We adopt predictive painting to interpolate well log data along seismic structure. Predictive painting is defined using plane-wave destruction filters that measure the local slopes of seismic events (Fomel, 2002). The plane-wave destruction operator can be written in linear operator notation
where s is a group of seismic traces from a seismic image (
), r is the destruction residual, and
, the destruction operator, is defined as
where is the identity operator and describes the prediction of trace j from trace i by shifting along the local slope of the seismic data. Slopes can be estimated in this way by minimizing the prediction residual operator r using regularized least-squares optimization. The prediction of one trace from another trace (Fomel, 2010) can be defined as
where is the unknown trace and is the reference trace. The predictive painting operator is defined as:
Predictive painting spreads information along local seismic structures to generate volumes of well log data from a single well log reference trace providing a method to predict an expected log profile in a location with no well log data.