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  • Articles  (5)
  • stratigraphy  (3)
  • calculus of variations  (2)
  • 2020-2023
  • 2010-2014
  • 1970-1974  (5)
  • 1965-1969
  • 1935-1939
  • Mathematics  (5)
  • Geosciences  (3)
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  • Articles  (5)
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  • Mathematics  (5)
  • Geosciences  (3)
  • 1
    Electronic Resource
    Electronic Resource
    A lithologic data-recording form for a computer-based well-data system (1972)
    Springer
    Mathematical geology 4 (1972), S. 61-72 
    Details
    ISSN: 1573-8868
    Keywords: data processing ; data recording ; data files ; lithology ; petroleum ; stratigraphy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Well-data files maintained by petroleum companies and service companies are important sources of data for exploration geologists. To make these data readily accessible and useful for computer studies, three preliminary steps are necessary: (1) systematic data gathering and recording, (2) storage for ready retrieval, and (3) preparation of analysis programs. One important source of geologic data is lithologic descriptions of well cuttings and cores. The practical lithologic data-recording form described here is used routinely at the well site and in the laboratory. It is designed in an 80-column format and uses codes for lithologic characteristics, porosity, and hydrocarbon shows, and forms part of an integrated well-data file. This datarecording form has the advantages that descriptions are made according to a standardized format convenient to use at the well site, and the data are subsequently available in raw form relatively free from interpretive bias. A library of analysis and display programs can be assembled for utilization of the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083194
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  • 2
    Electronic Resource
    Electronic Resource
    Z-trend maps for quick recognition of geologic patterns (1971)
    Springer
    Mathematical geology 3 (1971), S. 171-181 
    Details
    ISSN: 1573-8868
    Keywords: Fourier analysis ; graphics ; mapping ; spatial filtering ; trend analysis ; stratigraphy ; structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Z-trend maps are a simplified lineprinter version of spatially filtered maps designed to give a quick visual appraisal of trends. The printout shows a “yes-no” configuration by a printed character or a blank so that the map has a conspicuous pattern. This pattern reflects the presence, position, and trend of the desired features. If a reasonable symbol density ratio is used the results can be visually pleasing thus enhancing trend recognition. Z-trending can be adapted to any map with stationary properties but is most easily applied to data that have been filtered with a bandpass operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02045959
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  • 3
    Electronic Resource
    Electronic Resource
    Stratigraphic correlation of subsurface geologic data by computer (1972)
    Springer
    Mathematical geology 4 (1972), S. 331-343 
    Details
    ISSN: 1573-8868
    Keywords: cross correlation ; mapping ; plotting ; statistics ; stratigraphy ; structure ; electric logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Manual, semiautomatic, and fully automatic procedures for correlating subsurface data are reviewed. Special emphasis is placed on the use of electric-log data, including that of the dipmeter log, in this discussion. The Holgate method is described for its use in “fine-tuning” or refining gross correlations. A procedure for creating a matrix map for empirically establishing correlation between sets of data is described, and idealized models are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114094
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  • 4
    Electronic Resource
    Electronic Resource
    Parameter variation for the solution of two-point boundary-value problems and applications in the calculus of variations (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 164-178 
    Details
    ISSN: 1573-2878
    Keywords: Two-point boundary-value problems ; calculus of variations ; numerical methods ; differential equations ; computing methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the parameter variation method, a scalar parameterk, kε[0, 1], is introduced into the differential equations. The parameterk is inserted in such a way that, whenk=0, the solution of the boundary-value problem is known or readily calculated and, whenk=1, the problem is identical with the original problem. Thus, bydeforming the solution step-by-step throughk-space fromk=0 tok=1, the original problem may be solved. These solutions then provide good starting values for any convergent, iterative scheme such as the Newton-Raphson method. The method is applied to the solution of problems with various types of boundary-value specifications and is further extended to take account of situations arising in the solution of problems from variational calculus (e.g., total elapsed time not specified, optimum control not a simple function of the variables).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935537
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  • 5
    Electronic Resource
    Electronic Resource
    A lower closure theorem for abstract control problems withL p-bounded controls (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 521-528 
    Details
    ISSN: 1573-2878
    Keywords: Lower closure theorems ; generalized control theory ; control theory ; calculus of variations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A lower closure theorem for an abstract control problem is proved. The functional isJ(ϕ,u)=∝ G f 0(t, (Mϕ)(t),u(t))dt and the state equations areNϕ(t)=f(t, (Mϕ)(t),u(t)). It is shown that, if {(ϕ k ,u k)} is a sequence of admissible controlsu k and corre-sponding trajectories ϕ k such that lim infJ(ϕ k ,u k)〈+∞ and such that ϕ k → ϕ weakly,Mϕ k →Mϕ strongly,Nϕ k →Nϕ weakly, and {u k} is bounded in someL p norm, then there is a controlu such that (ϕ,u) is admissible and lim infJ(ϕ k ,u k)≧J(ϕ,u).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932846
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