I plan to use GSLIB Deutsch and Journel (1992) to perform both the kriging of the well velocity with the seismic velocity as a trend and the sequential Gaussian simulation (sGs) to calculate a measure of the local and global uncertainties about the estimated model.

The kriging estimated value of the velocity based on the well data and using the seismic velocity model as a linear trend is

(8) |

where coefficients are estimated by solving
the kriging with a trend (KT) system (9), and are the velocities of the *N* neighboring points located at position
used to determine . The KT system is made of
(*N*+3) equations:

(9) |

where is the covariance of the velocity
at location and location , and *a*_{i} are the
coefficients of the linear trend:

(10) |

A covariance model
is therefore needed and will be inferred from the semi-variogram model of the well velocity. By definition, is equal to *C*(0)-*C*(*h*).
The sGs will also allow me to estimate a range of equiprobable velocity
models that will require some interpretation in order to produce a measure of
the uncertainty about the estimated velocity model.

The sGs procedure is based on the normal score transform of the velocity random variable , assuming that the transformed variable is multi-normal. When the multi-normality hypothesis cannot be retained, I will use an indicator simulation instead of the Gaussian approach.

11/12/1997