ABSTRACT Multiple removal is essential for seismic imaging in marine seismic processing. After prediction of multiple models, adaptive multiple subtraction is an important procedure for multiple removal. Generally, adaptive multiple subtraction can be conducted by the iterative reweighted least-squares (IRLS) algorithm with an [Formula: see text]-norm minimization constraint of primaries. We have developed a machine-learning algorithm into adaptive multiple subtraction, which is implemented based on support vector regression (SVR). Our SVR-based method contains training and prediction stages. During the training stage, an SVR function is estimated by solving a dual optimization problem with the feature vectors of the predicted multiples and the target values of the original data. The SVR function can transform predicted multiples nonlinearly for a better match between the predicted multiples and the true multiples. Furthermore, we use the SVR function to estimate multiples in the prediction stage by inputting the feature vectors of predicted multiples. Then, multiple-removal results are obtained by subtracting the estimated multiples directly from the original data. Synthetic and field data examples demonstrate that our SVR-based method can better balance multiple removal and primary preservation than the IRLS-based method.
Resolving a portfolio optimization problem with investment timing through using the analytic hierarchy process, support vector regression and a genetic algorithm
