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Revista de la Asociación Argentina de Sedimentología

versión impresa ISSN 1853-6360

Rev. Asoc. Argent. Sedimentol. vol.8 no.2 La Plata jul./dic. 2001

 

ARTÍCULOS

Characterization of fluvial hydrocarbon reservoirs and aquifers: problems and solutions

Caracterización de reservorios de hidrocarburos y acuíferos fluviales: Problemas y Soluciones.

 

John S. Bridge

Department of Geological Sciences, Binghamton University, P.O. Box 6000, Binghamton, NY 13902-6000, USA.

Email: jbridge@binghamton.edu

 


Abstract

Fluvial deposits are important hydrocarbon reservoirs and aquifers in many parts of the world. In order to assess, develop and manage these resources, it is necessary to determine the three-dimensional geometry, orientation, spatial distribution and total volume of the reservoirs/aquifers. Such characterization of reservoirs/aquifers normally involves (1) analysis of well logs, cuttings, cores and seismic data (2) correlation of strata between wells, and (3) modeling of the three-dimensional volume between wells. These procedures require a great deal of geological knowledge. Unfortunately, current approaches to reservoir/aquifer characterization are problematical in many cases.
Specific fluvial depositional forms (e.g., channel bars, crevasse splays, lacustrine deltas) are commonly interpreted from well logs and cores, because it is thought that deposits associated with particular depositional forms will have particular geometries and reservoir quality. However, it is very difficult to unambiguously interpret fluvial depositional forms from such one-dimensional data, and it is questionable that a particular depositional form will have a distinctive stratal geometry. In particular, it is not possible to distinguish braided river deposits from meandering river deposits based on their vertical facies sequences. Also, it is a common myth that there is a relationship between channel-belt width/thickness, channel pattern, grain size of sediment load, and bank stability. However, with very careful analysis, the lateral extent of subsurface channel-belt deposits and overbank deposits can be estimated from their facies, thickness, and proportion observed in well logs and cores.
Correlation of fluvial lithostratigraphic units (e.g., channel-belt sandstone bodies) between wells is commonly based on untenable assumptions. The result is normally that stratigraphic units appear much more laterally continuous than they really are. Before attempting correlation, it is desirable to estimate the likely lateral extent and thickness variation of stratigraphic units, based on the interpretation of available well logs and cores mentioned above. Then, it is wise to set up multiple working hypotheses for the correlation. Estimation of the geometry of stratigraphic units is aided by use of modern analogs, ancient analogs, and depositional models. Modern analogs are superior aids because it is possible to describe fluvial morphology and deposits directly and unambiguously. Ancient analogs are less reliable, because their origin must be interpreted, and because outcrops are commonly not large enough to allow definition of the facies geometry (e.g., channel-belt width). Depositional models can be used to help estimate the lateral extent of stratigraphic units (e.g., zones of high or low net-to-gross). However, such models may be only two-dimensional, not quantitative, or do not represent depositional processes and products correctly. Sequence stratigraphic models are particularly problematical in these regards.
In order to characterize the three-dimensional volume between wells, it is common to make use of ancient analogs in combination with object-based stochastic models. The geometry and proportion of stratigraphic objects such as channel-belt sandstone bodies are determined statistically from well data and ancient analogs, and these objects are located in space using their known positions in wells and using quasi-random placement between wells. Although this method honors well data, the shapes and locations of objects can be very unrealistic. Process-based (forward) models are capable of producing much more realistic stratigraphy, and have much greater predictive value, but it is very difficult to fit such models to well data exactly. For this reason, process-based models are not routinely used for reservoir/aquifer modeling. However, it has been shown recently that hybrid process-based and stochastic models can potentially be fitted exactly to well data using a trial-and-error approach with new optimization procedures (genetic algorithms).

Keywords: Fluvial reservoirs and aquifers; Well logs and cores; Stratigraphic correlation; 3-D alluvial architecture models

