Xmap8: Three-Dimensional GIS for Geology and Geophysics

Jonathan M. Lees
Dept. Geology and Geophysics
Yale University, New Haven CT 06520-8109
(accepted for publication SRL, May, 1995)

INTRODUCTION

Manipulation and interactive exploration of a variety of spatial information is now commonplace in most computational environments where geology and geophysics are integrated. Sophisticated Geographical Information Systems (GIS) for arranging two- dimensional (2-D) overlays to portray quantitative relationships of spatial information come in the form of commercial products, such as ArcInfo (Environmental Systems Research Institute, 1993). Simpler programs for mapping and displaying digital images, such as GMT (Smith and Wessel, 1990; Wessel and Smith, 1991) are now used extensively in the academic community. One aspect that is lacking in most commercial approaches to GIS is the incorporation of a third (or forth) dimension. Other software exists to manipulate three- dimensional objects and raster images(AVS or IDL for example), although these are often expensive and so general that they require a significant learning period to be useful. Geographic information is by its nature two-dimensional (2-D). Usually information is stored in terms of a location on a map, along with attributes associated with each object. Most GIS systems allow users to store and manipulate points, 2-D objects, and 2-D raster images. A typical GIS software package allows users to plot various data sets overlaying each other, performing statistical analysis of different combinations of objects and combining data to form new objects, among other functions. Demographers and geographers find 2-D GIS systems more than adequate to handle many problems dealing with distributions over 2-D regions. For geologists and geophysicists, however, the restriction imposed by the inherent two-dimensionality of common GIS systems is severe. As earth scientists, we typically deal with data that has three spatial coordinates, and sometimes a fourth time coordinate. For example, seismologists studying earthquake hypocenter distributions in space and time, need a platform that integrates the power of a GIS approach in four-dimensions. Seismic three-dimensional modeling is now common in the form of 3-D velocity analysis (seismic tomography). The 3-D field is an extension of 2-D raster images to multidimensional raster grids (hyper-slabs). How do 3-D velocity fields relate to the three dimensional distribution of seismicity? How do Bouguer gravity anomalies distribute relative to the distribution of earthquakes, surface geology, topography and 3-D raster grids describing subsurface structures? Examples from my own work include studying the relationship of seismicity to the 3-D distribution of seismic velocity anomalies along the San Andreas Fault (Lees, 1990; Lees and Malin, 1990; Lees and Nicholson, 1993; Nicholson and Lees, 1992) and delineation of a possible magma system at Mt. St. Helens (Lees, 1992; Lees and Crosson, 1989) . While traditional 2-D GIS systems handle the plotting of geologic maps quite well, they are deficient if subsurface geologic information is available, such as from bore-holes well-logs or seismic reflection horizons. What geophysicists need is a simple interactive platform to examine, query, and manipulate various data sets in the 3-D context.

The "interactive" aspect of a GIS system is crucial to its value as a research tool. Interactive analysis has a two-fold meaning: 1) the user should be able to choose, during program execution, which data are displayed, and 2) during visual exploration of the 3-D data, the user needs access to information regarding the geographic location and attributes of selected objects. Both of these operations should be easy, i.e. should require no more than a menu selection, a point-and-click, or a simple dialogue response to the GIS program. We need to be able to explore our data in ways that allow us to simultaneously "see" all the data and at the same time not be overwhelmed by the shear volume of information. If we are able to interactively select and change displayed information we will not have to anticipate, a priori, what parts of our data are most revealing. This approach provides an element of serendipity in data exploration which I hold to be essential for scientific discovery. Furthermore, I anticipate that in the future, earth scientists will publish 3-D data sets along with programs similar to that presented here which allow readers to interact with data so they may verify conclusions drawn by authors without being restricted to the limited presentation provided by traditional print journals. In this paper I present an introduction to a new program, Xmap8, for accomplishing some of the rudimentary data manipulations required for 3-D GIS. An example of a fairly complex GIS type figure produced by Xmap8, involving a number of different types of data, is illustrated in Figure 1 (cover figure). As a seismologist, I have directed the program at problems which earthquake seismologists or structural geologists might approach. In this figure a combination of geologic information is combined with seismological data, producing a very information packed display. Using Xmap8 one can turn on (or off) any one of several overlays to reduce the density of information, allowing subtle features, or combinations of features, to reveal themselves. Other data such as potential field maps, tomographic images of seismic velocity, or station P-delay times could be easily added to this data set and manipulated with Xmap8.

BACKGROUND

Three-dimensional GIS works slightly differently than traditional two-dimensional GIS systems. The 2-D systems typically work with a set of 2-D overlays which are draped over each other forming a single image such as figure 1. Users can manipulate images and query a data-base about specific objects being displayed to understand their relationships. In 3-D there may be several layers of data to be analyzed simultaneously and retrievable by interactive queries. Since we can only view the data as 2-D projections on a page or computer screen, examining 3-D relationships are difficult unless one has the means to take arbitrary slices through sections of data space.

