1887

Abstract

Summary

The paper deals with the problem of determining model conditions that correspond to experimental data on the geological objects properties, as applied to the variational-grid method of geomapping. The peculiarity of the problem lies in the fact that the model conditions are given in the form of partial differential equations, and it is necessary to define two or more such equations for determine the uniqueness of the solution. We propose an approach based on the definition of orthogonal hyperplanes in the multidimensional space of the first, second derivatives, and values of the function being mapped, which are most consistent with the available data. in the absence of experimental definitions of the values of the derivatives, an iterative method of their sequential refinement is proposed. The method was tested using examples of restoring model conditions corresponding to a series of periodic solutions. The problem mathematical formulation general nature and the possibility of optimizing the computational scheme determine the prospects of the approach considered for restoring model conditions in a wider class of functions.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201900524
2019-03-25
2024-04-19
Loading full text...

Full text loading...

References

  1. Волков, А.М.
    [1988] Геологическое картирование нефтегазоносных территорий с помощью ЭВМ. Недра, Москва
    [Google Scholar]
  2. Плавник, А.Г.
    [2010] Обобщенная сплайн-аппроксимационная постановка задачи картирования свойств геологических объектов. Геология и геофизика, 51(7), 1027–1037.
    [Google Scholar]
  3. Плавник, А.Г. и Сидоров, А.Н.
    [2018] Картирование свойств геологических объектов с учетом анизотропии на основе моделирования деформационного преобразования. Математическое моделирование, 30(3), 19–36.
    [Google Scholar]
  4. Sidorov, A.N., Plavnik, A.G., Sidorov, A.A. and ShutovM.S. [2014] Use of Variational Methods in Geological Mapping. Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg, 325–328.
    [Google Scholar]
  5. Plavnik, A.G.
    [2010] Generalized spline-approximation problem formulation for spatial data modeling in geosciences. Russ. Geol. Geophys., 51(7), 801–807.
    [Google Scholar]
  6. Plavnik, A.G. and Sidorov, A.N.
    [2018] Mapping the Properties of Geological Objects with Allowance for Anisotropy Based on the Simulation of the Deformation Transformation. Math. Model. Comput. Simulations, 10(5), 629–638.
    [Google Scholar]
  7. Sidorov, A.N., Plavnik, A.G., Sidorov, A.A. and ShutovM.S.
    [2014] Use of Variational Methods in Geological Mapping. Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg, 325–328.
    [Google Scholar]
  8. Volkov, A.M.
    [1988] Geologicheskoe kartirovanie neftegazonosnykh territorii s pomoshchiu EVM. Nedra, Moscow.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201900524
Loading
/content/papers/10.3997/2214-4609.201900524
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error