Identifying waves in seismic sections sometimes requires the waves to be separated. The geophysicist has a variety of complementary filters at his disposal that can be used to perform optimum separations if they are carefully chosen and combined. The first part of this article was devoted to the principle and methods of wave separation. Wave separation methods can be divided up into three categories : acceptance region methods, inversion methods and matrix methods. The tau-p method and f-k filtering belong to the first category while the parametric method belongs to the second one. Matrix filtering by means of the cross-spectral matrix (SMF : Spectral Matrix Filtering), the singular value decomposition (SVD) and the Karhunen-Loeve method (KLT-Karhunen-Loeve Transform) belong to the third group. Matrix methods are used both to separate waves and to break data down into a signal space and a noise space. Here in the second part, we use synthetic data to compare how well the SVD and SMF methods perform in separating waves with only one eigenvector. We show that SMF filtering can be made much more effective by introducing models and present the SMF method with adapted or constrained models. We also introduce a field example of wave separation by conventional SMF filtering, then a synthetic example and two field examples of wave separation by SMF filtering with models. We demonstrate the advantages of using different wave separation methods together (f-k, KLT and SMF) to achieve optimum separation. The data that serve to illustrate this are full waveform acoustic data acquired in a horizontal drain hole. A VSP-type well survey is used to compare the different methods : f-k, SVD, SMF and the parametric method. The last example shows how SMF processing can be used for anisotropy measurement. The f-k filter requires a large number of traces that have been distance sampled at short intervals. The more stable the wave that is being extracted and the more clearly located it is in the f-k domain, the more efficient the filter is. The method is very cost-effective in CPU time. The KLT or SVD filter requires flattening the wave that is to be extracted, which must additionally be of greater amplitude. Filtering is carried out without any edge effect and the wave amplitude variations are preserved. It serves to separate the normal incidence wave from the other waves and the noise. The SMF filter (spectral matrix) is expensive in CPU time It makes the hypothesis that the wave is locally stable and does not require the data to be flattened. It can be used to separate very close neighboring waves without resorting to restrictive a priori hypotheses. It gives a measurement of time delays and also provides a measurement of variations in amplitude and phase spectra during propagation. This measurement is much better than the one supplied by the Wiener method, since it operates on all the traces. Additionally, it is used to separate data into a signal space and a noise space. The parametric method is the most expensive as regards time. It is simple to implement and requires no flattening or preparation of data. It extracts the waves according to chosen parameters, especially time delays. It is particularly recommended in offset vertical seismic profiling where the slowness of upgoing waves is unknown. It is robust with respect to some input parameters if the noise is low in comparison to the signal that is to be extracted. Many applications to field data have illustrated the effectiveness of these wave separation techniques. However, application to a new type of data often requires performance to be monitored to choose the best method
