Stochastic Signal Processing > Probability models
  • Step 1: ALPHA Example.
    The probability model used for modelling support and information effects identified on regionalized variable ALPHA considers each alpha sample as a unique realization of a random variable Z of x, output of a random function Z at location x. The probability model is a stationary model. It assumes that:
    • Average and variance of Z of x are constant and the same over the whole field
    • Spatial covariance of Z of x is a mathematical function only depending of distance h between two points inside the whole field.
    The probability model enables to mathematically compute the decrease of variance related to the support and information effects identified on the ALPHA data set.

  • Step 2: Depth Conversion Example.
    The probability model used for depth converting time interpreted horizons considers the well depth marker data as a unique realization of a random variable Z of x, output of a random function Z at location x. The probability model is a non stationary model. It assumes that:
    Average and variance of Z of x are varying in space according to the shape of the time interpretation and the considered velocity law.
    The probability model enables to mathematically compute the best estimation of the depth of the horizon at any location x of the field.