Resumen expandido

Los depósitos fluviales son importantes reservorios de hidrocarburos y acuíferos en muchas regiones del mundo. A fin de valorar, desarrollar y utilizar estos recursos es necesario determinar la geometría tridimensional, la orientación, la distribución espacial y el volumen total de los reservorios y acuíferos. Generalmente, este tipo de caracterización de reservorios y acuíferos involucra, (1) el análisis de perfiles de pozos, cuttings, testigos corona y datos sísmicos, (2) la correlación de estratos entre pozos, y (3) el modelado tridimensional de los depósitos entre los pozos. Estos procedimientos requieren una elaboración del conocimiento geológico. Desafortunadamente, en muchos casos las propuestas actuales para la caracterización de los reservorios y acuíferos son problemáticas.
Las formas fluviales de depositación (ejemplos: barras de canal, crevasse splays, deltas lacustres) son interpretadas comúnmente a partir de perfiles de pozo y testigos corona, ya que se piensa que los depósitos asociados con formas depositacionales determinadas tendrán geometrías particulares y una calidad de reservorio determinada. Sin embargo, es muy difícil interpretar inequívocamente las formas depositacionales fluviales a partir de estos datos unidimensionales y es cuestionable suponer que una forma depositacional particular tendrá una geometría estratal distintiva. En especial, no es posible distinguir depósitos de ríos enlazados de depósitos de ríos meandrantes en base a sus secuencias verticales de facies. Además, es un mito popular que hay una relación entre ancho/profundidad de la faja de canales, diseño del canal, tamaño de grano de la carga de lecho y estabilidad de los márgenes. Sin embargo, mediante un análisis muy detallado de las facies, el espesor y la proporción observados en los perfiles de pozo y testigos corona puede ser estimada la extensión en subsuelo de los depósitos de las fajas de canales y de los depósitos de albardón.
La correlación de unidades litoestratigráficas fluviales (por ejemplo: cuerpos de areniscas de faja de canales) entre pozos está basada comúnmente en suposiciones insostenibles. Normalmente, el resultado de estas correlaciones es que las unidades estratigráficas parecen mucho más continuas lateralmente de lo que son en realidad. Antes de intentar la correlación, es conveniente estimar la probable extensión lateral y las variaciones de espesor de las unidades estratigráficas, basándose en el análisis de los perfiles de pozo y testigos corona mencionados anteriormente. A partir de estas estimaciones es necesario establecer múltiples hipótesis de trabajo para realizar la correlación. La estimación de la geometría de las unidades estratigráficas es factible mediante el uso de análogos actuales, análogos antiguos y modelos depositacionales. Los estimadores más útiles son los obtenidos de análogos modernos porque en ellos es posible describir sin ambigüedades la morfología y los depósitos fluviales. Los análogos antiguos son menos confiables debido a que su origen debe ser interpretado y porque los afloramientos no son lo suficientemente extensos como para permitir la definición de las geometrías de las facies (por ejemplo: ancho de la faja de canales). Los modelos depositacionales pueden ser utilizados para ayudar a estimar la extensión lateral de las unidades estratigráficas (por ejemplo: zonas de alta o baja relación porcentual entre espesor útil y espesor total del reservorio, net-to-gross). Sin embargo, tales modelos pueden ser análogos inapropiados, ya que son solamente 2-D, no cuantitativos, o no representan correctamente los procesos y productos depositacionales. En estos análisis, los modelos de secuencia estratigráfica son particularmente problemáticos.
A fin de caracterizar el volumen de los depósitos entre los pozos, es común utilizar los análogos antiguos en combinación con objetos basados en modelos estocásticos. La geometría y la proporción de los objetos estratigráficos, tales como cuerpos de areniscas de faja de canal, son determinados estadísticamente a partir de datos de pozo y análogos antiguos, estos objetos son ubicados en el espacio utilizando sus posiciones conocidas en los pozos y un emplazamiento cuasi aleatorio entre los pozos. Aunque este método señala la importancia de los datos de pozos, las formas y ubicaciones de los objetos son muy poco realistas. Los modelos basados en procesos (ver más adelante) son capaces de producir estratigrafías mucho más realistas y tienen un mayor valor predictivo pero es muy difícil adecuar exactamente estos modelos a los datos de pozos. Por esta razón, los modelos basados en procesos no son usados rutinariamente en el modelado de reservorios y acuíferos. Sin embargo, recientemente ha sido demostrado que potencialmente los modelos híbridos, entre estocásticos y basados en procesos, pueden ser ajustados con exactitud a los datos de pozos utilizando una aproximación por prueba y error con nuevos procedimientos de optimización (algoritmos genéticos).
Los depósitos fluviales son importantes reservorios de hidrocarburos y acuíferos en muchas regiones del mundo. A fin de valorar, desarrollar y utilizar estos recursos es necesario determinar la geometría tridimensional, la orientación, la distribución espacial y el volumen total de los reservorios y acuíferos. Generalmente, este tipo de caracterización de reservorios y acuíferos involucra, (1) el análisis de perfiles de pozos, cuttings, testigos corona y datos sísmicos, (2) la correlación de estratos entre pozos, y (3) el modelado tridimensional de los depósitos entre los pozos. Estos procedimientos requieren una elaboración del conocimiento geológico. Desafortunadamente, en muchos casos las propuestas actuales para la caracterización de los reservorios y acuíferos son problemáticas.
Las formas fluviales de depositación (ejemplos: barras de canal, crevasse splays, deltas lacustres) son interpretadas comúnmente a partir de perfiles de pozo y testigos corona, ya que se piensa que los depósitos asociados con formas depositacionales determinadas tendrán geometrías particulares y una calidad de reservorio determinada. Sin embargo, es muy difícil interpretar inequívocamente las formas depositacionales fluviales a partir de estos datos unidimensionales y es cuestionable suponer que una forma depositacional particular tendrá una geometría estratal distintiva. En especial, no es posible distinguir depósitos de ríos enlazados de depósitos de ríos meandrantes en base a sus secuencias verticales de facies. Además, es un mito popular que hay una relación entre ancho/profundidad de la faja de canales, diseño del canal, tamaño de grano de la carga de lecho y estabilidad de los márgenes. Sin embargo, mediante un análisis muy detallado de las facies, el espesor y la proporción observados en los perfiles de pozo y testigos corona puede ser estimada la extensión en subsuelo de los depósitos de las fajas de canales y de los depósitos de albardón.
La correlación de unidades litoestratigráficas fluviales (por ejemplo: cuerpos de areniscas de faja de canales) entre pozos está basada comúnmente en suposiciones insostenibles. Normalmente, el resultado de estas correlaciones es que las unidades estratigráficas parecen mucho más continuas lateralmente de lo que son en realidad. Antes de intentar la correlación, es conveniente estimar la probable extensión lateral y las variaciones de espesor de las unidades estratigráficas, basándose en el análisis de los perfiles de pozo y testigos corona mencionados anteriormente. A partir de estas estimaciones es necesario establecer múltiples hipótesis de trabajo para realizar la correlación. La estimación de la geometría de las unidades estratigráficas es factible mediante el uso de análogos actuales, análogos antiguos y modelos depositacionales. Los estimadores más útiles son los obtenidos de análogos modernos porque en ellos es posible describir sin ambigüedades la morfología y los depósitos fluviales.
Los análogos antiguos son menos confiables debido a que su origen debe ser interpretado y porque los afloramientos no son lo suficientemente extensos como para permitir la definición de las geometrías de las facies (por ejemplo: ancho de la faja de canales). Los modelos depositacionales pueden ser utilizados para ayudar a estimar la extensión lateral de las unidades estratigráficas (por ejemplo: zonas de alta o baja relación porcentual entre espesor útil y espesor total del reservorio, net-to-gross). Sin embargo, tales modelos pueden ser análogos inapropiados, ya que son solamente 2- D, no cuantitativos, o no representan correctamente los procesos y productos depositacionales. En estos análisis, los modelos de secuencia estratigráfica son particularmente problemáticos.
A fin de caracterizar el volumen de los depósitos entre los pozos, es común utilizar los análogos antiguos en combinación con objetos basados en modelos estocásticos. La geometría y la proporción de los objetos estratigráficos, tales como cuerpos de areniscas de faja de canal, son determinados estadísticamente a partir de datos de pozo y análogos antiguos, estos objetos son ubicados en el espacio utilizando sus posiciones conocidas en los pozos y un emplazamiento cuasi aleatorio entre los pozos. Aunque este método señala la importancia de los datos de pozos, las formas y ubicaciones de los objetos son muy poco realistas. Los modelos basados en procesos (ver más adelante) son capaces de producir estratigrafías mucho más realistas y tienen un mayor valor predictivo pero es muy difícil adecuar exactamente estos modelos a los datos de pozos. Por esta razón, los modelos basados en procesos no son usados rutinariamente en el modelado de reservorios y acuíferos. Sin embargo, recientemente ha sido demostrado que potencialmente los modelos híbridos, entre estocásticos y basados en procesos, pueden ser ajustados con exactitud a los datos de pozos utilizando una aproximación por prueba y error con nuevos procedimientos de optimización (algoritmos genéticos).

Palabras claves: Reservorios y acuíferos fluviales; Perfiles de pozo y testigos corona; Correlación estratigráfica; Modelos de arquitectura aluvial 3-D.


 

Introduction

Fluvial deposits are important hydrocarbon reservoirs in many parts of the world (e.g., Alaska, Argentina, southern USA and Gulf of Mexico, North Sea, China, Venezuela). Also, fluvial deposits are commonly important aquifers. In order to assess, develop, and manage these resources, it is necessary to determine: (1) the total volume of reservoir or aquifer in a particular volume of the sedimentary basin (the net-to-gross), and; (2) the three-dimensional geometry, orientation and spatial distribution of the sedimentary rocks that form the reservoirs or aquifers. In fluvial deposits, reservoir or aquifer rocks are mainly channel-belt sandstones and gravelstones (conglomerates), with subordinate sandstones attributable to crevasse splays and levees. Determination of the stratigraphic properties (characterization) of a reservoir or aquifer generally entails the following steps: (1) analysis of well logs, cuttings and cores in order to describe and interpret the nature and origin of the rocks; (2) stratigraphic correlation of well logs and cores in order to assess the continuity of distinctive rock types (facies) between wells; (3) use of seismic data to assess the orientation and structural continuity of relatively thick (> 100 m thick) sequences of strata, and to recognize distinctive seismic patterns that can be related to distinctive sedimentary facies; (4) modeling of the geometry and distribution of lithofacies in the three-dimensional space between wells, and; (5) distribution of rock properties such as porosity and permeability as a function of lithofacies or using stochastic models. Successful completion of these steps involves a great deal of geological knowledge, the use of a range of stratigraphic models, and many assumptions that are difficult to test. Some methods of fluvial reservoir/aquifer characterization that are in common use are ill-conceived and unjustifiable. In this review, I will explain and justify this criticism, and attempt to offer constructive alternatives to reservoir/aquifer characterization. The comments in this review also have general implications for describing and interpreting fluvial deposits.

Analysis of well logs and cores

Description and interpretation of distinctive rock types (facies)

Well logs and cores are used to describe or interpret the spatial distribution of sedimentary rock composition, texture, sedimentary structures, porosity and permeability, the nature of the fluids in the void spaces, and the thickness of the different rock types (e.g., sandstone, shale, coal). It is common practice to interpret the specific fluvial depositional environment (e.g., channel bar, crevasse splay, levee, floodbasin) of the various lithofacies or petrofacies using vertical trends in grain size or some other sedimentary or petrophysical property. The objective is to use this interpretation to help estimate the three-dimensional geometry and connectivity of the reservoir rocks and permeability barriers. The assumptions in this practice are: (1) it is possible to interpret specific fluvial depositional environments from vertical logs, and; (2) there is an unambiguous relationship between the geometry and sedimentary processes of a specific depositional environment and the threedimensional geometry of the deposits formed in that environment. Both of these assumptions are suspect, as explained below.

