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‡Present address: ExxonMobil Production Company, Houston, Texas 77002, USA

Many important geotechnical issues (e.g., groundwater supply and contamination, subsurface waste disposal, hydrocarbon exploration and production) require a detailed understanding of porosity and permeability in subsurface clastic formations (= reservoir quality). Reservoir quality depends on the size, shape, and packing of sand grains as they are originally deposited, as well as diagenetic changes during burial. Obtaining enough samples to fully characterize the target formation is prohibitively expensive or physically impossible. Therefore, reservoir quality estimates must be extrapolated from analogues (± sparse samples) or derived from models. Forward-modeling approaches to predicting diagenetic effects on reservoir quality are well established, but they require information about the character of deposited sand, including mean grain size, sorting, matrix content, and composition of diagenetically relevant particles (i.e., all rock fragments, not just lithic fragments). In cases where deposited sand characteristics are not known, they must be estimated. To this end, we advocate an integrated genetic analysis, which simultaneously predicts multiple sand characteristics as a function of many environmental controls, including tectonic setting, provenance lithotype abundance, climate, regional topographic gradient, hinterland transport distance, basin transport distance, basin subsidence rate, and depositional environment. We have implemented this analytic procedure as a Bayesian belief network–based forward model that successfully predicts sand composition and texture in diverse settings, including provenance areas dominated by either volcanic, high-grade metamorphic, or sedimentary lithologic assemblages; climates ranging from tropical to desert; and a range of alluvial/fluvial drainage types represented by small steep drainages as well as continental-scale big rivers.

INTRODUCTION

Why Predict Sand Character?

Many important geotechnical issues require a detailed understanding of the porosity and permeability of subsurface clastic formations. We will refer to these characteristics as reservoir quality. Some pertinent reservoir quality questions include: (1) What are the draw-down and recharge rates of aquifers that supply domestic and agricultural water? (2) How quickly, and in what direction, will groundwater contaminants flow? (3) What is the reserve size and potential recovery efficiency of an oil field?

In all these cases, obtaining enough samples to fully characterize the porosity and permeability of the target formation is prohibitively expensive or physically impossible. Therefore, estimates of reservoir quality must either be extrapolated from analogues ± sparse samples or derived from models. The environmental and economic costs of faulty estimates can be substantial.

Therefore, it is desirable to have a consistent, systematic, and broadly applicable method to predict reservoir quality in places where direct observations are not possible. Many tools exist to predict reservoir quality if sand character (i.e., composition, texture, and matrix content) and burial and thermal history are known (e.g., Lander and Walderhaug, 1999; Perez et al., 1999; Bray et al., 2000; Bonnell and Lander, 2003). These tools are only as good as their input data; if there is no way to directly observe sand character, or if the range of sand character is not fully captured by available samples and analogues, then sand character must be estimated. The accuracy of porosity and permeability predictions is limited by the accuracy of the predicted sand character.

Because reservoir quality depends on the pore network, many features of the solid particles that define the pore network must be known. For example, the grain-size distribution and matrix content determine depositional porosity. Loss of depositional porosity is governed by the ductility of the grains and by the potential for the grains to grow diagenetic cement. An estimate of the bulk mineralogy (e.g., a Gazzi-Dickinson point count) of one grain size (e.g., medium sand) does not provide enough information to effectively model reservoir quality; the sizes and physical characteristics of all grains (especially rock fragments) are critical controls on compaction and cementation.

We advocate integrated genetic analysis as the best way to make sand character predictions because it accounts for the most important factors responsible for sand generation and evolution from the sediment source to the site of ultimate deposition.

Terminology

It is important to note our use of particular geologic terms to eliminate confusion or misconception. We consider provenance to include all aspects of the system responsible for sand generation and evolution (Suttner, 1974). We refer to the rocks that are decomposed to produce sand as provenance lithotypes. We use the term hinterland to indicate all portions of Earth's surface that contribute sediment to a particular basin, and basin to indicate the areas that accumulate large volumes of sediment due to subsidence. We use the terms hinterland and basin rather than the currently popular terms source and sink because “source” has a very particular meaning in our industry (i.e., organic-rich sediments that can generate hydrocarbons), whereas hinterland and basin are generally understood in the way we have defined them here. Our usage of hinterland should not be confused with tectonic or structural connotations, but rather taken in its literal sense of “territory behind the coast.”

Integrated Genetic Analysis

Integrated genetic analysis is a holistic analytical approach that recognizes the relationships among environmental conditions and the spectrum of sand types that may result as a function of variations in these conditions. There is no unique solution that corresponds with a given sandstone composition and texture, but by analyzing all the controlling factors and processes in concert, “a problem that appears to be hopelessly complex...does not need to be so” (Krynine, 1943, p. 3). It is possible not only to decipher an observed sand's history, but it is also possible to predict the composition and texture that should result from a particular history.

At least since James Hutton, sedimentary geologists have recognized that sand character depends on the entire history of sand generation and evolution. The basic conceptual framework of the sand-producing system was first laid out in Henry Clifton Sorby's Anniversary Address of the President to the Geological Society of London (Sorby, 1880). Periodically since then, other workers have described the systematic genetic relationships in flow charts or schematic representations (e.g., Krynine, 1943; Potter and Siever, 1956; Folk, 1974; Potter, 1978; Johnsson, 1993). The community generally accepts the following basic factors that control sand generation and evolution, as summarized in Figure 1: tectonics, which governs the assemblage of rock types and geomorphic character of the hinterland; weathering, both intensity and duration; transport, including weathering during storage and abrasion; and deposition, including hydrodynamic sorting effects.

Figure 1. Generally accepted factors controlling sediment generation and evolution.

Figure 1. Generally accepted factors controlling sediment generation and evolution.

Despite general agreement as to the basic factors, there is not yet a holistic and quantitative process to use general environmental knowledge about the sand genetic system to make specific predictions of sand character.

CONCEPTUAL FRAMEWORK AND ANALYTIC PHILOSOPHY

Genetic Context

In order to turn the broadly accepted, but ill-specified, concept model of sand generation and evolution into a tool for quantitative prediction, we define and quantify key aspects of provenance that control sand character (Fig. 2), including: (1) provenance lithotypes, (2) regional topographic gradient, (3) climate (weathering potential and transport potential), (4) transport distance in the hinterland, (5) transport distance in the basin, (6) basin subsidence, and (7) depositional facies.

Figure 2. Key genetic factors captured by the Sand Generation and Evolution Model (SandGEM).

Figure 2. Key genetic factors captured by the Sand Generation and Evolution Model (SandGEM).

Tectonic Setting

The first and most important step in understanding sand generation and evolution is a fundamental analysis of tectonic setting (Dickinson and Yarborough, 1978; Ingersoll and Busby, 1995). Tectonic setting provides a framework in which to interpret or make assumptions about: the rocks from which sediments are derived; the processes by which sediments are generated and evolved; and the depositional environments in which sediments have been deposited. All of the factors except for climate and depositional environment are directly determined by the plate-tectonic setting and geodynamic context. Even climate and depositional environment are moderated by tectonics, through the influence of landmass distribution and topography on global atmospheric and oceanic circulation (e.g., Poulsen et al., 1998; Motoi et al., 2005; Clark et al. 2005) and on local drainage patterns (e.g., Rossetti, 2004; Jones et al., 2004).

The integrated genetic approach presented here diverges from earlier studies correlating tectonics with sand composition (Dickinson and Suczek, 1979; Dickinson et al., 1983; Ingersoll and Busby, 1995) by emphasizing the tectonics of the hinterland as much as, if not more than, the tectonics of the sedimentary basin. Often, the tectonic settings of the basin and hinterland are tightly linked, for example, in foreland basins associated with fold-and-thrust belts (Critelli, 1999; Critelli et al., 2003), but just as often, particularly in the case of very large drainage basins, the tectonic setting of the depositional basin may be substantially disconnected from the hinterland. For example, the Barba-dos forearc basin clearly receives input from the adjacent South American continent (Faugeres et al., 1997; Mahabir et al., 2004), as well as from the arc system itself; the “anomalously quartzose” (Marsaglia and Ingersoll, 1992) sediments of this basin reflect the assemblage of provenance lithotypes in the hinterland, part of which is a function of a different tectonic setting than the one that formed the basin. We contend that once sand has reached the edge of a sedimentary basin, its composition has already been largely determined by its hinterland and transport heritage.

