IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 28, NO. 4, JULY 1990 71 1

Integration of Geophysical and Geological Data Using Evidential Belief Function

WOOIL M. MOON, SENIOR MEMBER, IEEE

Abstract-Several methods are available for integrating geophysical, geological, and remote sensing data sets and also for integrating them with additional information such as newly observed geophysical and geological data. Several published reports discuss successful applica- tion of different types of spatial information integration techniques in- cluding the geographical information system (GIs). There have also been theoretical developments including Bayesian approach in updat- ing old data sets with newly acquired information. However, weak- nesses and problems still exist. Many geological and geophysical data sets often have only partial coverage and in almost all cases have very different spatial resolution. These cause serious difficulties in certain cases. In this research the partial belief function approach is examined as a means to integrate one set of airborne and/or ground geophysical data with other available geological and geophysical data sets, and to update the existing information successively with newly observed data over target areas. In theory, the Dempster-Shafer method appears to be the most suitable method, but in practice several difficulties arise that must be overcome. One of the major difficulties is the dependency of the partial belief function on exploration targets, which can only be defined, at present, in a case-by-case approach.

Ground EM

Satellite lmaoe

Fig. 1. Schematic diagram of geological and geophysical data-set layers to be integrated.

I. INTRODUCTION HE INTEGRATION of geophysical, remote sensing, T and geological data has a long history-as old as the

first geologist who tried to map outcrop rocks and draw the field information on a topographic map. This classical approach has been successful for simple tasks and re- quired very little theory or research. However, with rapid advances in computer and spatial information processing techniques, digital geographical information systems (GIs’s) have been developed to an unprecedented level of public acceptance. The effectiveness of the powerful computer-based GIS and accompanying mathematical theory is generating renewed interest in information in- tegration in the earth science and remote sensing disci- plines. The huge volume of remote sensing and geophys- ical data from airborne and space-borne platforms has also encouraged the development of efficient GIs-type meth- ods of data integration. Another very effective way of in- tegrating large volumes of spatial data sets is the use of an AI/Expert system [8]. In either case, the mathematical foundation is based on a probabilistic scheme or on the Dempster-Shafer rule [2]-[4], [8], [111, [131, [141.

Manuscript received October 20, 1989; revised February 6, 1990. Thls work was supported by National Science and Engineering Research Coun- cil of Canada Operating Grant A-7400.

The author is with the Geophysics Department, University of Manitoba, Winnipeg, MB, Canada R3T 2N2.

IEEE Log Number 9035825.

In earth sciences, the most widely used digital data sets beside the satellite images include geological maps (lith- ological and structural), airborne magnetic (total field and gradient) maps, grayity maps (in less extent), and other geophysical data sets (Fig. 1). Available geological and geophysical maps and remotely sensed image data sets, however, have often very limited coverage in a chosen target area. In this paper, the GIs-type approach of inte- grating remote sensing and other geoscience data will first be briefly reviewed, and theoretical aspects of the statis- tical and evidential belief function approaches will be dis- cussed, with examples. An example with real geological and geophysical data sets from northern Manitoba, Can- ada, has demonstrated that the Dempster-Shafer approach of integrating spatial data can be very effective for re- source exploration application.

11. GIS AND DATA INTEGRATION A number of recent papers have dealt with GIS as a tool

for geological and remote sensing data integration [3], [4]. Many of the basic functions in GIS such as preparation techniques for remote sensing and geological data inven- tory, base maps, thematic compilation, and map integra- tion can be utilized directly in geological remote sensing and geological data integration [6]. Some of the technical problems involved in GIs systems, such as sliver errors, resolution inconsistencies, and inconsistent map classes

0196-2892/90/0700-0711$01.00 O 1990 IEEE

7 12 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL 28, NO 4, JULY 1990

are now mostly resolved by efficient resampling and ad- vanced interpolation techniques and optimized systematic integration approaches. However, further difficulties do exist: thematic boundary variability, transition zones, and, of course, the dilemma of questionable and missing data. Some difficulties have also arisen in vector and raster rep- resentation of data sets and transformation techniques.

