This paper appears in

Marine and Coastal Geographical Information Systems
edited by D.J. Wright and D.J. Bartlett
pages 117-128, 2000.

Copyright © reserved by Dawn Wright and Taylor & Francis publishers.
May be freely distributed electronically in whole or in part, but please keep this notice attached and do not alter the text.


Spatial Reasoning for
Marine Geology and Geophysics

Dawn J. Wright


Despite the general success of GIS in marine science as evidenced by the chapters in this volume, there are still remain constructive critics who are asking the "hard" questions, among them:

These questions are being raised particularly in the marine geology and geophysics (MG&G) community, where GIS appears to be at a crossroads. There is now a basic understanding of the utility of GIS for display, management, and mapping, particularly at sea where effective decisions may save thousands of dollars of ship time (e.g., Wright, 1996; Fox and Bobbitt, 1999; Hatcher, 1999; Su, 1999). However, many still wonder what all the excitement is about beyond this. Some answers to the above questions and dilemmas may be found in more cross-disciplinary communication. In other words, the challenge may be how best to communicate the concepts of geographic information science to practitioners in the newest application domains of GIS, deep-water marine science included. GISci is the "science behind the systems," including questions of spatial analysis (special statistical techniques variant under changes of location), spatial data structures, accuracy, error, meaning, cognition, visualisation, and more (for the most comprehensive treatment of GISci see Longley et al., 1999). Pursuant to GISci is the notion of "spatial reasoning," defined by Berry (1995) as a situation where the process and procedures of manipulating maps transcend the mere mechanics of GIS interaction (input, display and management), leading the user to think spatially using the "language" of spatial statistics, spatial process models, and spatial analysis functions in GIS. This is how to move beyond mere display to see an additional or greater value of GIS

It is the purpose of this chapter to briefly introduce, primarily to those MG&G practitioners not intimate with GIS software documentation or the GISci literature, the notion of spatial reasoning by way of outlining the analytical functionality common in most commercial packages. As MG&G is the speciality of the author, the examples presented in the paper are of that nature. Recommended studies for other subdisciplines include Manley and Tallet (1990), Mason et al. (1994) and Lucas (1999 and references therein) for physical oceanographers; Hansen et al. (1991) and Bobbitt et al. (1997) for chemical oceanographers; and May et al. (1996), Meaden and Chi (1996), Bobbitt et al. (1997), and Moses and Finn (1997) for marine biologists.


Recent trends in GIS software architecture design (i.e., the framework for how the input/capture, management, manipulation/analysis, output/display subsystems of the GIS are constructed) have focused more on application domains than on a generic GIS. The architecture of each subsystem of the GIS is based on a particular data model, which provides a formal means of representing information. Peuquet (1988) defines a data model more specifically as a general description of the specific sets of entities (the phenomena of interest in reality) or objects (the phenomena of interest as digitally represented in the database) and the relationships between these sets. Geographical data models are therefore the sets of entities and relationships between them used to represent geographic variation in the discrete, digital world of a computer database (Goodchild, 1992). The geographical data model determines the constructs for storage, the operations for manipulation, and the integration constraints for determining the validity of data to be stored within the GIS. Differing ways of viewing the occupation of geographic space have resulted in the layer (field), object, or network data models for a GIS (Goodchild, 1992; Nyerges, 1993). Li (1999), Gold (1999) and Varma (1999) address the nature of data models and the manifestations of them most suitable for marine applications.Unfortunately, these alternative data models are still not readily available in most commercial GIS packages.

