Study And Applications Of Adaptive Multiple Subtraction Based On L₁Norm

In seismic data processing the occurrence of multiple is always a great problem, especially in marine seismic exploration. Multiples have some negative influences on velocity model building, seismic imaging, seismic attribute analysis (for instance, AVO), structural interpretation, and so on. The main method of multiple elimination can be roughly divided into two categories. One is filtering methods which can deal with simple multiple; the other is wave field prediction and subtraction methods which are good at eliminating complex multiple.Wave field prediction and subtraction methods which current applied, mostly through the least squares method to match the prediction and the actual multiple, the requirements of effectively use is that should meet the assumption which the residual have minimum energy and to be orthogonal to multiple, also known as L2norm method. During matching subtraction, when multiple events are not orthogonal to primary events and the signal after multiple elimination has no minimum energy, the least-square adaptive matching filtering method can’t get correct matching results and so multiple elimination will produce some deviation. However, this paper makes a study of the multiple subtractions based on L1norm which can cope with these situations very well by using the weighted method to effectively avoid the assumption. Therefore, this choice is robust to "large" amplitude differences when measuring data misfit.L1norm situation unable to obtain extreme value because of its first derivative discontinuous. So the solution is approximated by a hybrid L1/L2norm minimized with the iteratively reweighted least squares (IRLS) method. The hybrid norm is obtained by applying a simple weight to the data residual. This technique is an excellent approximation to the L1norm. On application of the solution based on L2norm in the initial iterative, can effectively solve the nonlinear problems of the method.Based on a detailed theoretical analysis, a one-dimensional single channel model has been established to verify the two method’s application characteristics. At the meantime, it was compared and analyzed the L2norm method which combined with synthetic and field dataset processing. Horizontal stratigraphic model show that L1norm method can get better results and more robust, after processing through iterative. The complex stratigraphic model, the Pluto1.5model and one of the field data results also show that the L1-norm matching method can not only attenuate the multiples, but also preserve the primaries simultaneously.