These technical difficulties are expected to be ironed- out with evolution of the new computer systems and more sophisticated GI§. One of the more serious theoretical problems appears to be precise representation of infor- mation on each data set prior to data integration. In GIs, a given plane of data is generally reclassified or general- ized before merging. The reclassification or generaliza- tion of attributes is itself not a technically difficult process [6]. When it comes to reassigning observed information on each data set, considerable difficulty and misunder- standing exist as to how each class should represent what range of signal power or mapped information. In most GIs’s available today, points, lines, and/or polygons rep- resent either a certain information or feature or absence of them. In this approach, any map information is repre- sented as a binary map of ( 0 , 1) . This approach poses serious problems for most geophysical survey data, where each contour interval represents a range of particular field values. Another difficulty arises from missing data. If, for example, a geological map shows only 10% outcrop dis- tribution and the rest is covered by glacial deposits, in- tegration of the basement geology with other data must have a formalism to represent the interpreter’s ignorance or missed information.

In a recent development called “weights of evidence” mapping, each input map is converted into binary form where the two map classes are determined by the target objectives [3], [4]. In the binary map analysis, for ex- ample, the score for gold occurrence is set to one while nonoccurrence is set to zero, and a GIS system such as SPANS’ can be used to integrate geological, geophysical and mineral occurrence data and to evaluate a certain tar- get potential [4]. The weights of evidence modeling and binary map approach is appealing due to its simplicity; however, this method breaks down when the weights of evidence are required for data sets with continuously varying data values or for data sets which do not exist (unsurveyed or unexplored) [4], [151, 1171.

111. EVIDENTIAL REASONING AND THE DEMPSTER- SHAFER METHOD

Several methods are available for combining the infor- mation content from multiple sources of remote sensing image data and other spatial data such as geological and geophysical data, The Bayesian approach or probabilistic scheme 131, [4], [14] and the Dempster-Shafer-type or- thogonal sum combination rule approach [14], 1171 ap- pears to be most popular. The applicability of these two schemes in mixed multispectral data situation is reviewed

‘Registered@ service mark of the TYDAC Technology Inc.

and evaluated by Lee et al. [ 111. In this paper, application of the Dempster-Shafer method for the integration of geo- logical and geophysical data is examined with a real data set.

In the following discussion, digital map inventory prep- aration (geological and geophysical), creation of a base map, resampling, interpolation, and geocoding are as- sumed to have been carried out, and theoretical aspects only will be emphasized. It will also be assumed that each plane of information has originated from multiple but dis- parate sources. The information level of evidences can then either have a varying degree of certainty to several environmental possibilities, or be incorrect or incom- plete. If one can assign a degree of belief to each evi- dence, as in the evidential theory of belief, evidences with a varying degree of certainty can be represented by partial belief functions [ 161.

Suppose environmental possibilities e l , e2, . . . , e, ex- ist such that

E = {el , e2, 1 , e n ) .

Then each proposition is completely defined by the subset of E containing exactly those environmental possibilities where the proposition is true. If, in a given data set, geo- logical formations e, and e, + cannot be distinguished in terms of at least one proposition of interest, they should be replaced by a single environmental element. The prop- osition: “an ultramafic stock is located at (x, yl” then corresponds to the subset of environmental possibilities, that some kind of ultramafic rock is located at (x, y ). Now a geophysicist can represent one’s partial belief through a Bayesian distribution over E. This is done by distributing a unit of belief among the elements of E attributing com- mensurately greater amounts to the more likely elements. If one designates this distribution by the mapping “dist,” then

dist: E + LO, 11

c dist (e ) = 1 0.

This induces a probability on every proposition X defined over each layer of digital information (Fig. 1) such that, for all X c E,

e E 1 %

and it follows that

Pr ( X ) = 1.0 - Pr (1 X).

The problem with this approach is that the geophysicist has to determine a precise probability for every proposi- tion for each map layer no matter how impoverished the evidence. This would not be such a problem if a rich source of statistical data were available for each map layer from which these probabilities could be estimated. Un- fortunately, in most cases, each digital information layer of geological and geophysical data base is often incom- plete, and the Bayesian statistics tend to prefer disjunction

713 MOON: INTEGRATION OF DATA USING EVIDENTIAL BELIEF FUNCTION

of the mutually exclusive propositions which often results in unrealistic probability of certain propositions.