Schematic Representation

Our Sand Generation and Evolution Model (SandGEM) is shown in Figure 3. Each pair of boxes connected by an arrow in this diagram represents a small portion of the sand generation and evolution system that we can describe (however crudely) with a quantitative relationship that can be calibrated to observations of the real world. The network provides a formal, structured system to account for the complex real-life web of processes and products. The rest of this paper is devoted to explaining why we have chosen these particular relationships to describe the system, what observations support our description of the relationships, and how we can use this model to make predictions about sand character in reservoirs.

Figure 3. Functional relationships among key genetic factors (dark gray nodes) and sand character as described by the Sand Generation and Evolution Model (SandGEM).

Figure 3. Functional relationships among key genetic factors (dark gray nodes) and sand character as described by the Sand Generation and Evolution Model (SandGEM).

Key Variables

Provenance Lithotype

Provenance lithotype (Figs. 2 and 3) is the single most important genetic factor (Heins, 1993). Accumulations of sand that are large enough to be economically significant hydrocarbon reservoirs rarely are derived from only one rock type; we assume that they come from drainage systems that were (or are) large enough and complex enough to encompass numerous lithotypes (typically large second-order to third-order settings, in the sense of Ingersoll et al. [1993]). There are natural associations of provenance lithotypes that are determined by tectonic setting (Kearey and Vine, 1996; Cox and Hart, 1986). In the absence of other information, the Provenance Lithotype assemblage can be inferred from tectonic setting alone (Kairo and Heins, 2004). The relevant tectonic setting is the one that assembled and exposed the provenance lithotypes from which sediments were derived and that determined drainage and basin geometries at the time the reservoir sediments in questions were generated and deposited.

We discriminate among the Lithotypes based on: (1) propensity to create sand-sized detritus (akin to the sand generation index of Palomares and Arribas [1993]); and (2) the relative abundances of quartz, feldspars, micas, rock fragments, and clay among the detritus.

Both of these characteristics depend on the mineralogy and texture of the Provenance Lithotypes.

Regional Topographic Gradient

Regional Topographic Gradient (Figs. 2 and 3) is defined as the average gradient of major rivers that supply sediment to the basin. The regional topographic gradient influences how quickly water flows over and through the landscape and how quickly sediment can be exported from the weathering zone on top of bedrock (Ritter et al., 2002). The velocity of water and sediment influences: the duration, and therefore the cumulative intensity, of initial weathering in the regolith; and the power of the transport system to move sediment (Walling and Webb, 1996).

Climate

Climate (Figs. 2 and 3) is defined by the level and variability of wetness and temperature when and where the sand formed in the hinterland. The interaction of temperature and precipitation over seasons and longer-term climate cycles determines the potential of the environment to do chemical work in transforming provenance lithotypes into sediment and influences the potential of the environment to do physical work in moving the sediments toward the basin.

Temperature has two different effects. Increasing temperatures, if all other factors are equal, will increase mineral-dissolution reaction rates exponentially (Lasaga, 1984). However, increasing temperature also increases evaporation, all other things being equal, so the amount of water available to facilitate dissolution reactions will decrease (Willmott, 1977). Precipitation that is evaporated is also less available to do physical work moving sediment than precipitation that is not evaporated (Wischmeier and Smith, 1978). The seasonal variability of effective precipitation is also important. Cecil and Edgar (2003) observed that sediment transport reaches a maximum when effective precipitation is concentrated into a small fraction of the year; these observations are consistent with the classic observation of Langbein and Schumm (1958) that solid-sediment yields are highest in areas with moderate precipitation, because those climates have the most highly seasonal precipitation patterns.

We capture the time-dependent interaction of temperature and precipitation as Climate Weathering Potential and Climate Flushing Potential (Fig. 3). A method for calculating dimensionless weathering potential and flushing potential indices is described under Network Structure, and in Appendix A. Weathering and flushing potential indices have no intrinsic physical meaning, but they can be compared to levels of dissolved, suspended, and bed load in modern rivers (Curtis et al., 1973; Walling, 1987; Summerfield and Hulton, 1994; Ludwig and Probst, 1996; Milliman, 1997; Hovius, 1998; Schaller et al., 2001; Syvitski et al., 2003; Walling and Fang, 2003) to quantify relationships between climatic styles and sediment yields.

Hinterland Transport Distance

Hinterland Transport Distance (Figs. 2 and 3) is defined as the average distance sediment travels from its site of initial generation to the depositional base level. Hinterland Transport Distance reflects the size of the drainage capture area and the characteristics of the drainage network (Strahler, 1964; Roth et al., 1996). Hinterland Transport Distance is an important control on the potential for the system to store sediment, during which time it can be modified (Johnsson and Meade, 1990; Johnsson, 1993), and on the potential for the system to segregate different grain sizes (Vogel et al., 1992; Robinson and Slingerland, 1998a, 1998b; Gasparini et al., 2004).

Basin Fluvial Transport Distance

Basin Fluvial Transport Distance (Figs. 2 and 3) is defined as the average distance sediment travels across the subsiding depositional basin to the end of the fluvial system. In the case of a fluvial/alluvial basin, the end of the fluvial system is the final point of deposition. The maximum grain size that can be delivered to the basin by a river is, in part, a function of the distance the sediment travels by river within the subsiding basin (e.g., Robinson and Slingerland, 1998a, 1998b).

Rate of Basin Subsidence

Rate of Basin Subsidence (Figs. 2 and 3) is defined as the rate of subsidence of the bottom of the basin (not the sediment-water interface). This rate is approximated by the thickness of sedimentary strata that is preserved in a given time period (essentially the rate of change in structural accommodation). Basin Subsidence controls the regional slope of the depositional basin and is a primary factor in creating accommodation space.

Depositional Facies

Depositional Facies (Figs. 2 and 3) is defined as the deposits of distinct hydrodynamic regimes within generalized environments of deposition. The hydrodynamic regime influences mean grain size, sorting, and the matrix content of deposits (Hsü, 2004). Depositional Facies are the buildings blocks of a depositional environment, but are not necessarily linked to specific environments (e.g., channel deposits can occur in many depositional settings, but they all represent a unidirectional-flow-traction transport plus suspended-load transport.) Absolute grain size is determined by the grain-size mix delivered to the basin; hydrodynamic processes subsequently segregate the delivered mix by facies.

Physical Boundaries

Hinterland

If the boundaries of the hinterland are known, then a precise estimate of provenance lithotype abundance can be made, rather than generically inferred from tectonic setting. In this case, the default approximation is that the modern geologic map (minus units younger than the formation of interest) represents the lithotypes from which the sand was generated. The best possible estimate of hinterland boundary and relative abundance of provenance lithotypes (essentially a paleogeologic map) takes all sources of paleogeographic information into account, including geomorphology (wind gaps, water gaps, etc.), patterns of regional unconformity and facies distribution, paleocurrents, structural styles and patterns, and thermochronology; an example of such a reconstruction is provided by Tokarev (2005) and Tokarev and Gostin (2003).

Basin

The shape and position of the basin in which deposits of interest are found changes through time as the rates and limits of structural subsidence change. The genetic elements must relate in time and space to a distinct body of sediment in the basin, which is defined by formal upper and lower stratigraphic boundaries and distinct lateral boundaries.

Evolutionary Stages

To simplify the naturally complex system of sand derivation and modification while maintaining a genetic approach, we distinguish among three stages in the evolution of sediments: generation, transport, and deposition. In our model, we attempt to characterize texture and composition at each of these stages (Fig. 3).

Generated Sediment

Generated Sediment (Figs. 2 and 3) is an abstraction for the bulk character of all sediment in the regolith and/or soils upon disintegration of provenance lithotypes. The extent to which Generated Sediment differs from the Provenance Lithotypes depends on the intensity and duration of weathering processes, which in turn depend primarily on climate (for intensity) and topography (for duration) (Heins, 1993, 1995).

Transported Sediment

Transported Sediment (Figs. 2 and 3) is an abstraction for the bulk character of all sediments in the hinterland alluvial-fluvial transport network, just prior to delivery to the basin margin (i.e., the boundary between areas of net erosion and net deposition). Transported Sediments are generated sediments that have been reduced in size, had some components removed by dissolution, and had others transformed to clay. The extent to which Transported Sediment differs from Generated Sediment depends on the intensity and duration of weathering processes during storage (Johnsson and Meade, 1990; Johnsson, 1993) and on hydrodynamic segregation during transport (Vogel et al., 1992; Robinson and Slingerland, 1998a, 1998b; Gasparini et al., 2004).