The tension between domain-dependent and domain-independent GIS lies in the fundamental differences between chosen data models (e.g., Knapp, 1991). On one hand, the commercial sector, which must of course consider commercial profit, caters to domain-specific niches in the GIS market (a transportation GIS, a hydrology GIS, an epidemiology GIS, etc.) and stays with one class of data model to fit the chosen applications of its best customers. For example, the layer (field) data model of Arc/INFO™ has remained basically unchanged, with features such as TIN, GRID and dynamic segmentation added to it over the years. Analysis modules for hydrology, location-allocation, and land-based spatial statistics, among others, have been included in recent revisions of Arc/INFO, within the layer data model context, to meet the needs of the largest, most profitable application domains. At the other end of the spectrum is the creation of a superstructure, standardised GIS data model that would provide linkages across narrow application domains. One of the challenges here is the development of a data model that is representative of a myriad of data sets, while at the same time simple to understand, flexible and capable of answering new types of queries without changing data structures. This is currently being addressed by the Open GIS Consortium, Inc., the objectives of which are to provide a shared data environment through the implementation of a generic GIS data model and a user workbench with needed tools and data to support a variety of applications (Buehler, 1994;

Linking data models to the data in question (terrestrial or marine) depends on the nature of GIS architecture. For example, with MG&G data sets come from a variety of sources, including a number of different instruments (Figure 8.1), all with different attributes, making it difficult to define a uniform data structure applicable to all. Developing or changing data models within a GIS to better fit the data can be accomplished if the tools or commitment is there. However, it appears that the tools are developed only if the marketplace acts to spur on that development. There is a dilemma with such development for advanced marine science oriented systems, as such systems use suffers from a lack of marketplace and benefactor. Therefore, the best alternative currently is to try to make one's data fit within the confines of the existing data model and functionality of the GIS. However despite the challenges involved in linking data to data model and system architecture (Burrough, 1992), many researchers have successfully integrated remotely-sensed and in-situ MG&G data into a GIS and found the application to be not only feasible but essential for the success of the research or project in question. Those who are most successful have discovered functionality that is somewhat buried within the GIS. Having found it though, has reaped benefits, particularly when it can be linked to data analysis packages such as GMT or Matlab™, or to scientific visualisation packages (e.g., Goldfinger, 1999).

Figure 8.1 Hierarchy of possible MG&G information sources for GIS.



Below are three major examples of MG&G spatial problems that are useful to approach with spatial reasoning in GIS. They come mainly from insights gained from several decades of investigation along fast- spreading portions of the global mid-ocean ridge (particularly two of the best-studied sections of the East Pacific Rise (EPR) at 9° -10° N and 17° -18° S; Figure 8.2). These investigations have provided a wealth of geographically referenced data, results and data-driven theoretical (often numerical) studies.

Figure 8.2 Location of the main northern (9° -10° N) and southern (17° -18° S) study sites on the East Pacific Rise.

1. The exploration of large volumes of spatially and temporally variable data to facilitate previously undiscovered relations between already-existing data. For example, during a recent results-based workshop for the EPR 9° N region (RIDGE Symposia on the Results of Field Studies Along the East Pacific Rise, 9°-10°N, 1998), it was apparent to all involved that the amount of spatially- reference data and accompanying results already in existence for this region of the ocean floor are: (1) staggering in its amount; and (2) diffusely distributed in the minds and journal articles of individual scientists (D. Toomey, pers. comm., 1999).

2. Detecting changes in observables that span several orders of spatial and temporal magnitude at the crests of mid-ocean ridges, particularly discrete magmatic events and the resulting distribution of hydrothermal vent sites.

3. Determining the relations between the subseafloor expression of magmatic systems and the nature of diking and eruptive events. Two topics of particular interest in the MG&G community are the physical structure of axial magma chambers (e.g., Sinton and Detrick, 1992) and the nature of hydrothermal convection (e.g., Davis et al., 1996). However, studies of these entities are usually conducted independently of each other. For instance, seismologists have focused on imaging seismic velocity and attenuation of the ridge crest in order to map the spatial dimensions and physical properties (temperature and melt fraction) of axial magma chambers (e.g., Toomey et al., 1994; Dunn and Toomey, 1997). Geologists and geochemists have been equally focused on mapping the surface expression and chemistry of active vent fields (e.g. Haymon et al., 1991, 1997), from which attempts are made to infer how deep and in what geometry fluids are penetrating the crust (e.g., Wilcock, 1998). Such independently conducted studies are linked by a common process (the interaction of hydrothermal fluids with an evolving magmatic system) and should be linked in a common spatial analysis environment.


