USGS

Digital Mapping Techniques '99 -- Workshop Proceedings
U.S. Geological Survey Open-File Report 99-386

The Geometry of a Geologic Map Database

By Ronald R. Wahl

U.S. Geological Survey
Box 25046
Denver Federal Center, MS 913
Denver, CO 80225
Telephone: (303) 236-1320
Fax: (303) 236-0214
e-mail: rwahl@usgs.gov

INTRODUCTION

One objective of the Geologic Mapping Act (GMA) of 1992 (re-authorized in 1997) calls for the establishment of standards for digital geologic mapping both for paper plotting and for a computer-readable database. One response of the U.S. Geological Survey (USGS) and the National Cooperative Geologic Mapping Program (NCGMP) to Office of Management and Budget Circular A16, Executive Order 12096 and the GMA, will be to establish a national digital geologic map database for use at a scale of 1:100,000. This work is to be conducted under the National Geologic Map Database Project (NGMDB) of the NCGMP.

In August 1996, in St. Louis, Missouri, the Digital Geologic Mapping Committee of the Association of American State Geologists (AASG) and NGMDB of the USGS, formed several working groups to devise standards and guidelines for various concepts that make up a geologic map in digital form. Information about these working groups is available at the NGMDB project web site, http://ncgmp.usgs.gov/ngmdbproject/. One element of the geologic map database standards effort that has had little attention is map geometry.

Figure 1

Figure 1. The Greater Yellowstone Area.

The NGMDB needs to test the concept of a national geologic map database at a scale of 1:100,000. The Greater Yellowstone Area (GYA) is a region in which such a geologic database, built as a proof of concept, would add much to the understanding of the GYA ecosystem. The GYA encompasses an area five degrees in longitude (108 West to 113 West) and four degrees in latitude (42 North to 46 North). Forty 30' by 60' 1:100,000-scale quadrangle maps cover the GYA (figure 1). I anticipate that this pilot database will be used to supply geologic data for the GYA Science Initiative, a new part of the Integrated Natural Resources Science program (INATURES) of the USGS, which has become a part of the Department of Interior's Place-Based Science Program.

The NGMDB has the opportunity to test the results of its standards efforts on a database that is needed in the region by various interest groups, and that when integrated with other geospatial data sets of the GYA will prove to be vital for ecosystem management there. However, to insure the continued usefulness of the database, the geologic data in the database must be updatable and the GIS system must be able to keep careful track of the revisions as they are made. In addition, digital map databases from the state geological surveys of Idaho, Montana, and Wyoming will be integrated into the database. Each state survey will most likely have different ways of representing the geometry of their products.

Figure 2. The Cody, Wyoming 1:100,000-scale geologic map.
[To view larger image, click on thumbnail.]

To support the GYA database effort, I am converting unpublished "legacy" geologic map materials of W.G. Pierce for the geologic map of the Cody, Wyoming 2-degree sheet that lies on the east side of Yellowstone National Park in the northeast corner of the GYA (figure 1). These materials were originally compiled at a scale of 1:125,000. The density of line work and the level of geologic detail allow the capture of the data at a scale of 1:100,000. In particular, I am working with the unpublished Cody, Wyoming 1:100,000-scale quadrangle, which is in the northwestern quadrant of the Cody 2-degree map.

The Cody, WY 1:100,000-scale geologic map data exists as a film positive that was compiled by W.G. Pierce (1997) for the geologic map of the Cody 2-degree quadrangle (figure 2). Time constraints preclude the use of the seven published 15' geologic quadrangle maps as the primary source materials for the 1:100,000-scale map. The three other 1:100,000-scale pieces of the Cody 2-degree sheet are also unpublished and exist only as film positives. Large-scale source materials for these maps have yet to be located.