Deposited Sediment

Deposited Sediment (Figs. 2 and 3) forms the prospective reservoir, the character of which we wish to predict. Whereas the transition from Generated to Transported sediment represents the removal and transformation of grains; the transition from Transported to Deposited sediment represents the fractionation of the bulk population of Transported Sediments into different Depositional Facies according to hydrodynamic processes. Deposited Sediment, in each Depositional Facies, differs from Transported Sediment because some grain types are preferentially associated with some grain sizes (Krynine, 1948; Bokman, 1955; Crook, 1960; Kairo et al., 1993). Deposited texture depends on the relative ability of each depositional environment to segregate grains of a particular size.

Sand-Generating Processes

As outlined in Figure 3, we simplify all of the processes that are responsible for converting Provenance Lithotypes into Generated Sediment as the Generative Modification Potential, which is a function of Climate Weathering Potential and Regional Topographic Gradient. Generative Modification Potential is conceptually equivalent to the cumulative chemical weathering index (CCWI) of Grantham and Velbel (1988). Even though CCWI was not an appropriate predictor of sand composition in the particular genetic context examined by Grantham and Velbel (Heins, 1992, 1993), the fundamental reasoning behind the CCWI is sound: generated sediments differ from their parent rocks most significantly when the chemical power of the environment is high (due to higher temperature and/or precipitation) and when the residence time in the environment is high (due to lower topographic gradient).

Transport Processes

Total Flushing Potential

Total Flushing Potential (Fig. 3) quantifies the ability of the hinterland alluvial-fluvial network to move sediment to the basin. Total Flushing Potential is a function of the amount of water available to move sediment (as described by climate flushing potential) convolved with gravitational potential energy (as described by regional topographic gradient). Total Flushing Potential will be higher when Climate Flushing Potential and Regional Topographic Gradient variables are both higher, and vice versa. Between Climate Flushing Potential and Regional Topographic Gradient, Regional Topographic Gradient is considered to be a more important control on Total Flushing Potential, to honor the observations of Walling (1987), which showed that sediment delivery rates are high in mountainous areas across many climatic zones.

Fluvial Storage Potential

Fluvial Storage Potential (Fig. 3) is a measure of the propensity for sediment to be stored in fans, floodplains, terraces, bars, etc., along the alluvial-fluvial transport system of the hinterland. The array of factors that govern the likelihood of a sedimentary particle to be stored is broad, and these factors interact in complex ways (see Ritter et al., 2002, chapter 5, for an overview of relevant literature). An actual calculation of storage probability is only possible at the most conceptual level (Malmon et al., 2003). Nevertheless, fluvial storage is such an important process to determine sediment character (Johnsson and Meade, 1990) that it must be captured in the network.

We abstract all of the controlling factors into the effects of Total Flushing Potential and Hinterland Transport Distance. Fluvial Storage Potential is higher when Total Flushing Potential is lower and Hinterland Transport Distance is longer, and vice versa. Between Total Flushing Potential and Hinterland Transport Distance, Hinterland Transport Distance is considered to be a more important control on Fluvial Storage Potential, because any single flushing episode is highly unlikely to move a particle completely through any but the shortest system; rather, sediment tends to be exchanged between channels and storage sites (Dunne et al., 1998); thus the total number of flushing events, and thus the total amount of time, required to clear a particle through the system increases with Hinterland Transport Distance, regardless of Total Flushing Potential.

Selective Transport Fining

Selective Transport Fining (Fig. 3) is the portion of downstream reduction of grain size that can be attributed to differential transport of grains with different sizes and densities, which we simplify to be a function of Hinterland Transport Distance only. The longer the transport distance, the more opportunities are available for sediment to be temporarily stored; at each step of deposition and remobilization, sediments have an opportunity to be hydrodynamically segregated and different size classes preferentially retained or removed (e.g., Shih and Komar, 1990; Vogel et al., 1992; Robinson and Slingerland, 1998a, 1998b; Gasparini et al., 1999).

Transport Modification Potential

Transport Modification Potential (Fig. 3) is a measure of the ability of the hinterland environment to change Generated Sand Composition and to produce clay. Transport Modification Potential is a function of Fluvial Storage Potential (the duration of modification) and Climate Weathering Potential (the intensity of modification). Transport Modification Potential is higher when both duration and intensity are higher, and vice versa. Between Climate Weathering Potential and Fluvial Storage Potential, Fluvial Storage Potential is considered to be a more important control on Transport Modification Potential, because of observations that sediment traveling a short time and/or distance is only slightly modified, even in hot, wet climate conditions (Krynine, 1935; Ruxton, 1970), whereas sediment that is stored can be highly modified under a range of climate conditions (Suttner et al., 1981; Johnsson et al., 1988; Robinson and Johnsson, 1997).

Total Transport Fining

Total Transport Fining (Fig. 3) quantifies the ability of the hinterland alluvial-fluvial transport system to reduce the grain size of Transported Sediments by both physical (Selective Transport Fining) and chemical (Transport Modification Potential) processes. Total Transport Fining is higher when either physical or chemical modification is higher. Selective Transport Fining and Transport Modification Potential are considered to be equally responsible for Total Transport Fining.

Depositional Processes

Maximum Grain Size

Maximum Grain Size (Fig. 3) represents an upper limit on the grain size of sediment that can pass from the hinterland to the basin, which we consider to be a function of Rate of Basin Subsidence and Basin Fluvial Transport Distance; together, these factors determine the gradient in the basin, and thus the gravitational potential available to move sediment. Under some circumstances, coarser grain sizes may be sequestered near the basin margin, while the finer fractions of the delivered grain size distribution can be transported to more basin-ward environments of deposition (Robinson and Slingerland, 1998a, 1998b). Longer transport distances and slower subsidence rates (lower gradient) favor more effective trapping of a larger proportion of the coarse tail of the grain-size distribution.

Depositional Fining and Sorting Potentials

Depositional Fining Potential (Fig. 3) quantifies the propensity for a particular Depositional Facies to segregate grains that are finer, on average, than the mean grain size of the Delivered Grain Size and Sorting, whereas Depositional Sorting Potential (Fig. 3) is a measure of the propensity for a particular Depositional Facies to segregate a grain population that is better sorted, on average, than the sorting of the Delivered Grain Size and Sorting.

Deposition Modification Potential

Depositional Modification Potential (Fig. 3) is named in parallel with Generative Modification Potential and Transport Modification Potential to reflect the power of the environment to modify sand composition. Depositional Modification Potential is a function of the ability of Deposited Grain Size and Sorting to reflect the control of grain size on composition (Krynine, 1948; Bokman, 1955; Crook, 1960; Kairo et al., 1993).

MODEL IMPLEMENTATION

Bayesian Inference

We have codified our understanding of the generally accepted relationships between genetic controls and the character of reservoir sands in a Bayesian Belief Network (BBN). Bayes Rule (Bayes, 1763) states that the probability of two things (A,B) occurring together is equal to the probability of A given B, times the probability of B (and vice versa). Alternative symbolic formulations of the rule are given in Equations 1 and 2:  

formula
and  
formula

Bayes Rule provides a convenient bookkeeping device to keep track of a web of conditional probabilities; if you know the probability of B, given that A is true, and you know the probability of A, then you can calculate a probability of B. There is no limit to how many conditional states you may concatenate.

As a practical matter, formal models using Bayes Rule describe the world in nodes, which exist in discrete states that are comprehensive and mutually exclusive (Norsys, 2006). For example: the weather can be sunny or rainy, the speed of a car can be fast or slow; a road could be straight or curved; the pavement could be wet or dry. The states of the nodes have probabalistic relationships with each other, which can be exploited for predictive purposes. In the current example, the nodes may be arranged as in Figure 4. Nodes can be parent, child, or both. Nodes with arrows coming out are parent nodes. Nodes with arrows coming in are child nodes. Nodes that are parent only (weather condition, road type) are called root nodes or inputs. Nodes that are child only (crash risk) are leaf nodes or outputs. The rest are intermediate nodes, which are both child and parent. The probability of states in each child node depends on the probability of states in the parent node, i.e., the P(A), and on a conditional probability table (i.e, the P[B|A]). The conditional probability table for the crash risk node of this example is provided in Table 1. The structure of the network describes the fundamental relationships; the values in the conditional probability tables quantify the details of those relationships. The conditional-probability tables are specified by the builder of the network; they can be based on expert opinion or physical models, crudely estimated from sparse data, inferred by sophisticated statistical means from abundant data, or anything in between.

