable number of undiscovered deposits. 

More scientists are using both approaches (deterministic 

and probabilistic) together, as evidenced by two reports that 

75° 70°

40°

35°

30°

Figure 1. U.S. Atlantic Continental Shelf, showing location of study 

area and approximate locations of survey areas (letters) with marine 

sand deposits either used as data sources or mentioned in text. a, 

attached shoal field, Del.; b, Canaveral Shoal, Fla.; c, shoals F–M, 

Md.; d, Fenwick, Isle of Wright, and Weaver Shoals, Md.; e, Greater 

Gulf, Little Gulf Banks, and shoals B–D, Md.; f, areas 1–4, N.C.; g, 

shoals A–N, N.J.; h, BI–A to BI–O, N.J.; i, Avalon Shoal and Inner 

Sand Ridge, N.J.; j, Edisto Beach shoal and Gaskin Bank, S.C.; k, 

Joiner Bank shoal, S.C.; l, Sandbridge Shoal, Va. See table 1 for 

references associated with each survey area. 

4 Contributions to Industrial-Minerals Research 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

assess earthquakes (Krinitzsky, 2003) and landslides (Leynaud, and others, 2004). MCS in mineral-resource assessment 

has been applied to coal (Orheim, 1982), petroleum (Crovelli, 

1985), and metals (Spanski, 1992). 

MCS methodology has been particularly useful to some 

marine researchers. One of the most common applications is 

by scientists investigating landslides in the marine environment. Submarine slides, which are commonly triggered by 

earthquakes of M>7, can trigger tsunamis, for which Watts 

(2004) estimated amplitudes by using an MCS and a distribution of mass-failure size off southern California. One 

conclusion is that 26–33 percent of all earthquakes generate 

landslides with tsunamis larger than those that would have 

been generated by the earthquakes directly. In this study, 

stochastic simulation was used to supplement deterministic 

methods involving limited equilibrium and finite elements. 

An MCS was used to incorporate the uncertainties in bottom 

parameters for the part of the study that particularly focused 

on “the performance function defining the boundary between 

safe and unsafe (failure) domains” of the sea floor (Leynaud 

and others, 2004, p. 464). 

Other applications of MCS methodology include its use 

to predict seacliff recession in the United Kingdom (Lee and 

others, 2001). Research by Lund and others (2003) resulted 

in a new approach that provides better estimates of activity 

coefficients in seawater by using an MCS. Activity coefficients are used in the study of seawater chemistry to calculate mineral solubilities, dissociation constants, and complex 

formation, among other characteristics. As illustrated and 

described below, a new MCS program and associated 

models are now available for use in resource assessments of 

cape- and ridge-associated marine sand deposits off the U.S. 

Atlantic coast (fig. 1). These modeling techniques may be 

applicable elsewhere in the United States and the world, as 

appropriate. 

MCS Applications in MineralResource Assessments 

As described above, Singer (1993) defines a three-part 

approach to quantitative mineral-resource assessment. Cox 

and Singer (1986) prepared the first large compilation of 

grade-and-tonnage models needed for an MCS for both 

metallic and a few industrial minerals. Root and others (1992) 

described an MCS computer program that uses the products 

of quantitative mineral-resource assessments. Drew (1997) 

provided an insightful overview of some past progress and 

pitfalls in execution of this style of quantitative assessment. 

The MCS provides a distribution of undiscovered quantities 

of metals (or industrial minerals). Bliss and others (2003) also 

explored how aggregate assessment might proceed where the 

MCS is used as a sampling method of quantitative models 

that allows the total amount of aggregate to be calculated. The 

MCS needs to be iterated a sufficient number of times that the 

distribution of resulting values is stable. Depending on the 

complexity of the calculation, several thousand iterations may 

be sufficient, whereas Root and others (1992) recommend that 

4,999 iterations are applicable to the data provided in Singer’s 

(1993) three-part approach. 

The result of an MCS is a statistical distribution that can 

be used to probabilistically estimate the amount of marine 

sand that may be present in an assessment area. Although 

assessment studies predict resources yet to be extracted, 

several other factors come into play when the resources are 

actually under evaluation for development. For example, 

although the estimated marine sand resources may be present, they may not be extractable, owing to inaccessibility, 

unsuitability for dredging, preemptive use, or other economic 

factors, including transportation distance. These factors, 

however, could be addressed by constructing a second set of 

models that consider extraction and transportation and might 

be comparable to the model which provides a simplified economic filter applicable to massive sulfide deposits (Singer and 

others, 2000) or open-pit mining and heap-leach recovery of 

copper (Long and Singer, 2001). 

Cape- and Ridge-Associated Marine 

Sand Deposits 

Basic Data 

Acquiring sufficient high-quality data for model construction can be a major challenge, owing to cost and general 

nonavailability. Data about deposits included those deposits 

that various State and Federal agencies have considered possible sources of marine sand and are described in the various compilations used as data sources. Nearly all deposits 

have volumes of >1 million m3, whereas the smallest deposit 

included in the dataset has a volume of 560,000 m3. Other 

deposit variables listed above have values that represent 

characteristics of the material within the deposits reported in 

these compilations. One difficulty is that some agencies have 

included deposits in their reports with considerable amounts 

of nonsand sediment. 

Poor-quality data can be partly compensated for by collecting a large dataset, and this approach has been used in 

modeling marine sand deposits. To achieve this compensation, data from sand deposits in several different geologic 

settings have been compiled, but only those for cape- and 

ridge-associated marine sand deposits are used here. Some of 

these deposits are adjacent to one another but result from different geologic processes, and so we have treated them separately for modeling purposes; other deposits occur in isolation 

from other marine sand deposits. The data used here for modeling purposes are from published reports and other publicly 

available documents, including several reports prepared by 

State agencies with funding from the U.S. Minerals Management Service. Reports by the U.S. Army Corps of Engineers, 

as well as journal articles, provided additional data. Data have 

been compiled on >200 marine sand deposits, including those 

Modeling Cape- and Ridge-Associated Marine Sand Deposits 5 
along the eastern seaboard from Massachusetts to Florida, in 

the U.S. Gulf of Mexico, and in southern California; other 

data were obtained for marine sand deposits in Nova Scotia, 

Puerto Rico, and Hong Kong. Some of these data may be 

more appropriate for sand and gravel modeling, not sand 

modeling, and may have been included in error, owing to an 

absence of grain-size information. Thus, a subset of the larger 

dataset has been used to construct models for cape- and ridgeassociated marine sand deposits. 

The data initially considered 60 sites believed to contain 

marine cape- and ridge-associated marine sand deposits, all 

on the U.S. Atlantic Continental Shelf (fig. 1; table 1), that 

were chosen by using the criteria of S.J. Williams (verbal 

commun., 2007) and the descriptive model presented in 

appendix A. 

Several different procedures were used to test the data 

during model preparation. One concern was about the six 

deposits in South Carolina, where five deposits have volume 

data. These five deposits were discovered to have only small 

volumes, and so all data from these six sites were excluded 

from the models. (See subsection below entitled “Volume 

Model.”) In addition, comparisons were also made among 

data variables for survey areas grouped by State with data 

from four or more deposits. The single deposit reported 

in Delaware was included with the Maryland dataset, and 

the single deposits reported in Virginia and Florida were 

excluded. Deposits were compared by using a nonparametric 

Wilcoxon test or a Kruskal-Wallis test if three or more datasets were available (Conover, 1999). Nonparametric tests 

were also used, given both the small number of observations 

and the uncertainty in the type of distribution some of the 

variables may have. Values are replaced with ranks in these 

tests. Significance is reported for the test results from the JMP 

software (SAS Institute, Inc., 2002), a statistical package that 

uses a one-way chi-squared (χ2

) approximation at a specified 

degree of freedom (DF), the number of observations (n), and 

the probability p of obtaining by chance a χ2 value larger than 

the one calculated. Differences among variable ranks grouped 

by State are significant at the 1-percent-confidence level. 

Significant differences among variables grouped by State are 

readily recognized in the standardized scores calculated by 

the JMP program (SAS Institute Inc., 2002, p. 112.) 

Several deposits of this type probably occur elsewhere. 

Cape- and ridge-associated marine sand deposits are considered to be among the best sources of good-quality sand useful 

in beach nourishment. Several of the variables reported for 

those deposits include area, volume, thickness, median grain 

size (reported in Φ units), grain sorting (also reported in Φ

units), and the proportion of sand-dominated facies. Not all 

variables are reported for all 54 deposits. 

