The areal distributions of hydrocarbons and other components of rock bodies have been mapped in an attempt to relate their distributions to economic concentrations of hydrocarbons and other components. These components are dispersed three-dimensionally; their vertical distribution may be as important as (or more important than) their areal concentration. Distribution patterns in three dimensions are difficult to portray; this has handicapped efforts to relate the distribution patterns to economic drilling objectives.

Response surface analysis provides a rapid method of displaying three-dimensional relations within rock bodies. The variable of interest--for example, percent organic carbon--is regressed upon a linear combination of the three geographic axes. The resulting linear equation is a least-squares expression of the relation between the dependent variable and the spatial coordinates. In practice, a polynomial expansion of the linear equation commonly is used to provide a better representation of the data. Other linear equations may be more appropriate in specific cases; trigonometric functions, for example, may be introduced to simulate the effect of bedding.

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Measurements of organic carbon from the Lower Cretaceous Mowry Shale in Wyoming provide an illustration of the effects that can be obtained using different linear models in the regression. Relations between the distribution patterns and location of Lower Cretaceous hydrocarbon fields in this region can be shown graphically on the models.

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