TABLE 1. CONDITIONAL PROBABILITY TABLE FOR CRASH RISK

Figure 4. Example Bayesian network describing the relationships among weather condition, road type, and crash risk. Nodes with arrows coming out are “parent” nodes, which provide information about the probability of causes, whereas nodes with arrows coming in are “child” nodes, which provide information about effects. Nodes without parents are known as “root” or “input” nodes, whereas nodes without children are known as “leaf” or “output” nodes.

Figure 4. Example Bayesian network describing the relationships among weather condition, road type, and crash risk. Nodes with arrows coming out are “parent” nodes, which provide information about the probability of causes, whereas nodes with arrows coming in are “child” nodes, which provide information about effects. Nodes without parents are known as “root” or “input” nodes, whereas nodes without children are known as “leaf” or “output” nodes.

A BBN can accommodate the fact that a single cause may have several effects, each of which may have contrasting, or even contradictory, contributions to the leaf nodes. For example, a weather condition of sunny correlates with better road conditions (which lower crash risk), and with higher car speeds (which increase crash risk). The network provides a convenient means for keeping track of the ultimate relationship of weather condition on crash risk, even in the face of complex interaction of effects.

Network Structure

The schematic diagram of our model presented in Figure 3 and Tables 2 and 3 is also the structure of our BBN. This BBN is constructed with seven input nodes, which represent the key genetic elements governing sand character, and three output nodes which represent sand composition; sand texture; and detrital matrix content.

TABLE 2. NODES IN THE SAND GENERATION AND EVOLUTION BAYESIAN NETWORK

TABLE 3. PARENT-CHILD RELATIONSHIPS AMONG NODES IN THE SAND GENERATION AND EVOLUTION BAYESIAN NETWORK

In between the input and output nodes are a series of intermediate nodes that describe the interactions of the genetic elements and their ultimate influence on the output nodes. Some of the intermediate nodes of the network depend quite directly on the input nodes; they either are children of input nodes, or have only one intermediate node between them and an input node. We informally refer to these as moderately derived nodes. The rest of the intermediate nodes are far removed from the input nodes by several intervening nodes. We informally refer to these as highly derived nodes. The intermediate nodes listed in Table 2 are listed in order of increasing distance from the input nodes (equivalent to higher stream numbers of Shreve, 1966). The node “Deposited Grain Size and Sorting” is an output, in the informal sense that it is a feature of sand character that we wish to predict, although it is not a leaf node.

In this model, input and output nodes have precisely defined states with quantitative limits, whereas intermediate nodes related to processes have qualitative states that capture end members and intermediate states along a less-well-defined continuum.

“Tectonic setting” and “provenance lithotype assemblage” are shown in Figure 3 with dotted line connections, because they are not formal nodes. In real life, tectonic setting is the fundamental control on most aspects of the sand generation and evolution system, particularly on the assemblage of rocks exposed at the surface, from which the sediment will be derived. We constructed a library of provenance lithotype assemblages associated with different modern and ancient tectonic settings to use as analogs in cases where time or data restrictions prohibit reconstructing a paleogeologic map. For our purposes, we classified every rock type that can produce significant quantities of sand into 21 exhaustive and mutually exclusive categories (Table 4). We use information about the provenance lithotype assemblage, including relative abundance of each rock type, mineralogic composition (Table 5), and chemical composition (Table 6) to calculate the conditional probabilities that govern the nodes Generated Sand Composition, Generated Grain-Size Distribution, and Generated Clay Abundance.

TABLE 4. PROVENANCE LITHOTYPE NAMES Code

TABLE 5. PROVENANCE LITHOTYPE MINERALOGICAL CHARACTERISTICS

TABLE 6. PROVENANCE LITHOTYPE MAJOR-ELEMENT OXIDE CHARACTERISTICS (WT%)

Generated, Transported, and Delivered Sediments

In the model, we distinguish among generated, transported, and deposited sediments. Each kind of sediment is described by three nodes in the BBN: one for sand composition, one for sand texture, and one for mud. Each of the sand composition nodes has the same 66 states, corresponding to 10% increments in quartz–feldspar–rock fragment (QFR) ternary space (Fig. 5). Although each node state refers to a fixed proportion of Q, F, and R, the actual composition associated with each node state consists of 25 different grain types (Table 7). We calculated the specific 25-component mixture associated with each of the 66 ternary compositions with a separate spreadsheet, outside of the network.

TABLE 7. SANDGEM GRAIN TYPES

Figure 5. Operational definition of quartz–feldspar–rock fragment (QFR) sand composition states in the Sand Generation and Evolution Model (SandGEM).

Figure 5. Operational definition of quartz–feldspar–rock fragment (QFR) sand composition states in the Sand Generation and Evolution Model (SandGEM).

Generated and transported texture-node states correspond to specific grain-size distributions within standard categories from granules to coarse silt (Table 8), whereas deposited texture-node states refer to more generalized verbal descriptions of grain size and sorting (Tables 8 and 9). The number of grain-size distributions or size-sorting categories in each texture node is fixed, but the relative abundance of each grain size within each distribution (for generated and transported), or the numerical value of mean grain size and sorting (for deposited), is calculated with a separate spreadsheet, outside of the network.

TABLE 8. GRAIN-SIZE CATEGORIES

TABLE 9. SORTING CATEGORIES

Generated Sediment

The three nodes that describe generated sediments are generated sand composition, generated grain-size distribution, and generated clay abundance (Fig. 3; Tables 2 and 3). The node Generated Sand Composition has 66 states. The precise 25-component composition, and the conditional probability, for each state is calculated as a function of Provenance Lithotype relative abundance and Generative Modification Potential.

The node Generated Grain-Size Distribution has nine states (Fig. 6), which represent the coarsest, most likely, and finest possible outcomes produced by weathering the estimated provenance lithotype assemblage of the hinterland under high, moderate, and low states of Generative Modification Potential (Table 10), respectively. The calculations are based on observed grain-size distributions for soils derived from specific Provenance Lithotypes under various climatic and topographic conditions, weighted by the estimated abundance of each Provenance Lithotype. Soil grain-size observations were drawn from a variety of published databases, including Soil Survey Staff (1997), Batjes (2002), Cooper et al. (2005), and the International Soil Research and Information Center's Soil Information System (ISIS, http://lime.isric.nl/index.cfm?contentid = 218, verified 28 December 2005).

TABLE 10. DEFINITION OF GENERATED GRAIN-SIZE DISTRIBUTIONS

Figure 6. Detailed view of node states for generative modification potential, generated grain-size distribution, and generated clay abundance. Node states of Generated Grain Size Distribution GGSD1-9 represent nine possible grain-size distributions that could be generated from the Provenance Lithotype assemblage of the hinterland. The precise definition of each grain-size distribution is calculated separately, outside the network.

Figure 6. Detailed view of node states for generative modification potential, generated grain-size distribution, and generated clay abundance. Node states of Generated Grain Size Distribution GGSD1-9 represent nine possible grain-size distributions that could be generated from the Provenance Lithotype assemblage of the hinterland. The precise definition of each grain-size distribution is calculated separately, outside the network.

The node Generated Clay Abundance has three states: high, moderate, and low (Fig. 6). The conditional probability table is calculated according to: (1) the relative ability of each Provenance Lithotype to generate clay (based on the major-element geochemistry; Table 6), weighted by the relative abundance of each provenance lithotype; and (2) the level of Generative Modification Potential. Higher levels of Generative Modification Potential favor greater clay generation, within the constraints imposed by the aluminum, alkali, and alkali-earth content of the Provenance Lithotype assemblage.

Transported Sediment

The three nodes that describe transported sediments are Transported Sand Composition, Transported Grain-Size Distribution, and Transported Clay Abundance (Fig. 3; Tables 2 and 3).

The node Transported Sand Composition has 66 states. The precise 25-component composition, and the conditional probability, for each state is calculated as a function of the Generated Sand Composition and Transport Modification Potential.

The node Transported Grain-Size Distribution has 27 states (Fig. 7), which represent the coarsest, most likely, and finest possible outcomes produced by modifying the nine generated grain-size distributions under high, moderate, and low states of total transport fining, respectively. The calculated relative abundance of each grain size in each Transported Grain-Size Distribution depends on the relative abundance of that grain size in the correlative Generated Grain-Size Distribution and three Empirical Transform Functions that describe possible evolutionary pathways for each grain size under each level of Total Transport Fining. An example of Empirical Transformation Functions for low Total Transport Fining is provided in Table 11. Each of the Empirical Transformation Functions is calibrated to real world observations of modern stream sediments derived from known sources (D. Novák, 2005, personal commun., ExxonMobil Upstream Research Co.). The conditional probability table for Transported Grain Size Distribution is constructed so that low Total Transport Fining favors the coarsest calculated grain-size distributions, whereas high favors the finest.