To illustrate some of the details of Xmap8 I start by considering the kinds of objects one needs to solve interdisciplinary, 3-D problems in geology and geophysics. As in 2-D analysis, one starts with a surface base map consisting of points, lines, and filled polygons. The base map typically includes political boundaries, geographic indicators, faults traces, surface geologic units, volcanic vents etc. These are stored in an ASCII data base (as are all Xmap8 data) which contains attributes associated with each map element indicating location, name, color or other identifying features defined by the user. Next, three-dimensional information may be added as points, lines, surfaces, and layered raster images in a 3-D coordinate system. Because Xmap8 was designed initially for seismological applications, point data in the form of seismic stations and earthquake hypocenters are treated as special separate cases of generic 3-D point data. Three dimensional line data comes in many guises, for example: geothermal or oil field lithologic information along deviated bore-holes, fields of vectors representing flow, line drawings outlining features of a geologic interpretation, or lines following a seismic horizon on a reflection/refraction line. A fault plane may be described as a surface or combination of surfaces. In Xmap8, 3-D structures are stored as sets of planar polygons (wire-frame structures), although they do not have to be contiguous, so that torn faults or subduction slabs can be represented. The final set of objects needed for 3-D GIS are 2-D and 3-D raster images. These can be imported using several standard image formats, such as netCDF. A contouring package is included which can take irregularly spaced 2-D data, perform gridding and draw contours of the surface over the base map (Smith and Wessel, 1990; Wessel and Smith, 1991) .

PROGRAM OPERATIONS

The "gestalt" of Xmap8 for 3-D GIS generally runs like this: The program accepts, either on the command line or via menu driven dialogue boxes, names of files containing geographic objects and other parameters which describe the data base. The main window is a map view showing objects projected on the horizontal surface. If a 3-D raster is included (Figure 1), one can scroll through the model (in depth) layer by layer. The unique aspect of Xmap8 is that from the map view one can define a cross section (with arbitrary dip and width) slicing through all the 3-D objects in the database. An example is provided in Figure 2, as a cross section through Mount St. Helens. This means we can observe, in depth, the spatial relationship between hypocenter distributions, fault planes, geologic wire-frame models, tomographic images, bore-hole data, etc., with a simple point-and-drag mouse operation. Numerous cross sections can be viewed simultaneously along with map a map view. Furthermore, since information is stored in a (primitive) data base, the user has interactive access to specific features. For example, one can lasso (in map or cross section view) a subset of hypocenters to see their detailed parameters, or store them later for further analysis, or one can click on a location and find out what the seismic velocity is from the raster image. In cross section view, contour data can be projected along with surface geologic features, deviated bore-hole information and wire-frame structures. In addition to the generic objects described above, some unique facilities make Xmap8 particularly useful for geophysicists. Special attention has been paid to the plotting of focal mechanisms. Several choices for plotting fault plane solutions are provided including strike-dip of fault plane, P and/or T-axes, and fault plane trace or traditional beach balls. Since the choice of a fault plane may be ambiguous, the program allows one to switch designated fault and auxiliary planes. The ability to quickly, and intelligently, sort through a large data set allows researchers to define details of smaller, secondary faulting associated with large events like Joshua Tree-Landers.

Spinning facilities (rotation of objects about arbitrary axes) are currently available in many data management, statistical, and CAD programs. Xmap8 has a spin module, optimized to provide specific information with which geologists are concerned: the final strike and dip of a particular view, after numerous rotations about arbitrary axes. Fault planes of aligned seismicity can be determined quickly and quantitatively. Figure 3 is a view of the seismicity under Mount St. Helens from the northwest above ground looking to the southeast. The 3-D wire-frame model of a possible stoping region above a proposed magma chamber was rotated appropriately. Events are plotted such that their size is proportional to the distance away from the plane of view.

Xmap8 has a number of other handy features and as the need becomes apparent yet more will be added. For example, viewing earthquake hypocenters plotted in animated time sequence on a base map or cross section may be useful and can now be done. Time intervals between events are used to simulate true time sequences of aftershock activity. There is a special module for handling bore-hole lithology or well log data including apparent dip from dip-meter data. Labels and legends can be placed on views and PostScript hardcopy output can be made of any view.

CONCLUSION

Besides the personal data exploring capabilities of GIS, programs such as Xmap8 can provide new capabilities to exchange complex data sets in a simple format for scientific discussion. I imagine future electronic publication of results relating three dimensional distribution of earthquake hypocenters, gravity, geology, 3-D tomographic inversions, and seismic reflection/refraction lines will be common place. If such data are published in a standardized format, programs such as Xmap8 can be used to view and interact with data in 3-D. Compared to limited, 2-D views in paper publications, prepared by authors not anticipating the importance of different viewing angles, the value of interactive programs like Xmap8 is obvious. Readers of such "electronic" publications will be able to examine, thoroughly, claims of spatial relationships made by authors.