In addressing the above spatial problems mapping is an essential, sometimes formidable, first step. However, if a user is to move beyond mapping ("What is where and how do I change the colours in my legend, zoom in, zoom out, etc.?") to spatial reasoning ("Why is it there?"), a road map to GIS usability is extremely helpful. In other words, what are the functions or operations that enable a specific application to solve problems and/or aid in interpreting data? Five major classes of GIS functionality (in the order that are often employed) are data input/capture, data storage/management, data manipulation, data analysis, and data output/display. Nyerges (1993), for example, provides an exhaustive compilation of GIS functions suitable for environmental applications.

The all-important data analysis functions focus on developing and synthesising spatial relationships in data in order to solve spatial problems, to answer scientific questions. They range from simple models integrated within a GIS context (i.e., fully embedded within GIS architecture) to elaborate models that are coupled or "hot-linked" to a GIS environment. Many of the current concerns with the analytical functions in GIS are with the design tradeoff between integration and/or coupling by way of a special language interface (Densham, 1991; Burrough, 1988; Fedra, 1993; Nyerges, 1993).

Four commonly used spatial analysis procedures in GIS are data interpolation, contour generation, buffer zone generation and theme merging. MG&G practitioners have found the inverse distance weighted (IDW) and triangulated irregular network (TIN) functions in GIS to be very useful for interpolating irregularly spaced cruise and ROV dive data and matching them to evenly distributed grid data (e.g., Su, 1999). Quick contour generation from grids of bathymetry, temperature, salinity, etc. make for efficient comparison to point and line observations already loaded into the GIS. Buffering (the creation of polygons around existing points, lines, or areas) of sampling sites or ship track lines are integral to estimating the accurate spatial extent of data collection (e.g., Wright et al., 1995). Merge functions allow two or more individual or cruise data sets to be combined for further analysis (e.g., Hatcher and Maher, 1999; Su, 1999). GIS packages now come with an additional host of spatial analysis functions (e.g., point pattern analysis, spatial interaction models, calculations of Geary's and Moran's indices of spatial autocorrelation, network analyses) that have been traditionally used in terrestrial applications but hold great promise for MG&G studies, particularly at hydrothermal vent sites. Examples of primary data GIS analysis functions for MG&G applications are provided in Table 8.1.

Table 8.1 GIS analytical functionality for spatial problems in MG&G (listed alphabetically by likely names of commands, modules, or index terms in documentation of various GIS packages; actual Arc/INFO commands or functions listed in capital letters). Categories guidedby Nyerges (1993).

Azimuth: compute azimuth, bearings, and geographic point locations.

Significance tests: t- test, chi-square.

Buffers: compute distances from point, line, and polygon.

Simulation: conditional simulation in 2-D and


Descriptive nonspatial statistics: e.g., frequency analysis, measures of dispersion (variance, standard deviation, confidence intervals), measures of central

tendency (mean, median, mode), range, percentile.

Single mathematical operations: perform exponential, logarithm, natural logarithm, absolute value, sine, cosine, tangent, arcsine, arc cosine, arctangent on the grid cell.

Distance analysis: calculate distances between features, create grids of distances from source, create polygones of distance zones (e.g., BUFFER, REGIONBUFFER, NEAR, POINTDISTANCE, NODEDISTANCE, EUCLIDEANDISTANCE, PATHDISTANCE)

Slope/aspect: computer slope and aspect based on a fitting a plane (e.g., SLOPE, ASPECT), compute slope and aspect based on fitting a curve (e.g., CURVATURE).

Group mathematical operations: perform addition, subtraction, multiplication, division, minimum, maximum on the grid cell for two or more data categories.

Spatial interobject measurement: interobject calculations for distance and direction point to point, point to line, polygon perimeter, percent of total area, percentiles, range, midrange.