GEOMETRY AND THE DIGITAL GEOLOGIC MAP

Problems concerning the capture of the geometry of a geologic map database have arisen as I continue to compile the Cody 1:100,000-scale geologic map. The problems fall into three general categories. They are:

  1. Capture of the "art" and at times subtle geologic concepts that the original compiler wished to portray.

  2. Map-capture resolution and positional accuracy, and the relationship to National Map Accuracy Standards (USBB, 1947) and National Map Revision Standards (USGS-NMD, 1998).

  3. Structure of the digital geologic map data and the specifics of a data exchange or transfer format to allow users (within and outside the GYA) with a number of different viewers and GIS tools to utilize the data easily.

It is clear, that although geospatial data can be transferred using standard transfer formats, the representation of geospatial objects such as polygons and lines contained in a digital geologic map database is not standardized.

CURRENT STATUS OF ACCURACY STANDARDS

As of this writing no report has been released by anyone including the AASG/USGS standards groups mentioned above, proposing any standards for map geometry including standards for geologic map accuracy, or map resolution. General policies for digital geologic map products have been issued inside the USGS, but outside the USGS only proposed guidelines exist for groups producing digital geologic map data (see Soller, Duncan, Ellis, Giglierano, and Hess, this volume). These guidelines do not mention map geometry. The OpenGIS consortium (OpenGIS, 1999), in their abstract series of documents, has published a framework about which map geometry and accuracy standards for the digital representation of geologic maps may be formed. In addition, the National Mapping Division (NMD) of the USGS published a document which details standards for updating already published 1:24,000-scale topographic maps (USGS-NMD, 1998; Lemen, this volume). For now, the National Map Accuracy Standard (USBB, 1947) and the update document might be used to determine the accuracy with which geologic objects can be placed on a map until a more appropriate standard is developed.

Figure 3

Figure 3. Linework near Pat O¹Hara Mountain, southern part of the Cody, WY 1:100,000-scale map.

Problem 1: The capture of the geologic map "art" and concepts

Since the aforementioned 1996 meeting, I have expressed a concern that the "art" of a geologic map should be preserved as much as possible when the map is converted to a GIS database. The following example shows one of the connections between geologic "art" and concepts. Some 1:62,500-scale published geologic data near Pat O'Hara Mountain in the southeastern part of the Cody, WY 1:100,000-scale quadrangle, shows a number of older rocks units concealed by surficial materials. When these data were compiled on the 1:100,000-scale map, some but not all of these surficial deposits were omitted (figure 3). I think that Pierce eliminated these surficial units because he wanted to show the relationships among the older rocks and associated structures clearly. Maybe a future compiler of the Cody 1:100,000-scale map might want to show these surficial units. In doing so, however, the compiler would again have to answer the question: "What are the important geologic concepts that I am trying to portray and how might this best be done?". My objective in converting Pierce's original map to a digital form is to faithfully reproduce what Pierce recorded on his original map.

In studying the data from this locale on the Cody quadrangle, I conclude that there are no standard ways to represent linear data with characteristics more subtle than the primary attributes of "contact" or "fault". An implicit assumption is made for rock units older (or different) from Quaternary alluvium, that lines attributed as contacts show the top of one formation and the bottom of another. This information is indirectly found in age attributes in the data model. But what happens if the ages that are given for two formations are both "lower Cretaceous" and they are in contact in one place but not in another on the same map? I suggest that lines labeled as contacts be labeled in addition with other information that would add geologic and geometric attributes such as "unit top" or "unit bottom".

Another related question has arisen while capturing the Cody geology. The lines were automatically generated from a cleaned-up raster scan file by LT4X, a raster-to-vector conversion package used currently by the USGS-NMD. To reduce the angularity of such lines, the final vector data set was smoothed using B-splines. The result was that, after the import into Arc/Info, the lines representing contacts, faults, or dikes that had shown the slightest "wiggle" in them as raster lines had too many vertices. However, at map scale, the lines look "good" or smooth.

