In order to interpolate the rock properties predicted by several well logs, Karimi and Fomel (2015) used a weighted summation of the painting predictions.
The weights were calculated by radial basis function (RBF)
, whose value decays along the increasing distance (Micchelli, 1984).
An inverse quadratic form of the RBF is:
(2)
Then the interpolation can be calculated as below:
(3)
where
is the result of spreading well log at well location
into the seismic data and
represents the total number of used wells.
We propose to extend the definition of
from simply the horizontal distance
to the geologic distance that is measured along the seismic horizon:
(4)
in which
,
are points along a seismic horizon
;
is the curve length of the horizon, it can be calculated by
given local slope estimation
;
is fault attribute and
represents the distance penalty parameter, this term exaggerates the distance across fault.
The geologic distance indicates the decay of information confidence from the reference trace.
We perform this integration efficiently by accumulative predictive painting.
2024-07-04