In the evidential belief function approach, a proposition X is represented by an interval between Spt (X)and Pls (X) , where Spt (X) represents the degree to which the evidence supports the proposition X , and Pls ( X ) repre- sents the degree to which the evidence remains plausible. This evidential interval is a subinterval of the closed real interval [0, 11. The difference Pls ( X ) - Spt ( X ) rep- resents residual ignorance of the given subset of environ- mental elements. If one has accurate and exact informa- tion, the evidential interval collapses to a point on [ 0, l 3 . The binary map approach of integrating geological data 131, [4], and many other data integration methods using GIS implicitly assume such hypothetical limits.

A unit of belief over a set of propositions can be dis- tributed as a mass distribution where the focal proposi- tions need not be mutually exclusive, such that

mass: 2’ -+ [0, 11

C mass ( F ) = 1.0

mass (0, 0 ) = 0.0.

FE

Note here that the sum of the mass attributed to proposi- tions that imply X (Spt ( X ) ) plus the sum of the mass attributed to propositions that imply i X (Spt ( X ) ) do not necessarily equal 1.0, since some mass might be at- tributed to propositions that imply neither.

If rock formations represented by F could be included in the proposition X , an evidential interval can be induced on the probability of X such that

Spt ( X I = C mass ( F ) F G X

Pls ( X ) = 1.0 - Spt ( 1 X )

= 1.0 - C mass ( F ) F C - X

and

v x c E

Spt ( X ) s Pr ( X ) 5 PIS (X). Viewed intuitively, more mass is attributed to the most precise proposition that a body of evidence supports. The Bayesian approach requires that a precise probability be assigned to each evidence (e.g., type of rock), no matter how noisy the data (e.g., uncertainty in identifying the rock types) are and no matter how little statistical data (e.g., insufficient number of outcrops) are available [14]. In the Dempster-Shafer approach, one computes Spt ( X ) and PIS ( X ) based on an understanding of the proposi- tional dependencies that exist within the environment un- der study. If a mass is attributed to some proposition X and it is not known whether X implies another proposition Y or 1 Y, then the judgment can be suspended and the integration process branches to an available vertical op- tion. Mass ( X ) neither increases Spt ( X ) nor decreases

PIS ( X ) , but contributes to the evidential interval. This ability to represent ignorance gives the Dempster-Shafer approach a clear advantage over the Bayesian approach, which breaks down. In the Dempster-Shafer approach, Dempster’s rule does not require that one body of evi- dence supports a single proposition with certainty. The rule can take arbitrary complex mass distributions massl and mass2, and as long as they are not completely contra- dictory with respect to each other and can produce a third mass distribution mass3. Therefore, given F, and F2 in a digital map layer

F1, F 2 s E, a new mass distribution mass3 representing the pooled mass distribution from mass1 and mass2 is defined as

mass3 (0) = 0

and

for all nonempty F3 C E, where

k = C mass1 ( F , ) mass2 ( ~ 2 ) 1.0. A n F z = O

Since Dempster’s rule is both commutative and associa- tive, the order and grouping of combinations are imma- terial. This fact allows results to be obtained through hier- archical combinations of partial results with whatever degree of parallelism, not depending on the nature of map layers.

In the Dempster-Shafer approach, some information as a measure of conflict k can also be provided in regard to gross error during the data integration. The measure of conflict k provides degree to which the combined infor- mation or the new compilation map is contradictory to- ward the propositions. Given several bodies of evidence, one can expect that those containing gross errors will tend to be farther away from the other bodies of evidence than those with measurement errors. One can use a clustering algorithm to sort out those bodies of evidence containing gross errors.

One of the problems with the Dempster-Shafer ap- proach is that one must maintain each body of information independently because of the complexity of the method to combine information correctly with known dependencies. Most remote sensing and geophysical data sets are fortu- nately evidentially independent, and the problem of over- weighting one information or evidence does not require special attention [ 131, [ 141.

IV. TEST EXAMPLES

Four real data sets (airborne EM, airborne total field magnetic, ground EM, and bedrock geology maps) of the Farley Lake area of Manitoba, Canada, were selected for this study. The total study area is approximately 36 km2 and is divided into 100 x 100 pixels (Fig. 2). The explo- ration targets chosen were for test purposes only, and they

7 14 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 28, NO. 4, JULY 1990

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‘\ /

n 1 Y

FARLEY LAKE

MARN~E LAKE

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L O C A T I O N OF TEST AREA

Fig. 2. Location map of the test area in northern Manitoba, Canada

were the iron ore deposit and the base metal deposit. Since no basic theoretical development of the systematic and quantitative geological, geophysical, and statistical infor- mation base for mineral exploration was carried out, the statistical assignment of a partial belief function to each information is less exact and may even be arbitrary. How- ever, actual assignment of belief functions to varying de- grees of an anomaly or any other specific geophysical in- formation has followed a general empirical approach, based on the theory of mineral deposits. Nevertheless there should not be any confusion in regard to the inte- gration method being proposed in this research.

