Mathematical Geology, VoL 9, No. 4, 1977

Estimation of the Probability of Success in Petroleum Exploration 1 John C. Davis 2 A probabilistic nwdel for oil exploration can be developed by assessing the conditional relationship between perceived geologic variables and the subsequent discovery of petroleum. Such a model includes two probabilistic components, the first reflecting the association between a geologic condition (structural closure, for example) and the occurrence o f oil, and the second reflecting the uncertainty associated with the estimation o f geologic variables in areas o f limited control Estimates of the conditional relationship between geologic variables and subsequent production can be found by analyzing the exploration history of a "training area" judged to be geologically shnilar to the exploration area. The geologic variables are assessed over the training area using an historical subset of the available data, whose density corresponds to the present control density in the exploration area. The success or failure of wells drilled in the training area subsequent to the time corresponding to the historical subset provides empirical estimates o f the probability o f success conditional upon geology. Uncertainty in perception o f geological conditions may be estimated from the distribution o f errors made in geologic assessment using the historical subset o f control wells. These errors may be expressed as a linear function o f distance from available control. Alternatively, the uncertainty may be found by calculating the semivariogram o f the geologic variables used in the analysis: the two procedures will yieM approximately equivalent results. The empirical probability functions may then be transferred to the exploration area and used to estimate the likelihood of success o f specific exploration plays. These estimates will reflect both the conditional relationship between the geological variables used to guide exploration and the uncertainty resulting from lack of control. The technique is illustrated with case histories front the midContinent area o f the U.S.A. KEY WORDS: conditional probability, petroleum exploration, map reliability, discriminant analysis.

INTRODUCTION P e t r o l e u m p r o s p e c t s a r e e v a l u a t e d o n t h e basis o f t h e i r p o t e n t i a l w o r t h . T h e e c o n o m i c a n a l y s i s m a y be i n t u i t i v e o r h i g h l y f o r m a l i z e d , b u t t h e u l t i m a t e d e c i s i o n o f w h e t h e r to drill o r n o t is b a s e d o n a n a s s e s s m e n t o f t h e p r o b a b l e financial r e t u r n f r o m t h e w i l d c a t drilling. T h e f i n a n c i a l a n a l y s i s o f a p r o s p e c t may b e q u i t e i n v o l v e d , c o n s i d e r i n g s u c h f a c t o r s as t h e p r o b a b l e f u t u r e p r i c e Manuscript received 1 September 1976. This paper was presented at Symposium 116.3, "Quantitative Strategy for Exploration," held as part of the 25th International Geological Congress, Sydney, Australia, August 1976. -~ Kansas Geological Survey, Lawrence, Kansas 66044. 409

~ 1977 Plenum Publishing Corp., 227 West 17th Street, New York, N.Y'. 1001I. To promote freer access to published material in the spirit of the 1976 Copyright Law, Plenum sells reprint articles from all its journals. This availabiIityunderlines the fact that no part of this publication may be reproduced, stored in a retrieval system or transm ned in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher Shipment is prompt; rate per article is S7.50.

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of oil, discount rates, variables in drilling and leasing costs, and many other factors. The most important assumption in the financial analysis, however, is of the probability that a discovery will be made. This probability must be assumed by the decision-maker or, more desirably, supplied by the geologist who has developed the prospect. It is standard practice in many companies to require the exploration geologist to evaluate the probability of success of his wildcat prospects. These probabilities are subjective, based on the geologist's knowledge or beliefs about the geologic controls influencing the accumulation of petroleum in the area, and are tempered by the subjective appraisals of reviewers and managers in the decision chain. In common with other subjective assessments, these j0dgments of the probability of success tend to be inconsistent from person to person, and even from time to time within an individual. The desirability of probability assessments which are not subjective is apparent. However, few serious efforts have been made to develop such probabilities in petroleum exploration. Ideally, success probabilities should be conditional upon geologic variables, because these influence the migration and entrapment of hydrocarbons, and often can be measured with greater reliability than can the presence of petroleum itself. Although it is possible to estimate probabilities of success for individual prospects without consideration of alternatives, a more general approach would involve assessing the probabilities of success over an entire region of interest. Such probabilities might be expressed as a continuous probability surface which could be mapped. However, probabilities which form a continuous surface obviously must be derived from geologic variables which are themselves continuous. This restriction is not severe, as most of the geologic variables used as exploration guides can be regarded as spatially continuous. Examples include structural configuration, either measured directly or by geophysical methods; variation in lithology within a rock unit; and changes in geochemical composition of pore fluids. The K O X Experiments