I am experimenting with the "GENERALIZE" and "SPLINE" commands in Arc/Info. I use the "GENERALIZE" command to eliminate the extra vertices in faults and dikes; and the "SPLINE" command with an appropriate value for the grain tolerance along with the "GENERALIZE" command with the "BENDSIMPLIFY" option to eliminate extraneous vertices in contacts. I am also experimenting with values for the "line simplification distance" option and the grain tolerance. Careful use of the "GENERALIZE" command and the "SPLINE" command should produce smooth contact lines and straight faults and dikes that matches the original linework of the author.

Lastly, in some places, rock units that were mapped separately on the 15' geologic source maps are combined when the outcrops of individual units are too small to be seen at 1:100,000. I have left them as Pierce compiled them. I have done this so that the "art", which is only partially map esthetics, and his geologic concepts would be kept intact.

Figure 4

Figure 4. Very short lines shown over original raster scan.

Problem 2: Map resolution and digital geology

The use of an autovectorizer such as LT4X to convert raster scans of map data to a vector format can introduce extraneous lines as vectors. One problem occurs at line intersections. Line intersections are not always "clean" as a raster scan. As a result, Very Short Lines (VSL), lines less than 50 meters in length (at a scale of 1:100,000) are inserted at some intersections, especially if two lines as pixels meet at a shallow angle (figure 4a). However, line intersections are not the only case where VSLs are found. They also occur in places where line intersections as interpreted from the scan are close together. When drawn on a map and then scanned, lines have an actual width that lines as vectors do not. In order to check for all VSLs, each line that was 50 meters or less in length was selected and displayed on a 1:100,000-scale plot of the line data. I then had to choose to delete the VSL or leave it in no matter what its origin was and perhaps even add to its length so that a later check would not select this line (figure 4b). This latter choice might allow a fault to traverse an area very close to other line intersections without intersecting nearby contacts at nodes and thereby change a geologic interpretation.

The choice of 50 meters for a VSL was in origin a choice based on experience. I have learned since that the NMAS (USBB, 1947) document specifies that 90% of all objects shall be within 1/50th of an inch of the true position when placing objects on a map at a scale smaller than 1:20,000. This corresponds to 50.8 meters at a scale of 1:100,000. A point of confusion may arise because USGS-NMD uses similar terms in the Federal Geographic Data Committee (FGDC, 1998) metadata standard as follows:

  1. Resolution (abscissa and ordinate): means the resolution of the digitizing or scanning device. Since NMD uses digitizers and scanners that have a resolution of 0.001 inches, NMD reports the resolution for 1:100,000-scale DLG data as 2.54 meters. This is not the same as:

  2. Positional accuracy: NMD uses NMAS (USBB, 1947).

In addition, the Geography Department at the University of California at Santa Barbara (UCSB) teaches a concept called "map resolution" in their GIS classes. UCSB defines map resolution to be linear distance below which objects cannot be accurately located relative to other objects on a map of a given scale. The rule of thumb taught to UCSB students is as follows:

(Map scale denominator) / 2*1000 = map resolution, in meters.

Then, map resolution would be 50 meters for a 1:100,000-scale map, and 12 meters for a 1:24,000-scale map. More recently, NMD states in the map revision document (USGS-NMD, 1998) that locations of revisions to preexisting maps especially from aerial photography may be in error by as much as 22.2 meters (forty feet) of its actual position on a 1:24,000-scale map. If this is scaled for a 1:100,000-scale map, this positional inaccuracy might be as large as 88.8 meters. Moreover, one might argue that the digital geologic map layer is a revision or an addition to a preexisting map, the topographic map. In this case, the accuracy with which digital geology can be located on 1:100,000-scale topographic base maps may be on the order of 100 meters.

The understanding or lack thereof about these foregoing concepts in this section by the geologic mapping community has great consequences for digital geologic map compilation and its subsequent use as a thematic map layer.

Problem 3: The transfer of digital geologic geometry

The compilation of lines and polygons representing the geology of the Cody, WY 1:100,000-scale map will be done in one layer or coverage. There are advantages to this method of compilation. Lines that have multiple attributes both as linear features and polygon boundaries can be easily edited and updated. Unfortunately, this is not the case for point data. While my study of the features on the Cody materials shows no geologic features to symbolize as points, other 1:100,000-scale geologic maps include such features.