TABLE 11. EXAMPLE EMPIRICAL TRANSFORM FUNCTION

Figure 7. Detailed view of node states for Generated and Transported grain-size distribution, and total transport fining. Node states of Transported Grain Size Distribution TGSD1L-9H represent twenty-seven possible grain-size distributions that could be generated from the nine Generated Grain Size Distributions, if each is subjected to Low, Moderate, or High Total Transport Fining. The precise definition of each grain-size distribution is calculated separately, outside the network.

Figure 7. Detailed view of node states for Generated and Transported grain-size distribution, and total transport fining. Node states of Transported Grain Size Distribution TGSD1L-9H represent twenty-seven possible grain-size distributions that could be generated from the nine Generated Grain Size Distributions, if each is subjected to Low, Moderate, or High Total Transport Fining. The precise definition of each grain-size distribution is calculated separately, outside the network.

The node Transported Clay Abundance has three states (Fig. 7), representing the cumulative amount of clay produced during generation and transport. The conditional probability table is calculated according to: (1) the amount of initial clay generation; (2) the clay-generating potential of the Generated Sand Compositions; and (3) the Transport Modification Potential. The highest level of Transported Clay Abundance is favored by high Generated Clay Abundance, high probability of quartz-deficient Generated Sand Composition, and high Transport Modification Potential.

Deposited Sediment

The four nodes that describe deposited sediments are Deposited Sand Composition, Deposited Grain Size and Sorting, and Deposited Matrix Abundance (Fig. 3; Tables 2 and 3).

The node Deposited Sand Composition has 66 states. The precise 25-component composition, and the conditional probability, for each state is calculated as a function of the Transported Sand Composition and Deposition Modification Potential.

The nodes Delivered Grain Size and Sorting and Deposited Grain Size and Sorting each have 42 states (Fig. 8), which represent all combinations of the grain sizes granules through very fine sand (Table 8) and the sorting levels very well to extremely poorly sorted (Table 9). Delivered Grain Size and Sorting is a function of Transported Grain-Size Distribution and Maximum Grain Size. The calculated grain-size distribution associated with each state of Transported Grain-Size Distribution is truncated at the grain size specified by Maximum Grain Size, and the mean grain size and sorting for the new grain-size distribution is calculated (Table 12). The conditional probability table is constructed based on the relative frequency of each grain-size/sorting combination among the calculated values. Deposited Grain Size and Sorting is a function of Delivered Grain Size and Sorting, Depositional Fining Potential, and Depositional Sorting Potential (Fig. 8). Because some grain-size/sorting combinations are not observed in nature (Griffiths, 1951), the conditional probability table is constructed so that unobserved combinations have zero, or extremely low, probabilities. Higher values of Depositional Fining Potential favor finer grain-size/sorting combinations, whereas higher values of Depositional Sorting Potential favor better-sorted grain-size/sorting combinations.

TABLE 12. EXAMPLE OF TRANSPORTED TO DELIVERED GRAIN-SIZE DISTRIBUTION TRANSFORMATION

Figure 8. Detailed view of node states for delivered and deposited grain size and sorting. Codes for grain size (g, vc, c, m, f, vf) are defined in Table 8 and those for sorting (xp, vp, p, m, mw, w, vw) are defined in Table 9.

Figure 8. Detailed view of node states for delivered and deposited grain size and sorting. Codes for grain size (g, vc, c, m, f, vf) are defined in Table 8 and those for sorting (xp, vp, p, m, mw, w, vw) are defined in Table 9.

Matrix is considered to be detrital clastic material that is enough smaller than framework grains to occlude intergranular pore throats. We only consider three levels to be important: insufficient to affect permeability, intermediate, sufficient to substantially eliminate permeability. The exact numerical values associated with each level depend on the relative grain size of the system and can be estimated with the methods of Panda and Lake (1994, 1995). The node deposited matrix abundance has three states: low (typically 0%–2%), moderate (typically 2%–10%), and high (typically 10%–25%). Deposited Matrix Abundance is a function of Transported Clay Abundance and Depositional Facies. The conditional probability table is constructed so that higher values of Transported Clay Abundance and Depositional Facies associated with lower values of net-to-gross (e.g., Walker and James, 1992) favor higher values of deposited matrix abundance.

Input Nodes

Regional Topographic Gradient

The states of Regional Topographic Gradient (Table 13; Fig. 9) are high (m/km), moderate (cm/km), and low (mm/km). Generative Modification Potential and Flushing Potential are the children of Regional Topographic Gradient.

TABLE 13. REGIONAL TOPOGRAPHIC GRADIENT NODE STATES

Figure 9. Operational definition of regional topographic gradient in the Sand Generation and Evolution Model (SandGEM), illustrated with a digital elevation model of South America (USGS Hydro1k DEM for South America, visualized at http://edcdaac.usgs.gov/gtopo30/hydro/sa_dem_img.asp [accessed 14 October 2005]).

Figure 9. Operational definition of regional topographic gradient in the Sand Generation and Evolution Model (SandGEM), illustrated with a digital elevation model of South America (USGS Hydro1k DEM for South America, visualized at http://edcdaac.usgs.gov/gtopo30/hydro/sa_dem_img.asp [accessed 14 October 2005]).

Climate: Weathering Potential and Flushing Potential

Weathering Potential and Flushing Potential are characterized by the discrete, qualitative, states high, moderate, and low (Fig. 10, 11). We used information about the level and variability of wetness and temperature to make quantitative estimates of weathering potential index and transport potential index (Appendix A) to guide the selection of the qualitative states.

Figure 10. Examples of weathering potential index (WPI) and flushing potential index (FPI) calculated for modern and ancient climate. Locations include: Mombasa, Coast, Kenya; Astoria, Oregon, USA; Ulaan Baatar, Töv, Mongolia; Aberdeen, Scotland, UK; Dakar, Dakar, Senegal, Cox's Bazaar, Chittagong, Bangladesh; Lae, Morobe, Papua New Guinea; Quibdo, Chocó, Colombia. Climate conditions for the mid-Cretaceous were estimated from West et al. (2005).

Figure 10. Examples of weathering potential index (WPI) and flushing potential index (FPI) calculated for modern and ancient climate. Locations include: Mombasa, Coast, Kenya; Astoria, Oregon, USA; Ulaan Baatar, Töv, Mongolia; Aberdeen, Scotland, UK; Dakar, Dakar, Senegal, Cox's Bazaar, Chittagong, Bangladesh; Lae, Morobe, Papua New Guinea; Quibdo, Chocó, Colombia. Climate conditions for the mid-Cretaceous were estimated from West et al. (2005).

Figure 11. Detailed view of node states for input nodes and their immediate child nodes.

Figure 11. Detailed view of node states for input nodes and their immediate child nodes.

The Weathering Potential Index (WPI, Appendix A) accounts for two different effects of temperature. Increasing temperatures, if all other factors are equal, will increase mineral-dissolution reaction rates exponentially (Lasaga, 1984). However, increasing temperature also increases evaporation, so the amount of water available to facilitate dissolution reactions will decrease, all other things being equal (Willmott, 1977). WPI provides a bookkeeping device to account for these opposite tendencies. Values of WPI for modern climate (and for plausible ancient climates) range between 0 (least potential to chemically modify silicate minerals) and ∼256 (greatest potential).

The Flushing Potential Index (FPI, Appendix A) acknowledges that precipitation that is evaporated is less available to do physical work moving sediment than precipitation that is not evaporated (Wischmeier and Smith, 1978). It also accommodates the observations of Cecil and others (Cecil and Edgar, 2003) that sediment transport reaches a maximum when effective precipitation is concentrated into a small fraction of the year. Values of FPI range from −1.2 (lowest potential to transport sediment) to +1.2 (highest potential).