The Kansas Geological Survey has undertaken an extensive research project into methods for estimating the probability of success in drilling ventures which are conditional upon geologic variables. The research effort, called the Kansas Oil Exploration (KOX) Project, extended from 1972 to the present time. The approach chosen was tailored to analysis of the Kansas portion of the mid-Continent petroleum province, but the general principles are widely applicable. Although Kansas oil production is now at a mature stage, the degree of exploitation varies across the state. It is possible to contrast local areas of advanced maturity with neighboring regions which are still at

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an early stage o f their exploration. The exploration history of the more mature regions allows estimation of probabilities of success which can then be used in the prediction of probabilities of success in future drilling in immature areas. Efforts have been concentrated on the use of geologic variables which have demonstrated utility for exploration in the mid-Continent region. Wherever possible, methodologies are used which are already familiar to practicing explorationists in Kansas. In this way, the derived probabilities are meaningful to the exploration geologists themselves, and their actions more likely to be influenced by knowledge o f these probabilities. The K O X research included investigation of three methodologies which were field-tested in three exploration areas (Fig. 1). The first experiment, conducted by Alfredo Prelat (1974), was an attempt to relate structural

Figure 2. Cellular grid superimposed on Lansing Group structure map in Stafford Co., Kansas, made using all wildcats and selected field wells drilled prior to 1946. Grid contains 144 cells, each 2 × 2 miles square. From Prelat (1974).

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configuration of the Pennsylvanian Lansing-Kansas City Group to oil production from that unit in Stafford County, of central Kansas. The Lansing-Kansas City is a limestone which contains numerous reservoirs. Prelat attempted to subjectively classify the geologic structure within small areas into categories such as "anticline," "nose," "homocline," or "syncline." The record of drilling successes within each of these classes of structures then provided an estimate of the probability of success. Structure was assessed from computer-contoured maps subdivided into geographic cells (Fig. 2). A series of maps were made using data available at five-year time intervals from 1935 to 1970. Historically later maps are based on more complete information, so the mapped surfaces in general are more complex and structures are more readily classified. Prelat's study represents an intermediate stage between purely subjective assessment of probabilities and the more objective procedures desired. The primary difficulties are the result of inconsistency in the classification of structures within geographic cells and the necessity of dividing the area into discrete cells rather than treating the map area as a continuum. A similar but more ambitious variant of this approach was used in an EXXON study of the San Joaquin Valley (Grender, Rapoport, and Segers, 1974). They divided the sedimentary basin into a series of three-dimensional cells and subjectively classified the structure and lithologic content of each cell. The results of drilling through various cells provided "petroleum ratings" which can be regarded as probabilities. Similar studies, using surface geology in the exploration for minerals, have been published by Harris (1965, 1969) and by Agterberg et al. (1972). A second KOX test project was also concerned with analysis of structural traps in the Lansing-Kansas City Group, but in Graham County, an area of northwestern Kansas (Hambleton, Davis, and Doveton, 1975). An attempt was made to avoid any element of subjectivity by using various quantitative measures of local structure. Because these measures of local structure could be assessed continuously across the area, it was not necessary to segment the map into discrete cells. By relating magnitudes of the structural measurements with drilling success ratios, maps could be made of the probability of success as a continuous variable across the exploration area. The third KOX experiment was conducted by Doveton (1973, 1976) in a part of Stafford County, Kansas, using the Mississippian "B" unit, an informal stratigraphic designation tbr an interval composed of mixed Chert and shale. Primary factors controlling hydrocarbon entrapment in the Mississippian "B" are stratigraphic variations. This experiment was designed ':o assess methods for using lithologic data and for combining multiple variables into a single expression of the probability of success which could be mapped.