The correlations between variables for the full dataset 

reported here are considered significant at the 1-percentconfidence level. Interpretation of the reported correlations 

is uncertain, given the small number of observations in the 

dataset. However, correlations between variables need to 

be recognized and require MCS programs to be modified if 

correlated variables are used together. One variable, deposit 

thickness, was tested differently, owing to rejection of normal 

and log-normal distributions—a common observation in 

thickness data for other deposit types. Thickness data were 

compared with other variables in this study by using nonparametric procedures; that is, the values were ordered and 

replaced with ranks before analysis. Note that the proportion 

of sand-dominated facies, if not reported, is assigned as 100 

percent. Many deposits lack data on the proportion of sanddominated facies. 

Modeling Sand-Deposit Variables 

Introduction 

We used seven variables describing cape- and ridge-associated marine sand deposits to construct models, five of which 

proved useful to assess quantitatively marine sand deposits. 

The models can be used as a reference to compare observations in permissive tracts that may suggest the presence of 

one or more undiscovered deposits. Five models suitable for 

this application are those using the following variables: (1) 

area, (2) thickness, (3) mean grain size, (4) grain sorting, and 

(5) spatial density. As described below, the area and spatialdensity models can be particularly useful. Two models used 

by the MCS program are (1) volume and (2) sand-dominated 

facies. A detailed discussion follows about these and other 

variables useful in assessing cape- and ridge-associated 

marine sand deposits. 

Area Model 

Area data are available for 47 of the 54 cape- and ridgeassociated sand deposits in the study area (fig. 1). The areas 

of individual deposits range from 0.24 to 239 km2. The areas 

of deposits along the coasts of Maryland (n=14), North 

Carolina (n=4), and New Jersey (n=29) are not significantly 

different (χ2=2.63, DF=2, p>χ2=0.27). The dataset can be 

limited by several factors, including arbitrary truncation due 

to water depth, jurisdictional boundaries, and other externally 

imposed conditions. The area data (fig. 2) are right skewed 

so that the x-axis layout is transformed and the data pattern 

is shown as if it had a log-normal distribution. (See app. 

B on figure format and the use of statistical distributions.) 

Areas are displayed in figure 2 both as a histogram and as a 

normal quantile-quantile (or Q–Q) plot. To test the assumption of log normality suggested in the upper part of figure 2, 

a Shapiro-Wilk W test (Conover, 1999) was run, yielding a W 

value of 0.983 and an associated probability of <0.855, and 

so the assumption that the statistical distribution is log normal 

cannot be rejected at the 1-percent-confidence level. 

The area model, shown in a form suitable for computer 

simulation if so needed (that is, cumulatively, so that each 

data point has an explicit associated probability), is plotted in 

figure 3, along with the log-normal distribution as a line fitted 

to the data points. Values at 0.1, 0.5, and 0.9 probabilities (fig. 

6 Contributions to Industrial-Minerals Research 
Table 1. Areas of cape- and ridge-associated marine sand deposits on the U.S. Atlantic Continental Shelf 

considered in this study.

 [Letter preceding name denotes survey location in figure 1] 

Nation and Area name Reference State 

USDE (a) Attached shoal field McKenna and Ramsey (2002)

USFL (b) Canaveral Shoal Nocita and others (1990)

USMD (c) Shoal F Conkwright and Gast (1995)

USMD (c) Shoal G Conkwright and Gast (1995)

USMD (c) Shoal H Conkwright and Gast (1995)

USMD (c) Shoal I Conkwright and Gast (1995)

USMD (c) Shoal J Conkwright and Gast (1995)

USMD (c) Shoal K Conkwright and Gast (1995)

USMD (c) Shoal L Conkwright and Gast (1995)

USMD (c) Shoal M Conkwright and Gast (1995)

USMD (d) Fenwick Shoal Conkwright and others (2000)

USMD (d) Isle of Wright Shoal Conkwright and others (2000)

USMD (d) Weaver Shoal Conkwright and others (2000)

USMD (e) Greater Gulf Bank Conkwright and Williams (1996

USMD (e) Little Gulf Bank Conkwright and Williams (1996)

USMD (e) Shoal B Conkwright and Williams (1996)

USMD (e) Shoal C Conkwright and Williams (1996)

USMD (e) Shoal D Conkwright and Williams (1996)

USNC (f) Area 1 Hoffman (1998); Boss and Hoffman (2001)

USNC (f) Area 2 Hoffman (1998); Boss and Hoffman (2001)

USNC (f) Area 3 Hoffman (1998); Boss and Hoffman (2001)

USNC (f) Area 4 Hoffman (1998); Boss and Hoffman (2001)

USNJ (g) Shoal A Meisburger and Williams (1980)

USNJ (g) Shoal B Meisburger and Williams (1980)

USNJ (g) Shoal C Meisburger and Williams (1980)

USNJ (g) Shoal D Meisburger and Williams (1980)

USNJ (g) Shoal E Meisburger and Williams (1980)

USNJ (g) Shoal F Meisburger and Williams (1980)

USNJ (g) Shoal G Meisburger and Williams (1980)

USNJ (g) Shoal H Meisburger and Williams (1980)

USNJ (g) Shoal I Meisburger and Williams (1980)

USNJ (g) Shoal J Meisburger and Williams (1980)

USNJ (g) Shoal K Meisburger and Williams (1980)

USNJ (g) Shoal L Meisburger and Williams (1980)

USNJ (g) Shoal M Meisburger and Williams (1980)

USNJ (g) Shoal N Meisburger and Williams (1980)

USNJ (h) BI–A Meisburger and Williams (1982)

USNJ (h) BI–B Meisburger and Williams (1982)

USNJ (h) BI–C Meisburger and Williams (1982)

USNJ (h) BI–D Meisburger and Williams (1982)

USNJ (h) BI–E Meisburger and Williams (1982)

USNJ (h) BI–F Meisburger and Williams (1982)

USNJ (h) BI–G Meisburger and Williams (1982)

USNJ (h) BI–H Meisburger and Williams (1982)

USNJ (h) BI–I Meisburger and Williams (1982)

USNJ (h) BI–J Meisburger and Williams (1982)

USNJ (h) BI–K Meisburger and Williams (1982)

USNJ (h) BI–L Meisburger and Williams (1982)

USNJ (h) BI–M Meisburger and Williams (1982)

USNJ (h) BI–N Meisburger and Williams (1982)

USNJ (h) BI–O Meisburger and Williams (1982)

USNJ (i) Avalon Shoal Smith (1996)

USNJ (i) Inner Sand Ridge Smith (1996)

USSC (j) Edisto Beach (Shoal) Van Dolah and others (1998)

USSC (j) Gaskin Bank Van Dolah and others (1998)

USSC (j) Hunting Island Van Dolah and others (1998) 

USSC (j) Pawleys Island Van Dolah and others (1998)

USSC (j) Seabrook Island Van Dolah and others (1998)

USSC (k) Joiner Bank shoal Wright and others (1999)

USVA (l) Sandbridge Shoal Maa and Hobbs (1998) 

Modeling Cape- and Ridge-Associated Marine Sand Deposits 7 
 

 

 

 

 

 

 

 

 

 

 

 

 

3) are from the statistical distribution. For example, the capeand ridge-associated marine sand deposits represented by this 

distribution have a median area of 10 km2—in other words, 

there is a 50-percent chance that a marine sand deposit will 

have an area of ≥10 km2. Furthermore, there is a 90-percent 

chance that it will have an area of ≥1.7 km2, and a 10-percent 

chance that it will have an area of ≥53 km2. The mean area 

is substantially larger than the median of data for these capeand ridge-associated sand deposits, or 22 km2

. The area model 

is particularly useful in visualizing how many undiscovered 

deposits are likely in a permissive tract. (See above description of part 3 of the approach of Singer, 1993.) 

Several significant correlations are suggested between 

log-normal area and other variables in the dataset. However, 

no correlation was found between log-normal deposit area 

and mean grain sorting (r=0.14, n=21), where is r is the correlation coefficient and n is the number of observations with 

both variables. There is a negative correlation (at the 1-percent-confidence level) between log-normal area and mean 

grain size (r=−0.51, n=32), suggesting that deposits with a 

larger area may have a smaller mean grain size. One of the 

strongest positive correlations (at the 1-percent-confidence 

level) is between deposit area and volume (r=0.92, n=47). If 

the area of a recognized cape- and ridge-associated marine 

sand deposit is known, the volume can be estimated by using 

the equation 

log10 V = 0.43 + 0.855 log10 A, (1) 

where V is the volume (in millions of cubic meters) and A 

is the area (in square kilometers). In fact, 84 percent of the 

variation in deposit volume can be explained by knowledge of 

the deposit area, comparable to a regression model of onshore 

fluvial sand and gravel deposits (Bliss and Page, 1994). 