Inferential nonspatial statistics: e.g., correlation, regression, analysis of variance, and discriminant analysis (e.g., CORRELATION, REGRESSION, SCATTERGRAM, HISTOGRAM, STATISTICS).

Spatial intraobject measurement: individual object calculation for line length, polygon area, surface volume, polygon perimeter, percent of total area, etc.

Inferential spatial statistics: e.g., trend analysis, autocorrelation, Geary and Moran indices, Pearson's correlation coefficient (e.g., GEARY, MORAN).

Superimpose: superimpose one feature on another with replacement.

Interpolation: Inverse distance weighted, spline, trend interpolation (e.g., IDW, SPLINE, TOPOGRID, TREND), conversions of TINs instead of points to grids (e.g., TINLATTICE).

Territory designation: creation of polygons around points, calculation of distance territories, (e.g., THEISSEN, ALLOCATE, EUCLIDEANALLOCATION).

Kriging computations: ordinary, stationary, and nonstationary kriging, kriging in 1-D, 2-D, and 3-D for scattered points, grids of points, and irregular grids. (e.g., KRIGING).

Triangulated Irregular Network (TIN) production: TIN modelling with geologic fault specification.

Merging: merge attribute information automatically or manually as a result of composite process; two attributes associated with same area.

Traverses: define open and closed traverses, trace flow through networks of connected nodes and arcs (e.g., TRACE).

Model structuring: model-structuring environment that links parts of numerical/process model to the GIS environment through a special language interface.

Variogram: variogram calculations (e.g., SEMIVARIOGRAM).

Multivariate statistics: output regression coefficients for a regression model, maximum likelihood classification(e.g., REGRESSION, SAMPLE, STACKSTATS, DENDEROGRAM, MLCLASSIFY).

Visibility: identify visual exposure and perform viewshed analysis on a surface (VISIBILITY, VIEWSHD, VISDECODE, SURFACEVIEWSHED, SURFACESIGHTING).

Nearest neighbour: compute closest geographic phenomenon to each phenomenon of a particular kind.

Weighting: weight features by category in the overlay process.

Overlay operators: point, line, area object on/in point, line, and area object, data operators for Boolean AND, OR, NOT; for point in polygon point on line, line in polygon, and polygon in polygon.

Zonal Functions: calculate sizes and shapes of regions (ZONALAREA, ZONALPERIMETER, ZONALTHICKNESS, ZONALSTATS, ZONALGEOMETRY)

Replacement: replace cell values with new value reflecting mathematical combination of neighbourhood cell values such as average, maximum, minimum, total, most frequent, least frequent, standard deviation.


It has been established quite readily that the data entry/capture, data management, and data display/output functions in a GIS can support MG&G. These are probably the most obvious of the support functions, and oftentimes are the only capabilities of a GIS that are recognised. Although not the focus of this chapter, examples of primary GIS data manipulation functions, often the direct precursors to analysis, are listed Table 8.2 for reference.

Table 8.2 GIS data manipulation functions for spatial problems in MG&G (listed alphabetically by likely names of commands, modules, or index terms in the documentation of various GIS packages; categories guidedby Nyerges, 1993).

Spatial Co-ordinate Manipulation


Adjustments: mathematical adjustment of co-ordinate data using rotation, translation, or scaling.

Merging: interactive or automatic merging of geometrically adjacent spatial objects to resolve gaps or overlaps with user-specified tolerance.

Compression or decompression: of raster-formatted data with techniques such as run length encoding or quadtree.

Resampling: modify grid cell size through resampling.

Co-ordinate geometry: generate boundaries from survey data; intersect liens, bisect lines.

Smoothing: smooth line data to extract general sinuosity.

Co-ordinate recovery: recovery of geographic seafloor co-ordinates from photographic data using single photo resection/intersection together with bathymetric data.

Spatial selective retrieval: retrieval of data based on spatial criteria such as rectangular, circular, or polygonal window, point proximity, or feature name.