Mappers that I know usually delete rock outcrops that show as a point unless such features are a topographically or geologically important feature. They then "cartoon in" a line or polygon to represent these features. However, Reynolds (1971) used small triangles to indicate formation outcrops that were too small to show on a 1:24,000-scale map. The locations of these outcrops were important data that show the reason that inferred unit contacts were drawn as shown on the map. It is not possible with most GIS systems to use point data formats to represent spatial features in a layer with polygon or line data. For example, any attempt to include data points in an Arc/Info coverage that contains polygon and line data results in problems if one issues a "BUILD" or "CLEAN" command. All of the data points then become label points, and the effect of these commands cannot be undone.

Digital geologic map analysts prefer polygon and line data in the same coverage while working in Arc/Info. However, a "casual" user of ArcView who imports such a map coverage will be surprised to learn that strictly line information may be left behind. In ArcView, line data and polygon data cannot exist in the same file. Other GIS systems do not allow attribution of polygon boundaries with more that one attribute. A line that is a polygon boundary cannot also be a fault in these cases.

The preceding discussion becomes more complex when one looks at existing and proposed standards for the simple geometric terms: polygon and line. The definitions of these terms differ among software vendors and standards organizations. The interested reader can look at some of the various standards listed below:

  1. OpenGIS: http://www.opengis.org/techno/specs.htm

  2. SDTS: http://mcmcweb.er.usgs.gov/sdts/

  3. SAIF: http://www.elp.gov.bc.ca/~srmb/saif32/

A possible solution to these problems comes first from asking the question: What type of spatial data geometric objects do modern GIS systems handle best? In my opinion, these systems handle polygons, of whatever type, best. Then notice that USGS-NMD publishes point data in DLG files by including points as lines composed of two vertices that lie on top of one another. These two ideas lead to a further idea that would allow the representation of both point and linear features as polygons.

Figure 5

Figure 5. Point and line objects captured as polygons.

To represent points as polygons, image a circle whose radius is twice the grain tolerance (in Arc/Info terms) (figure 5a). The circumference could be attributed as a "scratch" line, which means that the circumference of the circle would not be drawn. Marker symbols then could use the label point at the center to symbolize an attribute of the point. Circles of the recommended size would have little effect on the measured area of a containing polygon and would not be seen unless the circumference was drawn. I would call such a structure a "dot".

Extending the idea to two dimensions (a line), imagine a linear feature that is enclosed by a "flexible" rectangle whose width would be four times the grain tolerance with the line representing the linear feature running down the center of the rectangle (figure 5b). This would make two polygons, one on either side of the central line that could be labeled "right" and "left" to show the direction that the line should be traversed. I would call this construct a "wire". Problems would arise with the implementation of such constructs, but they would allow point and linear features to be carried in the same coverage in all GIS systems. A wire would allow a linear feature to be clipped and still keep the directional information intact. Linear feature decoration would be applied to the central line without interruption. The perimeter of the wire could be a scratch boundary when necessary. Unfortunately the "Dynamic Segmentation" feature of Arc/Info that would perform most of the same functions is proprietary and does not directly allow an import into other GIS systems.

The wire construct would be of great value in the geologic map database of the GYA, because there are five different forms that dikes are recorded on geologic maps here (I am including sills in this discussion). They are:

  1. Dikes that have a width that can be shown in true size on the map.

  2. Dikes that are too narrow to show the actual width, but use a polygon form to keep the geometry of the dike and its relation to other rock outcrops and structures.

  3. Dikes as lines. A line may represent more than one dike.

  4. Dikes that are too numerous and too small to show individually, but the map compiler wants to show the dike pattern directions and concentration.

  5. Dikes that are too numerous and too small to show individually and even the pattern of the dikes cannot be seen, and the map compiler wants to show the presence of dikes.