Thickness Model 

Thickness data are available for 34 of the 54 cape- and 

ridge-associated marine deposits in the study area (fig. 1). 

The dataset shows no pattern that fits a statistical distribution, 

and considerable uncertainty exists, given how this dataset 

was collected. The thicknesses of deposits along the coasts of 

North Carolina (n=4) and New Jersey (n=29) are not significantly different (χ2 

=0.15, DF=1, p>χ2 =0.70). Available thickness data may facilitate determining whether the data from a 

target area indicate a possible undiscovered deposit. 

Data on deposit thickness have similar limitations to 

those for deposit area. In addition, many thicknesses are 

measured from the top of first indication of sand to the 

bottom of the sampled core and do not represent the total 

thickness of sand in the deposits, and so the reported thicknesses are likely too small. Deposit thicknesses for cape- and 

ridge-associated marine sand deposits mostly range from 1 to 

5 m in the dataset—a narrow range of only 4 m; the median 

thickness is 2.3 m. 

Comparisons between thickness and the other variables 

in this study were by nonparametric methods, where ranks 

were substituted for values. Correlation between deposit 

thickness ranks and ranks of other variables was made by 

using Spearman’s ρ, which is simply Pearson’s r (or simply r, 

0.01 

0.05 

0.10 

0.25 

0.50 

0.75 

0.90 

0.95 

0.99 

3 

2 

1 

0 

-1 

-2 

-3 

-1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 

LOGARITHM OF AREA 

(IN SQUARE KILOMETERS) 

Figure 2. Histogram (lower part) and normal quantile-quantile plot 

(upper part) of area data for 47 of 54 cape- and ridge-associated 

marine sand deposits in survey areas (fig. 1). See appendix B and 

figure 13 for detailed discussion of format. 

PROBABILITY 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

1.7 10 53 

n=47 

0.2 0.3 0.4 0.6 0.8 1 2 3 4 5 6 8 20 30 50 200 300 10 70 100 

AREA, IN SQUARE KILOMETERS 

Figure 3. Area model of cape- and ridge-associated marine sand 

deposits. 

8 Contributions to Industrial-Minerals Research 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2. Phi (Φ) scale of grain sizes for sedimentary deposits 

Grain size 

(mm) Φ value Size term (after Wentworth, 1922) 

8.00–64.0 

4.000–8.00 

2.000–4.000 

1.000–2.000 

0.250–1.000 

0.250–0.500 

0.0313–0.125 

0.0625–0.125 

0.0039–0.0625 

0.0010–0.0039 

3 to 6 

2 to 3 

1 to 2 

0 to 1 

1 to 0 

2 to 1 

3 to 2 

4 to 3 

8 to 4 

10 to 8 

Medium to very coarse pebbles

Fine pebbles

Very fine pebbles (includes granules)

Very coarse sand

Coarse sand 

Medium sand 

Fine sand 

Very fine sand

Very fine to coarse silt

Clay 

as used elsewhere in this report) calculated on the ranks and 

average ranks (Conover, 1999). 

There is a positive and significant correlation between 33 

deposits with both area ranks and thickness ranks (ρ=0.500, 

p>0.003) at the 1-percent-confidence level, suggesting that 

the larger the area, the thicker the deposit. There is also a 

positive significant correlation between 34 deposits with both 

volume ranks and thickness ranks (ρ=0.77, p>0.001), suggesting that the larger the volume, the thicker the deposit. 

No correlations were noted between 23 deposits with both 

thickness ranks and mean-grain-size ranks (ρ=−0.40, p>0.06), 

and between 11 deposits with both thickness ranks and grainsorting ranks (ρ=−0.10, p>0.76). 

Mean-Grain-Size Model 

Data on mean grain sizes of sand are available for 36 of 

the 54 cape- and ridge-associated marine sand deposits in the 

study area (fig. 1). The mean grain sizes of deposits along 

the coasts of Maryland (n=13), and New Jersey (n=22) are 

not significantly different (χ2 =0.51, DF=1, p>χ2 =0.47). The 

combined dataset may facilitate determining whether target 

areas (that is, possible undiscovered deposits) are comparable. 

As proposed by Krumbein (1934), model grain sizes are in Φ

units, calculated as the negative logarithm (base 2) of the grain 

size (in millimeters). The result of the negative sign in the 

conversion is that as grain size decreases, Φ value increases. 

For example, for a grain size of 1 mm, Φ=0. Grain-size terms, 

grain sizes, and Φ values are summarized in table 2. 

End-use requirements differ because the mean grain 

size and the variation in sand-grain distributions need to 

be comparable to those of the sand on those beaches where 

the material is expected to be used. The median Φ value of 

“mean grain size” in cape- and ridge-associated marine sand 

deposits is 1.5 (coarse sand), and the Φ value of the middle 

80 percent of the grain-size distribution (that is, excluding 

the highest and lowest 10 percent of observations) ranges 

from 0.37 to 2.33 (fine to coarse sand). 

As noted for the area model, mean grain size is inversely 

correlated with area and volume. There is no significant correlation between mean grain size and grain sorting (r=−0.31, 

n=24). 

If the data (black squares, fig. 4) are normal, they are 

expected to group about the line. Recall that Φ units are logarithms to the base 2 and are transformed values by definition. 

The data points are also expected to fall within the Lilliefors 

confidence band (99-percent-confidence interval) bounded 

by the two curves on opposite sides of the diagonal. The patterns of data points on the Q–Q plot (upper part, fig. 4) does, 

indeed, suggest that the distribution may be log normal. To 

confirm this interpretation, a Shapiro-Wilk W test (Conover, 

1999) was run, which gave a W value of 0.944 with an associated probability of <0.067, and so the assumption that the 

distribution is log normal cannot be rejected at the 1-percentconfidence level. Note that the break in data values between 

mean grain sizes of Φ~0.6 and Φ=1.1 is also evident in grainsize distributions in the sediment in many onshore rivers and 

streams. This break, which was first recognized in 1980, is 

commonly expressed as an abrupt transition from gravel- to 

sand-dominated streambeds (Parker, 1998). 

The grain-size model, shown in a form suitable for computer simulation if so needed (fig. 5). (Recall that Φ value 

decreases as grain size increases.) Also shown in figure 5 

is the log-normal distribution as a curve fitted to the data 

points. Values at 0.9, 0.5, and 0.1 probabilities are from the 

statistical distribution. Thus, there is a 90-percent chance 

that a marine sand deposit will have a grain size of Φ≤0.63, 

a 50-percent chance that it will have a grain size of Φ≤1.3, 

and a 10-percent chance it will have a grain size of Φ≤2.0. 

Nearly all the data points fall within these grain sizes. 

Grain-Sorting Model 

Data on grain sorting or standard deviation of Φ value 

(see preceding subsection; Boggs, 1995) are available for 

only 24 of the 54 cape- and ridge-associated marine sand 

Modeling Cape- and Ridge-Associated Marine Sand Deposits 9 
 

 

 

 

 

 

 

 

 

 

 

 

deposits in the study area (fig. 1); all the data are from either 

Maryland or New Jersey. The grain sortings of deposits along 

the coasts of Maryland (n=13) and New Jersey (n=11) are significantly different (χ2 

=7.11, DF=1, p>χ2 =0.0077). Cape- and 

ridge-associated marine sand deposits along the New Jersey 

coast are more poorly sorted (median standard deviation of 

Φ value, 0.76) when compared to those along the Maryland 

coast (median standard deviation of Φ value, 0.55), making 

the model constructed here from combined data from both 

New Jersey and Maryland unsuitable for characterizing grain 

sorting in undiscovered deposits along either the Maryland 

or New Jersey coast. This model can be used in other coastal 

areas where data about grain sorting are unavailable or not 

significantly different from those used in the model. 

Sediment samples with a standard deviation of Φ≤0.35 are 

identified as very well sorted, as defined by Boggs (1995)—in 

other words, the grain sizes in the sample are all nearly the 

same. As the standard deviation of Φ value increases, the 

range of grain sizes in the sample also increases. When the 

standard deviation of Φ value is >4, the sample is described as 

extremely poorly sorted (Boggs, 1995). 

End-use requirements differ, but the grain sorting needs 

to be comparable to that in typical sand samples collected 

from the beaches where the material is expected to be used. 

