Multi-scale multi-point simulation using wavelet transform.

Zoya Romanenko and Théophile Gentilhomme and Guillaume Caumon. ( 2013 )
in: Proc. 33rd Gocad Meeting, Nancy

Abstract

Multiple point statistics methods are widely used in reservoir modeling, but their ability to take into account relations between different scales is limited. This limitation could be overcome by using wavelet transform, whose main property is to decompose a signal (image, property) into different scales (frequencies) at different locations. This allows the integration of different scale secondary data (for example, seismic data), which is often an issue for conventional algorithms. This paper introduces a 2d multiple point simulation algorithm based on discrete wavelet transform. It can be used for the simulation of both categorical and continuous properties. Direct sampling is used to simulate a property at the coarse scale of a secondary data. Then template matching is used to simulate wavelet coefficients from coarser to finer scales. Examples of meandering channels continuous property simulations show that the proposed method reproduces the conditioning data, the inter-scale relations and the spatial dependencies of the training image. It also reduces computational time compare to basic direct sampling algorithm due to coarse scale simulations.

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BibTeX Reference

@INPROCEEDINGS{RomanenkoGM2013,
    author = { Romanenko, Zoya and Gentilhomme, Théophile and Caumon, Guillaume },
     title = { Multi-scale multi-point simulation using wavelet transform. },
 booktitle = { Proc. 33rd Gocad Meeting, Nancy },
      year = { 2013 },
  abstract = { Multiple point statistics methods are widely used in reservoir modeling, but their ability to take into account relations between different scales is limited. This limitation could be overcome by using wavelet transform, whose main property is to decompose a signal (image, property) into different scales (frequencies) at different locations. This allows the integration of different scale secondary data (for example, seismic data), which is often an issue for conventional algorithms.
This paper introduces a 2d multiple point simulation algorithm based on discrete wavelet transform. It can be used for the simulation of both categorical and continuous properties. Direct sampling is used to simulate a property at the coarse scale of a secondary data. Then template matching is used to simulate wavelet coefficients from coarser to finer scales.
Examples of meandering channels continuous property simulations show that the proposed method reproduces the conditioning data, the inter-scale relations and the spatial dependencies of the training image. It also reduces computational time compare to basic direct sampling algorithm due to coarse scale simulations. }
}