The wire construct would allow the geometric relations of linear features like dikes and sills of the first three types to be kept in the geometry. The fourth and fifth dike types can at present best be shown as overlay polygons in another coverage. The number of dikes on the Cody 1:100,000-scale map alone discourages the recording of individual geometric relations in an attribute relations table. Such relationships might be more easily recorded in a form that is useable in a digital manner as a part of the spatial geometry of the coverage.

Figure 6

Figure 6. Three-tiered data delivery, with their Applications Programming Interfaces (APIs).

In addition, any solution to the problem of representing spatial two-dimensional data in one coverage will have to fit into a modern storage system that would allow multiple viewers and GIS systems to use such a database. It is becoming clear that this will be an environment that will be a multi-tiered storage and retrieval geospatial data system. Most of the proposed systems involve three major tiers of software. Figure 6 show the OpenGIS approach to the distribution of GIS data. They are:

  1. User software -- Viewers, editing, and analysis tools.

  2. GIS system software -- Arc/Info, AutoDesk Map, Intergraph, SmallWorld

  3. Relational database with SQL -- Oracle, Xybase, Informix

Translating software may be necessary in between each of the three tiers, using the main software systems application programming interfaces (APIs) shown in figure 6, to allow data to move smoothly from one of the tiers to another. With the advent of such systems and the likelihood of GIS data holders moving to this kind of a data archive, the spatial data produced by the geologic community must be in such a form that it will readily be useful in such an environment. This form includes an understanding of the geometric aspects of their products.

CONCLUSIONS

I have digitized and attributed the Cody, WY 1:100,000-scale materials to retain the art, esthetics, and geologic concepts recorded by the map author. I am producing a map database that when rendered as a map will have pleasing line work, and yet be useful to geoscience analysts. The cleanup and attribution of the map data will take into account the resolution of the digitizing method while capturing the source data using map accuracy standards, and the concept of map resolution as presented by UCSB as guides. In addition, digital map files for this product will be furnished in a sufficient number of formats to insure ease of use in a number of common viewers and GIS systems. The attribution of the map and the database follows the NGMDB data model preliminary standards version 4.3 using the "Curly tool" (Raines and Hastings, 1999) for the data entry and export into Arc/Info. The proposed North American data model standard for geologic maps is available at: http://geology.usgs.gov/dm/.

The future of the geologic database may be with Arc/Info version 8 on Windows NT systems using object models or with GIS systems like SmallWorld or even by the use of polygons to represent all geologic information in current GIS systems. A continuing study of current spatial geometry standards by one of the current AASG/USGS working groups or a new working group is needed to see how these spatial geometries fit the needs of digital geologic maps. Clearly much remains to be done to standardize digital geologic map geometry.

REFERENCES CITED

Federal Geographic Data Committee (FGDC), 1998, Content standard for digital geospatial metadata (CSDGM): http://www.fgdc.gov/metadata/contstan.html.

OpenGIS, 1999, http://www.opengis.org/techo/presentations/overview/side063.htm.

OpenGIS, 1998, http://www.opengis.org/techno/specs.htm (click on Topic 1).

Pierce, W.G., 1997, Geologic map of the Cody 1-degree by 2-degree quadrangle, northwestern Wyoming: U.S. Geological Survey Miscellaneous Investigations I-2500, scale 1:250,000.

Reynolds, Mitchell W., 1971, Geologic map of the Bairoil quadrangle, Sweetwater and Carbon counties, Wyoming: U.S. Geological Survey GQ-913, scale 1:24,000.

Raines, Gary L., and Hastings, Jordan T., 1999, Curly: Unpublished software tool produced under the auspices of the AASG/USGS geologic map data model working group, available at: http://geology.usgs.gov/dm/tools/Curly/.

US Bureau of the Budget (USBB), 1947, National Map Accuracy Standards: http://rockyweb.cr.usgs.gov/nmpstds/nmas.html.

USGS-NMD, 1998, Standards for revised primary series quadrangle maps (Draft for implementation): http://rockyweb.cr.usgs.gov/nmpstds/qmapstds.html.

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