The median standard deviation of Φ value for samples in this 

3 

dataset is 0.63, or moderately well sorted (Boggs, 1995). In 

all, 90 percent of deposits have a grain sorting of Φ≤0.80, 

or moderately well sorted, and 10 percent of deposits have 

a grain sorting of Φ≤0.47, or well to extremely well sorted. 

None of the deposits has a standard deviation of Φ value >1, 

or poorly sorted. 

As noted in previous discussions above, there is no correlation between grain sorting and area (r=0.14, n=21), thickness (r=−0.11, n=11), or mean grain size (r=−0.31, n=24). 

There also is no significant correlation between grain sorting 

and volume (r=−0.06, n=24). 

If the distribution is log normal, the data points are 

expected to group about the curve and to fall within the Lilliefors confidence band (99-percent-confidence interval) 

bounded by the two curves on opposite sides of the diagonal. 

The pattern of data point on the Q–Q plot (upper part, fig. 

6,) does, indeed, suggest that the distribution may be log 

normal. To confirm this interpretation, a Shapiro-Wilk W test 

(Conover, 1999) was run, which gave a W value of 0.979 with 

an associated probability of <0.87, and so the assumption 

that the distribution is normal (or log normal here) cannot be 

rejected at the 1-percent-confidence level. 

The gravel-sorting model, shown in a form suitable for 

computer simulation if so needed (fig. 7). Also shown in 

figure 7 is the log-normal distribution as a line fitted to the 

data points. Φ values at 0.9, 0.5, and 0.1 probabilities are 

from the statistical distribution. Thus, there is a 90-percent 

chance that a marine sand deposit will have a grain sorting of 

Φ≥0.46, a 50-percent chance that it will have a grain sorting 

of Φ≥0.63, and a ≥10-percent chance that it will have a grain 

0.01 

0.05 

0.10 

0.25 

0.50 

0.75 

0.90 

0.95 

0.99 sorting of Φ≥0.81. 

2 

1 

0 1 

0.9 

-1 

0.8 

-2 0.7 

-3 

PROBABILITY0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

1.75 2 2.25 2.5 2.75 3 

2.0 0.63 1.3

n=36

0 5.5 1.0 1.5 2.0 2.5 3.0 0 

0 .25 .5 .75 1 1.25 1.5 

MEAN GRAIN SIZE, IN Φ UNITS 

Figure 4. Histogram (lower part) and normal quantile-quantile MEAN GRAIN SIZE, IN Φ UNITS 

plot (upper part) of mean-grain-size data for 36 of 54 cape- and 

ridge-associated marine sand deposits in survey areas (fig. 1). See Figure 5. Mean-grain-size model of cape- and ridge-associated marine 

appendix B and figure 13 for detailed discussion of format. sand deposits. 

10 Contributions to Industrial-Minerals Research 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Volume Model 

Volume data were available for all 54 cape- and ridgeassociated marine sand deposits in the study area (fig. 1). As 

noted previously, five of the six deposits in South Carolina 

appeared to have considerably smaller volumes. The volumes 

of deposits along the coasts of Maryland (n=17), North Carolina (n=4), New Jersey (n=31) and South Carolina (n=5) are 

significantly different (χ2 =17.2, DF=3, p>χ2 =0.0006). The 

deposits in South Carolina have the lowest volume ranks as 

expressed by standardized scores and are clearly smaller than 

the other deposits in this study. Therefore, all the deposits 

in South Carolina were excluded in constructing the various 

models in this study. These six deposits may be members of a 

possible subpopulation of sediment-starved cape- and ridgeassociated marine sand deposits or some other deposit type that 

needs to be separately modeled. 

In contrast, the volumes of deposits along the coasts 

of Maryland (n=17), North Carolina (n=4), and New 

Jersey (n=31) are not significantly different (χ2 =5.4, DF=2, 

p>χ2 

=0.068). The combined data used in the volume model for 

PROBABILITY 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

0.46 0.63 0.81 

Well sorted Poorly sorted 

n=24 

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

GRAIN SORTING, IN Φ UNITS 

Figure 7. Grain-sorting model of cape- and ridge-associated marine 

sand deposits. 

0.01 

0.05 

0.10 

0.25 

0.50 

0.75 

0.90 

0.95 

0.99 

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 

GRAIN SORTING, IN Φ UNITS 

Figure 6. Histogram (lower part) and normal quantile-quantile plot 

(upper part) of grain sorting data for 24 of 54 cape- and ridge-associated 

marine sand deposits in survey areas (fig.1). See appendix B and figure 

13 for detailed discussion of format. 

3 

0.01 

0.05 

0.10 

0.25 

0.50 

0.75 

0.90 

0.95 

0.99 

3 

2 

2 

1 

1 

0 

0 

-1 

-1 

-2 

-2 

-3 

-3 

-0.5 .0 .5 1.0 1.5 2.0 2.5 3.0 

LOGARITHM OF VOLUME 

(IN CUBIC METERS) 

Figure 8. Histogram (lower part) and normal quantile-quantile plot 

(upper part) of volume data for 54 cape- and ridge-associated marine 

sand deposits in survey areas (fig. 1). See appendix B and figure 13 for 

detailed discussion of format. 

Modeling Cape- and Ridge-Associated Marine Sand Deposits 11 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.7 

1 

all the other deposits are skewed, suggesting that the volumes 

(in millions of cubic meters) need to be transformed logarithmically. The transformed values for marine sand are plotted 

in figure 8. The data points are also expected to fall within the 

Lilliefors confidence band (99-percent-confidence interval) 

bounded by the two curves on opposite sides of the diagonal. 

The pattern of data points on the Q–Q plot (fig. 8) does, indeed, 

suggest that the distribution may be log normal. To confirm this 

interpretation, a Shapiro-Wilk W test (Conover, 1999) was run, 

which gave a W value of 0.959 with an associated probability 

of <0.104, and so the assumption that the distribution is normal 

(or log normal here) cannot be rejected at the 1-percent-confidence level. Correlations between volume and the other variables considered in this study have been previously discussed. 

The volume model is in a form suitable for computer 

simulation if so needed (fig. 9). Also shown in figure 9 is the 

log-normal distribution as a line fitted to the data points. Values 

at 0.1, 0.5, and 0.9 probabilities (fig. 9) are from the statistical 

distribution. Thus, there is a 90-percent chance that a marine 

sand deposit will have a volume of ≥4.5 million m3, a 50-percent chance that it will have a volume of ≥22 million m3

, and 

a 10-percent chance that it will have a volume of ≥110 million 

m3. Half of the deposits have volumes of 11 to 52 million m3, 

on the basis of quantiles (fig. 8). The volume model is used 

by the MCS program to estimate the volumes of undiscovered 

deposits, although this model is not particularly useful in estimating the probable number of undiscovered deposits because 

deposit volumes are more difficult to visualize during assessment than deposit areas, as discussed above. 

Sand-Dominated-Facies Model 

Cape- and ridge-associated marine sand deposits identified 

as sources of sand-size material commonly contain other materials (non-sand-dominated facies) either finer or coarser than sand. 

Therefore, the volume model presented above will generally 

overestimate the amount of sand suitable for use because volume 

data also are likely to include some silt and gravel. These less 

suitable materials are either interbedded or directly mixed with 

the sand. The sand content of marine sand deposits is less commonly reported, possibly owing to an underlying assumption 

that the nonsand fractions are minor by definition and that many 

deposits containing ≤100 volume percent sand are not reported 

and so may be missing from the dataset. For modeling purposes 

here, the 39 deposits with reported volumes but for which data 

on sand content are unavailable have been assigned a sand content of 100 volume percent. Thus, the sand-dominated-facies 

model presented here may be biased, and so its use in an MCS 

may lead to a slight overprediction of the amount of sand in 

undiscovered cape- and ridge-associated marine sand deposits. 

No comparisons were made among the sand deposits grouped by 

State for the sand-dominated-facies dataset. 

Only 15 of the 54 cape- and ridge-associate marine sand 

deposits in the study area (fig. 1) had reported sand contents. 

All 54 deposits were used to construct a model in which 80 

percent have either a reported or an assigned sand content of 

100 volume percent. The resulting distribution of 11 deposits 

with sand-dominated facies of <100 volume percent is empirical (fig. 10) and cannot be tested in the same way as other variables. Unlike the other models, the model in figure 10 shows 

a distribution of sand-dominated facies for only 20 percent of 

the dataset. This type of distribution is also observed in several 

industrial-mineral-deposit types where high purity is sought 

and deposits are reported to have grades of 100 percent. 

