Three-Dimensional Modeling of Glacial Sediments Using Public Water-Well Data Records: an Integration of Interpretive and Geostatistical Approaches

Three-dimensional modeling of glacial sediments using public water-well data records: An integration of interpretive and geostatistical approaches

Erik R. Venteris Ohio Division of Geological Survey, 2045 Morse Road, Building C, Columbus, Ohio 43229, USA

ABSTRACT and geophysics) are needed to parameterize Three-dimensional modeling techniques are facies simulations. essential for the mapping of surfi cial materi- Despite their importance to environmen- als due to the complexity of glacial sediments. tal issues and mineral resources, surfi cial Keywords: glacial sediments, geostatistics, hy- The glacial stratigraphy in Ohio is the result sediments are largely unmapped at depth drofacies, water wells, hydrogeology. of a lengthy depositional and erosional history in the United States. Full three-dimensional involving several oscillations of the Laurentide (3D) models of these materials are needed to INTRODUCTION ice sheet. This complexity is especially refl ected support hydrologic modeling, geotechnical in the sediments of the buried valleys, which engineering, and mineral-resource inven- Maps and models of surfi cial materials are typically contain alternating deposits of till, tory applications. The main source of infor- key to solving current problems in geology and lacustrine sediments, and >100-m-thick out- mation for such models in the Midwestern the environmental sciences. Hydrologic stud- wash. Such valleys are often a major source of United States is lithology logs from public ies that address issues such as water supply groundwater and the subject of numerical mod- water-well records. Three-dimensional mod- and non-point source pollution require accurate eling studies involving contaminant distribution eling of lithology was conducted to elucidate and realistic representations of unconsolidated and water supply. Three-dimensional geologic the nature and quality of spatial information sediments at depth. Surfi cial materials maps models are required to defi ne the physical char- sourced from water wells. The modeling was are also essential to engineering and geologic acteristics of this highly heterogeneous fl ow conducted on an ~130-km2 area near Lake hazard investigations such as risk assessments medium. In addition, 3D models reduce the Erie in northeast Ohio that contained an end for seismic damage and landslides. Despite abstraction inherent in traditional maps and moraine superimposed on a buried glacial the importance of surfi cial deposits, mapping cross sections, making such models invaluable valley. An integrated approach to 3D model- at depth is rare across the United States. When for describing and illustrating complex glacial ing was adopted where traditional interpre- available, surfi cial models are typically in the geology to the general public. tive techniques were used to defi ne glacial form of two-dimensional (2D) maps drawn at The quality and quantity of available data cre- stratigraphic units (glacial outwash, till, county and state scales. Such maps are common ates serious challenges to the mapping and mod- etc.) with geostatistical simulation of lithofa- for states with glacial deposits. An additional eling of surfi cial sediments. The main source of cies conducted within the stratigraphic lay- source, the digital soil survey (SSURGO, avail- data at depth for this and similar studies is lithol- ers. Despite the large amount of variability able from the United States Department of Agri- ogy logs from public water-well records (Ohio and noise inherent in water-well data, there culture, Natural Resource Conservation Service Department of Natural Resources Division of were statistical patterns in the lithology (Gabriel et al., 1992)), provides information at Water (ODOW), 2007). Well records contain records related to glacial stratigraphy. In the county scale to an average depth of ~1.5 m. lithologic information (sediment type, thick- contrast, the well data provided only mini- For most areas, the depth below the surveyed ness, and color) fi led by private water-well com- mal information on facies geometry within soil to the bedrock interface is unmapped. The panies. These wells have a typical spatial den- these units. The spatial structure of facies Ohio Division of Geological Survey is conduct- sity of four wells per square kilometer, which in the vertical direction was based on thick- ing three-dimensional (3D) mapping of surfi - has been found to be insuffi cient to characterize ness statistics from the water-well data and cial materials, 1:100,000-scale, as a fi rst step the lateral spatial structure of alluvial and bur- on geologic interpretation for the horizontal toward fi lling this knowledge gap (Venteris, ied valley sediments by traditional geostatisti- direction. Several sequential indicator simu- 2007; Schumacher, G.A., Venteris, E.R., and cal structural analysis (Weissmann et al., 1999; lation models were conducted to investigate Swinford, E.M., unpublished data, 2007). In Ritzi et al., 2000). The depths of these wells the effect of grid-cell thickness, stratigraphic addition to this work, quantitative techniques vary widely, but rarely extend beyond 50 m, trimming, and length-to-thickness ratios on for mapping are being investigated to better often leaving large intervals of buried valleys the reproduction of thickness statistics. This understand the spatial variability of glacial with little or no data upon which to constrain case study confi rms that water wells are a sediments and the quality of geologic informa- models. In addition, the lithologic information viable data source for stratigraphic model- tion available from lithology logs sourced from contained in individual water wells ranges in ing, but better data sources (e.g., outcrops public water-well databases. quality, from highly detailed borings that can

Geosphere; December 2007; v. 3; no. 6; p. 456–468; doi: 10.1130/GES00090.1; 8 ﬁ gures; 5 tables.

