Optimization techniques for integrating spatial data

Two optimization techniques ta predict a spatial variable from any number of related spatial variables are presented. The applicability of the two different methods for petroleum-resource assessment is tested in a mature oil province of the Midcontinent (USA). The information on petroleum productivity, usually not directly accessible, is related indirectly to geological, geophysical, petrographical, and other observable data. This paper presents two approaches based on construction of a multivariate spatial model from the available data to determine a relationship for prediction. In the first approach, the variables are combined into a spatial model by an algebraic map-comparison/integration technique. Optimal weights for the map comparison function are determined by the Nelder-Mead downhill simplex algorithm in multidimensions. Geologic knowledge is necessary to provide a first guess of weights to start the automatization, because the solution is not unique. In the second approach, active set optimization for linear prediction of the target under positivity constraints is applied. Here, the procedure seems to select one variable from each data type (structure, isopachous, and petrophysical) eliminating data redundancy. Automating the determination of optimum combinations of different variables by applying optimization techniques is a valuable extension of the algebraic map-comparison/integration approach to analyzing spatial data. Because of the capability of handling multivariate data sets and partial retention of geographical information, the approaches can be useful in mineral-resource exploration.     

Comparison of British and American Carboniferous cyclic rock sequences

Classification is of interest to geologists as a convenient means of expressing ideas and concepts. Most classification schemes categorize a continuum into discrete classes or states based on some prominent character of the objects being classified. Unknowns then are identified as to their position within the classification scheme. Until recently most geologic classification schemes have been qualitative. With advent of the computer, applications of many quantitative statistical techniques have become practical. These techniques offer the advantages of repeatability and objectivity. This report gives results of the applications of several techniques for classifying Carboniferous cyclic rock sequences. Twenty sections were measured in detail in Great Britain and the United States. Particular importance was placed on noting transition from one lithology to another. Seven lithologic types were distinguished: (a) sandstone, (b) siltsone, (c) nonfossiliferous shale, (d) seatearth or underclay, (e) coal, (f) fossiliferous shale, and (g) limestone. It was noted also which part of the sequence was marine and which nonmarine. From the original data, the number of changes per 100 ft were calculated as well as an entropy index indicating the “orderliness” of the sequence and a matching index obtained by comparing the similarity in sequences of lithology between pairs of sections. The matching index is based on qualitative characters and in this regard belongs to a type of sequential analysis of scaleless nonnumeric data. The matching coefficients were clustered and displayed as dendrograms. A cluster analysis also was performed using nine variables (number of changes per 100 ft, entropy index, percentage thickness of sandstone, siltstone, nonfossiliferous shale, seatearth and coal, fossiliferous shale, and limestone, and percentage of nonmarine units) and the results displayed as dendrograms. In addition principal components analysis utilized the nine variables to determine if groups were present in the data. The first three principal components were interpreted geologically and a three-dimensional model constructed. Three loosely grouped clusters could be recognized in this display: (1) cyclic sequences associated with deltaic complexes, (2) sequences characteristic of deposition farther offshore, and (3) those composed mainly of marine sequences formed in an offshore open-marine environment.     

Meteorological excitation of the annual polar motion

Summary. Numerous studies have indicated that the annual term in the polar motion cannot be explained in any detail by meteorological/hydrological excitation and no reasonable alternative excitations have been put forward. Part of the problem has been that the hydrostatic adjustment of the oceans to the atmospheric pressure changes has traditionally been computed using the inverse barometer approach. This approach does not properly model the gravitational interaction between the atmosphere and oceans, and the inverse barometer theory is modified in this paper to account for this properly. The information necessary to compute the ocean tide and polar excitation caused by any change in the atmospheric pressure pattern is presented. The results of the application of this theory to two global atmospheric pressure data sets are examined and compared to results of other workers.
It is concluded that the atmosphere is observed well enough to answer the question of the annual excitation of polar motion and it is argued that the ground water excitation is the component with the largest error and remains the chief obstacle to the successful solution of this problem.