Prediction and Elimination of Multiples Based on Energy Flux Conservation Theorem and Prediction Operator Equation

The received wave field including primaries and all of the multiples can be associated with the reflection coefficients which are only primaries by a prediction operator and two equations: the energy flux conservation equation and the prediction operator equation that is developed from the Levinson recursion and can be easily solved by Li group method under a two-dimensional condition. Given reflection coefficients, the prediction operator can be obtained by solving the prediction operator equation. By the energy flux conservation equation, the reciprocal of the prediction operator times the conjugate of it, the wave field can be predicted, in which both of the surface multiples and the internal multiples are involved. On the other hand, if the wave field is given, based on the energy flux conservation equation solved by the 2D spectral factorization, a fully automated data-driven algorithm is developed to remove the surface multiples as well as the internal multiples.