The airborne EM map (Fig. 3(a)) covers only about two-thirds of the test area. Only a small portion in the northwest of the study is covered by ground EM survey [5] (Fig. 3(c)), the rest of the study area is not covered, and consequently no data are available. The geological map (Fig. 3(d)) again represents only approximate loca- tions of the basement rocks because of thick overburden and lakes. The aeromagnetic total field map has complete coverage of the test area (Fig. 3(b)).

One of the first steps of integrating different geophysi- cal and geological data sets involves digitizing the map information that is not already in digital form. The next step involves conversion of the digitized information lay- ers into probability distributions. At present, this partic- ular step depends on human experts for quantitative inter- pretation and assignment of appropriate probability to each information cell. As mentioned before, no systematic sta- tistical representation technique exists for this type of study. However, a review made of several hundred sets of geophysical survey data assessment files indicates that

slight changes in probability assignment by different hu- man experts, if they were qualified experts, appears to result in minor changes in the final support map.

The probability ranges assigned to each proposition were based on the authors’ intuitive and qualitative knowledge of the theory of mineral deposits. The two im- portant points to be noticed are: first, that probability as- signment, or weighting, in another approach, of the effi- ciency of different information layers for a chosen proposition must be made as carefully as possible; and secondly, the probability function assigned for each layer is relative. For the practical robust application of the method being proposed, geologists and geophysicists must develop a systematic methodology for quantitatively de- ducing information values of each geoscience data set for each chosen proposition. One way of systematically as- signing probability or belief can be made by using an ex- pert system, such as p-Prospector [12] for the geological information layer. For geophysical data interpretation, no such expert system is available at present, although an attempt is now being made to develop a geophysical equivalent [ 11.

In Dempster’s rule of combination, it is essential to keep the relative amount of basic probability numbers assigned in a reasonable sequence for each data set. In such a case, one can expect to obtain a reasonable result even when the absolute numbers assigned are not precise. However, algebraic independence of each data set is important in the theory. The linear dependence of different data sets tested in this study has not been exhaustively studied, but it was judged not to be a very serious problem. The two propositions tested in this study are 1) an iron ore deposit present, and 2) a base metal deposit is present. The prob- ability figures committed to these propositions from each data set are listed in parts a) and b) of Tables I-IV.

The results of integrating these four data sets using Dempster’s rule of combination are plotted in grey level and color plots (Figs. 4-7). The total belief plot repre- sents the pooling of individual beliefs committed to the chosen exploration targets from each data set. The highest support obtained for “iron formation” is located at the midwest part of the test area (Fig. 4(b)), in which location pyrrhotite ( >95%) was found by drilling. The lowest support is located in the lake areas and in the areas with evidence of less likelihood or no information. Fig. 4(a) shows the support distribution for a base metal deposit. The most favorable area for base metal predicted by the pooled belief is located in the vicinity of the upper left comer, where anomalies of ground EM were observed and in the east part of the test area where anomalies of air- borne EM were recorded.

A disbelief map shows the degree to which the propo- sition cannot be believed by the evidences. The highest disbelief for iron formation deposit is located in the south- east part of the test area and, for base metal, is located in the area where no anomalies of ground EM or airborne EM was detected (Fig. 5 ) . The ignorance plots show the degree to which the proposition is uncertain. The higher