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A common feature of the three KOX experiments is that all relied upon a "re-experience" approach. The results of wildcat drilling are commonly interpreted in hindsight. After a well has been drilled, it is usually easy to rationalize reasons for its success or failure. From the time of the rationalization, the geology of the prospect is regarded in the light of post-drill knowledge. However, any probabilistic assessments that might be useful in future exploration must be based upon the geologic conditions as they are interpreted prior to drilling of the well. Knowledge of the reasons for the success or failure of a wildcat provides little assistance in evaluating undrilled prospects. Were the geologic conditions that lead to a dry hole known in advance of drilling, obviously dry holes would never be drilled. This simple but basic concept has been overlooked in most studies which attempt to relate the outcome of exploratory ventures with geologic conditions. PERCEPTUAL

ERRORS

Probability estimates which are conditional upon perceived geology can be considered to be composed of two independent parts. The first is the probability that the geology is actually what it seems to be. The second is the conditional probability relating the geologic variables to the presence of oil. Both the perceptual and oil-occurrence probabilities must be assessed and combined for every prospect site which is to be evaluated. For consistency, it is essential that geologic variables used in probabilistic exploration be mapped by computer. Mapping algorithms are estimation procedures where values at as-yet-undrilled localities are estimated from known control points. Errors in the estimation procedures have been investigated by numerous authors including Switzer, Mohr, and Heitman (1964) and Matheron (1969, 1971) and his associates (Huijbregts, 1975; Huijbregts and Matheron, 1971; David, 1972). Universal kriging is a wellknown procedure which has as one of its objectives the estimation of the possible error in the contoured surface (Matheron, 1969). Basically, the method involves first estimating the form of the surface autocorrelation, and then using this autocorrelation to assess the error distribution at the interpolated points as a function of their distance from control points. Universal kriging was used in one of the K O X test areas by Olea (1972, 1974). Similar results can be obtained by an empirical method which requires using part of the data in an area to predict values of the map variable at "blind" locations where the true values are known. Differences between the known values and the true values can then be assessed. The spread in estimates around the true surface can be expressed as the root-mean-square (RMS) error. In the Graham County, Kansas, KOX experiment the LansingKansas City structural horizon was mapped using only the first 352 wells

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Figure 3. Structure map of top of Lansing Group as perceived in 1952, when 352 wells were drilled in Graham Co., Kansas, training area. From Hambleton, Davis, and Doveton (1975). drilled in the area (Fig. 3), The area was then remapped using 2758 wells available at the end of 1974 (Fig. 4). Thus, estimates of the perceptual error were obtained at 2406 locations. Figure 5 shows histograms of these errors expressed according to the distance from the estimated location to the nearest control point. These histograms can be replaced with normal error curves having the same means and standard deviations (Fig. 6). I f the standard Jeviations (or RMS) o f these error distributions are plotted as a function of Jistance from control, they fall on a straight line whose coefficients can be ~lsed to map uncertainty in perception as a function of distance from control Fig. 7). Note that the error relationship has an upper limit which is equal o the standard deviation of the m a p p e d surface itself. In the G r a h a m County experiment, the data on structural elevation ,vere divided into two parts on the basis of the date of drilling, This was done

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Figure 4. Current (1974) perception of structure of top of Lansing Group in Graham Co., Kansas, training area. Area now contains 2758 wells. From Hambleton, Davis, and Doveton (1975). so results obtained in G r a h a m County could be compared with the current activities in nearby Rawlins County, which is at a much earlier stage in its exploration history. However, a chronological separation of the data set is not essential. In Doveton's (1976) experiment with the Mississippian " B , " only 124 wells were available for mapping. Subdividing these wells on the basis of chronology would result in data sets too small for reliable estimates o f perceptual error. Instead, Doveton randomly selected wells from the complete data set and used these to map the entire area. The remaining wells were "blinds," where the estimated surface values were compared with the true values. The process was repeated several times, selecting random sets

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Figure 8. Root-mean-square (RMS) error in discriminant score map in Stafford Co., Kansas, area. Error is expressed as exponential function of distance from nearest control well. After Doveton (1976). The error function found by Doveton has a much steeper slope than hat used for the Graham County structural map. This is in part a result of *ae smaller sample size and also because the composite variable mapped by ~oveton is autocorrelated only over a limited spatial range. Selection of Geological Variables

he Graham County KOX experiment was concerned with establishing the ~obabilities o f success conditional upon a single geological variable-fuctural configuration. Although some reservoirs in the Lansing-Kansas ity Group are known to be stratigraphically controlled, all exploration in ,is area is based upon structural plays. Seismic reflection measurements of e top o f the limestone unit are extensively used to supplement structural aps made from well control. Since industrial practice in the area is based elusively on a structural trapping model, the Graham County experiment ~ployed only the single variable, structural configuration. However, explorationists do not explore on the basis of absolute struc~al relief, but rather for local structural features within restricted areas. ~at is, they are concerned with whether a positive structure of limited extent l anticline) is present at a specific locality. Prelat (1974) attempted to define :h local structures subjectively, with inconclusive results. Therefore, a rnber of procedures were evaluated for systematically isolating and measur-