Weathering and Flushing Potential Indices are dimensionless and have no intrinsic physical meaning, but they can be compared to levels of dissolved, suspended, and bed load in modern rivers (Curtis et al., 1973; Walling, 1987; Summerfield and Hulton, 1994; Ludwig and Probst, 1996; Milliman, 1997; Hovius, 1998; Schaller et al., 2001; Syvitski et al., 2003; Walling and Fang, 2003) in order to guide selection of the high, moderate, and low states in the Weathering and Transport Potential nodes of the network. Values of Weathering and Transport Potential indices (WPI and FPI) that characterize high, moderate, and low levels of Weathering and Transport Potential are summarized in Tables 14 and 15. Figure 10 shows these values graphically, along with modern and ancient examples of each state. Generative Modification Potential and Transport Modification Potential are the children of Climate Weathering Potential. Total Flushing Potential is the child of Climate Flushing Potential.

TABLE 14. WEATHERING POTENTIAL NODE STATES

TABLE 15. FLUSHING POTENTIAL NODE STATES

Hinterland Transport Distance

The states of Hinterland Transport Distance (Table 16; Fig. 11) are short, medium, and long, which equate to first-, second-, and third-order drainages in the sense of Ingersoll et al. (1993). The numerical cutoffs in Table 16 were established after Dutta and Suttner (1986a, 1986b). Fluvial Storage Potential and Selective Transport Fining are the children of Hinterland Transport Distance.

TABLE 16. HINTERLAND TRANSPORT DISTANCE NODE STATES

Basin Fluvial Transport Distance

The states of Basin Fluvial Transport Distance are short, intermediate, long, and very long (Table 17; Fig. 11). Maximum grain size is the child of basin fluvial transport distance.

TABLE 17. BASIN FLUVIAL TRANSPORT DISTANCE NODE STATES

Rate of Basin Subsidence

The states of Rate of Basin Subsidence (Table 18) are rapid and slow. Maximum Grain Size is the child of Rate of Basin Subsidence.

TABLE 18. BASIN SUBSIDENCE NODE STATES

Depositional Facies

Depositional Facies states are summarized in Table 19 and Figure 11. The Depositional Facies included in this model are limited to those likely to be significant hydrocarbon reservoir facies; the list is not intended to be exhaustive. Depositional Fining Potential and Depositional Sorting Potential are the children of Depositional Facies.

TABLE 19. DEPOSITIONAL FACIES CHARACTERISTICS

Sand-Generating Process Nodes

The states of Generative Modification Potential are high, moderate, and low (Fig. 6). The conditional probability table is constructed so that high Generative Modification Potential is virtually certain when Climate Weathering Potential is high (WPI > 128; see Appendix A) and Regional Topographic Gradient is low (mm/km; Table 12), whereas low Generative Modification Potential is virtually certain when Climate Weathering Potential is low and Regional Topographic Gradient is high. The logic behind conditional-probability assignment is described in Grantham and Velbel (1988).

Transport-Process Nodes

Total Flushing Potential

Total Flushing Potential states are high, moderate, and low. The conditional probability table for this node is constructed so that Total Flushing Potential is virtually certain to be high when Climate Flushing Potential and Regional Topographic Gradient are both high, whereas the Total Flushing Potential is virtually certain to be low when the parent nodes are both low. Between Climate Flushing Potential and Regional Topographic Gradient, Regional Topographic Gradient is considered to be a more important control on Total Flushing Potential.

Fluvial Storage Potential

Fluvial Storage Potential states are high, moderate, and low (Fig. 10). The conditional probability table for this node is constructed so that high Fluvial Storage Potential is virtually certain when Total Flushing Potential is low and Hinterland Transport Distance is long, whereas Total Flushing Potential is virtually certain to be high when Total Flushing Power is high and Hinterland Transport Distance is short. Between Total Flushing Power and Hinterland Transport Distance, Hinterland Transport Distance is considered to be a more important control on Fluvial Storage Potential.

Selective Transport Fining

Selective Transport Fining states are much, some, and none. Hinterland Transport Distance is the only parent of Selective Transport Fining. The longer the transport distance, the more opportunities available for sediment to be temporarily stored; at each step of deposition and remobilization, sediments have an opportunity to be hydrodynamically segregated and different size classes preferentially retained or removed. Total Transport Fining is the child of Selective Transport Fining.

Transport Modification Potential

Transport Modification Potential states are high, moderate, and low. The conditional probability table is constructed so that high Transport Modification Potential is virtually certain when both of the parent nodes are high, whereas low is virtually certain when the parent nodes are both low. Between Climate Weathering Potential and Fluvial Storage Potential, Fluvial Storage Potential is considered to be a more important control on Transport Modification Potential.

Total Transport Fining

Total Transport Fining states are high, moderate, and low (Fig. 7). The conditional probability table is constructed so that high Total Transport Fining is virtually certain when both of the parent nodes are high, whereas low Total Transport Fining is virtually certain when the parent nodes are both low. Selective Transport Fining and Transport Modification Potential are considered to be equally responsible for Total Transport Fining.

Depositional-Process Nodes

Maximum Grain Size

Maximum Grain Size states are granules, very coarse sand, coarse sand, and medium sand (size definitions in Table 8). The conditional probability table is constructed so that longer transport distances and slower subsidence rates (lower gradient) favor more effective trapping of a larger proportion of the coarse tail of the grain-size distribution.

Depositional Fining and Sorting Potential

Depositional Fining Potential and Depositional Sorting Potential states are low, moderate, and high (Fig. 10). The conditional probability table is calibrated to match observations (Table 19). In general, any depositional facies will have some probability for every level of fining and sorting potential, with the most likely value in Table 19 receiving the largest single probability.

Depositional Modification Potential

Depositional Modification Potential states are very coarse–coarse, medium, and fine–very fine; these are considered to be the scale at which compositional variation as a function of grain size will operate. The conditional probability table is set according to grain-size/grain-type relationships derived from a proprietary database of more than 260,000 point counts in which both grain size and grain type have been recorded on a point-by-point basis for samples from a wide range of hydrocarbon reservoirs, adjusted for the Provenance Lithotype assemblage in the hinterland. The simultaneous collection of grain size and grain type on a point-by-point basis is trivial when using an automated data collection system like the one described by Cipriani et al. (this volume).

EXAMPLE PREDICTIONS

The effectiveness of this forward modeling approach can be tested against observations of modern sand, where the genetic factors of tectonic setting, provenance lithotype abundance, climate, uplift, transport distance, etc., can be well documented. Paul Potter and co-workers have accumulated a large set of South American fluvial and beach sand data (Potter, 1993, 1994) that is appropriate for this purpose. ExxonMobil has also funded studies to obtain appropriate data to test the model, including Menacherry (2006) and Menacherry et al. (2006). Next we compare observations made in studies of Brazilian beach sand, Chilean fluvial sand, and Australian alluvial sand with predictions from SandGEM.

Graphical Conventions

The predictions consist of a probability distribution for all of the potential outcomes. The figures that follow graphically depict the probability distribution as a contoured probability density surface, or grid equivalent (Fig. 12). The contours or shading levels represent three levels of probability: Black depicts the single most likely outcome; gray depicts the next most likely outcomes, up to a cumulative probability of 68%, which is equivalent to the area under a standard normal curve within one standard deviation from the mean; and (3) white depicts the next most likely outcomes, up to a cumulative probability of 95%, which is equivalent to the area under a standard normal curve within two standard deviations from the mean.

Figure 12. Graphical convention for displaying probability density surfaces in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation), as contours (A) or grids (B).

Figure 12. Graphical convention for displaying probability density surfaces in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation), as contours (A) or grids (B).

Brazilian Beach Sand Composition

Observations

The Brazilian beach sands were selected from Potter's Atlantic coastal samples between 0° and 30°S. The data are presented in Table 20, with Potter's original point-count data recast into categories that can be compared to SandGEM predictions. All of the data reported in Potter (1993) and summarized in Potter (1994) were point-counted by Paul Potter from samples he and his co-workers collected, mostly in the early 1980's. Each sample was counted twice: the first count consisted of 200 framework-grain points, counted in the categories of Table 21; the second count consisted of 100 rock-fragment points, counted in the categories of Table 22 (Franzinelli and Potter, 1983). The data presented in Table 20 translate Potter (1993) data into SandGEM categories according to the scheme in Table 23. The beach sands were not characterized for texture, but all samples were collected from medium to fine sand on the berm (Potter, 1986).