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TABLE I PROBABILITY ASSIGNMENT FOR AIRBORNE EM DATA

P r i or i t y support Plausibility

a) Exploration Target Base Metal

B 0 4 0 9 C 0 35 0.9 D 0 30 0.9 E 0 20 0 9

Band 0 15 0 9 No anomaly 0 1 0 7

b) Exploration Target Iron Formation

B 0 25 0 9 C 0 2 0 9 D 0 15 0 9

E and band 0 1 0 9 No anomaly 0 1 0 75

TABLE 11 PROBABILITY ASSIGNMENT FOR AEROMAGNETIC DATA

Field Value ( y ) support Plausibility

a) Exploration Target. Base Metal

> 3000

< 500 500-3000

0 1 0.15 0.15

b) Exploration Target: Iron Formation > 3000

500-3000 < 500

0.35 0.15 0.1

0.. 8 0 8 0.9

0.85 0.85 0.9

TABLE I11 PROBABILITY ASSIGNMENT FOR GROUND EM DATA

Value support Plausibility

> 20 10-20 3-10 < 3

> 20 10-20 3-10 < 3

a) Exploration Target Base Metal 0.35 0 3 0 2 0.85 0 1 0.65

b) Exploration Taget. Iron Formation

0 3 0 9 0 2 0.9 0 15 0 9 0 1 0.8

ignorance represents the fact th evidence or less ef- ficient evidence exists for the position. Usually, the areas of high ignorance req rther survey or fur- ther examination. The highes e is in lake areas or areas with no data for either proposition (Fig. 6). Plau- sibility i s defined as the mathematical sum of support and ignorance. It can in reality be interpreted as an upper boundary of probability for the given proposition in each case. The high plausibility areas can, in practice, be in- terpreted as areas with conditionally high support that re- quire more information. Because of the lack of ground

INS ON GEOSCIENCE AND REMOTE SENSING, VOL 28, NO 4, JULY 1990

TABLE IV PROBABILITY ASSIGNMENT FOR BEDROCK GEOLOGY MAP

Rock Type Support Plausibility

a) Exploration Target Base Metal

Magnetite-bearing slate 0 15 0 8 Andesite and basalt 0 2 0 85 Tuff, agglomerate, and volcanic breccia 0 2 0 9 Granodiorite 0 2 0 9 Granite and granite gneiss 0 2 0 9 Gabbro, norite and hornblendite 0 15 0 8 Diorite and quartz diorite 0 1 0 9 Rhyolite and trachyte 0 2 0 9

b) Exploration Target Iron Formation

Magnetite-bearing slate 0 35 0 85 Andesite and basalt 0 2 0 9 Tuff, agglomerate, and volcanic breccia 0 25 0 85 Granodiorite 0 1 0 75 Granite and granite gneiss 0 1 0 7 Gabbro, norite and hornblendite 0 15 0 9 Diorite and quartz diorite 0 2 0 9 Rhyolite and trachyte 0 1 0 8

data over lakes in the study area, the high plausibility areas are located in the lake areas, as shown in Fig. 7.

V. DISCUSSION AND CONCLUSION

In the Dempster-Shafer approach of integrating infor- mation, one must first be able to reason over possibilities and also about the interrelation between several sets of available information. The human perceptualireasoning system already has a multisensor data integration capa- bility embedded in it. With this capability, an explora- tionist (geologist or geophysicist) can actively cue sen- sors and a personal knowledge base, seeking confirmation and/or refuting evidences related to the exploration target entities.

In geophysical, geological, and remote sensing tasks, many data sets are incomplete a statistically unbal- anced, even though the rate of inc se in the volume of newly available data is alarmingly high. One approach to solving this problem will be a planned interactive ap- proach of exploration, which is, at present, practically impossible. The Dempster-Shafer approach provides an optimal theoretical basis for integrating remote sensing, geological, and geophysical data sets. The straightfor- ward approach of the GIS technique, the binary map ap- proach [3], [4], fuzzy logic [l], and the Bayesian ap- proach of updating old data sets [ 3 ] , [4], [15] are also valid and will provide a methodology, but the choice should be made by the user depending on the expected accuracy of the expected outcome and exploration ob- jects. As demonstrated with test data sets, the Dempster- Shafer approach has clearly outlined the most probable exploration target area. Moreover, a small iron ore de- posit was found under thick overburden in the case of the iron ore proposition example, and, similarly, a gold ore showing and a massive pyrrhotite body have been discov- ered in the “base metal” proposition example. One of the

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Fig. 4. (a) Support distribution for base metal proposition. (b) Support distribution for iron formation proposition. In this support map, recent discoveries of iron formation (Fe) and gold (Au) deposit are marked.

718 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 28, NO. 4, JULY 1990

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difficulties, however, of applying the Dempster-Shafer approach in geological/geophysical remote sensing lies in the variation of the evidential belief function which de- pends critically on the final exploration target.