Difficulties interpreting fluvial depositional environments from well logs and cores

A simple view of fluvial deposits, as seen in well logs and cores, is that the thickest (say, meters thick) sandstone-gravelstone bodies are deposits of channel belts, and very thick bodies (say, tens of meters thick) may be superimposed (amalgamated) channel belts. Thinner sandstones bodies (dm to m thick) interbedded with shales might be taken as overbank deposits such as crevasse splays, levees, lacustrine deltas, or fills of floodplain-drainage channels. Thick sequences of shale with minor sandstones would be floodbasin deposits (Fig. 1). However, it is difficult to distinguish: (1) relatively thin parts of isolated channel-belt sandstone bodies (e.g., parts of channel fills, or shallow parts of the channel) from the thicker overbank sandstone bodies; (2) floodbasin muds from muddy channel fills, and; (3) the different types of overbank sandstone bodies (Fig.1).


Figure 1. Example of interpreted gamma ray logs from the Travis Peak Formation, East Texas Basin (from Tye, 1991). Interpretations of depositional environment were aided by cores from well S.F.E. No.2. The sandstone bodies vary in thickness, and the thicker ones are in most cases interpreted as channel-belts. The thinner, overbank sandstones were interpreted by Tye (1991) as either crevasse splays or lacustrine deltas. The sandstone bodies may fine upward, coarsen upward or appear "blocky", irrespective of their thickness and interpretation. It is possible that some of the overbank sandstones are channel-belt sandstones, and vice versa. Also, it is possible that some of the mudstone could be deposited in channel fills or as upper-bar deposits within channel belts (Bridge and Tye, 2000). Notice also that, in correlating the stratigraphic units between wells, the tops and bases of sandstone bodies were not assumed to be horizontal.
Figura 1. Ejemplo de perfiles de rayos gama interpretados para la Formación Travis Peak, Cuenca East Texas (de Tye, 1991). Las interpretaciones del ambiente depositacional fueron apoyadas por testigos corona del pozo S.F.E. Nº2. Los cuerpos de areniscas varian de espesor y en la mayoría de los casos los más espesos se interpretaron como fajas de canales. Los cuerpos más delgados, las areniscas de albardón fueron interpretadas por Tye (1991) como crevasse splays o deltas lacustres. Los cuerpos de arenisca pueden ser granodecreciente, granocreciente o no presentar cambios (blocky) independientemente de su espesor e interpretación. Es posible que algunas de las areniscas de albardón sean areniscas de faja de canal y viceversa. Es posible además que algunos de los estratos de pelitas podrían estar depositados en los rellenos de canal o como depósitos de tope de barra dentro de las fajas de canales (Bridge and Tye, 2000). Note que también, en las correlaciones de las unidades estratigráficas entre pozos, las bases y techos de los cuerpos de areniscas no fueron tomados como horizontales.

The folly of trying to interpret paleochannel pattern from well logs and cores

Sandstone bodies interpreted from well logs are commonly classified as fining upward, coarsening upward, or "blocky". Fining-upward sandstone bodies might be interpreted as point-bar deposits or channel-fill deposits of a meandering river, whereas blocky sandstone bodies (no clear vertical trends in grain size) are commonly assigned to braided river bars (e.g., Galloway and Hobday, 1983, 1996; Flores et al., 1985). Coarsening-upward sandstone bodies might be interpreted as deposits of distributary-mouth bars, lacustrine deltas or progradational crevasse splays/levees. The reality is that all of these vertical sequence patterns can form in all of these depositional environments. Figures 2 and 3 show how the vertical variation of grain size, sedimentary structure, and thickness of single channel-belt deposits varies depending on the topographic features of the bars and channels, the position within a channel bar or channel fill, and the nature of channel migration (determining what parts of channel bars are preserved). Fining-upward, coarsening-upward, and "blocky" sequences can occur in any type of channel deposit. Therefore, it is not possible to distinguish the deposits of the different river patterns (braided, meandering) from single vertical logs.


Figure 2. Typical channel deposits, with gamma ray logs, from different parts of sandy channel bars and channel fills (from Bridge and Tye, 2000).
Figura 2. Depósitos típicos de canal, con perfiles de rayos gama, de distintos sectores de las barras arenosas y de los rellenos de canal (tomado de Bridge and Tye, 2000).


Figure 3. Topographic features of braided and meandering rivers: curved channels, unit bars, compound bars, cross-bar channels (modified from Bridge, 1993a).
Figura 3. Rasgos topográficos de ríos enlazados y meandrantes: canales curvados, barras unidad, barras compuestas, canales transversales en el tope de las barras (modificado de Bridge, 1993a).

Why is it so important to interpret ancient channel patterns such as braided, meandering, and anastomosing anyway? This preoccupation with determining ancient channel pattern is based on the misguided notion that different channel patterns are associated with distinctive sedimentary facies and geometry (e.g., Allen, 1965; Collinson, 1996; Galloway and Hobday, 1996; Miall, 1996; Selley, 1996). For example, meandering river deposits are commonly thought of as relatively fine-grained sandstones with ribbon-like geometries (low width/ thickness) set in voluminous muddy floodplain deposits. In contrast, braided river deposits are commonly thought of as relatively coarse-grained sandstones and/or gravelstones with sheet-like geometry (large width/thickness) with very little associated floodplain deposits. Anastomosing river deposits have been thought of as a connected network of channel sandstone bodies with low width/thickness set in a matrix of floodplain mud. There are some very serious misconceptions in all of this.

Attempts to distinguish meandering and braided river deposits based on their grainsize and geometry

This practice owes its origin to Schumm's (1963, 1971, 1972, 1977, 1981, 1985) classification of channel patterns. Schumm (followed by many sedimentologists such as Galloway and Hobday, 1983, 1996; Miall, 1996) postulated that rivers that transport large amounts of bed load relative to suspended load tend to have relatively low sinuosity and high degree of braiding. Such bed-load streams have been associated with relatively easily eroded banks of sand and gravel, large channel slope and large stream power, such that they are laterally unstable. In contrast, rivers with relatively large suspended loads were postulated to be characteristic of undivided rivers of higher sinuosity. Such suspended-load streams were associated with cohesive muddy banks, low stream gradient and power, and lateral stability. Schumm defined suspended- load channels as those carrying more than 97% suspended-sediment load (presumably at flood stage), whereas bed-load channels are defined as those carrying less than 89% suspended sediment. Such a definition of bed-load channels is misleading to say the least! The correlation between channel pattern, type of sediment load and bank stability is not generally supported by data. This mythical correlation probably arose because early studies of braided rivers were in mountainous areas of sandygravelly outwash and those of single-channel sinuous streams were from temperate lowlands (e.g., the U.S. Great Plains). In fact, many braided rivers are sandy and silty (e.g., Brahmaputra in Bangladesh, Yellow in China, Platte in Nebraska), and many single- channel, sinuous rivers are sandy and gravelly (Madison in Montana, South Esk in Scotland, Yukon in Alaska) (Rust, 1978; Jackson, 1978; Bridge, 1985). The key controls on whether or not a river is braided or meandering are the amounts of water and sediment supplied during seasonal floods (Fig. 4).


Figure 4. Qualitative variation of equilibrium channel patterns with channel-forming water discharge, valley slope, and sediment size. Valley slope can be thought of as a measure of sediment transport rate, because sediment transport rate increases with increasing slope and water discharge and with decreasing sediment size.
Figura 4. Variación cualitativa de los diseños de equilibrio de los canales con respecto al caudal de agua del canal formador, la pendiente del valle y el tamaño de sedimento. La pendiente del valle puede ser analizada como una medida de la tasa de transporte de sedimento debido a que la tasa de transporte de sedimento se incrementa con el incremento de la pendiente, el caudal de agua y con el decrecimiento del tamaño del sedimento.

