4 Building a Framework

The geometric framework is the foundation for static modeling. This orients the contaminated site in three dimensions relative to the defining boreholes.

4.1 Maps and Cross Sections

For many years, maps and cross sections formed the entire framework for static modeling. With modern computer software, this is now done in immersive 3D environments that facilitate spatial conceptualization. However, maps and cross sections still underpin the 3D interpretations in many ways. For this example, traditional maps and cross sections are used for the interpretation.

The Test Site is approximately 9 hectares in size and has been characterized by 14 boreholes. The boreholes are arranged in two roughly perpendicular transects and were drilled through unconsolidated sediments and terminated at the top of bedrock. The ground surface is between 70-73 meters above sea level, and slopes towards the south. Bedrock was encountered at depths ranging from 40 to 70 meters below ground surface. The geometric details used to construct the interpretation framework are shown in Figure 1 where the two cross sections have been arranged immediately next to the map, with everything drawn to scale.

The interpretation framework
Figure 1 – The interpretation framework (Brandenburg, 2020).

4.2 Surfaces

Geologic interpretation involves dividing the subsurface into layers. Stratigraphers are interested in horizons and zones representing specific geological times, structural geologists try to identify surfaces that were originally horizontal, and geophysicists look for layers with contrasting acoustic rock properties. No matter the basis, constructing three-dimensional surfaces is an essential part of subsurface geological modeling. The most robust way to do this is to contour the data defining the surface of interest, creating structural contours: maps with lines of equal elevation defining the geologic surface of interest. Structural contour maps are analogous to topographic contour maps.

Contouring by hand (Figure 2) instead of relying on a computer algorithm has the benefit of incorporating human understanding of typical geologic characteristics, whereas software does not have the benefit of common sense in areas of sparse data. Hand-contoured maps are useful as quality control on contours generated using computer software, particularly for surfaces that are discontinuous because of faulting.

Photo showing drawing structural contours by hand
Figure 2 – Drawing structural contours by hand is a reliable method for geologic interpretation (Brandenburg, 2020).

At the Test Site, detailed lithological logs were generated for each borehole using a combination of samples collected during drilling and those collected by borehole sensing devices (Figure 3). Here, lithological logs were generated using a Cone Penetrometer Test (CPT): a method of directly sensing changes in the mechanical properties of the unconsolidated materials during drilling. CPT is commonly employed for environmental investigations and has the benefit of producing logs in discrete intervals rather than a continuous curve. For the Test Site, the discrete lithological logs differentiate between bedrock and six classes of clay, silt, sand, and gravel.

Discrete lithological logs
Figure 3 – Discrete lithological logs at the Test Site. The surface contours show the elevation of the ground surface above sea level (Brandenburg, 2020).

Analysis of the logs reveals fining upward sediments thinning over a bedrock high. The key surfaces identified are the top of the bedrock, and a laterally continuous clay separating the coarser strata from shallower silts and clays. Based on slightly artesian conditions observed when installing the monitoring wells, the clay layer behaves as a leaky aquitard. This is mapped as stratigraphic horizon H01 as shown in Figure 4. Based on familiarity with similar sites in the region, the horizon is mapped as a roughly symmetrical anticline.

Stratigraphic Horizon H01
Figure 4 – Stratigraphic Horizon H01. The surface contours show the elevation of stratigraphic horizon H01 above sea level (Brandenburg, 2020).

The bedrock in this location is known to be faulted by northeast-southwest trending normal faults. The scarp was identified by a coarse-grained unit present at the base of borehole W-04 but not observed in other wells. The stratigraphic interval thickness between H01 and Bedrock is thicker in wells W-04, CPT–7 and W-02 compared to the thickness in wells CPT-6, CPT-5 and W-05. This indicates that the fault is a growth fault that most likely does not reach the H01 level. This results in the need for an offset in the bedrock surface in the contour map shown in Figure 5.

This type of small buried fault scarp is common, particularly in tectonically active areas such as the Western United States. Interpretation of faults in boreholes is another rich topic beyond the scope of this book. At the Test Site, the fault is important in that the sandy section is thicker and coarser on the downthrown side of the fault. If this feature were important to the project (e.g., if there was DNAPL contamination), geophysical methods that are sensitive to the depth of the sediment/bedrock interface could be employed.

The structured surface defining the top of bedrock
Figure 5 – The structured surface defining the top of bedrock. The surface contours show the elevation of the top of bedrock above sea level. Contours are discontinuous across the fault (Brandenburg, 2020, gw-project.org)

In the petroleum industry, static models are focused on the portion of the reservoir with mobile fluids. In this Test Site example, the section of interest is the coarse strata between the top of bedrock and H01. In oil and gas appraisal, the volume of rock bound between those surfaces would be referred to as the reservoir. Here, it is the aquifer. In some groundwater projects the nature of the fine-grained material is important in order to characterize their ability to store or release water, or their chemistry and potential for transferring chemical constituents via diffusion.

4.3 Gridding

Next, the surfaces defined along the cross-sections are extended using an interpolation technique (referred to as gridding) in order to define a two-dimensional plan view of their elevation. This provides an elevation for each surface of interest at regular grid intervals across the entire site and is needed for three-dimensional simulations. The simplest grid-construction method is to use point observations like the elevation of a stratum in particular wells as direct input to gridding algorithms, which can be done in commercial programs such as EVS or Surfer. These programs are primarily intended for data visualization but can be also be used to prepare gridded surfaces for models.

The quality of input data is very important to this process. The ideal dataset contains points that are evenly spaced, cover the entire area that will be gridded, and have been reviewed for inconsistencies and validated. Given such a dataset, most algorithms will produce the same gridded surface. Use of sparse, irregularly spaced and internally inconsistent data is a major source of error in geologic modeling. The output of different gridding algorithms can vary drastically in the response to inconsistent data and data outliers. Some common gridding artifacts are bull’s eyes around single data points and surfaces that extend significantly beyond the limits of the original data (See Box 1 for examples).

In situations with sparse or irregular data, a systematic and ideally geology-based method is required to guide the gridding algorithm in this “white space” between observations. Software available for this type of 3D geologic modeling, for example Visual MODFLOW Flex and RockWorks. For the Test Site, the relatively simple method of digitizing hand-drawn contours to create additional data points for the gridding algorithm is used since it requires no special software (Figure 6).

Gridding algorithms need guidance in areas with sparse data.
Figure 6 – Gridding algorithms need guidance in areas with sparse data. Here, hand-drawn contours are digitized to provide data to the gridding algorithm (Brandenburg, 2020).

In the Test Site model, the hand contoured data were digitized then gridded with 20 by 20 grid node discretization (grid cells are approximately 15 meters by 15 meters). This ‘20×20 grid’ is used for calculations throughout the rest of the book.

Gridded surfaces for top bedrock and H01
Figure 7 – Gridded surfaces for top bedrock (left) and H01 (right). Each square is an interpolated value of the elevation of the surface with its magnitude indicated by the color of the square. Plotted with the Open Source Generic Mapping Tools (GMT) (Brandenburg, 2020).


Geologic Frameworks for Groundwater Flow Models Copyright © 2020 by J.P. Brandenburg. All Rights Reserved.