Locational classification: grouping of data values to summarise the location of an object such as a deepsea vehicle trackline of a particular line number.

Structure conversion: conversion of vector to raster, raster to vector, or quadtrees to vector with locational referencing.

Locational transformation: transformation of seafloor survey bearing and distance data to geographic co-ordinates using least-squares adjustment of traverse to ground control; e.g., from latitude/longitude to transponder net co- ordinates and vice versa.


Attribute Manipulation


Arithmetic calculation: calculate an arithmetic value based on any other values (i.e., add, subtract, multiply, divide).

Attribute selective retrieval: retrieval of data based on thematic criteria such as attribute of vehicle trackline or Boolean combination of attributes.

Attribute classification: grouping of attribute data values into classes.

Class generalisation: grouping data categories into the same class based on characteristics of those categories.

Spatial Co-ordinate and Attribute Manipulation


Contouring: generate contours from irregularly or regularly spaced data; constrain contour generation by break lines; e.g., shoreline, faults, ridges.

Object conversion: point, line, area, grid cell or attribute conversion to point, line, area, grid cell or attribute.

Gridding: generate grid data from TIN; generate a grid from contours.

Rescaling: rescaling of raster data values.


In working with the spatial analytical functionality outlined above the GIS may raise as many questions as it answers. However, this should lead not only to the increased spatial awareness of the user but in improvements and extensions of the GIS. Indeed this is a natural component of spatial reasoning: the realisation that improvements in the mechanics of GIS interaction are challenging the user to think more intently about the conceptual process and actual procedures of manipulating and analysing maps. Spatial reasoning is moving beyond mapping and spatial database management to modelling of relationships between and among mapped variables. It is looking at maps as numbers and relationships first, and as pictures second. Spatial reasoning is also facilitated by spatial dialogue which is important for MG&G practitioners who often collaborate with many other colleagues while at sea or on shore. A GIS that is "intelligent" can help achieve this dialogue by producing a variety of outcomes that make users examine the differences and reasons for the differences in various outputs. The intelligent GIS (characterized by a fairly "intelligent" user interface as in Su, 1999) will further facilitate spatial reasoning by guiding users through the spatial operations and models they use, and by encouraging them to try various routes to a similar end.

Goodchild (1999) discusses a range of advantages and disadvantages of GIS as a software tool for global change research that were identified at the Specialist Meeting of NCGIA Research Initiative 15 (Goodchild et al., 1995). There are many, many parallels here to the MG&G community and it may be useful to consider some of the points of consensus that were reached among global change scientists (many of whom are oceanographers). One point was that a larger academic perspective of GIS might be important in order to understand all of the ramifications of its current usage, and to help users to understand and implement the notion of spatial reasoning. There have now emerged now at least three distinct perspective that are identifiable in the current use of the term "GIS" (Wright et al., 1997; Goodchild, 1999):

Of the three the second perspective of GIS may be the most constructive with regard to MG&G as GIS is joined by other geographic information technologies such as mapping packages, remote sensing processing packages, in a broader category. As Goodchild (1999) puts it for the global change community: "the use of GIS in no longer an issue: ...research has no choice but to use computers and digital data; and the vast majority of the types of data needed.. are geographically referenced." This raises a final important point with regard to spatial reasoning: the understanding not only of the basic questions that a GIS (the tool) can answer (Berry, 1995), but also a knowledge of the best combinations of GIS with other data analysis tools. This is not to suggest that GIS will always be the best or the only tool to use. For many scientists there are various statistical and mathematical packages, or home-grown analytical programs, that are much more supportive of complex process modelling than GIS. However, they may not have robust mapping and data integration capabilities. Again, it is the "science" that should supersede, but be supported by, the "system."


This paper benefited greatly from numerous discussions with and input from Douglas Toomey, an MG&G practitioner at the University of Oregon, and computer scientists Janice Cuny (University of Oregon), and Judy Cushing (Evergreen State College). The support of the National Science Foundation (grant OCE-9521039) is greatly acknowledged.


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