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ing local structures in the Graham County area. Methods included filterin for structures having specified wavelengths (Robinson, Charlesworth, an. L Ellis, 1969); use of context measures developed by Demirmen (1972, 1973a); and use of trend-surface residuals. Demirmen's techniques consisted c f determining the rate of curvature along radial lines placed over the surfac: (1973b). Statistics are calculated for these lines which allow characterizatio l of both the size and shape of local features. Unfortunately, both spatial filtering and Demirmen's methods require a very large set of control poinl~ spaced on a regular grid. This grid may be estimated by a contouring procedure, but the resulting set of points has no more degrees of freedom tha l the number of original data points used to make the contour map. Becaus.~ trend surfaces are global functions generated by comparatively few term.,, data requirements are not so extensive. In this application, a trend surface regarded as a crude high-pass filter whose output is a quantitative expressio l of local structure. Selection of the specific mathematical model used to define a local structure can be done on an empirical basis. Since the objective of the KO~ study was to measure some component of perceived structure and to use th : probabilistic experience gained to map an adjacent area of comparable siz,, complexity, and sampling density, the geologic variable selected should t:: the one which has the highest conditional relationship with oil occurrenc,. This empirical relationship can be found by calculating the percentage c ? producing wells within any structural magnitude class, or the percentage c f the area of any structural magnitude class which is underlain by petroleux 70

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Figure 9. Empirical probabilities of success conditional upon magnitude of third-order trend-surface residuals from Lansing Group structure in Graham Co., Kansas. Probabilities based on results of drilling 2333 wells after 1952.

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Figure 10. Empirical probabilities of success conditional upon magnitude of fourth-order trend-surface residuals. From Hambleton, Davis, and Doveton (1975). .~servoirs. Examples are shown in Figures 9, t0, and 11, which represent the .robabilities of success in third-, fourth-, and fifth-order trend-surface esiduals, and also in Figure 12, which represents the percentage o f producing ,'ells within areas defined by spatial filtering for features having a wavelength .f 2½ miles or less. The best separation between producing and dry regions • found by using fourth-order residuals as the measure of structural variation. Use of trend-surface residuals in this area has an added advantage; it is widely practiced procedure accepted by explorationists. Introduction of a ~ore complex methodology such as spatial filtering or context measurement ould be justified only if they produced a higher conditional relationship ith petroleum occurrence. Another advantage of trend-surface residuals is ~at separation of the structural surface into two components is a linear 60-

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Figure 1I. Empirical probabilities of success conditional upon magnitude of fifth-order trend-surface residuals.

John C. Davis

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Figure 12. Empirical probabilities of success conditional upon magnitude of spatial filter response. Filter designed to pass features having a wavelength of 2 1/2 miles or less. operation. Therefore the error function found for the surface itself is als, applicable to the residuals from that surface. In Doveton's (I 976) Mississippian " B " experiment, he used Demirmen ; (1972) context measurements to define local variations in the mapped surfac,. The small number of control points available for the study precluded a~ extensive empirical analysis of the alternative methodologies that was possibl in the Graham County test. The KOX Mississippian " B " experiment was designed to test method; utilizing multiple geological variables. In principle it would be possible t , map a series of geological variables, establish the conditional relationshit: ; between each of these variables and the occurrence o f oil, and then combin .~ the series of conditional probabilities. However, this would involve calcuhtion of a multidimensional contingency table and would require inordinal ." numbers of observations. Instead it was decided to attempt to combine a 1 of the geologic variables used into a composite variable which was most closel i related to the presence of oil. This can be done effectively by multiple di:criminant function analysis, a procedure also used by Abry (1975) in t study of oil production in the Tatum Basin of New Mexico. If the discrimin~ tion is based upon whether a well is a producer or a dry hole, the linear combination of geologic variables obtained will be the best possible fcr predicting the status of a prospect based on these same geologic variables. Doveton used a discriminant function based on six geologic variable These include the structural elevation o f the top o f the Mississippian " B , ' thickness o f the " B " unit, and an estimate of the proportion of shale in tt ; unit. The latter variable reflects the permeability o f the producing formatio~. Estimates of shale proportions were derived from measurements o f tl~: gamma-ray response in wells drilled through the interval.

