Stochastic Signal Processing > Spatial Data Conditioning
  • Step 1: Stationarity.
    Left image shows a Raw Time Map in figure a containing artefacts and noise. It is first decomposed into a non stationary trend in figure b and a stationary residual in figure c. The Trend is computed as a second order polynomial approximation inside a local moving neighbourhood.

  • Step 2: Spatial analysis.
    The experimental variograms are computed on the stationary residual shown in Figure a in 4 directions. They are fitted in figure b using a single nested anisotropic variogram model explained in figure c and containing a nugget effect plus a cubic 45 and a long inline range spherical model.
    The noise and artefacts are modelled with the nugget and the long range spherical variogram are interpreted as signature of the noise and the cubic model as the signature of the signal or contributive part of the time interpretation to the depth conversion.

  • Step 3: Factorial Kriging.
    Factorial Kriging is applied to best estimate the signal and noise components of the time residuals shown in figure a, b and c.
    The estimated signal residual is added to the time non stationary trend to obtain the conditioned time map.

  • Step 4: S D C results.
    The S D C output is the decomposition of the raw time map in figure a into its conditioned part contributive to the depth conversion in figure b and the removed noise non contributive to the depth conversion in figure c.