To appreciate the fact that channel pattern may not have a major influence on the geometry of a single channel-belt sandstone body, consider the Mississippi and Brahmaputra Rivers, classic examples of meandering and braided rivers, respectively. Both of these rivers flow through extensive floodplains. The width of the Mississippi River meander belt in the lower Mississippi Valley (Yazoo Basin) is 15 to 25 km, and the maximum thickness of the channel-belt deposits ranges from 20 to 40 m, giving an average channel-belt width/ thickness of about 650 (Bridge, 1999). In the Atchafalaya Basin and delta plain, the Mississippi channel-belt width is 10 to 15 km and the maximum thickness is about 50m, giving a maximum width/ thickness of about 300. The Brahmaputra channel belt is about 10 km wide, and 40 m in maximum thickness, giving a minimum width/thickness of about 250 (Bristow, 1987). It appears that the width/ thickness ratio of the meandering Mississippi channel belt is greater than that of the braided Brahmaputra, or at least comparable. The reason for the similar width/thickness ratios is not hard to understand. A braided river occupies several channels across the width of its channel belt simultaneously. A meandering river may only occupy one channel at a time, but the channel still wanders through a channel belt that may be comparable in width to a braided channel belt of the same thickness.

The significance of planar cross strata

It is commonly stated in the literature (e.g., Collinson, 1996; Miall, 1977, 1996) that planar cross strata produced by transverse unit bars is characteristic of braided rivers, but not meandering rivers. This is quite wrong (review in Bridge, 2002; Fig. 3). Transverse unit bars occur in all alluvial river types. Furthermore, it appears from recent studies that the deposits of most unit bars are composed of medium-scale trough cross strata formed by the dunes that migrate over the unit bars during high flow stages. Planar cross strata associated with migration of a unit bar with an avalanche face apparently only occurs at the margins of unit bars. However, this is a moot point when dealing with well logs or cores, because it is not possible to distinguish planar cross strata from trough cross strata when the sets are dm to m thick (i.e., medium-scale cross strata).

Relationship between discharge variability, channel pattern and deposits

Another common myth (perpetuated by Miall, 1977,1996, and many others) is that discharge variability is greater for braided rivers than for meandering rivers. This myth probably originated from the early studies of pro-glacial braided rivers in mountainous regions of North America, where discharge varied tremendously during snowmelt. In contrast, many single-channel rivers were studied in temperate lowland regions where discharge variations were moderated by groundwater supply. In fact, discharge variability does not have a major influence on the existence of the different channel patterns, because all patterns can be formed in laboratory channels at constant discharge. Moreover, many rivers with a given discharge regime show along-stream variations in channel pattern. However, variability of water and sediment supply during floods does have an influence on the nature of flood sedimentation units, and these units might be recognizable in well logs and cores (Fig. 2).
Related to this issue of discharge variability is the claim that extremes of discharge will have a strong influence on the nature of the river deposits. Specifically, the deposits of ephemeral rivers are considered to have certain distinctive features, such as a predominance of planar laminated and lowangle cross-stratified sandstone, and either a lack of well-defined channels or channels with high width/depth ratios (e.g., North and Taylor, 1996). These features are not restricted to ephemeral rivers. The key features that distinguish deposits of ephemeral rivers from those of perennial rivers are those that indicate that the channel flow ceased (i.e., plant roots and desiccation cracks in the bottom of channels). In reality, the main characteristics of channel deposits are controlled by flood conditions, and floods occur in ephemeral and perennial rivers alike.

Are anastomosing river deposits distinctive?

A distinction has been made between rivers where channels split around bars (braided) and those where channels split around floodplain areas (anastomosing or anabranching) (Lane, 1957; Brice, 1964, 1984; Chitale, 1970; Smith, 1976; Schumm, 1977, 1985; Knighton and Nanson, 1993; Nanson and Knighton, 1996; Makaske, 2001). The characteristic and definitive features of anastomosing (anabranching) channel segments are that they are longer than a curved channel segment around a single braid or point bar, and the patterns of flow and sediment transport in adjacent anastomosing segments are essentially independent of each other. This means that each anastomosing segment contains bars appropriate to the imposed discharge and sediment load, enabling assignment of its own channel pattern, based on degree of channel splitting around bars and sinuosity. This means also that the terms anastomosing and braiding are not mutually exclusive, as implied in the channel-pattern classifications of Rust (1978) and Miall (1992, 1996). In fact, many rivers are braided and/or meandering as well as anastomosing (Fig. 5). The term anastomosing belongs in classifications that describe how channel belts split and join on floodplains, such as distributive and tributive. The number of coexisting anastomosing or distributive channels is controlled by the nature of channel-belt deposition and avulsion rather than the water and sediment discharge in channels (which controls whether channels are meandering or braided). The nature of channel-belt deposition and avulsion has a major control on the superposition of channel belts, the preservation of overbank deposits, and the overall net-to-gross, as discussed below. Whether or not the ancient channel belt was braided or meandering is largely irrelevant when analyzing net-to-gross in the subsurface.


Figure 5. Brahmaputra River immediately north of its confluence with the Ganges River, showing braided channels and undivided sinuous channels that are also anastomosed. Scale bar is 20 km. Photo courtesy of C.S.Bristow, also published in Bridge (1993a).
Figura 5. Río Brahmaputra inmediatamente al norte de su confluencia con el río Ganges, se observan canales enlazados y monocanales sinuosos que también son anastomosados. La barra de escala es 20 km. La fotografía es cortesía de C.S. Bristow, también publicada en Bridge (1993a).

Superimposed channel bars and channel belts

Channel bars and channel fills can be superimposed within a single channel belt and by superposition of different channel belts (Fig. 6). Recognition of such superposition is not a simple task. Within a single channel belt, simple and compound bars can be superimposed in complicated ways that cannot be interpreted easily from well logs. It is very important to recognize superimposed channel belts in well logs and cores, because superimposed channel belts generally produce sandstone-gravelstone bodies with much larger width/thickness than single channel belts. It is not possible to rationally correlate channel-belt sandstone bodies between wells without assessing their degree of superposition, as discussed below.


Figure 6. Vertical sequences of lithofacies and gamma-ray logs for superimposed channels bars and channel belts (from Bridge and Tye, 2000).
Figura 6. Secuencias verticales de litofacies y perfiles de rayos gama correspondientes a barras de canal superpuestas y fajas de canales (tomado de Bridge and Tye, 2000).

Spatial variations in proportion of channelbelt deposits (net-to-gross)

The proportion and grain size of channel-belt deposits commonly vary vertically in wells, and vary between wells at a given stratigraphic level. For example, an increase in channel-deposit proportion may be associated with a zone of superimposed channel bars or channel belts. Variations in net-to-gross can occur over different spatial scales. For example, vertical variations in channel-deposit proportion over scales of tens of meters, hundreds of meters and kilometers have been documented (e.g., Willis, 1993a,b; Khan et al., 1997; Zaleha, 1997a,b). Spatial variations in alluvial architecture have been explained by a variety of different kinds of stratigraphic models (e.g., Leeder, 1978; Allen, 1978; Bridge and Leeder, 1979; Paola et al, 1992; Bridge and Mackey, 1993a; Shanley and McCabe, 1993, 1994; Wright and Marriott, 1993; Mackey and Bridge, 1995). There may be many different explanations for a given alluvial architecture, and great care must be taken to keep an open mind about the possible explanatory hypotheses. This is an important point, because choice of any particular interpretation of alluvial architecture has far-reaching implications for lateral correlation of stratigraphic units.