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provide reliable information on both strati- water wells and current geophysical techniques area, a major north-south bedrock valley. The graphic units and facies, to clearly erroneous typically do not provide information of suffi - feature is approximately four miles wide and records. Careful evaluation and interpretation of cient quantity or quality to allow explicit map- contains up to 100 m of glacial sediments. The the water-well data set is required before their ping at facies scales. The multiple realizations valley is fi lled with till (overlying) and sand use. Water-well data can occasionally be sup- generated by geostatistical simulation provide and gravel deposits interbedded with lacustrine plemented from detailed borings (from private a method of accounting for facies heterogene- and probably remnant till facies (Venteris, sector studies, the Ohio Environmental Protec- ity that directly incorporates the considerable 2007). The area has been mapped at the surface tion Agency, or the Ohio Department of Trans- uncertainty into the workfl ow. Finally, simulat- many times (White and Totten, 1979; Pavey et portation), which contain penetration tests and ing lithology types rather than fl ow parameters al., 1999), but studies at depth have not been full laboratory analysis of texture. Such detailed allows the direct comparison of modeling results published. records were not available for the immediate to traditional geological maps and models (Ven- study area. teris, 2007). METHODOLOGY This work seeks to create 3D models based This work seeks to better understand the on water-well data using a combination of potential uses and limitations of water-well data Preprocessing of Well Data stratigraphic interpretation and geostatistical for the creation of 3D models at the stratigraphic simulation. Geologic interpretation, confi rmed and facies scales. It is critical to obtain a bet- The fi rst step in modeling was to convert the by statistical analysis of the well data, is used ter understanding of the information contained water-well data to a format appropriate for geo- to defi ne regions where the assumption of sta- within this data set. For much of the state of statistical modeling. The water-well database tionarity is reasonable (Carle et al., 1998, Weiss- Ohio, and most of the industrialized world, sim- from ODOW consisted of lithologies described mann and Fogg, 1999; Ritzi et al., 2000; Proce ilar well databases represent the main source of using three-letter codes (for example, CLA for et al., 2004). Facies heterogeneity is then mod- information about the shallow subsurface. clay and DRF for drift). For this study area, there eled within the defi ned stratigraphic units using were sixty-fi ve different codes describing sedi- sequential indicator simulation (SISIM). Study Area ment, rock, and anthropogenic material such as Spatial variability in lithology and hydrologic fi ll. These descriptions required simplifi cation parameters at the facies scale is usually mod- A buried valley near Lake Erie was the focus for modeling, a process that included interpre- eled using indicator geostatistics (Journel, 1983; of this modeling exercise, which was initially tation and generalization. A lookup table was Carle and Fogg, 1996; Ritzi et al., 2000). In this conducted to support qualitative mapping of created to reclassify the lithologic descriptions approach, the sedimentary facies are divided portions of the Ashtabula 30 × 60-min quadran- into four main lithologies (clay, silt, sand, and into a set of categorical variables to be estimated gle (Venteris, 2007; Schumacher, G.A., Venteris, gravel). Subsequent comparisons between the or simulated. The set of indicators can vary in E.R., and Swinford, E.M., unpublished data, water-well data and more detailed lithology detail from several texture classes to binary 2007). In general, the study area (Fig. 1) is gla- logs from bridge borings for Ashtabula County approaches that divide textures into categories ciated with extensive deposits of Wisconsinan suggested that silt was grossly underrepresented of high and low conductivity. Simulated facies and some Illinoian-age drift at depth (White (Table 1). It was likely that the “clay” units of can then be assigned engineering or hydrologic and Totten, 1979). Near Lake Erie, ice proxi- the water-well records contained lithologies properties (porosity or saturated hydraulic con- mal (till, kames, and outwash) and lake deposits ranging from clay to silt. These four texture ductivity) by using average values or through (lacustrine deposits and beach ridges) cover the classes were modeled using sequential indica- further geostatistical simulation (Feyen and Portage escarpment (Brockman, 1998). Farther tor simulation (SISIM) techniques in Venteris Caers, 2006). inland, the depositional environment transitions (2007), where the goal was to aid decision The indicator simulation approach is justi- to till plains and buried valleys. A key feature making for qualitative mapping. For this work, fi ed on practical and theoretical grounds. Pre- of most buried valleys in this region is that they the goal was to create a model appropriate for vious studies of fl uid fl ow within consolidated were ice-dammed to the north (Bagley, 1953). groundwater modeling. Accordingly, the lithol- (Deutsch, 2003) and unconsolidated sediments These buried valleys are different than those ogies were further grouped into materials with (Ritzi et al., 2000; Weissmann et al., 2002; Carle studied to the south that drained into the Ohio high and low hydraulic conductivity (Fig. 2). et al., 2006) have demonstrated that accounting River (Ritzi et al., 2000). In general, the block- Ritzi et al. (2000) found that simple binary for the heterogeneity of facies within sedimen- ing of drainage resulted in the deposition of a models dividing the domain into fi ne-grained tary units is critical to realistic modeling (as greater amount of lacustrine facies and a higher (abbreviated m, representing clay and silt) and opposed to the simpler approach of assigning proportion of fi ne sediments than in valleys with coarse-grained (abbreviated s, representing sand average values of hydrologic parameters to free drainage. and gravel) hydrofacies captured most of the each stratigraphic unit). The generation of many The area where the Painesville end moraine important variation in hydraulic conductivity. In equiprobable models (realizations) greatly facil- is superimposed on the buried valley (in the addition, by defi ning categories that group clay itates uncertainty assessment. In addition, the southwest corner of the 1:24,000 Ashtabula with silt, the issue of the under-detection of silt indicator approach provides solutions to many South quadrangle) is the subject of this model- in the water-well data set was avoided. statistical diffi culties (Journel, 1983; Deutsch, ing study (Fig. 1). On the immediate surface, The wells were discretized in the vertical 2003). For example, hydraulic conductivities the study area contains end moraines, beach direction to facilitate modeling. Lithologies occur over a wide range of magnitudes and ridges, and lacustrine sediments. Till is the for wells in the original ODOW database are show strong partitioning between sediment dominant deposit, especially at depths below assigned over-depth ranges; the upper and types. Hence, the modeling of hydraulic con- 3 m. In general, the upper layer is a till with lower contacts for each lithologic unit are ductivity as a continuous variable presents dif- an average thickness of 12 m, which contains provided. After conversion to indicator codes, fi culties because assumptions of normality and- occasional sand and gravel lenses. Below this the water wells were discretized at 0.305-m stationarity are rarely met. On a practical level, till is the main subsurface feature of the study (one-foot) increments. The interval represents