Xmap8, its documentation and sample data sets are available via FTP over the Internet, at milne.geology.yale.edu (130.132.22.24) in directory pub/Xmap8. A summary of this article, the figures published here, a full reference manual, and other details of Xmap8 including a full set of UNIX man pages are available in html with a WWW browser at http://love.geology.yale.edu. Executable code is currently available for SUN Sparcstations running SUN OS-4.1.3 which will also work on Solaris-2.3 under the compatibility mode. The source code will be available in the future for easy porting to any X11 UNIX environment.

ACKNOWLEDGMENTS

The author acknowledges the efforts of Craig Nicholson, Geoff Ely, Jess McCullugh, Steve Malone and Bob Crosson for numerous comments and suggestions which significantly improved Xmap8. Portions of the code were developed by Bob Fischer, Peilin Jia and Mark Lindner. Thanks to Mark Alvarez for the original suggestion to develop this code. During program development the author was supported by NSF NEHRP grant EAR-9011441 and the donors of The Petroleum Research Fund, PRF 26595-G2, administered by the American Chemical Society.

BIBLIOGRAPHY

Bortugno, E. J. and T. E. Spittler (1986). Geologic Map of the San Bernardino Quadrangle:

Lees, J. M. (1990). Tomographic P-wave velocity images of the Loma Prieta earthquake asperity: Geophysical Research Letters: 17, 1433-1436.

Lees, J. M. (1992). The magma system of Mount St. Helens: Non-linear high resolution P-wave tomography: J. Volc. Geoth. Res: 53, 103-116.

Lees, J. M. and R. S. Crosson (1989). Tomographic inversion for three-dimensional velocity structure at Mount St. Helens using earthquake data: Journal of Geophysical Research: 94, 5716-5728.

Lees, J. M. and P. E. Malin (1990). Tomographic images of P-Wave velocity variation at Parkfield, California: Journal of Geophysical Research: 95, 21,793-21,804. Lees, J. M. and C. Nicholson (1993). Three-dimensional tomography of the 1992 Southern California sequence: Constraints on dynamic earthquake ruptures?: Geology: 21, 385-480.

Nicholson, C. and J. M. Lees (1992). Travel-time tomography in the northern Coachella Valley using aftershocks of the 1986 ML 5.9 North Palm Springs earthquake: Geophysical Research Letters: 19, 1-4.

Pallister, J. S., R. P. Hoblitt, D. R. Crandell and D. R. Mullineaux (1992). Mount St. Helens a decade after the 1980 eruptions: magmatic models, chemical cycles, and a revised hazards assessment: Bull. Volcanol.: 54, 126-146.

Smith, W. H. F. and P. Wessel (1990). Gridding with continuous curvature splines in tension: Geophysics: 55, 293-305.

Wessel, P. and W. H. F. Smith (1991). Free software helps map and display data: Eos (Transactions, American Geophysical Union): 72, 445-446.

FIGURE CAPTIONS

Figure 1(cover): Map view of the Landers/Joshua Tree aftershock sequence in the Mojave desert, showing color coded geologic structures and faults, hypocenters of events greater than magnitude 3 (circles), and the distribution of the Joshua Tree protable array (triangles). Geologic units were digitized and named according to the geologic maps (Bortugno and Spittler, 1986) . Tomographic velocity anomalies (Lees and Nicholson, 1993) , represented as percent perturbation in slowness are shown for 5- 8 km depth. Focal mechanisms for several large events (upper hemisphere, M>5) are displayed offset from their hypocenters. Note the correlation of the bend in the fault with the JHD (Jurrasic Hornblend Diorite) colored red.

Fig 2: Cross section through a tomographic image of Mt. St. Helens P-wave velocity anomalies (Lees, 1992) . Colors represent percent slowness perturbation from a layered half space. Focal mechanisms are front projections, color coded according to rake. Small yellow dots outline seismicity associated with magma movement and green triangles are stations plotted at their projected locations. Pink lines were digitized from an independant interpretation of the magma system (Pallister, et al., 1992) .

Fig 3: Mount St. Helens stoping region in spin module. View is from northwest above the ground looking southeast. The drawing shown in Figure 2 is rotated along with the hypocenters. A 3-D wireframe model (light gray) of the stoping region above the magma chamber is rotated and projected. Events are plotted such that their size is proportional to distance away from plane of view so that closer objects appear larger and provide depth perception. The angles the rotated axes make with a vector pointing into the page (unrotated Z-axis) are printed for reference.