Stochastic simulation of complex geology is addressed through discrete wavelet transformation (DWT) that handles multiscale spatial characteristics in datasets and training images. The simulation of the proposed approach is performed on the frequency (wavelet) domain. A multiscale, multipoint simulation algorithm is proposed in this paper in which the scaling image and wavelet images across the scale are simulated jointly. The inverse DWT reconstructs simulated realizations of an attribute of interest in the space domain. The proposed algorithm reduces the computational time required for simulating large domain as compared to spatial domain multipoint simulation algorithm since the simulation is performed in the wavelet domain in which numbers of nodes to be simulated are significantly less as compared to spatial domain nodes. The algorithm is tested with an exhaustive dataset using unconditional simulation in two-dimensional data set. The realisations generated perform well and reproduce the statistics of the training image. The study conducted comparing the spatial domain filtersim multiplepoint simulation algorithm suggests that the proposed multiscale, multipoint algorithm generates equally good realisations at much lower computational cost.


Article metrics loading...

Loading full text...

Full text loading...


  1. Arpat, G. and Caers, J.
    [2007] Conditional simulation with patterns. Mathematical Geology, 39(2), 177–203.
    [Google Scholar]
  2. Chatterjee, S., Dimitrakopoulos, R. and Mustafa, H.
    [2012] Dimensional reduction of pattern-based simulation using wavelet analysis. Mathematical Geosciences, 44, 374–.
    [Google Scholar]
  3. Chatterjee, S. and Dimitrakopoulos, R.
    [2012] Multi-scale stochastic simulation with wavelet-based approach, Computers and Geosciences, 45, 189–.
    [Google Scholar]
  4. Gloaguen, E. and Dimitrakopoulos, R.
    [2009] Two dimensional conditional simulation based on the wavelet decomposition of training images. Mathematical Geosciences, 41(7), 679–701.
    [Google Scholar]
  5. Goovaerts, P.
    [1998] Geostatistics for Natural Resources Evaluation (Applied Geostatistics Series). Oxford University Press, New York.
    [Google Scholar]
  6. Honarkhah, M. and Caers, J.
    [2010] Stochastic simulation of patterns using distance-based pattern modelling. Mathematical Geosciences, 42, 517–.
    [Google Scholar]
  7. Journel, A.
    [2007] Roadblocks to the evaluation of ore reserved–The simulation overpass and putting more geology into numerical models of deposit. In: R.Dimitrakopoulos (Ed.) Orebody modeling and strategic mine planning, AusIIMM, Melbourn, 2nd Edition, Spectrum Series, 14, 29–32.
    [Google Scholar]
  8. Mallat, S.
    [1998] A wavelet tour of signal processing. Academic Press, San Diego, CA.
    [Google Scholar]
  9. Mao, S. and Journel, A.G.
    [2009] Generation of a reference petrophysical and seismic 3D data set: The Stanford V reservoir. Stanford Center for Reservoir Forecasting Annual Meeting. http://ekofisk.stanford.edu/SCRF.html (1999), Accessed 23 February2014.
    [Google Scholar]
  10. Strebelle, S.
    [2002] Conditional simulation of complex geological structures using multiple-point statistics, Mathematical Geology, 34(1), 1-21.
    [Google Scholar]
  11. Tran, T., Mueller, U.A. and Bloom, L.M.
    [2002] Multi-scale conditional simulation of two-dimensional random processes using Haar wavelets. Proceedings of GAA Symposium, Perth, 56–78.
    [Google Scholar]
  12. Vannucci, M. and Corradi, F.
    [1999] Covariance structure of wavelet coefficients: theory and models in a Bayesian perspective. J.R. Statis. Soc., 61, 986–.
    [Google Scholar]
  13. Zhang, T., Switzer, P. and Journel, A.
    [2006] Filter-based classification of training image patterns for spatial simulation. Mathematical Geology, 38(1), 63–80.
    [Google Scholar]

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