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Figure 1. Preliminary model of the subsurface geology at the head of the Grand River, Ashtabula County, Ohio. Water wells used in the study are marked. This is a portion of the “stack” map for the 1:100,000-scale Ashtabula quadrangle. The map is currently under review and revi- sion. Some key abbreviations: A = alluvium; IC = ice contact; TG = Wisconsinan till unit, high in silt; TE = Wisconsinan till unit, high in clay; SG = sand and gravel; LC = silt and clay (generally lacustrine); L = silt (generally lacustrine); Sh = shale bedrock; S = Sand; CG = buried- valley deposit with undifferentiated lithology. Detailed information on how these maps are created is available from Venteris (2007).

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TABLE 1. COMPARISON BETWEEN WATER-WELL AND BRIDGE-BORING TEXTURES FOR ASHTABULA COUNTY (2) p, from p, from bridge Break used Texture class water well boring method for class where φ is 3 or 1.5 for the exponential and spherical models, respectively, and a is the structural Clay 0.6 0.37 >40% k range of the autovariogram. Combining equa- Silt 0.004 0.26 >40% tions one and two gives the result Sand 0.18 0.07 >40% Gravel 0.21 0.07 >30% sand, >10% gravel (3) Note: The comparison contains many sources of bias because the water-well data generally extend to greater depths than the Ohio Department of Transportation boring data, and the which relates the autovariogram range to the spatial distribution of bridge borings is mainly in valley bottoms near streams and rivers. mean facies length and proportion. However, it is clear the silt is grossly underrepresented. The column titled “Break used for class” gives the textural percentage used to define each lithologic class in the bridge borings. Solutions to Equation 3 were obtained from statistics calculated from the discretized water- well data, grouped by the till and glaciofl u- vial stratigraphic units described earlier in the minimum thickness of data in the original on the southeast, bottom edge of the map; this paper. The proportions and mean vertical records. therefore, it was removed, and the bedrock lengths (thicknesses) were calculated for each topography was reinterpreted. facies. Clustering bias was checked using the Stratigraphic Modeling DECLUS routine in GSLIB software (Deutsch Statistical and Geostatistical Modeling of and Journel, 1998) and was found not to be an A stratigraphic 3D model was developed Facies important source of error. Structural lengths for for the study area based on the water wells the simulations were based on the mean thick- and geologic interpretation. In general, the The general modeling approach was to cre- ness of facies s. This approach differs from that study area was interpreted as containing a ate a series of 3D grid models (voxel or “brick” of Ritzi et al. (2000) and Proce et al. (2004), glacial till layer overlying a glaciofl uvial sys- models) using SISIM (using SGeMS software, where facies m was used to avoid the potential tem. Thin (<3 m) surface features apparent in v1.4; Remy et al., 2006). The key task was spec- bias in s due to incomplete penetration. In this Figure 1 were not incorporated into the strati- ifying the facies proportions and spatial struc- study area, the majority of the wells penetrate to graphic model. The top of the till layer was tures for input into the simulation algorithm. bedrock. Also, for the till layer, the thickness of defi ned by a digital elevation model (Powers Spatial structures for the models were defi ned facies m is largely controlled by the layer geom- et al., 2002). The elevation of the interface using the approach of Ritzi (2000). Typical geo- etry, which is not stationary. Facies s, within between the glaciofl uvial system and overly- statistical practice is to defi ne spatial structures the till, is a minor constituent, and hence is less ing till was determined through analysis and empirically by the calculation of an experimen- affected by thickness variations in the till sheet. interpretation of the water-well data. The data tal variogram from the data and then fi tting As in previous studies, constraining the struc- were processed initially to extract the bottom a model variogram for use in estimation and tural model in the horizontal direction proved of the fi rst recorded clay layer for each loca- simulation. However, it is well established that diffi cult. Experimental variography did not tion. This was used as the fi rst approximation variograms derived from water-well data are provide a useful model, and there was no geo- of the depth of till. An iterative process fol- unreliable (Weissmann et al., 1999; Ritzi, 2000; physical or outcrop information available. In the lowed wherein an interpolated surface was Ritzi et al., 2000), and alternative methods are absence of information on the lateral extent of created (kriging using Geostatistical Analyst, needed to model spatial structure. Experimental facies, sensitivity studies were conducted over ESRI, 2007), and each data point was evalu- variography was attempted on this data set but length-to-thickness ratios ranging from 1 to 1 to ated for potential exclusion. Wells with val- did not produce useful variograms, especially 500 to 1. A single realization was generated for ues signifi cantly above or below the probable in the horizontal direction. Accordingly, length each ratio using the same random seed number. elevation of the till/glaciofl uvial interface statistics from the well logs were converted to It was found that ratios ranging from 1 to 1 to were removed, and the surface was recalcu- structural ranges for input into SISIM (Ritzi, 100 to 1 remained faithful to the model propor- lated. In effect, the position of the interface 2000). The approach is outlined below. Firstly, tions, with the range of mean thickness of facies at unreliable wells (often too shallow due to Carle and Fogg (1996) showed that the mean s being 0.20 m for the till layer and 0.5 m for sand lenses or too deep due to over-general- facies (k) length (l) in a given direction (u) is the glaciofl uvial layer. Large length-to-thick- ized records) was interpolated from the reli- related to the derivative of the autovariogram at ness ratios (>100 to 1) decreased the propor- able values at surrounding wells. During this the origin tions and thickness of facies s. Over the studied process, fi ve wells were considered errone- range of length-to-thickness ratios, maxima in ous and removed from all subsequent model- (1) occurred at a ratio of 10 to 1 for facies s in the ing. The bottom of the glaciofl uvial system till layer, and 25 to 1 in the glaciofl uvial layer. In

