INFLUENCE OF INITIAL DATA REPRESENTATION ON THE RESULTS OF SIMULATION BY DOUBLE KRIGING METHOD

Abstract

The relevance. When solving inverse geophysical problems, the important task is to construct petrophysical parameters volumetric models. The greatest difficulties in developing the methods for solving this problem are determined by the inhomogeneity of the real geological environment, and their accuracy is defined by the inadequacy of the borehole observations grid. This article presents a new method, the distinguishing feature of which is the joint use of seismic exploration and well logging data. It is based on the geostatistical approach experience and solving the described problems uses the assumption that seismic and borehole data measured within a single geological object can have similar covariance properties. The reliability and effectiveness of the double kriging method have not been previously published, although their research is required for application of the method. One of the first questions here is to assess the impact of the input data representativeness. The main aim is to consider the influence of the input data representativeness on the modeling quality by the double kriging method and possible ways of developing a quantitative measure of the representativeness estimation. Objects: model of the seismic attribute cube; 3D CDP and GWL data of the Kontorovichsky Tomsk region deposit. Methods: theory of random processes, methods of linear algebra, statistical modelling and simulation experiment. Results. The authors have proved analytically that using the representative data sample entails a simulation error equal to zero. They proved analytically and practically that in the presence of an unrepresentative data sample, the simulation error and the Lagrange multiplier are directly proportional to the weight coefficients of the lacking data. On the basis of this fact, it was suggested that the Lagrange multiplier can be used as a measure of the used sample representativeness. This suggestion was practically verified on the Kontorovichskoe field materials of the Tomsk region, within the framework of which a simulation by double kriging method was carried out using three, five and seven wells. With the increase in the sample from three to seven wells, the value of the Lagrange multiplier was decreased, which confirmed the correctness of the proposed assumption.

Keywords

• statistical modelling
• seismic exploration
• kriging
• petrophysical modeling