Release:
2019, Vol. 5. №2About the author:
Andrey G. Plavnik, Dr. Sci. (Tech.), Chief Researcher, West Siberian Branch of Trofimuk Institute of Petroleum Geology and Geophysics of Siberian Branch Russian Academy of Sciences, Tyumen, Russia; Professor, Department of Oil and Gas Geology, Institute of Geology and Oil and Gas Production, Industrial University of Tyumen, Tyumen, Russia; plavnikag@ipgg.sbras.ru, https://orcid.org/0000-0001-8099-4874Abstract:
The variety of geological objects properties and the nature of their formation determine the presence and usage of a large number of different mapping methods, as well as the need to choose the method that is most suitable for each specific data set.
The problem is that the predictive properties of the results depend on the compliance or non-compliance of the model conditions used in the mapping methods with real laws. One of the approaches involves mapping according to the training data, with the subsequent comparison of the constructed maps predictive properties according to the examination data. Such an approach requires multivariate, computationally expensive calculations.
Under these conditions, determining the appropriate model conditions from the observed data is relevant in the development of geological mapping methods.
Within the framework of the variational-grid geological mapping method, there is considered the problem of determining model conditions that describe the spatial regularities of mapping parameters change in the form of partial differential equations and are consistent with observed set of experimental data on the properties of geological objects. A special feature of the problem is the need to define two or more equations to ensure uniqueness of the solution.
In this paper, the authors propose an approach based on the search for a parameter space including the values of the function being mapped, its first and second derivatives such a system of orthogonal hyperplanes that consistent for available experimental data with greatest degree. Direct implementation of this approach is complicated by the fact that the necessary values of the derivatives are not actually determined experimentally. Under these conditions, an iterative method is used to sequentially refine the values of the derivatives and restore the model conditions. The method has been successfully tested on examples of the reconstruction of partial differential equations 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.
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