was deﬁ ned by the bedrock topography map where pk is the facies proportion, and h is the the absence of reliable information on the lateral (Fig. 2), which was created mainly by hand lag or separation vector. Taking the derivative of extent of facies, these ratios were used in further contouring (Powers and Swinford, 2004). The the spherical or exponential model variograms simulation experiments. Subsequent analysis bedrock topography contours were edited to (Deutsch and Journel, 1998) at h = 0 and using was focused on the reproduction of thickness account for new unpublished data collected c = pk(1 – pk) (for a binary variable) to deﬁ ne statistics, and detailed analysis of horizontal using seismic refraction. The new study was the positive variance contribution term (c), lengths was postponed until better constraining inconsistent with a side valley that was drawn yields the equation information becomes available.

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TABLE 2. SUMMARY OF THE GRID DIMENSIONS USED IN THIS STUDY parameters. The model for spatial structure was Dim x Dim y Dim z Dim x Dim y Dim z based on the statistics generated from the well Grid Nx Ny Nz (ft) (ft) (ft) (m) (m) (m) data (Table 3) and the results of previous heu- A 150 150 780 50 50 0.5 15.24 15.24 0.15 ristic analysis (Ritzi, 2000). The facies for mod- B 150 150 780 50 50 1.0 15.24 15.24 0.30 eling and the functional form (linear, spherical, C 182 191 190 200 200 2.0 60.98 60.98 0.61 D 182 191 127 200 200 3.0 60.98 60.98 0.91 and exponential) of the variogram must be cho- E 182 191 95 200 200 4.0 60.98 60.98 1.22 sen for each stratigraphic unit. The glacioﬂ uvial Note: Nx, Ny, and Nz represent the number of cells along each axis, respectively. Columns system had a cv greater than one, so the expo- headed with Dim (dimension) give the axial lengths of each cell in both feet and meters. nential structural model was appropriate. The structural range was nearly identical between facies m and s (Table 3). The till layer was more problematic because the cv was nearly one, Conditional and unconditional simulations proportion and spatial structure of facies were and the structural ranges were not the same were conducted to explore several modeling similar. Therefore, the stratigraphic model was between the facies (the proportion of s in the issues. Several grid dimensions were used in this at least partially validated if the statistics calcu- till layer was so small that it had little practi- study and are summarized in Table 2. Uncondi- lated from the well data show contrasts between cal importance, and it was modeled mainly for tional simulations conducted on grids A and B the units. The proportion of facies s and the illustrative purposes). Facies s was chosen for