Proposed procedure for interpreting channeldeposits in well logs, image logs, and cores

When interpreting channel deposits in vertical logs, it is important to estimate maximum and mean bankfull-channel depth with some confidence, because these parameters are commonly used to estimate the width of subsurface channels and channel belts (Bridge and Tye, 2000). Quantitative estimation of channel depth from subsurface data requires three preliminary steps. First, major channel-belt sandstones and gravelstones must be distinguished from floodplain sandstones. This is not always an easy task, because of the gradation in thickness and facies between these types of sediment bodies. Second, it is essential to try to recognize the different scales of channel deposits: cross sets, flood sedimentation units, unit-bar deposits, compound-bar deposits, individual channel belts, and compound channel belts. This must be done by inspection of spatial variations in grain size, sedimentary structures, paleocurrents and degree of disruption. It is very difficult to do this using data from one well. As shown above, it is easy to confuse flood-sedimentation units with bar deposits, and to confuse individual channel belts with superimposed channel belts. Third, the thickness of as many untruncated channel bars or fills (from the tops of channel belts) as possible must be measured to get an idea of the range of maximum channel depths.
Maximum bankfull-channel depth is commonly estimated from the (decompacted) thickness of untruncated channel-bar and channel-fill deposits. It is not always easy to correctly identify untruncated channel-bar and channel-fill deposits in logs or cores. Furthermore, the thickness of such channel sandstones is generally less than the bank-full channel depth (Bridge and Mackey, 1993b). The presence of sandy-muddy upper-bar deposits, and the uncertainty in distinguishing these from proximal overbank deposits makes it difficult to identify paleo-bankfull level. Thick channel-fill mudstones above thin channel-bar sandstones can look very similar to overbank deposits. Furthermore, maximum channel depth and bar thickness vary in space quite markedly (by at least a factor of two) in channel belts, such that limited data from a single well may not be representative. An independent means of estimating bankfull flow depth would be beneficial. This is possible using an understanding of the relationship between dune height and thickness of associated cross sets, and of the known relationship between dune height and water depth.
The method for calculating the distribution of dune height from the distribution of cross-set thickness is described by Bridge (1997), Leclair et al. (1997) and Leclair and Bridge (2001). The method is based on the justifiable assumption that the distribution of cross-set thickness is due primarily to variability in dune height, and that variation in deposition rate plays a minor role. This method is also limited to homogeneous cosets of cross strata, meaning that there are no obvious spatial changes in the type of strata or mean grain size. The assumption is, therefore, that such cross sets were formed by migration of dunes whose mean geometry did not vary appreciably in time and space. To use this method, the thickness,
s, of as many cross sets as possible should be measured, such that the mean set thickness, sm, can be calculated. Mean dune height, Hm , is approximately equal to 3 sm . To avoid confusing cross strata of dune origin with solitary sets formed by unit bars, abnormally thick, isolated cross sets should be avoided. As dune height is expected to vary with position on channel bars, cross-set thickness measured in different positions in the vertical profile should be grouped into subsets. Mean dune height generally increases with formative flow depth, d. It appears that, for all types of river dunes (including those not in equilibrium with the flow), d/Hm averages between 6 and 10. Although estimation of flow depth from dune height is imprecise, such an estimate is still a useful complement to flow depth calculated from channel-bar thickness.

Re-interpretation of the geometry and spatial distribution of subsurface fluvial sandstone bodies

There are many examples in the literature of interpretation of river-channel deposits using data from cores and well logs (e.g., various papers in the volumes edited by Barwis et al., 1990; Ethridge and Flores, 1981; Ethridge et al., 1987; Galloway and Hobday, 1996; Lomando and Harris, 1988; Miall and Tyler, 1991; Selley, 1996). In most examples, a range of possible interpretations of well logs is not considered, and the cores are not described in sufficient detail to allow use of the methods proposed here. In particular, the thickness of medium-scale cross sets is rarely presented. However, Bridge and Tye (2000) demonstrated how application of the new techniques discussed here had an impact upon previous interpretations of paleochannel depths, channel-belt widths, and fluvial sandstone-body dimensions and connectedness.

Stratigraphic correlation of well logs and cores: use of seismic data
Method of correlation

Correlation of lithofacies between wells is normally accomplished within a framework of regional stratigraphic markers established using seismic sections, well logs and cores. In order to facilitate correlation, it is common practice to plot the stratigraphic markers as horizontal surfaces. Lithostratigraphic correlation must entail certain assumptions about, or models of, the geometry and lateral continuity of lithofacies such as channel-belt sandstone bodies or floodplain shales (Fig. 1, 7 and 8). For example, must the tops and bases of correlated sandstone bodies be horizontal and parallel? If they are not horizontal and parallel, how inclined can the boundaries be relative to the datum, and how variable can the thickness of a sandstone body be? What is a reasonable lateral extent in any given direction? These are very difficult questions to answer. In many cases, the assumptions made in correlation are either not stated explicitly, or are based on various kinds of stratigraphic models. If correlating stratigraphic sequences that are less than the order of 100 m thick, seismic data will be of limited use in resolving the lateral continuity of strata and the presence of small faults. Stratigraphic resolution using seismic data improves as interval thickness and impedance contrast increase. Therefore, an infinite number of correlations is possible, but only one will be used in practice.


Figure 7. Different ways of correlating rock units between two wells, depending on assumptions about the physical continuity and orientation of unit boundaries.
Figura 7. Diferentes formas de correlacionar unidades de roca entre dos pozos, dependiendo de las suposiciones de la continuidad física y de la orientación de los límites de la unidad.


Figure 8. Correlation of two wells within the Ness Formation of the Brent Field, UK North Sea (from Bryant and Flint, 1993). GR = Gamma Ray; FDC = Density Log; CNL = Compensated Neutron Log. Coals have been used as correlation markers. There has been some imaginative definitions of the shapes and lateral extents of channel sands and crevasse splay sands.
Figura 8. Correlación de dos pozos en la Formación Ness del Distrito Brent, Mar del Norte-Inglaterra (de Bryant and Flint, 1993). GR = Rayos Gama; FDC = Perfil de Densidad; CNL = Perfil Compensado de Neutrones. Las capas de carbón han sido utilizadas como niveles de correlación. Algunas de las definiciones de las formas y extensiones laterales de las arenas de canal y de las arenas de crevasse splay han sido imaginativas.

Using well-to-well correlation to estimate lateral extent of reservoirs or aquifers

It is ironic, but not surprising, that the most common method for estimating channel-belt widths and orientations is by correlating specific channelbelt sandstone bodies between well logs (e.g., Nanz, 1954; Berg, 1968; Cornish, 1984; Tye, 1991). With this technique, there is generally no attempt to predict reasonable geometries and lateral extents of different lithofacies from analysis of well logs. The minimum possible width of sediment bodies that can be resolved by this method is the well spacing. This approach to estimating lateral extent lithofacies is commonly compromised by simplistic or erroneous assumptions, such as: (1) basal erosion surfaces and tops of channel-belt sandstone bodies are flat; (2) sandstone bodies positioned at the same stratigraphic level must be connected between adjacent wells; (3) sandstone body width/thickness ratios are closely related to paleochannel pattern, and; (4) vertical sequences through channel deposits indicate the paleochannel pattern and hence the geometry of channel-belt sandstone bodies.
Concerning assumption (1), the depositional models discussed above clearly show that the basal erosion surfaces and tops of channel belts are not generally flat. Concerning assumption (2), sandstone bodies at the same stratigraphic level in adjacent wells are not necessarily connected, and some assessment of the probability of connection is required, perhaps using empirical data on channelbelt width/maximum channel depth. However, if two sandstone bodies are indeed continuous between wells, they are not necessarily from a single channel belt. This is of particular concern if sandstone-body proportion exceeds 0.4 (Bridge and Mackey, 1993b). Assumptions (3) and (4) were shown to be wrong above.
In order to rationalize the correlation process as much as possible, it is desirable to use interpretations of depositional environments and stratigraphic models to constrain the correlation assumptions. In the case of isolated channel belts, it is unlikely that the tops and bases will be horizontal and parallel. Data from modern and ancient analogs can be used to assess these characteristics. Models and real-world examples of channel belts indicate that their thickness may vary laterally by a factor of at least two, and that there are systematic lateral variations in thickness. A range of likely channel-belt widths can be obtained from the thickness of single channel belts, as indicated below. It may turn out that sandstone bodies at the same stratigraphic level should not be correlated over the distance between two wells if this distance greatly exceeds the expected lateral extent of a channel belt. There needs to be much more work done on the geometry of different lithofacies in modern fluvial environments, if modern analogs are to be used to predict the geometry of subsurface fluvial sediment bodies.