Comparisons between data on sand-dominated facies and 

other variables in this study were not made, given that 80 percent of the recorded sand contents are 100 volume percent and 

that 72 percent of these deposits in the dataset had their sand 

content assigned. 

The sand-dominated-facies model, shown in a form suitable for computer simulation if needed (fig. 10), has a median 

4.5 22 110

n=54 

0.6 0.8 1 2 3 4 5 7 20 40 60 200 400 700 10 100 

1 

n=54 

64 

0.975 0.9 

0.8 0.95 

0.925 

PROBABILITY 

0.3 0.825 

0.2 0.8 

0.1 

PROBABILITY

0.6 0.9 

0.5 0.875 

0.85 

0.775 

20 30 40 50 60 70 80 90 100

SAND-DOMINATED FACIES, IN PERCENT 

VOLUME, IN MILLIONS OF CUBIC METERS Figure 10. Sand-dominated-facies model of cape- and ridge-associFigure 9. Volume model of cape- and ridge-associated marine sand ated marine sand deposits. 42 of 54 deposits that are composed of 100 

deposits. volume percent sand are not shown. 

12 Contributions to Industrial-Minerals Research 

0.4 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3. Mineral-deposit density (MDD value) of cape- and ridge-associated marine sand deposits in 


three survey areas (fig. 1).
 

[MDD values in number of deposits per 1,000 km2]
 

Survey area 

(fig. 1) 

Area 

(km2) MDD Reference 

Maryland Shoal Field I–III 944 17.0 Conkwright and Grast 

(1995), Conkwright and 

Williams (1996a). 

Cape May, N.J. 1,235 14.6 Meisburger and Williams 

(1980b). 

Offshore Nags Head, Kitty 640 9.4 Hoffman (1998). 

Hawk, and Kill Devils 

Hills, N.C.

sand content of 100 volume percent. Thus, there is a 90-percent 

chance that a marine sand deposit will contain ≥64 volume 

percent sand, and a 10-percent chance that it will contain 100 

volume percent sand. 

Spatial-Density Model 

Spatial-density models of mineral deposits suitable for 

mineral-resource assessment are a relatively new undertaking 

in quantitative mineral-deposit modeling. They are particularly useful in meeting the requirement of part 3 of Singer’s 

(1993) approach described above; however, they are but one 

of about a half-dozen guidelines that are suitable for subjectively estimating the probable number of undiscovered 

deposits (Singer, 2007, table 1). An estimate of the probable 

number of undiscovered deposits is a key input variable 

needed to run the MCS. Instead of subjectively estimating the 

probable number of undiscovered deposits, a type of spatial 

model can also be used. The spatial model can also be used as 

a guide to subjective estimation if desirable. Called a mineraldeposit-density (MDD) model, it is simply the number of 

deposits per some standard unit of area (generally reported as 

number of deposits per 1,000 km2

) in a well-explored area. 

Like an assessment tract, all of the area is permissible. Construction of a spatial-density model requires the deposits to 

be defined in the same way as for other quantitative models. 

An important purpose of the MDD model is to allow for an 

independent estimate of the probable number of undiscovered 

deposits for assessment purposes. Research in MDD modeling began in the 1980s (Bliss and others, 1987; Bliss and 

Menzie, 1993), and a final report that summarizes most of 

this effort, as well as the results of new investigations, was 

published by Singer and others (2001). Typical MDD values 

for both metallic- and industrial-mineral deposits range from 

1 to 10 deposits per 1,000 km2; the full range of MDD values 

is from 0.01 to 100 deposits per 1,000 km2. In a recently 

completed, new interim MDD model for one type of onshore 

sand and gravel deposits in a resource assessment of Afghanistan, MDD values in six areas range from 0.1 to 1.0 sand and 

gravel deposit per 1,000 km2

 (Bliss and Bolm, 2007). 

We used three studies of areas with cape- and ridgeassociated marine sand deposits to calculate three MDD 

values for three survey areas (fig. 1; table 3). These values 

should be used carefully because these survey areas were 

selected not for their absence but for their presence of marine 

sand deposits! Thus, the three survey areas can be expected 

to have higher MDD values than if they have been selected 

at random within some predefined area permissive for marine 

sand deposits. The boundaries of the survey areas were not 

set by geologic conditions but were arbitrarily selected by 

those conducting the survey and so are likely nested within 

a much larger area permissive for cape- and ridge-associated 

marine sand deposits. These MDD values should be used as 

a guide to estimating the probable number of undiscovered 

deposits, with an understanding that they may be too high for 

some parts of permissive tracts for cape- and ridge-associated 

marine sand deposits. 

Estimating the Number of 

Undiscovered Deposits 

Perhaps no task in mineral-resource assessment is perceived to be more challenging than that of subjectively estimating of the probable number of undiscovered deposits. 

However, such a task must be undertaken by an assessment 

team if an MCS is to be run and a probabilistic distribution of 

marine sand resources is to be provided. An important requirement is that the characteristics of the undiscovered deposits be 

comparable to all the characteristics in the models described 

above. Therefore, nearly all the undiscovered deposits are 

expected to have volumes of >1 million m3 (fig. 8). 

Several tools are available to help in making these estimates, including spatial-density models as described above. 

A common approach to estimating the probable number of 

undiscovered deposits is to assemble an assessment team. 

Estimates are to be made cumulatively at three probabilities: 

Modeling Cape- and Ridge-Associated Marine Sand Deposits 13 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4. Probable number of undiscovered marine sand deposits estimated by three assessment-team 

members for a hypothetical assessment tract. 

Level of estimate 

Assessment-team members Consensuses 

A B C 

90-percent chance of at least: 

50-percent chance of at least: 

10-percent chance of at least: 

1 

1 

2 

1 

2 

5 

2 

4 

8 

1 

2 

4 

0.9 (most likely), 0.5, and 0.1 (least likely). In an example of 

a hypothetical assessment area somewhere on a continental 

shelf (table 4), three assessment-team members have provided independent estimates of the numbers of undiscovered 

cape- and ridge-associated marine sand deposits. In this 

example, assessment team member A is pessimistic about the 

number of undiscovered deposits, while member C is optimistic. Team member A believes that there is a good chance 

of at least one deposit but that there is also is no more than a 

50-percent chance of at least one deposit. All three estimators, 

however, are fairly certain that there is at least one undiscovered deposit, although assessment-team member C believes 

that there is a 90-percent chance of at least two deposits. To 

achieve consensus, each assessment-team member needs to 

present arguments and evidence in support of his estimate. 

The consensus is not necessarily an average but represents 

an agreement among the assessment-team members. Singer 

(2007) noted that assessment-team estimates are likely to be 

better than those provided by individual estimators. 

How do assessment team members make these estimates 

and reach a consensus? What type of evidence do they use? 

Singer (2007, table 1) presented six techniques used by past 

assessment teams to estimate the probable numbers of undiscovered deposits, albeit almost all past assessments involve 

estimating the probable number of undiscovered metallicmineral deposits on shore. In some assessments (Menzie and 

Singer, 1990), individual occurrences, prospects, and other 

indications of mineralization of a specific deposit type are 

assigned individual probabilities, and the results are combined. 

Each assessment-team member notes the similarity of a given 

target to known mineral deposits of the type under assessment and his estimate is based on that experience. Has the 

area been well explored? If not, then the evidence for a target 

may suggest the presence of an undiscovered deposit. Better 

assessment-team members are those with a long involvement 

both in the mineral-deposit type under evaluation and in the 

areas being assessed. Using the frequency of deposits in wellexplored areas (or MDD models described previously), both 

published and from experience, can help guide the estimates. 

In our estimate of marine sand resources, evidence of 

undiscovered deposits would be suggested by geologic setting as described by various remote-sensing and geophysical 

methods, bathymetric geomorphology, grain-size data, and 

other site-specific features. The assessment team may evaluate all of these characteristics in making its estimates and later 

suggest why one set of arguments for a specific set of estimates of the number of undiscovered deposits is more compelling than another. Well-explored parts of an assessment 

area should not be forgotten during these discussions. Again, 

assessment-team members need to recall that all undiscovered 

deposits are expected to have characteristics that fall somewhere within the range of values—that is, at least half of the 

undiscovered deposits would have volumes larger than the 

median in the volume model (fig. 9) described above. 

Assessment teams also need to understand that MSC 

results will be more sensitive to the grade-and-tonnage model 

(or volume model in this application) than to small errors in 

the estimate of the probable number of undiscovered deposits (Singer, 2007). Therefore, the selection of appropriate 

marine-sand-deposit types by the assessment team is most 

important. 