were used to explore the impact of cell thick- coeffi cient of variation (cv) are less in the till this layer because the thickness of m is known ness on the of generated facies. The dimen- layer than in the underlying glaciofl uvial system not to be constant over the domain due to the sions of these test grids were chosen to mini- (Table 3), confi rming that the model delineates geometry of the till sheet (Fig. 3). Models using mize the effect of the top and bottom bounding a contrast in facies structure. both exponential and spherical variograms were surfaces on the simulation and thickness statistics Sand and gravel deposits were found at conducted for the till layer. (Emery, 2004). Three simulations with different depth throughout nearly the entire study area The values of from the models showed seed numbers were conducted on the B grid to (Fig. 4), raising interpretive questions. In sensitivity to the thickness of the grid cells. For compare length statistics between runs with oth- particular, facies s was common below the grid A, the cells were thinner than the minimum erwise identical parameters. Finally, conditional northeast-southwest-trending Painesville end recorded thickness in the well data, and this was and unconditional simulations were run over the moraine (prominent topographic high appar- strongly refl ected in the results. For the till layer, entire domain of the well data (grids C, D, and E) ent in Fig. 3). The origin of the sand and gravel the mean and median thicknesses were too thin, with grids of reduced resolution. Facies propor- core was unknown, but determining its nature and there was a greater proportion of facies m tions and thickness distributions were generated remained important for hydrofacies modeling. (Table 4). The model for the glaciofl uvial system for all simulation runs to compare the results. The core may be an old beach ridge that was matched the proportions correctly but was also subsequently covered with till or an erosional too thin. The grid with a 1-ft interval (B) was RESULTS remnant from a larger glaciofl uvial deposit. more appropriate for comparison because the Arbitrarily, the latter interpretation was adopted minimum thickness for the model and well data Glacial Stratigraphy for this model. Facies simulations were based were equal. Accordingly, the match between the on the assumption that there was an ice proxi- models and the well data was improved. There The hypothesized stratigraphic model was mal glaciofl uvial deposit covering the study was additional, if minor, improvement when a layer of Wisconsinan till over a glaciofl uvial area that was subsequently truncated (the till/ using the exponential over the spherical model system (Fig. 3). This preliminary conceptual glaciofl uvial interface is interpreted as an ero- for the till layer. Overall, was increased and model was developed from geomorphic rela- sional surface). By this interpretation, the spa- the quantiles matched better, although they tionships apparent in surface maps and a few tial structure of facies was assumed constant were still too thin (Table 4). The model and detailed borings outside of the study area (in the throughout the glaciofl uvial layer. well histograms were of similar shape (Figs. 5 same buried valley; Venteris, 2007). Ultimately, and 6). However, histograms for the wells from the stratigraphy should be tested with addi- Preliminary Unconditioned Simulations both stratigraphic units show a larger propor- tional detailed borings and perhaps geophysical tion of middle and extreme thicknesses than the data. However, for this work, the main use of Unconditioned simulations were conducted simulation models. For all models, the standard stratigraphy was to delineate regions where the to help choose the structural model and grid deviation of thickness was much less than the well data. TABLE 3. STATISTICAL SUMMARY OF PROPORTIONS (p), THICKNESS STATISTICS Additional runs were conducted with different random seed numbers to illustrate the variability (MEAN THICKNESS ( ) AND COEFFICIENT OF VARIATION (c )), AND v in the thickness statistics between realizations. STRUCTURAL RANGES (a ) CALCULATED FROM THE WELL DATA v Most of the variation between runs with differ- Glaciofluvial layer Till layer ent seed numbers occurs at the tail end of the Facies m Facies s Facies m Facies s distribution, above the third quartile (Table 4). p 0.66 0.34 0.94 0.06 5.24 2.77 12.01 2.68 Simulations over the Full Domain

cv 1.29 1.47 0.66 0.94 Further simulation was conducted to make av spherical 2.67 2.74 1.08 3.77 models for visualization and to investigate the av exponential 5.35 5.48 2.16 7.55 effects of trimming the models to stratigraphy

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TABLE 4. SUMMARY STATISTICS ON THE THICKNESS OF FACIES S FROM THE PRELIMINARY UNCONDITIONED SIMULATIONS Grid Standard deviation Mean Minimum Quartile 1 Median Quartile 3 Maximum Proportion Glaciofluvial Well data 4.09 2.77 0.31 0.61 1.22 3.05 35.06 0.34 Glaciofluvial A 1.10 1.10 0.15 0.31 0.76 1.37 17.84 0.34 Glaciofluvial, run 1 B 1.70 1.66 0.31 0.61 0.92 2.13 24.70 0.35 Glaciofluvial, run 2 B 1.72 1.68 0.31 0.61 0.92 2.13 28.35 0.35 Glaciofluvial, run 3 B 1.69 1.65 0.31 0.61 0.92 2.13 28.35 0.34