Geometry of modern channel-belt deposits

Several attempts have been made to predict channel-belt width in the subsurface using empirical equations derived from modern rivers that relate maximum channel depth, channel width, and channel-belt width (Collinson, 1978; Lorenz et al., 1985, 1991; Fielding and Crane, 1987; Davies et al., 1993; discussed by Bridge and Mackey, 1993b). This approach requires reliable estimates of maximum bankfull-channel depth from one-dimensional subsurface data. As discussed previously, correct estimation of maximum bankfull-channel depth is not straightforward, because complete channel-bar or channel-fill sequences may be difficult to identify, and the thickness of the sandstone-gravelstone parts of these coarse members is not always as great as the bankfullchannel depth. Furthermore, within a single channel belt, maximum channel depth and bar thickness can vary spatially by a factor of at least 2 (Bridge, 1993a; Salter, 1993). Therefore, limited data from a single well may not be representative.
Empirical regression equations relating maximum channel depth, channel width, and channel-belt width have large standard errors, and are dependent on channel-pattern parameters such as channel-bend wavelength and sinuosity (Bridge and Mackey, 1993b). Most of the empirical equations used to date (Collinson, 1978; Lorenz et al., 1985, 1991; Fielding and Crane, 1987; Davies et al., 1993) do not include such dependencies. Channel-bend wavelength and sinuosity are actually very difficult to reconstruct from outcrops and are impossible to determine from well data. Lorenz et al. (1985) used empirical equations derived from rivers with sinuosity greater than 1.7, and assumed that sandstone bodies in both outcrops and subsurface strata were deposited in highly sinuous rivers. Equations presented in Bridge and Mackey (1993b: their Table 2) are based on larger data sets than previous equations or on theoretical principles. Channel-belt widths predicted by these equations agreed with those observed in outcrops by Bridge et al. (2000).

Use of outcrop analogs to aid well-to-wellcorrelation

The geometry and lithofacies of channel and channel-belt deposits determined in outcrops are commonly used as analogs for subsurface strata (Collinson, 1978; Walderhaug and Mjos, 1991; Lowry and Raheim, 1991; Cuevas Gozalo and Martinius, 1993; Dreyer, 1993; Dreyer et al., 1993; Robinson and McCabe, 1997; Bridge et al., 2000). Despite the popularity of this approach, it has many pitfalls. First, it must be established that the depositional setting interpreted for the subsurface strata is indeed analogous to that interpreted for the outcrops. This requires two interpretation steps, the reliability of which depends on the quality of the outcrops, of the subsurface data, and of the depositional models used for interpretation. It is difficult to make detailed interpretations of depositional environments using typical subsurface data. Because our understanding of modern depositional environments is incomplete, most depositional models are qualitative, lacking in detail, and not fully three-dimensional (Bridge, 1985, 1993b). The deficiency of most depositional models severely limits their use in detailed interpretation of ancient deposits. Rarely are outcrops extensive enough to allow unambiguous determination of the three-dimensional geometry and orientation of channels and channel belts. Channel-belt width is particularly difficult to determine, even in large outcrops (Geehan and Underwood, 1993). Moreover, channel-belt width and thickness are known to vary spatially within one channel belt and between different channel belts. In general, limited data from a few large exposures are unlikely to be generally representative of fluvial-deltaic channel belts. This is why it is desirable to use analog data from Holocene depositional environments, where channel-belt dimensions can be determined easily, and the relationship between the nature of the deposits and the geometry, flow and sedimentary processes of the environment can be established unambiguously.

Amplitude analysis of 3-D seismic horizon slices

Amplitude analysis of 3-D seismic horizon slices (Weber, 1993; Hardage et al., 1994, 1996; Burnett, 1996) is the only method capable of yielding directly the width of channel belts, and imaging the channel pattern (sinuosity, channel splitting) of subsurface sandstone bodies (Fig. 9). This is also the only method that can be used to predict the spatial distribution of channel-belt thickness and lithofacies. However, high quality 3-D seismic data are rarely available, the most sandstone bodies of interest are too thin and buried too deeply to be completely resolved using seismic data.


Figure 9. Amplitude analysis of a 3-D seismic horizon slice showing the width of a channel belt and channel pattern of subsurface channel sandstone bodies. The cross section shows correlated logs and the position of the horizon slice. Log 3 cuts through the variablewidth, straight channel belt trending north-south. Logs 4 to 6 cut through a point bar and channel fill of a slightly older channel belt.
Figura 9. Análisis de amplitud de una sección horizontal de sísmica 3-D mostrando el ancho de la faja de canales y el diseño de los canales de los cuerpos de areniscas de canal en subsuelo. Las secciones transversales muestran los perfiles correlacionados y la posición de la sección horizontal. El perfil 3 atraviesa longitudinalmente la faja de canal de ancho variable en dirección norte-sur. Los perfiles 4 y 6 atraviesan una barra de punta y el relleno de canal de una faja de canal un poco más antigua.

Estimating width of superimposed cannel belts from subsurface data

When correlating channel-belt sandstone bodies between wells, it is critical to be able to distinguish connected channel belts. Two connected channel belts may be up to twice the width of a single channel belt. Bridge and Mackey (1993b) used their revised two-dimensional model of alluvial architecture (Bridge and Mackey, 1993a) to study the width and thickness of sandstone (or gravelstone) bodies comprising single or connected channel belts. The width and thickness of sandstone bodies depend critically on the proportion of channel-belt deposits in the stratigraphic interval, as this proportion controls the degree of connectedness of individual channel belts. For low values of channel-deposit proportion (less than about 0.4), channel belts are unconnected, sandstone-body width equals channel-belt width, and sandstone-body thickness equals aggraded channel-belt thickness (Fig. 10). As channel-deposit proportion increases, some channel belts become connected, the mean and standard deviation of sandstone-body width and thickness increase, and their frequency distributions become polymodal with the largest modes at the lowest values of width and thickness. As channel-deposit proportion continues to increase, the distributions are still polymodal but the larger modes are at higher values of width and thickness (Fig. 10). If channel-deposit proportion exceeds about 0.75, all channel belts are connected, and the single sandstone body has a width equal to floodplain width and a thickness equivalent to the whole section.


Figure 10. Relationships between channel-belt deposit proportion and connectedness, and the width and thickness of channel-belt sandstone bodies (based on Bridge and Mackey, 1993b).
Figura 10. Relaciones entre la proporción de los depósitos de la faja de canales, la interconexión, el ancho y el espesor de los cuerpos de areniscas de la faja de canales (basado en Bridge and Mackey, 1993b).

Channel-deposit proportion, width and thickness increase as bank-full channel depth and channel-belt width increase, and as floodplain width, aggradation rate and avulsion period decrease. Channel-deposit proportion is also influenced by depth of burial (degree of compaction) and tectonic tilting of the floodplain. For example, channel-deposit proportion and connectedness of channel belts increase on the down-tilted sides of floodplains but are reduced on the up-tilted sides.
The three-dimensional model of alluvial architecture of Mackey and Bridge (1995) gives results that are generally similar to those described above for two-dimensional models. However, the three-dimensional model predicts that channeldeposit proportion and connectedness, and the dimensions of channel sandstone bodies, vary with distance from points of channel-belt splitting (due to avulsion). Upstream of avulsion points, sandstone bodies have lower than average width/ thickness because of aggradation in a fixed channel belt. Immediately down valley from avulsion points, channel belts are connected, resulting in sandstone bodies with higher than average width/thickness. Because of this, relationships between channeldeposit proportion and connectedness and sandstone-body dimensions derived from 2-D models are strictly applicable only to parts of the floodplain located some distance down valley from avulsion points.