Setting Up the MCS, Using MarineSand-Assessment Data 

The MCS method provides a probabilistic estimate of 

marine sand resources within permissive tracts. The overall 

structure of the MCS program (fig. 11) and its results follow 

the procedure outlined by Root and others (1992), which 

includes using 4,999 iterations in the simulation. The simulation values for presentation were calculated with the JMP 

software, a statistical package (SAS Institute, Inc., 2002). 

In the hypothetical MCS exercise that follows, two 

distribution models are used to predict resource values for 

cape- and ridge-associated marine sand deposits: (1) deposit 

volume and (2) sand content, together with an estimate of 

the probable number of undiscovered deposits, using the 

consensus values listed in table 4 and summarized in table 

5. In this hypothetical example, the empirical option is used 

so that unrealistically large values of grade and tonnage are 

avoided. The values are selected from the data used and not 

from the statistical distribution that can be used to describe 

the data. However, the piecewise linear-distribution approximation used by Root and others (1992) was not used. Instead, 

14 Contributions to Industrial-Minerals Research 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5. Probabilities of numbers of undiscovered marine sand deposits estimated 

for a hypothetical assessment tract. 

Level of estimate Expressed as Consensuses 

90-percent chance of at least: N(0.9) 1 

50-percent chance of at least: N(0.5) 2 

10-percent chance of at least: N(0.1) 4 

the data values used to construct the models were directly 

mapped onto a uniform distribution where each variable was 

assigned an equal discrete probability range. 

Executing the MCS Program 

Step 1. How many cape- and ridge-associated marine 

sand deposits are present?—Within each of the 4,999 iterations, the MCS program also executes between zero and four 

subiterations to estimate the probable number of undiscovered 

deposits within each iteration selected by the program (table 6), 

using the product of the allocation procedure and the empirical 

option described by Root and others (1992) and the estimates 

listed in table 5. The probable number of undiscovered deposits 

 START

 with n

 iterations 

Number of deposits 

(MDD model) 

Randomnumber 

generator 

Randomnumber 

generator 

Size of deposit 

(volume model) 

= No. of subiterations 

Subiterations

 completed? 

NO 

YES 

Total sand and gravel

 for subiteration 

Add to simulated 

distribution 

YES 

NO 

Randomnumber 

generator 

Adjust deposit volume 

(sand-dominatedfacies Model) 

Have all program 

iterations been run? 

Output simulated 

distribution with 

n iterations 

Figure 11. Schematic flowchart illustrating overall structure of Monte 

Carlo simulation program. 

follows a default distribution guided by the three probability 

estimates listed in table 4. Values between these three estimates 

are selected so that they are “approximately in the middle of all 

possible choices” as graphically and mathematically presented 

by Root and others (1992, p. 130–131, fig. 4). 

Step 2. What is the volume of each cape- and ridge-associated marine sand deposit?—Given one or more deposits 

within a specific iteration, each deposit is assigned a volume by 

using the volume model (fig. 9). Random numbers between 0 

and 1 generated by the program are used to select corresponding volumes in the volume model. With the empirical option 

Table 6. Default distribution of undiscovered 

marine sand deposits and probabilities used 

in a Monte Carlo simulation. 

Default number 

of deposits Probability 

0

1

2

3

4

0.067

0.233

0.3

0.2

0.2

as used here, the reported values are used directly in the MCS 

and not the fitted statistical distribution, so that each of the 54 

deposit volumes is assumed to be equally likely, and the chance 

of selection is equally divided among all 54 values. Therefore, 

all the volumes in the model are equally likely, whereby there 

is 1 chance in 54 of selection during the MCS, or a probability 

of 0.0185 (1/54). For example, if the random number generated 

is exactly 0.5, the volume selected for the deposit is 22 million 

m3

, or the median volume. The program as described in this 

section is executed for all the deposits described in step 1, and 

volumes are selected by the program for all deposits predicted 

to be present per iteration. In this example, the first iteration 

includes three deposits, and so three volumes are selected for 

each of the three subiterations. 

Step 3. What proportion of each cape- and ridgeassociated marine sand deposit is actually sand?—The 

sand content of each simulated deposit is determined by using 

the data in the sand-dominated-facies model (fig. 10). The 

selection process is similar to that used in step 2, where the 

Modeling Cape- and Ridge-Associated Marine Sand Deposits 15 
empirical option is used. Of the 54 marine sand deposits in the 

study area (fig. 1), slightly fewer than 80 percent have either 

reported or assigned values of 100 volume percent. For the 

rest of the data, each of the 11 values other than 100 percent 

volume in the sand-dominated-facies model is assumed to be 

equally likely, and so the chance of selection is equally divided 

among all 11 values, or 1.8 percent (1/54). For example, if the 

random number generated is 0.1, sand content is selected to be 

100 volume percent, multiplied by the volume selected from 

the volume model. In this example, the deposit volume is not 

reduced. All three volumes in the first iteration are modified in 

this step, if needed. 

Step 4. Determine whether all deposits predicted in 

the iteration have been created, compute a total volume, 

and output the results after 4,999 iterations have been 

executed.—In the first iteration, the final volumes of the three 

deposits are summed and transferred to the output dataset. The 

resulting dataset, after all 4,999 iterations have been run, is then 

transferred to the JMP program for analysis, and the result is 

reported as a cumulative probability distribution (fig. 12) for 

the cape- and ridge-associated marine sand deposits calculated 

by the MCS, which is the expected distribution of undiscovered 

deposits in the assessment area. There is a 90-percent chance 

that the assessment area contains ≥5.0 million m3

 of marine 

sand, a 50-percent chance that it contains ≥59 million m3 of 

marine sand, and a 10-percent chance that it contains ≥200 million m3

 of marine sand. The mean volume of sand predicted 

is 93 million m3. As noted in the section above entitled “Introduction,” ~920 million m3

 of marine sand has been extracted 

and used since the 1920s. The mean volume of undiscovered 

marine sand in this hypothetical assessment is 93 million m3, 

or 10 percent of the volume of marine sand used in the past 80 

years in the United States. PROBABILITY 

1 n=4,999 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 93 

0.3 

0.2 

0.1 

5.0 59 200

0 

1 10 100 1000 2 3 4 5 7 20 40 60 200 300 500 

SAND VOLUME, IN MILLIONS OF CUBIC METERS 

Figure. 12. Cumulative distribution of predicted sand resources in 

cape- and ridge-associated sand deposits in a hypothetical survey 

area (fig. 1). Blue dot, mean estimated resource of 93 million m3 of sand. 

Summary 

Quantitative mineral-resource assessment is now possible 

for one type of marine sand deposit—cape- and ridge-associated marine sand deposits. We have presented a set of models 

that can be used to screen data from target areas that are suspected to contain undiscovered deposits. Using the number 

of targets observed plus guidance provided by several preliminary MDD models, the probable number of undiscovered 

deposits can be subjectively estimated. These estimates are 

to be made in areas that have seabed geomorphology, marine 

conditions, and other evidence that suggesting that this specific deposit type may be present. With estimates of the probable number of undiscovered deposits available, an MCS can 

be run with those values plus the distribution of values in two 

new models that describe the volume and proportion of sanddominated facies typical of cape- and ridge-associated marine 

sand deposits. The MCS produces a cumulative probabilistic 

distribution of sand resources yet to be discovered—information of interest to marine-sand users both private and public, 

economists, and continental-shelf-resource managers. 

Conclusions 

Production of material from marine sand deposits is 

likely to be limited by various economic and environmental 

factors, including maximum water depth, end-use criteria, 

and conditions dictated in State and Federal regulations 

not explicitly considered but that may have played a part 

in estimating the probable number of undiscovered deposits. For example, current U.S. dredging equipment suitable 

for extracting offshore sand is suitable to work in depths 

no greater than ~40 m; however, extraction at this depth is 

unlikely because the maximum depth at which marine sand 

can be extracted economically is 30 m along the U.S. Atlantic 

coast. Another important factor that can restrict or eliminate 

development of sand resources is that their locations are 

preemptively used to meet other government and economic 

needs, as described in the descriptive model (see app. A). 

Another concern is that marine sand deposits containing >10 volume percent mud and clay or ≥10 volume percent 

gravel are unlikely to be suitable sources of sand for beach 

replenishment or other uses. Some deposits in the dataset 

used to construct models contain considerably more that 10 

volume percent nonsand facies materials, albeit dredging 

procedures may still permit exclusion of these undesirable 

materials. The most suitable sand has a grain-size distribution 

(texture and sorting) comparable to that of the native beach 

where is to be used. Recreational users in the United States 

prefer sand beaches that are white (Leatherman, 1997), and 

this statement may be true elsewhere in world, including New 

Zealand, where “lighter sand colours [are] generally preferred” (Dahm, 2002, p. ii). 