Till Well data 2.50 2.68 0.31 0.76 1.83 4.12 15.24 0.06 Till A 0.82 0.77 0.15 0.31 0.46 0.92 10.67 0.09 Till, spherical model B 0.78 1.15 0.31 0.60 0.91 1.52 9.14 0.07 Till, run 1 B 0.90 1.27 0.31 0.61 0.91 1.83 9.45 0.06 Till, run 2 B 0.90 1.27 0.31 0.61 0.92 1.83 10.67 0.06 Till, run 3 B 0.90 1.26 0.31 0.61 0.92 1.83 10.37 0.06 Note: The exponential variogram model was used for runs one through three for the till layer.

and data conditioning on the thickness sta- earlier studies (e.g., Carle et al., 1998). How- software (Carle, 1998). The usual justifi ca- tistics. Initial attempts at modeling used the ever, the comparative analysis of histograms tions for annealing are to improve the fi t of the dimensions of grid B (extended to cover the presented here illustrated the issue in more realizations to the input parameters (propor- entire domain), but produced fi les that were too detail. The results were sensitive to the thick- tions, etc.), improve the results of groundwater large for effi cient visualization on a personal ness of the grid cells. The vertical cell size set simulations, or bring the realizations closer to computer (using EVS-Pro software (Ctech, the minimum thickness of the model distribu- the geologists’ concept of facies heterogeneity 2007)). Therefore, a coarser grid (C) was used tion, and many single cell thicknesses were (Deutsch, 2003). Alternate simulation algo- for these experiments. generated. The potential error from choosing an rithms and post-processing are beyond the Thickness statistics were relatively insensi- inappropriate vertical resolution was especially scope of this paper because there is little inde- tive to data conditioning and stratigraphic trim- apparent when it was set below that of the well pendent information outside of the thickness ming. Using a thicker grid cell (0.61 m) further data. Also, in cell-based modeling, each thick- statistics to evaluate competing models. Also, increased the mean, standard deviation, and ness for a sedimentary layer is defi ned by a the results contained confl icting information as quantile thicknesses of all runs, bringing the series of adjacent cells with like lithology. The to the quality of fi t of the SISIM models to the distributions in closer agreement with the well probability of a continuous series of facies over well data. Clearly, the mean and standard devia- data (Table 5). Trimming the realizations by the a given length decreases as cell size decreases tion of facies thickness did not match, but these stratigraphic surfaces (Figs. 7 and 8) reduced because there are more chances to interrupt the measures of center and spread are intended for the mean and maximum thickness of facies s for sequence. Mean thickness was made to match normal distributions (the distributions are not both layers, but the effect was not large. Like- the well data by progressively increasing the truly log normal; therefore, simple transforms wise, data conditioning had little effect on the thickness of the grid cells (Table 5). Doing so do not address the issue). For grid resolutions distribution of thicknesses other than forcing a improved the fi t of the average length and stan- B and C, the fi t of the overall distributions as match between maximum thicknesses between dard deviation, but degraded the fi t for all quan- measured by the quantiles seems reasonable, the model and well data. tiles except the maximum. especially when considering the quality of There are many proposed solutions to the well data. However, unconditioned SISIM DISCUSSION improving the match between the model outputs a thickness distribution of consistent input and output parameters such as simu- shape (Figs. 5 and 6), and any deviation of the That SISIM does not reproduce the length lated annealing (Deutsch and Journel, 1998) well histogram from that shape cannot be accu- statistics of the input data is well known from and the quenching step contained in TPROGS rately reproduced by SISIM alone.

TABLE 5. SUMMARY STATISTICS ON THE THICKNESS OF FACIES S FROM SIMULATIONS CONDUCTED OVER THE ENTIRE STUDY DOMAIN Data Standard Grid conditioned? deviation Mean Minimum Quartile 1 Median Quartile 3 Maximum Proportion Glaciofluvial C n 1.87 2.39 0.61 1.22 1.83 3.05 26.89 0.34 Glaciofluvial, trimmed C n 1.70 2.16 0.61 1.22 1.83 3.05 19.51 0.34 Glaciofluvial, trimmed C y 1.67 2.15 0.61 1.22 1.83 3.05 35.37 0.34 Glaciofluvial D n 2.31 2.98 0.92 0.92 2.74 3.66 36.65 0.34 Glaciofluvial E n 2.62 3.42 1.22 1.22 2.44 4.88 34.15 0.34 Glaciofluvial, 100 to 1 C y 1.95 2.08 0.61 0.61 1.22 2.44 20.12 0.37

Till C n 0.81 1.55 0.61 1.22 1.22 1.83 9.15 0.06 Till, trimmed C n 0.78 1.44 0.61 0.61 1.21 1.83 7.13 0.06 Till, trimmed C y 0.79 1.45 0.61 0.61 1.22 1.83 15.24 0.06 Till D n 1.14 2.11 0.92 0.92 1.83 2.74 11.89 0.06 Till E n 1.40 2.58 1.22 1.22 2.44 3.66 15.85 0.06 Till, 100 to 1 C y 1.43 1.65 0.61 0.61 1.22 1.83 13.42 0.07 Note: The rows labeled “Glaciofluvial, 100 to 1” and “Till, 100 to 1” represent the models based on the thickness ratio from qualitative geologic mapping.