Correlation using sequence-stratigraphicmodels

Correlation of lithofacies associations between wells may be aided by other kinds of stratigraphic models, such as sequence-stratigraphic models (Fig.11). Sequence-stratigraphic models (e.g., Jervey, 1988; Posamentier and Vail, 1988; Posamentier et al., 1988; Ross, 1990; Shanley and McCabe, 1993, 1994; Wright and Marriott, 1993) predict the effects of relative sea-level change on alluvial deposition rate and alluvial architecture, and are therefore potentially applicable to near-coastal fluvial successions. There are substantial differences between these models, and all of them can be criticized. Most of these models are severely limited because they are qualitative, essentially two-dimensional, and do not account for all of the factors that influence alluvial architecture. Actually, eustatic sea-level change may not have the influence on alluvial systems that has been assumed in the past. Factors such as climate, vegetation and tectonism may also have an important influence on rivers and floodplains during eustatic sea-level change (Schumm, 1993; Wescott, 1993; Blum, 1994; Koss et al., 1994; Leeder and Stewart, 1996; Miall, 1996; Blum and Price, 1998; Ethridge et al., 1998; Blum and Tornqvist, 2000). Miall (1986, 1991, 1996) has criticized some of the earlier models (e.g., Jervey, 1988; Posamentier et al., 1988) for the effects of sea-level change on near-coastal alluvial deposition. His main point is that a relative fall in sea level is not normally associated with alluvial aggradation, except for the newly exposed part of the sea bed, and even then only under special circumstances. In fact, whether or not a river valley is incised or aggraded during sea-level fall depends, among other things, on the slope of the exposed shelf relative to that of the river valley (Pitman, 1986; Pitman and Golovchenko, 1988; Schumm, 1993; Leeder and Stewart, 1996). In general, the effects of sea-level change are expected to decrease up-valley (Saucier, 1981, 1994; Autin et al., 1991; Schumm, 1993; Shanley and McCabe, 1994). Only three-dimensional models can describe these effects (Bridge, 1999: Karssenberg et al, 2001b).
Most alluvial sequence-stratigraphic models have an erosional base to the sequence (Shanley and McCabe, 1993, 1994; Wright and Marriott, 1993; Gibling and Bird, 1994; Miall, 1996; Fig. 11). This is ascribed to river incision arising from relative fall in base level and exposure of a slope that is steeper than the river slope upstream. Although incision may be associated with base-level fall near the coast, incision further inland may not be associated with falling base level (Blum, 1994; Blum and Price, 1998: Blum and Tornqvist, 2000). Therefore, the basal erosion surface of the sequence may not be coeval with, or coincident with, erosion surfaces inland. The erosional base of the sequence in these models is overlain by amalgamated fluvial channel deposits (the so-called lowstand systems tract: LST) that are ascribed to deposition under conditions of low deposition rate and restricted floodplain width (due to valley incision). Many workers assume that zones of high channel-deposit proportion (high net-to-gross) in alluvial deposits represent these basal parts of sequences, and that the basal erosion surface of the lowest sandstone body represents an incised valley (e.g., Aitken and Flint, 1995). In many cases, evidence for an incised valley is lacking. Criteria for incised valleys include (Dalrymple et al., 1994): (1) erosional relief that is greater than the thickness of a single channel fill; (2) multiple, vertically stacked channel bars within the valley; (3) evidence for extended periods of non deposition (mature paleosols) on interfluves; (4) alluvial channel deposits resting erosively upon shallow marine sands and muds. Commonly, a large amount of erosional relief on the base of a single channel deposit can be misinterpreted as an incised valley margin (Salter, 1993; Best and Ashworth, 1997).
Falling sea level (marine regression) does not necessarily result in valley incision near the coast. The land exposed by marine regression may experience erosion or deposition depending on the slope of the exposed surfaces (Schumm, 1993; Wescott, 1993; Wood et al., 1993). Erosion will occur on relatively steep slopes given enough time and flow competence. However, erosion of channels and floodplains is a long-term process, and the shortterm response may be to increase sinuosity of rivers. Also, upstream avulsion may cause channel abandonment before incision is complete (Leeder and Stewart, 1996). Incision of channels and floodplains is associated with terrace formation, reduction of valley width, and up-valley migration of knick-points. Avulsion frequency is expected to be low in areas of erosion. Channel-deposit proportion and connectedness may increase during sea-level lowstand because of reduced deposition rate (or erosion) and reduced floodplain width. However, channel-deposit proportion may decrease as a result of reduced avulsion frequency, or if the channel-belt width and thickness were reduced as a result of a decrease in water discharge. Sequence stratigraphic models must account for changes in all of these factors that influence alluvial architecture.


Figure 11. Examples of alluvial sequence-stratigraphic models (upper model from Shanley and McCabe, 1993; lower model from Wright and Marriott, 1993).
Figura 11. Ejemplos de modelos de secuencia estratigráfica aluvial (modelo superior de Shanley and McCabe, 1993; modelo inferior de Wright and Marriot, 1993).

Thick and laterally extensive amalgamated channel deposits are commonly important oil and gas reservoirs. Therefore, it is important to interpret such deposits accurately when predicting their thickness, lateral extent, and bounding facies. If zones of high channel-deposit proportion are incorrectly interpreted as incised valley fills, their extent normal to the valley direction will be underestimated, and their extent parallel to the valley will be overestimated. There are many examples in the literature where zones of high channel-deposit proportion are not associated with filling of incised valleys. For example, they may be associated with high deposition rates and high avulsion frequencies of large channels on megafans (Willis, 1993a,b; Khan et al, 1997; Zaleha, 1997a,b). In this case, their lateral extent may be considerable.
According to the sequence-stratigraphic models, the deposits above the lowstand systems tract were deposited under conditions of relatively high deposition rate on a broad alluvial plain, associated with rising relative base level and drowning of incised valleys (the so-called transgressive systems tract: TST). The channeldeposit proportion and connectedness are taken to be relatively low as a result. According to Gibling and Bird (1994), coal is likely to occur at the top of the TST, immediately below the so-called maximumflooding surface. Paleosols are likely to reflect high groundwater table. Deposits associated with the maximum-flooding surface may contain evidence of marine influence.
During relative sea-level rise, slopes of rivers and floodplains are reduced near shore due to backwater effects, and the width and depth of valleys increase due to drowning. These changes result in reduced grain size of transported sediment, deposition, change in channel pattern, and increased frequency of avulsion. Tornqvist (1993, 1994) associated high avulsion frequency and anastomosing river patterns with periods of rapid base-level rise and deposition. Increases in avulsion frequency increase channel-deposit proportion and connectedness, but increases in deposition rate and width of floodplains decrease them. It is also necessary to know how channel-belt geometry changes during sea-level change in order to adequately predict channel-deposit proportion. In the case of the Mississippi coastal plain, the channeldeposit proportion in the Holocene deposits is low mainly because of high floodplain width relative to channel-belt width. However, in the coeval deposits of the lower Mississippi Valley, the channel-deposit proportion is very high because of low floodplain width relative to channel-belt width (Bridge, 1999).
The highstand systems tract (HST) is also associated with relatively low channel-deposit proportion according to Shanley and McCabe (1993). However, Wright and Marriott (1993) predict an increase in channel-deposit proportion in the HST, and an increase in soil maturity, both related to reduced deposition rate.
Based on the comments above, it is unlikely that extant alluvial sequence-stratigraphic models are generally applicable. Karssenberg et al (2001b) have attempted to improve upon this situation by producing a 3-D model that takes account of most of the factors that control alluvial architecture during changing base level.