TABLE 20. OBSERVED BRAZILIAN BEACH SAND COMPOSITION

TABLE 21. PETROGRAPHIC CATEGORIES FOR 200-POINT COUNTS OF FRAMEWORK GRAINS IN POTTER (1993)

TABLE 22. PETROGRAPHIC CATEGORIES FOR 100-POINT COUNTS OF ROCK FRAGMENTS IN POTTER (1993)

TABLE 23. TRANSLATION SCHEME FOR POTTER TO SANDGEM PETROGRAPHIC CATEGORIES

Environmental Conditions

The provenance lithotype assemblage from which these sands were derived is composed (in order of importance) of: low- to medium-grade metasediments and schists; plutons and high-grade gneisses; volcanics; and sedimentary rocks. The precise details are quantified in Table 24. The values in Table 24 were measured by planimetry in Choubert et al. (1976); the precise abundance of lithotypes implied by each (litho)chronostra tigraphic unit of the map was calibrated in selected areas with information from 1:1,000,000 geologic maps in the series Carta Geológica do Brasil ao Milionésimo (Brazil, Divisão de Geologia e Mineralogia, Ministério das Minas e Energia, Departamento Nacional da Produção Mineral, 1974).

TABLE 24. PROVENANCE LITHOTYPE ABUNDANCE IN BRAZILIAN SHIELD

The environmental conditions that governed the generation and evolution of these sediments, as quantified by Sand-GEM input parameters, are summarized in Table 25. The region is characterized by moderate (compared to all of Earth history) weathering and flushing power, long transport distance over a low topographic gradient, and a small, slowly subsiding basin with a shoreface depositional facies. All of these factors tend to favor a highly mature sediment composition.

TABLE 25. ENVIRONMENTAL PARAMETERS FOR BRAZILIAN BEACH SAND PREDICTION

Prediction versus Observation

There is good agreement between prediction and observation for sand composition (Figs. 13 and 14; Tables 22,26, and 27). The model predicts that the single most likely composition is pure quartz and that the probability-weighted average quartz content should be 87.0%. In fact, quartz arenite (Q90–100F0-5R0-5; sensu Dott 1964) is by far the most likely composition (63 of 81 samples), and the average quartz content of all samples is 87.5%. The model predicts that plagioclase should be less abundant than alkali feldspar by a factor of ∼4. In fact, in almost all the samples (73 of 81), plagioclase is less abundant than alkali feldspar, with an average Fp:Fk of 0.240. Rock fragments are predicted to be virtually absent. In fact, rock fragments are virtually absent—52 of 81 samples have no rock fragments, and the average rock-fragment content of all the samples is 4.3%. No quantitative data are available about the sand texture, but the predicted texture (Fig. 15) corresponds to the qualitative description of grain size provided by Potter (1986).

TABLE 26. SANDGEM PREDICTION FOR BRAZILIAN BEACH SAND

Figure 13. Predicted and observed values for Brazilian beach sand composition in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation).

Figure 13. Predicted and observed values for Brazilian beach sand composition in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation).

Figure 14. Plot of predicted versus observed relative abundance of grain types for Brazilian beach sand. The x-axis values have been weighted by the probability of each predicted composition. The y-axis values represent the arithmetic average of values for all samples.

Figure 14. Plot of predicted versus observed relative abundance of grain types for Brazilian beach sand. The x-axis values have been weighted by the probability of each predicted composition. The y-axis values represent the arithmetic average of values for all samples.

Figure 15. Predicted sand texture for Brazilian beach sand. There are no published measurements to compare with the prediction, but Potter (1986) reported that the sands generally were “medium to fine grained.”

Figure 15. Predicted sand texture for Brazilian beach sand. There are no published measurements to compare with the prediction, but Potter (1986) reported that the sands generally were “medium to fine grained.”

Chilean Fluvial Sand

Observations

The Chilean fluvial sands were selected from Potter's samples on rivers that have their headwaters in the Andes, between 32 and 38°S; all the samples were taken in the Pampas Central, so the sands do not reflect any contribution from the Cordillera Costera. The compositional data from Potter (1993) are presented in Table 28. Grain-size data (collected for ExxonMobil by M.K. DeSantis at the University of Cincinnati) are presented in Table 29.

TABLE 29. OBSERVED CHILEAN FLUVIAL SAND TEXTURE

Environmental Conditions

The provenance lithotype assemblage from which these sands were derived is composed (in order of importance) of Cenozoic volcanics (∼80%), Mesozoic plutons (∼10%), and Mesozoic volcanic sediments (∼10%). The precise details are quantified in Table 30. The values in Table 30 were measured by planimetry in Choubert et al. (1976); the precise abundance of lithotypes implied by each (litho)chronostratigraphic unit of the map was calibrated in selected areas with information from Zeil (1964).

TABLE 30. PROVENANCE LITHOTYPE ABUNDANCE IN THE CHILEAN ANDES

The environmental conditions that governed the generation and evolution of these sediments, as quantified by SandGEM input parameters, are summarized in Table 31. The region is characterized by low weathering power, moderate flushing power, short transport distance over a high topographic gradient, and a small, slowly subsiding basin with fluvial depositional facies. All of these factors tend to favor highly immature sediment.

TABLE 31. ENVIRONMENTAL PARAMETERS FOR CHILEAN RIVER SAND PREDICTION

Prediction versus Observation

There is good agreement between prediction and observation for sand composition (Figs. 16 and 17; Tables 28, 32, and 33). Quartz and feldspar contents are predicted to be subequal and each below 10%. Rock fragments are predicted to be ∼78%, with virtually all rock fragments being volcanic. Plagioclase is predicted to be about twice as abundant as alkali feldspar. In fact, the observed sand composition conforms very closely to these predictions. The single most likely predicted sand texture (Fig. 18, Table 34) is medium-grained, moderately well sorted. In fact, every observation (Fig. 18; Table 29) fits this description.

TABLE 32. SANDGEM PREDICTION FOR CHILEAN SAND COMPOSITION

TABLE 33. COMPARISON OF PREDICTION AND OBSERVATION FOR CHILEAN RIVER SAND COMPOSITION

TABLE 34. SANDGEM PREDICTION FOR CHILEAN SAND TEXTURE

Figure 16. Predicted and observed values for Chilean fluvial sand composition in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation).

Figure 16. Predicted and observed values for Chilean fluvial sand composition in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation).

Figure 17. Plot of predicted versus observed relative abundance of grain types for Chilean fluvial sand. The x-axis values have been weighted by the probability of each predicted composition. The y-axis values represent the arithmetic average of values for all samples.

Figure 17. Plot of predicted versus observed relative abundance of grain types for Chilean fluvial sand. The x-axis values have been weighted by the probability of each predicted composition. The y-axis values represent the arithmetic average of values for all samples.

Figure 18. Predicted and observed sand texture for Chilean fluvial sand (std—standard deviation).

Figure 18. Predicted and observed sand texture for Chilean fluvial sand (std—standard deviation).

Australian Alluvial Sand

Observations

The Australian dryland sands were collected from the drainage of Umbum Creek, which heads in the Davenport Ranges and deposits sand into Lake Eyre, South Australia (Reilly et al., 2003). Petrographic data from Menacherry (2006) are presented in Table 35.

TABLE 35. OBSERVED AUSTRALIAN ALLUVIAL SAND COMPOSITION AND TEXTURE

Environmental Conditions

The provenance lithotype assemblage from which these sands were derived is composed (in order of importance) of Cenozoic sands and silicretes, Mesozoic sandstones, and Proterozoic metasediments, volcanics, and plutons (Menacherry, 2006). The precise details are quantified in Table 36. The environmental conditions that governed the generation and evolution of these sediments, as quantified by SandGEM input parameters, are summarized in Table 37. The region is characterized by low weathering and flushing power, short transport distance over a low topographic gradient, and a small, slowly subsiding basin with confined alluvial depositional facies.

TABLE 36. PROVENANCE LITHOTYPE ABUNDANCE IN THE UMBUM CREEK DRAINAGE, AUSTRALIA

TABLE 37. ENVIRONMENTAL PARAMETERS FOR AUSTRALIAN ALLUVIAL SAND PREDICTION

Prediction versus Observation: Sand Composition

There is good agreement between predictions and observations (Figs. 19 and 20; Tables 35, 38, and 39). The sands are predicted to be composed of roughly two-thirds quartz and one-quarter rock fragments, dominated by sedimentary rock fragments. Among the feldspars, plagioclase is predicted to be 2.5 times more abundant than alkali feldspar. The observations are very close to the predicted values, although plagioclase is actually only ∼1.5 times more abundant than alkali feldspar.

TABLE 38. SANDGEM PREDICTION FOR AUSTRALIAN ALLUVIAL SAND COMPOSITION

TABLE 39. COMPARISON OF PREDICTION AND OBSERVATION FOR AUSTRALIAN ALLUVIAL SAND

Figure 19. Predicted and observed values for Australian alluvial sand composition in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation).