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Figure 5. Histograms of thickness for the unconditioned SISIM model using grid B (left) and well data (right) for the glacioﬂ uvial system.

Figure 6. Histograms of thickness for the unconditioned SISIM model using grid B (left) and well data (right) for the till layer.

Geosphere, December 2007 465

Downloaded from http://pubs.geoscienceworld.org/gsa/geosphere/article-pdf/3/6/456/854355/i1553-040X-3-6-456.pdf by guest on 25 September 2021 Venteris Figure 7. 3D raster “brick-pile” model of a single SISIM realization (unconditioned), trimmed by the stratigraphic model. “brick-pile” model of a single SISIM realization 7. 3D raster Figure

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multi-model heterogeneous formations: Advances The modeling exercise illustrates the current Geostatistical simulation or other Monte Carlo in Water Resources, v. 29, p. 912–929, doi: 10.1016/ limited knowledge about the geology of the techniques provide a convenient method to j.advwatres.2005.08.002. study area and the gains in that knowledge that generate multiple equiprobable models upon Gabriel, W.J., Golden, M.L., Loomis, L.E., Steers, C.A., and Wright, P.N., 1992, Soil Survey Geographic Database can be made using water-well data. Firstly, the which to base uncertainty analyses. As in this (SSURGO) technology; revolutionizing the methods interpreted stratigraphy model of till on the gla- study, such simulations are often limited by the and philosophy for soil survey: Agronomy Abstracts, v. 84, p. 302. ciofl uvial system was very simple, but clearly lack of realistic models of the spatial structure Journel, A.G., 1983, Nonparametric estimation of spatial partitioned the data by proportion of facies. As of lithofacies, particularly the horizontal length distributions: Journal of the International Association a whole, the water-well data set provided mean- of layers. Facies studies based on detailed 3D for Mathematical Geology, v. 15, no. 3, p. 445–468, doi: 10.1007/BF01031292. ingful, if incomplete, information on glacial stra- outcrop models (as described in other papers in Ohio Department of Natural Resources Division of Water, tigraphy. Further study was needed to determine this special issue of Geosphere), close proximity 2007, Water Well Log Report: Accessed January 31, if the sand and gravels below the end moraine borings, and high-resolution geophysical data 2007, at http://www.dnr.state.oh.us/water/. Pavey, R.R., Goldthwait, R.P., Brockman, C.S., Hull, D.H., were from the same deposit as those found in are needed to create training images (Strebelle, Swinford, E.M., and Van Horn, R.G., 1999, Quaternary the buried valley. In contrast, the water-well data 2002) and geostatistical structure models to pro- Geology of Ohio: Ohio Division of Geological Survey Map M-2, scale 1:500,000. provided very limited information on lithofa- duce more realistic facies simulations for glacial Powers, D.M., Laine, J.F., and Pavey, R.R., 2002, (revised cies geometry. While it was possible to gener- sedimentary environments. 2003), Shaded elevation map of Ohio: Ohio Division of ate statistics on facies thickness, individual well Geological Survey Map MG-1, scale 1:500,000. ACKNOWLEDGMENTS Powers, D.M., and Swinford, E.M., 2004, Shaded drift records showed a wide range in quality due to thickness map of Ohio: Ohio Department of Natural lumping and splitting issues, fi ling of erroneous Resources, Division of Geological Survey, SG3, scale This work was partially supported by the Central locations, lithologies, etc. Such issues certainly 1:500,000. Great Lakes Geologic Mapping Coalition, United Proce, C.J., Ritzi, R.W., Dominic, D.F., and Dai, Z., 2004, created a bias in the length statistics, but that States Geological Survey Cooperative Agreement Modeling multiscale heterogeneity and aquifer inter- bias was not quantifi able without high-resolu- No. 04ERAG0061. Gary S. Weissmann and Robert connectivity: Ground Water, v. 42, no. 5, p. 658–670, tion, independent data. In addition, due to the W. Ritzi Jr. provided helpful reviews, which resulted doi: 10.1111/j.1745-6584.2004.tb02720.x. in signifi cant improvements to the modeling and the Remy, N., Bourcher, A., and Wu, J., 2006, S-GeMS Stanford spatial intensity and accuracy of the water-well Geostatistical Modeling Software, version 1.4: http:// manuscript. data, no information could be obtained from the sgems.sourceforge.net Ritzi, R.W., 2000, Behavior of indicator variograms and tran- well data on the lateral continuity of facies. The REFERENCES CITED sition probabilities in relation to the variance in lengths horizontal ranges could be based on the maxi- of hydrofacies: Water Resources Research, v. 36, mum thickness obtained from the sensitivity no. 11, p. 3375–3381, doi: 