(22) |

where s is a group of seismic traces from a seismic image ( ), r is the destruction residual, and , the destruction operator, is defined as

(23) |

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

(24) |

where is the unknown trace and is the reference trace. The predictive painting operator is defined as:

(25) |

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.

2019-05-07