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The geologic variables measured in each well pertain only to a single eographic location (or "locus"). In other words, measurements at a well tte record subsurface characteristics at a point and provide no information :bout how these properties change laterally. However, the accumulation of il or gas is governed not only by the presence of a suitable reservoir rock, ut also by a suitable trap configuration. Therefore, in addition to measuring ~servoir capabilities at points, it is necessary to estimate the lateral variation 1 the geologic variables. These lateral changes may be expressed as "context" ~aeasures. In the study done by Doveton, the measure of local context used vas Demirmen's (1972) "marginal polar slope." This expresses the rate of .urvature of the mapped surface within a one-mile square centered around ach test well. Use of context variables increased the number of geologic ariables from three to six. The variables ranked in order of decreasing importance in the linear

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discriminant function included: (1) lateral change in shale ratio; (2) loce thickness; (3) lateral change in thickness; (4) lateral change in structure! residual; (5) local shale ratio; (6) local structural residual value. Within th~ original data set, the probability o f correct classification of the location of producing well is 0.9 and the probability o f correct classification of a dry hot ~. location is 0.81. Discriminant function scores were calculated for each wel, then contoured. The resulting surface can be regarded as a composite measur o f the geology that is specifically keyed to oil occurrence. By tracing th contour line which coincides with the discriminant index, the area may b; divided into two discriminant score categories--one containing p o t e n t i a l t productive localities and the other containing unfavorable areas (Fig. 13). The discriminant score at each well is simply a linear combination c" the original geological variables measured in the Mississippian " B . " Since th • original variables may be considered as a continuous surface, their combina tion into a discriminant score is also a continuous surface. Although at eac well a discriminant score can be calculated directly, in areas between w e l l the discriminant value must be interpolated. Just as the interpolation c" original variables involves a degree of uncertainty, so does the contourin : of discriminant scores. This uncertainty must be considered if the discriminan : scores are to be used in a probabilistic fashion. COMBINING CONDITIONAL AND PERCEPTUAL PROBABILITIES At this point two probability distributions must be combined: one describin

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Estimation of the Probability of Success in Petroleum Exploration

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uncertainty in perception, the other describing the conditional relationip between perceived geology and the occurrence of oil. Figure 14, taken ~m the G r a h a m County test area, shows how this may be done. At any een location in the m a p area, the probability of success may be estimated sed upon the geologic variable or variables. However, the perception o f the ology at this unsampled location is subject to error, which is expressed as a nction of distance to the nearest available well control. In the example own, a perceived 30-ft positive structural residual is indicated at a distance mile from the nearest control point. The two error functions may be cornned to give the probability that the locality will be producing, considering

Figure 15. Probability map for Graham Co., Kansas, area, based on structure as perceived in 1952. Contour interval is 0.05 probability of discovery of oil. Areas having probabilities higher than ambient or background level are shaded. All oil fields in area are shown in black. Compare with Figure 3 to determine association of post-1952 fields with areas of high probability. From Hambleton, Davis, and Doveton (1975).

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the possibility that the perception of the structural surface may be in erro ". The more distant the prospective location is from a control point, the larg, r the perceptual error distribution becomes, and the greater the averagir g effect when the two probability distributions are combined. The end rest t is that at distant locations the probabilities become equal to the region 1 average success ratio or ambient background probability. This, of course, s intuitively expected. In those areas where too little information is availab e for reliable prediction, the best estimate of the probability o f success is simp y the regional average rate o f success. Since both the error function and the conditional probability can ~ e assessed for any point on a map, predictions of success can be made at a regular gridwork o f points which can in turn be used to create a conto~ r map. The final step in the probabilistic assessment is creation of a map o f tl e expected probabilities of success over the entire region. Such a map is shox~ a in Figure 15 for the G r a h a m County area. In the K O X research p r o g r a r , similar maps have been made for each of the other test areas, expressing tl e likely results o f continued exploration within these regions. Given the probability estimates contained within these maps, the explor; tion geologist now has the necessary input parameters for financial asses ments such as those described in the accompanying article by John Harbaug and in the book by Newendorp (1975). These probability assessments an t their contingent econometric analyses can provide a more rational basis fi r exploration decisions than has previously been possible. Petroleum explor;tion is an inherently probabilistic undertaking. Use of formal methods ~f probability analysis should result in a significant increase in the efficiency, f exploration. In addition, the requirement for careful analysis of the cotditional relationships between geologic variables and the occurrence , f petroleum should shed light on the basic nature o f oil generation, migratio , and entrapment. REFERENCES