ACKNOWLEDGMENT The author would like to thank Dr. G . F. Bonham-

Carter (Geological Survey of Canada, Ottawa, Canada) for the preprints and discussions during the early stages of this research and P. An, who digitized and processed the test data. I. Hosain (Department of Energy and Mines, Province of Manitoba, Canada) kindly provided the au- thors with the geological and geophysical data of the test area.

REFERENCES 111 P. An, “Development of a m EXPERT system for geophysical data

interpretation,” Ph.D. thesis proposal, Univ. of Manitoba, Winni- peg, MB, Canada, 1989.

[2] P. Blonda et al . , “Classification of multitemporal remotely sensed images based on a fuzzy logic technique,” in Proc. IGARSS ’89, pp.

[3] G. F. Bonham-Carter and F. P. Agterberg, “Application of a micro- computer based geographic information system to mineral potential mapping,” Micro-Computer in Geology, to be published.

[4] G. F. Bonham-Carter, F. P Agterberg, and D. F. Wright, “Integra- tion of geological data sets, for gold exploration in Nova Scotia,” Photo. Eng. Remote Sensing, vol. 54, pp. 1585-1592, 1988.

[5] R. Chevillard and B. Genaile, “Ground horizontal loop EM survey map,” Dept. Energy and Mines, Province of Manitoba, Assessment File 91436, 1970.

[6] J. Dangermond and C. Freedman, “Description of techniques for au- tomation of regional natural resources inventory,” in GIs for Re-

834-837.

720 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 28, NO. 4, JULY 1990

sources Management; A Compendium, W. J. Ripple, Ed., 1987, pp. 9-33.

[7] “Airborne total field magnetic map,” Geological Survey of Canada, Ottawa, Canada, Open File Rep. 1047, 1984.

[8] D. G. Goodenough, B. Baker, G. Plunkett, and D. Schanzer, “An expert system for using digital terrain models,” in Proc. IGARSS ’89,

[9] Int. Nickel Co., in “Airborne EM priority map,” Dept. Energy and Mines, Province of Manitoba, Winnipeg, Canada, Assessment File 91615, 1954.

[lo] H. Kim and P. H. Swain, “Multi-source data analysis in remote sens- ing and geographic information systems based on Shafer’s theory of belief,” in Proc. IGARSS ’89, pp. 829-832.

[ l l ] T. Lee, J. A. Richards, and P. H. Swain, “Probabilistic and eviden- tial approach to multisource data analysis,” IEEE Trans. Geosci. Re.- mote Sensing, vol. GE-25, pp. 283-293, 1987.

[12] R. B. McCammon, “The p-PROSPECTOR mineral consultant sys- tem,” U.S. Geol. Survey Bull., no. 1697, 1986.

[13] W. M. Moon, “Application of evidential belief theory in geological, geophysical and remote sensing data integration,” in Proc. IGARSS ’89, pp. 8838-8841.

[14] W. M. Moon and P. An, “Integration of remote sensing and geolog- ical digital data using Dempster-Shafer methods,” Geophys., to be published.

[15] G. S. K. Rao et al . , “Integration of remote sensing and geological information using Bayesian probability theory and GIS system, ” in

pp. 842-843.

Proc ERIM Conf Exploration Geology, Calgary, AB, Canada, to be published

Princeton Univ Press, 1976

evidences,” UCBiERL M79124, 1979, pp 1-12

[16] G Shafer, A Mathematical Theory of Evidence Princeton, NJ

[17] L A Zadeh, “On the validity of Dempster’s rule of combination of

* Wooil M. Moon (S’68-M’70-SM’86) received the B Sc degree in geology from Seoul National University, Seoul, South Korea, the B As degree in electrical engineering from the University of Toronto, Toronto, ON, Canada, the M Sc degree from Columbia University, New York, NY, and the Ph D degree in geophysics from the Univer- sity of British Columbia, in 1968, 1970, 1972, and 1976, respectively

From 1976 to 1979 he was a Postdoctoral Re- search Associate in the Department of Physics,

Memorial University of Newfoundland and University of Toronto In 1979 he joined the faculty at the University of Manitoba, where he is currently a Professor of Geophysics and Adjunct Professor of Electrical Engineering His current research interests include global satellite geophysics, geophys- ical imaging, and the AIiexpert system

Dr Moon is a member of the AGU, CGU, SEG, CSEG, CAP, CJRS, and RaS (London)