Figure 19. Predicted and observed values for Australian alluvial sand composition in quartz–feldspar–rock fragment (QFR) ternary space (std—standard deviation).

Figure 20. Plot of predicted versus observed relative abundance of grain types for Australian alluvial sand. The x-axis values have been weighted by the probability of each predicted composition. The y-axis values represent the arithmetic average of values for all samples.

Figure 20. Plot of predicted versus observed relative abundance of grain types for Australian alluvial sand. The x-axis values have been weighted by the probability of each predicted composition. The y-axis values represent the arithmetic average of values for all samples.

Prediction versus Observation: Sand Texture

The single most likely sand texture is medium grained and moderately sorted, with an expected range of variation up to one sorting category better or worse, and one grain size finer (Table 40). All of the observations fall very close to the most likely verbal description, and well within the predicted range of variation (Fig. 21).

TABLE 40. SANDGEM PREDICTION FOR AUSTRALIAN ALLUVIAL SAND TEXTURE

Figure 21. Predicted and observed sand texture for Australian alluvial sand.

Figure 21. Predicted and observed sand texture for Australian alluvial sand.

Summary of Predictions

The Sand Generation and Evolution Model (SandGEM) successfully predicts sand composition and texture in diverse environments that include: provenance lithotype assemblages dominated by either volcanic, high-grade metamorphic, or sedimentary rocks; tropical to desert climates; and drainage basins that range from local mountain catchments to continental scale. A probabalistic, forward modeling approach that synthesizes quantitative and qualitative understanding of sand generation and evolution processes gleaned from a wide range of disciplines has the ability to make accurate, quantitative predictions of sand character based on observations or estimates of a few key environmental features.

DISCUSSION

Benefits of Integrated Genetic Analysis for Sedimentary Petrology

Traditionally, sedimentary petrologists have taken an inductive approach in which they attempt to infer cause from effect (Pirsig, 1974). Typically, this means examining a restricted subset of a physical sample (e.g., medium sand), with one tool (e.g., Gazzi-Dickinson point count, zircon age-spectrum, chemical analysis, etc.) to infer one aspect of provenance sensu latu (e.g., tectonic setting). This is a sensible and economical approach for a broad range of problems, but there is an even broader range of problems for which this approach is inadequate; a short list of such problems in the field of reservoir quality was enumerated at the beginning of this article. For these problems, a deductive approach (inference of effect from cause) is required, because the physical sample is not available or not fully representative.

Integrated genetic analysis provides a framework for conducting more comprehensive, inductive studies, and it also provides a framework within which to integrate observations from restricted deductive studies. Bayesian networks, or other probabilistic quantitative tools, provide a productive avenue to investigate complex systems that previously have been considered intractable.

Productive Lines of Future Research

Climatic Effects on Weathering Intensity

Although intensive research has been focused on mineral dissolution in natural environments (e.g., White et al., 2001) and the laboratory (e.g., Arvidson et al., 2004), there is still a big gap in understanding how climate influences chemical work done on the landscape at large space and time scales, either directly through kinetic controls, or indirectly through influence on biologic controls (e.g., Anderson et al., 2004). For example, it is not intuitively obvious under what climatic condition the most intensive chemical weathering will occur; high temperatures and high precipitation both favor increased weathering, but high temperatures also promote faster evaporation and transpiration, so that the amount of water actually available to do chemical work decreases with increasing temperature (Strakhov, 1967). The net effect of the balance between the physical and chemical work of water is also not intuitively obvious; more water should promote more intense chemical weathering, but it also provides more transport power to decrease the duration of weathering. On the other hand, more water may also promote greater vegetation to reduce erosion and increase the duration of weathering (Schumm, 1981). Greater understanding of the fundamental controls on chemical weathering intensity, which determines the initial trajectory of sand generation, will help clarify sand evolutionary processes.

Landscape Evolution

The environmental factors and processes that feed into the Fluvial Storage Potential and Selective Transport Fining nodes of SandGEM currently are addressed by the landscape evolution community (e.g., Gasparini et al., 2006; Hasbargen and Paola, 2003; Pazzaglia, 2004; Willett et al., 2003). Sedimentary petrologists can make great strides in predicting composition and texture (or inferring provenance features from composition and texture) by working on the influence of landscape evolution on the time it takes for sediment to progress from generation to ultimate deposition, and on the character of deposited sediment.

Phytogeographic Evolution

All modern observations of climatic effects on, and landscape interaction with, sediment generation and evolution are made in the context of a fully vegetated world. These observations are probably only relevant back to the early Oligocene and the widespread distribution of grasses. Other significant step-changes in sedimentary response to environmental forcing probably occurred in the Late Cretaceous (extensive colonization of uplands and riparian areas made possible by angiosperms) and Middle Devonian (extensive colonization of coastal lowlands by terrestrial plants). Significantly more work must be done on the paleo-effect of plants on sediment generation and transport (e.g., Fraticelli et al., 2004) before modern sand generation and evolution principles can be applied confidently to the Mesozoic or Paleozoic.

TABLE 27. COMPARISON OF PREDICTION AND OBSERVATION FOR BRAZILIAN BEACH SAND

TABLE 28. OBSERVED CHILEAN FLUVIAL SAND COMPOSITION

APPENDIX A: CALCULATION OF WEATHERING POTENTIAL AND TRANSPORT POTENTIAL INDICES

Weathering Potential

The Weathering Potential Index (WPI) for a modern climate is calculated using mean monthly precipitation and temperature data. It is defined as:  

formula
where Pi = mean monthly precipitation for month i (mm); Ei = potential evaporation in month i (mm) calculated with Hamon's equation (Hamon, 1961; Haith and Shoemaker, 1987); E [thetas] = average activation energy of silicate mineral dissolution (J·mol−1), with a default value of 48.6 (after Lasaga, 1984; approximately the value for feldspar), which replicates van't Hoff's rule (doubling of reaction rates for every 10 °C increase in temperature) at Earth-surface conditions; R = universal gas constant (J·mol−1·°K−1); and i = mean temperature for month i (°K)  
formula
where Hi = hours of sunlight on the Julian day in the middle of month i, and es = saturation vapor pressure at i.  
formula
where ω s = sunset angle on the Julian day in the middle of month i.  
formula
where k, a, and b are constants, equal to 0.6112, 17.67, and 29.66, respectively (http://atmos.nmsu.edu/education_and_outreach/ encyclopedia/sat_vapor_pressure.htm, verified 14 October 2005).  
formula
where [phis] = latitude of the site (+ in Northern Hemisphere, – in Southern Hemisphere) and δ = solar declination (in radians) on the Julian day Ji, at the middle of month i = 23.45 × sin [360/365 × (284 + Ji)].

Transport Potential

The Flushing Potential Index (FPI) for a modern climate is calculated using mean monthly precipitation and temperature data. It is defined as:  

formula
where ni, flushing and ni,nonflushing are 1 or 0, depending if the effective precipitation in month i (Pi – Ei) is greater or less than a user-specified critical value. When ni, flushing = 0, then ni, flushing = 1, and vice versa. We typically set the critical value at 200 mm.

TABLE A1. SAMPLE WORKSHEET LAYOUT TO CALCULATE WEATHERING POTENTIAL INDEX (WPI) AND FLUSHING POTENTIAL INDEX (FPI) WITH DATA FROM POINTE NOIRE, CONGO

Example

The layout for a spreadsheet to calculate WPI and FPI, with mean monthly temperature and precipitation observations from Pointe Noire, Congo, is presented in Table A-1.

Our concepts have evolved from the ideas of H.C. Sorby, P.D. Krynine, J.C. Griffiths, R.L. Folk, P.E. Potter, W.R. Dick-inson, L.J. Suttner, R.V. Ingersoll, A. Basu, and M.J. Johnsson, among many others.

It would not be possible to employ these concepts without the pioneering work of applying Bayesian networks to geoscience inference done by A. Woronow, K.M. Love, J.F. Scheutte, and C.S. Kim at ExxonMobil Upstream Research Co. The concepts, methods, and tools described herein are the subject of United States and foreign patents by ExxonMobil Upstream Research.

Earlier versions of this manuscript benefited from the comments of R.G. Charles, M.W. French, P.E. Rumelhart, A. Seyedollali, and B.P. West. The final manuscript was greatly improved by the reviews of R.V. Ingersoll and G. Girty.

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Figures & Tables

Contents

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