Modeling of the three-dimensional Geometry and distribution of Facies between wells

Information derived from seismic profiles, cores, well logs, and well tests is rarely sufficient to provide comprehensive three-dimensional description and understanding of subsurface reservoir rocks. As a result, recourse is commonly made to outcrop analogs and quantitative depositional models. A common approach is to use interpreted outcrop analogs (discussed above) to provide supplementary data on sedimentary architecture, and to use stochastic, structure-imitating models conditioned by subsurface data to distribute the sediment types in 3-D space (reviews by Bryant and Flint, 1993; Koltermann and Gorelick, 1996; North, 1996; Anderson, 1997: Fig.12). Structure-imitating stochastic models do not simulate processes of deposition: they directly simulate the stratigraphy. Methods used are indicator geostatistics (e.g., Journel, 1983; Bierkens and Weerts, 1994), simulated annealing (e.g., Deutsch and Cockerham, 1994), Markov chains (e.g., Doveton, 1994, Carle et al., 1998), and Boolean object models that use probabilistic rules to define the geometry and location of stratigraphic units (e.g., Budding et al., 1992; Deutsch and Wang, 1996; Hirst et al., 1993; Holden et al., 1998). An advantage of these models is that they match the available data exactly. However, input parameters are very difficult to obtain, and the alluvial stratigraphy simulated is commonly very unrealistic (e.g., Tyler at al., 1994; Deutsch and Wang 1996; Holden et al., 1998). In the case of object-based models, the lack of realism is associated with the choices available for object shapes, and the essentially random placement of objects where well data are not available. For example, channel belts are modeled as one or more sinuous ribbons with channel-shaped bases (Fig. 13).


Figure 12. An example of use of a two-dimensional, object-based stochastic model (from Srivastava, 1994). The width and thickness of channel-belt sandstone bodies are normally obtained from Monte Carlo sampling from empirical distributions derived from outcrop analogs. Notice that the "sand bodies" have been given a channel-shaped form. Channel-belt sandstone bodies do not normally have this form.
Figura 12. Un ejemplo del uso de un modelo bidimensional estocástico basado en objetos (de Srivastava, 1994). El ancho y el espesor de los cuerpos de areniscas de faja de canales son obtenidos del muestreo Monte Carlo a partir de las distribuciones empíricas derivadas de análogos de afloramiento. Note que los «cuerpos de arena» han sido adjudicados a una forma de canal. Los cuerpos de areniscas de faja de canales normalmente no tienen esta forma.


Figure 13. (A) Example from the MOHERES software of a single channel belt consisting of four "channel beds" (from Tyler et al., 1994). In this software, internal elements such as channel bars and channel fills can be placed randomly within these "channel beds". This is not a realistic representation of the geometry of deposits in channel belts. Notice that the "channel beds" are not even in contact with eachother in places. (B) Example of a channel belt from Patagonia showing a single active channel and many abandoned channel bars and channel fills. The channel-bar deposits comprise most of the volume of this channel belt.
Figura 13. (A) Ejemplo del programa MOHERES consistente en una faja de canales simple con cuatro "lechos de canales" (de Tyler et al., 1994). En este programa, los elementos internos tales como barras de canal y relleno de canales pueden estar ubicados al azar dentro de los "lechos de canales". Esta no es una representación relista de la geometría de los depósitos en las fajas de canales. Note que los "lechos de canales" no están en contacto entre sí en otros sectores (figura inferior). (B) Ejemplo de una faja de canales de Patagonia mostrando un canal activo simple y muchas barras de canal abandonadas y rellenos de canal. Los depósitos de barras de canal conforman la mayor parte del volumen de esta faja de canales.

Unlike the structure-imitating models, process based models (sometimes referred to as processimitating models) simulate the sedimentary processes acting to produce a deposit (Koltermann and Gorelick, 1996; Anderson, 1997). Process-based models can be deterministic and/or stochastic, and empirical and/or theoretical. Examples of such models include random-walk sedimentation models of braided rivers (Webb, 1994), models based on the fundamental equations of fluid flow and sediment transport (e.g., Bridge, 1977, 1992; Tetzlaff and Harbaugh, 1989; Stam, 1996), and avulsionbased alluvial stratigraphy models (e.g., Bridge and Leeder, 1979; Mackey and Bridge, 1995; Heller and Paola, 1996). Process-based models are forward models in the sense that they predict the nature of deposits given a set of initial starting parameters. It is not known a priori what the deposits will look like. Advantages of process-based models are that they utilize fundamental physical principles to generate stratigraphy. Therefore, process-based models can help provide genetic interpretations of deposits, and can predict more realistic stratigraphy than structure-imitating (stochastic) models. However, a perceived disadvantage of process-based models is that it is difficult or impossible to make the simulated deposits fit observational data in sufficient detail (Clemetsen et al., 1990; North, 1996; Koltermann and Gorelick, 1996; Anderson, 1997). Therefore, process-based models have had limited application in quantitative simulation of reservoir stratigraphy.
Recent work shows, however, that fitting of process-based models to well data is possible in principle, using a trial-and-error approach with some optimization (Karssenberg et al., 2001a). Karssenburg et al. (2001a) fitted a simplified version of the Mackey-Bridge (1995) three-dimensional model of alluvial stratigraphy to five hypothetical wells (Fig. 14). The approach is to run the model many times, each time with different input defined using Monte Carlo simulation techniques. Successful runs are those where output fits well data within certain tolerance limits. Figure 15 shows the temporal evolution of the floodplain for one run of the process-based model with the simulated deposits fitting the five wells. On the basis of all of the realizations of the model that fit the wells, the probability of occurrence of channel-belt deposits within the area can be calculated (Fig. 16).


Figure 14. (A) Hypothetical model area with location of five wells (B) Hypothetical well data used for model fitting (from Karssenberg et al., 2001a).
Figura 14. (A) Área hipotética del modelo con la ubicación de cinco pozos, (B) Datos hipotéticos del pozo usados para ajustar el modelo (de Karssenberg et al., 2001a).


Figure 15. Model run that fits the well data. Each map shows position of the old and new channel belt, and the surface elevation (m) at the time of an avulsion (from Karssenberg et al., 2001a).
Figura 15. Modelo simulado que se ajusta a los datos de los pozos. Cada mapa muestra la posición de la faja de canales antigua y nueva, y la elevación de la superficie (m) en el momento de una avulsión (de Karssenberg et al., 2001a).


Figure 16. 3-D image of probability of occurrence of channel belt deposits based on model runs that fit the well data. Top figure shows volume with probability > 0.8. Bottom diagram shows transects through the 3-D block, with grayscale representing probability of occurrence of channel-belt deposits (from Karssenberg et al., 2001a).
Figura 16. Imagen 3-D de probabilidad de ocurrencia de los depósitos de faja de canales basada en los modelos simulados que se ajustan a los datos de los pozos. La figura en la parte superior muestra el volumen con probabilidad > 0,8. El diagrama de la base muestra las transectas a través del bloque 3-D, la escala de grises representa la probabilidad de ocurrencia de los depósitos de la faja de canales (de Karssenberg et al., 2001a).

It was concluded that using this trial-and-error approach in practice will require: (1) refinement of the process-based model; (2) improved algorithms for efficiently fitting the model to the data, and; (3) overcoming the anticipated large amounts of computing time. Recent progress on these three problems has facilitated the implementation of this inverse modeling approach and its application to real-world data. Moreover, the effectiveness of process-based models in simulating alluvial stratigraphy can now be compared with stochastic, structure-imitating models. The 3-D process-based model can be fitted to well data exactly by inverse modeling (Cross and Lessenger, 1999; Bornholdt et al, 1999; Karssenberg et al., 2001a). With inverse modeling, fitting of the model to well data is achieved by repeatedly running the model, comparing its output with well data, and adjusting the model input parameters until the model output fits the well data within specified tolerance limits. For each model run, a fitness function (called objective function or goal function by others) expresses the difference between model output and well data. The objective is to minimize the difference between the model output and well data, or to maximize the fitness function. Since the fitting procedure will put a high demand on computational resources, the choice of the fitting method and the software implementation of this method and the process-based model is critical in order to minimize run times.

Acknowledgements

Sincere thanks to my friend and colleague Bo Tye for many discussions of the issues raised in this review. Bo also generously reviewed the manuscript. Sincere thanks also to another friend and colleague, Sergio Georgieff, who invited me to write this paper, and who was responsible for the Spanish translations.

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