One unusual characteristic of marine sand deposits in 

comparison with most terrestrial mineral deposits (except 

some fluvial-channel sand and gravel deposits) is their capac16 Contributions to Industrial-Minerals Research 
 

ity to recover, given that they are in a dynamically maintained 

state. Some marine sand deposits have undergone repeated 

dredging, followed by recovery of the shoal at the same 

site (Hayes and Nairn, 2004). Therefore, some marine sand 

deposits may be considered a renewable resource. However, 

little monitoring and postdredging surveying is routinely 

done on dredge borrowsites, and much is unknown about how 

marine sand bodies form, evolve, and interact with adjacent 

sea-floor sediment. 

Assessing potential mineral resources is an important 

function provided by geologists and others in government. 

Considerable care needs to be taken to ensure that the assessment is internally consistent. For example, in this assessment 

and the subsequent MCS, the predicted sand resources are 

only those expected to occur in cape- and ridge-associated 

marine sand deposits. The sources in all other types of marine 

sand deposits (for example, blanket deposits, channel fill, 

ebb- and flood-tidal deltas) are beyond the scope of this 

report. 

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Modeling Cape- and Ridge-Associated Marine Sand Deposits 19 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix A. An Interim Descriptive 

Model for Cape- and Ridge-Associated 

Marine Sand Deposits 

By S. Jeffress Williams and James D. Bliss 

Introduction 

Descriptive models allow users to classify mineral 

deposits into types for use during a mineral-resource assessment. As noted by Barton (1993, p. 8), “a mineral deposit 

model is a systematically arranged body of information that 

describes some or all of the essential characteristics of a particular feature or phenomenon; it presents an idealized condition within which essential elements may be distinguished 

and from which extraneous elements may be recognized 

and excluded.” The following descriptive model provides 

an interim guide to help users recognize cape- and ridgeassociated marine sand deposits as applied to the mineralresource assessment of the U.S. Atlantic Continental Shelf. 

Construction of descriptive models like those of Cox and 

Singer (1986) for marine sand deposits has never before been 

attempted. This interim model is expected to be replaced by 

one or more improved descriptive models of marine sand 

deposits suitable for use in future mineral-resource assessments of marine aggregate resources. 

Most marine sand deposits occur in the depositional 

system within which they are created or dynamically maintained. Therefore, parts of the genetic model, including tides, 

currents, wave intensities, and river discharges, are directly 

observable. Other evidence for the presence of the marine 

sand deposits is obtained from associated marine sedimentary 

deposits and sea-floor bathymetry, generally of Holocene age. 

Some Pleistocene deposits in deeper water may no longer be 

associated with their genetic processes. Some genetic processes are local and directly related to deposit formation (currents, tidal strength), whereas others are regional, including 

some that occur inland or along the edge between the marine 

and terrestrial setting, such as those that also form beaches. 

Most of the information in the literature describing 

cape- and ridge-associated marine sand deposits is not about 

that part of these bedforms suitable as a source of sand for 

extraction but about the capes and sand ridges as recognizable bathymetric feature. Surveys of marine sand deposits 

reveal that much of the material present in sand-ridge fields, 

specifically in ridges, is unsuitable for economic use. Some 

sand bodies are inadequate in thickness or area, or both, to 

justify extraction; in other places, the sand characteristics (for 

example, grain size, sorting) are incompatible with expected 

end uses. The expected proportion of the area underlain by 

sand deposits within survey areas of marine sand-ridge fields 

may be as small as 16 percent. In addition, a few of the sand 

deposits described as possible sources of marine sand contain 

considerable amounts of silt-size material (see subsection 

above entitled “Sand-Dominated-Facies Model”). 

Although the quantitative models presented above consider only deposits found on the U.S. Atlantic Continental 

Shelf, this descriptive model includes deposits on sand 

ridges in marine areas of Canada, the United Kingdom, the 

Netherlands, Japan, Korea, China, and the Mediterranean 

Sea. Recognition and classification of sea-floor sand ridges 

for the purpose of probabilistic assessment has just begun, 

and proper classification of associated sand deposits is still 

unclear. Inclusion of possible deposits of the type under 

assessment outside the study area (fig. 1) helps users understand that this deposit type is likely present in other similar 

marine settings, and helps develop a broader perspective on 

these deposits and the possible locations of associated undiscovered sand resources. 

The following descriptive model provides information 

predominantly about cape- and ridge-associated deposits, the 

hosts for the sand bodies in which most marine sand deposits 

consistent with the quantitative models occur, and not about the 

contained sand deposits. 

Brief Description 

Deposit synonyms: Regularly to irregularly spaced 

linear ridges that become curved at the mouths of estuaries 

and embayments; ridges may be either attached to or detached 

from onshore beaches and barrier island systems. 

Principal commodities produced: Sand-size rounded 

grains; deeper water deposits may be coarser (Goff and others, 

2005). 

Byproducts (other commodities): Gravel. 

End uses (of produced commodities): Beach nourishment, 

coastal and wetland restoration, and shore protection. 

Typical deposits: See table 1 for deposits on the upper 

U.S. Atlantic coast and Continental Shelf; see also Sable 

Island Bank, Nova Scotia, Canada (Hayes and Nairn, 2004). 

Relative importance of deposit type (the proportion of 

the world supply of the produced commodity supplied by this 

deposit type): Unknown but important for areas along the U.S. 

Atlantic Continental Shelf and more limited parts of the Gulf 

of Mexico. 

Associated/related deposit types (other deposit types 

spatially or genetically associated with this deposit type): 

Marine sand and gravel deposits of various types; ilmenite 

beach deposits. 

Regional and Local Geologic Attributes 

Tectonic-margin type: Trailing edge. 

Coastal classification: Transgressive, with mixed-energy 

wave-dominated marine environment coupled with barrier 

islands cut by migrating tidal-inlet systems (McBride and 

Moslow, 1991). Mesotidal (mean range, 2–4 m) areas like 

those in parts of the North Sea may be permissive; a sand 

deposit does not form on prograding delta fronts or macrotidal 

coasts (mean range, >4 m). 

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Continental-shelf properties: Wide sandy continental 

shelf; numerous bathymetric irregularities. 

Coastal terrestrial features: Barrier-island chains with 

inlets (McBride and Moslow, 1991); absence of large sedimentloaded rivers with large deltas; estuaries with capes and spits at 

mouth; extensive sand beaches; headlands may be present and 

related to ridge formation (Dyer and Huntley, 1999). 

Coastal marine and associated processes: 

(a) Sources of sand: Transgressive seas rework terrestrial 

sand or sand-and-gravel deposits, both fluvial and glacial, and 

onshore beach and dune deposits; delivery of fluvial sand and 

gravel is ongoing but insufficient to allow delta formation; 

shoreline erosion of bedrock and headlands. 

(b) Processes developing sand deposits: Wave-dominated, tide-dominated, or mixed wave- and tide-dominated 

(McBride and Moslow, 1991) longshore currents; ridges in all 

tidal seas with current velocities >0.5 m/s, given a sand source 

(Dyer and Huntley, 1999); formation as detached ridges for 

shorefaces of barrier islands and maintained by currents, either 

tide or storm driven (Hayes and Nairn, 2004). Deposition 

related to irregularities on the sea floor, including abandonment of ebb-tidal delta deposits with inlet migration (McBride 

and Moslow, 1991); tidal currents drive circulation of sand 

both around and over ridges (Dyer and Huntley, 1999). 

(c) Preservation and repositioning of sand deposits: 

Longshore currents result in ridge migration; sand waves are 

present on active ridges; relief increases with water depth 

(Harrison and others, 2003); upward refraction of waves 

up along detached sand-ridge sides. These processes result 

in sand transport over ridge crest and maintain ridges after 

detachment (Hayes and Nairn, 2004); migration of ridges may 

accelerate during storms. 

(d) Degradation, modification, and destruction of sand 

deposits: Moribund ridges in the Mediterranean Sea are 95 

to 110 m deep (Bassetti and others, 2006). At 50-m depth, 

ridges are no longer active on the U.S. Atlantic Continental 

Shelf (Goff and others, 2005); absence of large sand waves 

on flanks; round crested cross; slope of ≤1o; sandy or muddy 

swales (Dyer and Huntley, 1999); possibly coarse older and 

moribund deposits (Goff and others, 2005). 