10.1029/2000WR900139. Bagley, C.T., 1953, Subsurface study of glacial deposits at Ritzi, R.W., Bogle, J.L., Dominic, D.F., Greer, C.B., Klohe, analysis as presented above, or from geologic Cleveland, Ohio: The Ohio Journal of Science, v. 53, C.A., Masters, R.W., Means, B.P., Reboulet, E.C., Sle- interpretation. Geostatistical analysis based on no. 2, p. 65–71. sers, A.J., and Telford, J.A., 2000, Comparing statisti- Brockman, C.S., 1998, Physiographic regions of Ohio, Ohio cal models of physical heterogeneity in buried-valley the interpreted 3D map of the area (Venteris, Department of Natural Resources, Division of Geolog- aquifers: Water Resources Research, v. 36, no. 11, 2006) suggested a length-to-thickness ratio of ical Survey, Geologic Maps of Ohio series, http://www. p. 3179–3192, doi: 10.1029/2000WR900143. 100 to 1 for these sediments. Thickness statis- dnr.state.oh.us/geosurvey/pdf/physio.pdf. Strebelle, S., 2002, Conditional simulation of complex geo- Carle, S.F., 1998, Transition probability geostatistical soft- logical structures using multiple-point statistics: Math- tics generated from this model (Table 5) were ware, version 2.0: User’s manual: Davis, California, ematical Geology, v. 34, no. 1, p. 1–21, doi: 10.1023/ generally thinner than the previous runs based University of California, Davis. A:1014009426274. on smaller ratios, but the standard deviation was Carle, S.F., and Fogg, G.E., 1996, Transition probability- Venteris, E., 2007, Qualitative and quantitative 3D modeling based indicator geostatistics: Mathematical Geology, of surfi cial materials at multiple scales: Proceedings increased closer to the target values. v. 28, no. 4, p. 453–476, doi: 10.1007/BF02083656. from Digital Mapping Techniques 2006, Columbus, Carle, S.F., Labolle, E.M., Weissmann, G.S., Van Brocklin, Ohio (in press). D., and Fogg, G.E., 1998, Conditional simulation of Weissmann, G.S., and Fogg, G.E., 1999, Multi-scale alluvial CONCLUSIONS hydrofacies architecture: A transition probability/Mar- fan heterogeneity modeled with transition probability kov approach, in Fraser, G.S., and Davis, J.M., eds., geostatistics in a sequence stratigraphic framework: Due to the quantity and quality of available Hydrogeologic Models of Sedimentary Aquifers, Journal of Hydrology, v. 226, no. 1-2, p. 48–65, doi: Concepts in Hydrogeology and Environmental Geol- 10.1016/S0022-1694(99)00160-2. data, the effective modeling of surfi cial materi- ogy No. 1: SEPM (Society for Sedimentary Geology) Weissmann, G.S., Carle, S.F., and Fogg, G.E., 1999, Three- als necessitates the collaboration of geoscien- Special Publication, p. 147–170. dimensional hydrofacies modeling based on soil sur- tists from many disciplines and perspectives. Carle, S.F., Esser, B.K., and Moran, J.E., 2006, High-reso- veys and transition probability geostatistics: Water lution simulation of basin-scale nitrate transport con- Resources Research, v. 35, no. 6, p. 1761–1770, doi: Geostatistical modeling requires a stratigraphic sidering aquifer system heterogeneity: Geosphere, v. 2, 10.1029/1999WR900048. framework to defi ne regions of like spatial p. 195–209, doi: 10.1130/GES00032.1. Weissmann, G.S., Zhang, Y., LaBolle, E.M., and Fogg, Ctech, 2007, EVS-Pro 3D modeling software: http://www. G.E., 2002, Dispersion of groundwater age in an allu- structure (stationarity). Given the variable qual- ctech.com/ vial aquifer system: Water Resources Research, v. 38, ity of water-well records and the complexity of Deutsch, C.V., 2003, Geostatistical reservoir modeling: no. 10, p. 1198, doi: 10.1029/2001WR000907. glacial sedimentary environments, stratigraphic Oxford University Press [Oxford], 384 p. White, G.W., and Totten, S.M., 1979, Glacial geology of Deutsch, C.V., and Journel, A.G., 1998, GSLIB: Geosta- Ashtabula County, Ohio: Ohio Division of Geological mapping based on water-well data and geologic tistical Software Library and User’s Guide (2nd ed.): Survey Report of Investigations No. 112, 52 p. knowledge is a viable approach. The veracity Oxford University Press [Oxford], 369 p. of such stratigraphic modeling can at least be Emery, X., 2004, Properties and limitations of sequential indicator simulation: Stochastic Environmental partially checked through statistical analysis Research and Risk Assessment, v. 18, p. 414–424. of the well data. However, public water-well ESRI, 2007, ArcGIS and Geostatistical Analyst software: data are generally not of suffi cient resolution to http://www.esri.com/. MANUSCRIPT RECEIVED 5 FEBRUARY 2007 Feyen, L., and Caers, J., 2006, Quantifying geologi- REVISED MANUSCRIPT RECEIVED 24 MAY 2007 allow interpretive, explicit mapping of facies. cal uncertainty for fl ow and transport modeling in MANUSCRIPT ACCEPTED 22 JULY 2007

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