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emirmen, F., 1973b, Probabilistic study of oil occurrence based on geologic structure in Stafford County, south-central Kansas: Kansas Geol. Survey, Tech. Rept. Project KOX, Univ. Kansas, Lawrence, 188 p. oveton, J. H., 1973, Numerical analysis relating location of hydrocarbon traps to structure and stratigraphy of the Mississippian 'B' of Stafford County, south-central Kansas: Kansas Geol. Survey, Tech. Rept. Project KOX, Univ. Kansas, Lawrence, 56 p. )oveton, J. H., 1976, Linear discriminant analysis can be used as an oil-prospect exploration guideline: Oil and Gas Jour., v. 74, no. 18, p. 324-328. ;render, G. C., Rapoport, L. A., and Segers, R. G., 1974, Experiment in quantitative geologic modeling: Am. Assoc. Petroleum Geologists Bull., v. 58, no. 3, p. 488--498. Iambleton,W.W., Davis, J. C., and Doveton, J. H., 1975, Estimating exploration potential, in J. D. Haun (ed.), Methods of estimating the volume of undiscovered oil and gas resources: Am. Assoc. Petroleum Geologists, Studies in Geology No. 1, p. 171-185. tarbaugh, J. W., Doveton, J. H., and Davis, J. C., 1977, Probability methods in oil exploration: Wiley-Interscience, New York, 261 p. tarris, D. P., 1965, Multivariate statistical analysis--a decision tool for mineral exploration: Short Course and Symp. on Computers and Computer Applications in Mining and Exploration, v. 1 : Univ. Arizona, p. C1-C35. -larris, D. P., 1969, Alaska's base and precious metals resources: a probabilistic regional appraisal: 7th Intl. Symp. on Operations Research and Computer Applications in the Mineral Industries, Colorado School Mines Quarterly, v. 64, no. 3, p. 295-327. quijbregts, C. J., 1975, Regionalized variables and quantitative analysis of spatial data, in J. C. Davis and M. J. McCullagh (eds.), Display and analysis of spatial data: John Wiley & Sons, Ltd., London, p. 38-53. -luijbregts, C. J., and Matheron, G., 1971, Universal kriging: an optimal method for contouring and trend surface analysis: Canadian Inst. of Mining and Metallurgy, CIM Special Vol. No. 12, p. 159-169. vlatheron, G., 1969, Le krigeage universet: Les Cahiers du Centre de Morphologie Math6matique de Fontainebleau, v. 1, 83 p. Vlatheron, G., 1971, The theory of regionalized variables and its applications: Les Cahiers du Centre de Morphologie Math6matique de Fontainebleau, v. 5, 211 p. qewendorp, P. D., 1975, Decision analysis for petroleum exploration: Petroleum Pub. Co., Tulsa, Oklahoma, 750 p. )lea, R. A., 1972, Application of regionalized variable theory to automatic contouring: Kansas Geol. Survey, Tech. Rept. Project KOX, Univ. Kansas, Lawrence, 191 p. (API Spec. Rept. Project 131). )lea, R. A., 1974, Optimal contour mapping using universal kriging: Jour. Geophysical Research, v. 79, no. 5, p. 695-702. 'relat, A., 1974, Statistical estimation of wildcat well outcome probabilities by visual analysis of structure contour maps of Stafford County, Kansas: Kansas Geol. Survey, Tech. Rept. Project KOX, Univ. Kansas, Lawrence, 103 p. ~obinson, J. E., Charlesworth, H. A. K., and Ellis, M. J., 1969, Structural analysis using spatial filtering in Interior Plains of south-central Alberta: Am. Assoc. Petroleum Geologists Bull., v. 53, no. 11, p. 2341-2367. ;witzer, P., Mohr, C. M., and Heitman, R. E., 1964, Statistical analyses of ocean terrain and contour plotting procedures: Project Trident Tech. Rept. 1440464, Arthur D. Little, Inc., Cambridge, Mass. (Contract NObsr-81564, Bur. Ships, Dept. Navy), 81 p.