Age range: Holocene; Pleistocene in deeper water (Berné 

and others, 2002); latest Pleistocene (11,900–11,600 ka in the 

Gulf of Lions, Mediterranean Sea; Bassetti and others, 2006). 

Water depth: Nearshore areas; including ridges 

expressed as shoals attached to beaches and barrier islands to 

possible maximum depth of 90 m on the U.S. Atlantic Continental Shelf; possibly as deep as 110 m in the Mediterranean 

Sea if those occurrences belong to this deposit type. 

Sea-floor bathymetry: Linear ridges parallel to predominate wave-approach direction; open shelf and at estuary entrances with and without recession (Dyer and Huntley, 

1999); typically observed in extensive regions of asymmetric 

ridges or shoals bounded by both steep (6o) and shallow (≤1o) 

slopes (Dyer and Huntley, 1999); contorted cape associated 

ridges; maximum length, 80 km, average width, 13 km; average height, tens of meters; ridge spacing proportional to width 

(Dyer and Huntley, 1999), increasing with water depth (Off, 

1963) in the Maryland sector: 3.7 to 12.1 km long, mostly 

8.3 to 13.9 km long; 0.9 to 2.8 km wide, mostly 1.4 to 2.3 km 

wide (Duane and others, 1972; Swift and Field, 1981); in the 

Korea Strait: maximum 63 km long, 3 to 9 km wide, and 22 m 

thick (Park and others, 2003). 

Related geomorphologic feature(s): Areas between 

active ridges with clean gravel (Dyer and Huntley, 1999). 

Associated sediment(s): Silt, gravelly silt; sandy silt, 

gravelly sand; clay-size material; interridge areas separated by 

swales of clean gravel (Dyer and Huntley, 1999). 

Sand-deposit mineralogy: Sand-size quartz, other durable 

and chemically inert minerals sought for use; colors, grain 

shape. 

Impurity mineralogy/materials: Clay and clay-size minerals, organic and shell debris, gravel, silt, carbonates. 

Typical sand deposit dimensions: See “Sea-Floor 

Bathymetry” item above for ridges hosting marine sand deposits; see text for sand-deposit thicknesses and areas. 

Maximum limitation of overburden: Unknown but 

dependent on dredging equipment used. 

Exploration data source(s): Vibracore, age determination; fossil assemblages. 

Geochemical signature(s): None known at present. 

Geophysical signature(s): Chirp seismic; seismic; sidescan sonar. 

Other exploration guide(s): Sand-ridge spacing increases 

with water depth. False positives include superficially appearing sand-ridge deposits that are erosional features where they 

are composed of fine sediment (deltaic, estuarine materials) as 

observed in deep (90 m) water in the East China Sea (Berné 

and others, 2002); erosional ridges also observed in Cretaceous 

sediment along the west coast of Long Island, N.Y. 

Most readily ascertainable regional attribute: Barrier 

islands with inlets along coastal zones, with lengths measured 

in hundreds of kilometers. 

Most readily ascertainable local attribute: Possibly 

exposed as a shoal at or near the water surface or within ridge 

fields readily recognized from bathymetry. 

Economic Limitations 

Physical/chemical properties affecting minability/use: 

Mean grain size and sorting of sand in sand deposit is best 

if compatible with the beach on which it is to be used; contamination with clay, silt, and coarse sediment is undesirable; 

grains should be rounded or possibly uneven in dependence on 

application. 

Compositional/mechanical processing and other 

restrictions: Maximum dredge equipment depth, 40 m; maximum economic depth of extraction, 30 m (U.S. Atlantic Continental Shelf). 

Preemptive-use limitations: Marine sand deposits of this 

type are common and of greatest utility as resources in nearshore parts of the Continental Shelf, and so also commonly in 

promising locations with many other uses: vessel navigation, 

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pipelines, drilling platforms, cables, military and homeland 

security facilities, wind farms, and other related activities. 

These sand bodies too commonly serve as valuable marine 

benthic habitats and may be characterized as Essential Fish 

Habitats and off limits to such activities as dredging. These 

uses will commonly preclude the use of all or significant parts 

of these sand deposits as a resource. 

Distance to transportation, processing, and end use: 

The U.S. Army Corps of Engineers estimates dredging and 

transport costs of marine sand at $4.00/yd3 ($5.20/m3) within 

1 mi (1.6 km) of the U.S. Atlantic coast, with each additional 

mile adding $1.00/yd3 ($1.30/m3) to a maximum distance of 

5 miles (8 km) (Weggel, in Leatherman, 1989), the maximum 

possible distance for a floating-pipe dredge system. Beyond 

this distance, sand is dredged and transported by hopper dredge 

or by barge, then by truck, to location at an additional cost of 

$2.00/yd3 ($3.00/m3). The final cost of dredged sand is largely 

determined by transportation distance. Material containing >10 

volume percent clay or gravel is likely unsuitable for use as 

beach nourishment. 

Spatial properties important in exploration and exploitation: Sand-ridge geometry changes from long and thin 

(length-to-width ratio, 9:1) in shallow water to short and thick 

(length-to-width ratio, 3:1) in deeper water (≥15 m) (Swift 

and Field, 1981). Note that this specification applies to the full 

ridge and may not be applicable to the contained sand deposits 

that may be suitable for extraction. 

Environmental/health concerns related to deposit type 

(asbestosis, silicosis; other environmental problems; types and 

extent of ecologic disruption): Until about 2004, most sand 

extraction was from deposits in 5- to 15-m-deep water and at 

depths at which associated physical and biologic impacts are 

expected to be greatest (Hayes and Nairn, 2004). Dredging 

can disrupt bottom ecosystems, create turbulence, and permanently modify sea-floor geometry, affecting currents, and may 

also result in remobilization of buried or sequestered industrial 

waste. 

Appendix B. Statistical Methods and 

Diagrams 

One way to test data collected for modeling is by determining whether the values can be treated as random samples drawn 

from a single population. Data from mineral deposits of the 

same type commonly include variables (volume, area) that can 

be described by using either a log-normal or a normal distribution. Statistical rejection of these distributions may suggest that 

some of the deposits are misclassified or that errors related to 

data reporting or collection exist. Testing of data in this way is 

important in screening processes during modeling, as illustrated 

in figure 13, which plots the same dataset expressed in two different ways. The values in the histogram shown in green in the 

lower part of the figure are also the same values shown as data 

points in the upper part of the figure. The upper part of the figure 

is called a normal quantile-quantile (Q–Q) plot. These figures 

help explore how well the normal distribution describes the data. 

The normal distribution is expected to have a symmetrical, bellshaped curve, as shown by the red line on the histogram in the 

lower part of the figure. The distribution is described by using 

two variables: the mean and the standard deviation. The mean 

is the value at the peak of the curve, and the standard deviation 

describes how values are distributed about the mean; thus, the 

larger the standard deviation, the greater the spread in values, 

and the broader the bell mouth. The normal distribution also 

can be expressed as a “standard normal distribution,” where the 

value of the mean is set to 0 and the standard deviation is set to 

1 with values both positive and negative. These values are also 

called a normal score, as given along the right vertical axis of 

the Q–Q plot. The normal distribution, when scaled as a standard normal distribution, produces a straight line, as shown in 

the upper part of the figure (the same red line shown overlaying 

the histogram in the lower part of the figure). The black data 

points are expected to fall near the line if they can be described 

by using a normal distribution. If the data points fall outside the 

Lilliefors confidence boundaries located above and below the 

normal-distribution curve in the Q–Q plot, this result suggests 

that the assumption of a normal distribution would be rejected at 

the one-percent-confidence level. Note that the probability scale 

adjacent to the normal score also has values so distributed as to 

accommodate a bell-shaped shown as a straight line, and lists the 

probabilities in increasing order. See standard statistics textbooks 

for more information about the widely used normal distribution. 

0.01 

0.05 

0.10 

0.25 

0.50 

0.75 

0.90 

0.95 

0.99 

-3 

-2 

-1 

0 

1 

2 

3 

Lilliefors 

confidence 

boundary

 Normal 

distribution 

Normal score 

Probability scale 

-1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 

LOGARITHM OF AREA

 (IN SQUARE KILOMETERS)
 

Figure 13. Same histogram (lower part) and normal quantilequantile (Q–Q) plot (upper part) for 47 of 54 cape- and ridgeassociated marine sand deposits as in figure 2, with normaldistribution curves and Lilliefors confidence boundary indicated. 

22 Contributions to Industrial-Minerals Research