· · · Institutional Repository

Surface-related multiple reflections are often considered noise in the seismic reflection measurements. By seismic processes, such as migration and inversion, they can be mistakenly seen as primary reflections and give an erroneous image of the earth. Therefore, a method is needed to separate the multiples from the primaries. This thesis describes a primary estimation method named estimation of primaries by sparse inversion (EPSI). The interesting aspect of this method is that it does not see the multiples as noise, but uses the multiples to come to a better estimation of the primaries. Other wave equation based primary estimation methods first predict the multiples and then adaptively subtract them from the data. During this adaptive subtraction primary energy may be removed. EPSI tries to explain the total data, both primaries and multiples, in terms of primary impulse responses. By doing so an adaptive subtraction of multiples is avoided. In fact EPSI is a large-scale inversion process that estimates primaries such that they and their corresponding multiples explain the total data. To constrain this process, a sparseness constraint is used, which assumes that our estimated primaries have a certain amplitude distribution (large and small ones). A general characteristic of wave equation based primary estimation methods is that the near-offset data are very important for estimating water column reverberations, especially in shallow water. However, it is not possible to record the near-offset data and, therefore, most wave equation based primary estimation methods have great difficulties with shallow water marine data. A major advantage of EPSI is that it can reconstruct the missing near-offset data from information in the multiples and, therefore, show a good primary estimation result on shallow water marine data. Furthermore, the EPSI method can be extended to other measurement configurations, exploiting a similar relation between primaries and surface multiples. In this thesis both passive and blended seismic data have been considered. For passive seismic data multiples are used to obtain an estimate of the subsurface responses, usually by a cross-correlation process. This cross-correlation process relies on the assumption that the surface has been illuminated uniformly by subsurface sources in terms of incident angles and strength. If this is not the case the cross-correlation process cannot give a true amplitude estimation of the subsurface response. Furthermore, there are cross terms in the cross-correlation result that are not related to actual subsurface inhomogeneities. In this thesis it is demonstrated that, with some modifications to the algorithm, EPSI can obtain true amplitude subsurface responses without the uniform surface illumination assumption. The EPSI method will go beyond the cross-correlation process and will estimate primaries only from the multiples in the available signal. The estimated primary impulse responses, with point sources and receivers at the surface, can be used directly in traditional imaging schemes. This thesis demonstrates that for the situation of blended acquisition, meaning that different sources are shooting in a time-overlapping fashion, multiples can be used to 'deblend' the seismic measurements. With some modifications the EPSI method can be used for blended seismic data. As output EPSI gives unblended primary impulse responses with point sources and receivers at the surface, which can be used directly in traditional imaging schemes. The feasibility of the EPSI method is demonstrated in this thesis by a successful application of the method to two marine field datasets, one with a moderate water depth and one with shallow water. It demonstrates that for deeper water EPSI can compete with the standard surface-related multiple elimination (SRME) method, where for the shallow water EPSI clearly shows better results than SRME. The latter is mainly attributed to the fact that near offset reconstruction, which plays a crucial role in shallow water data, is included in the EPSI method.

For passive seismic data, surface multiples are used to obtain an estimate of the subsurface responses, usually by a crosscorrelation process. This crosscorrelation process relies on the assumption that the surface has been uniformly illuminated by subsurface sources in terms of incident angles and strengths. If this is not the case, the crosscorrelation process cannot give a true amplitude estimation of the subsurface response. Furthermore, cross terms in the crosscorrelation result are not related to actual subsurface inhomogeneities. We have developed a method that can obtain true amplitude subsurface responses without a uniform surface-illumination assumption. Our methodology goes beyond the crosscorrelation process and estimates primaries only from the surface-related multiples in the available signal. We use the recently introduced estimation of primaries by sparse inversion (EPSI) methodology, in which the primary impulse responses are considered to be the unknowns in a large-scale inversion process. With some modifications, the EPSI method can be used for passive seismic data. The output of this process is primary impulse responses with point sources and receivers at the surface, which can be used directly in traditional imaging schemes. The methodology was tested on 2D synthetic data.

ost wave-equation-based multiple removal algorithms are based on prediction and subtraction of multiples. Especially for shallow water, the prediction strongly relies on a correct interpolation of the missing near offsets. The subtraction of predicted multiples from the data can easily lead to the distortion of primaries if primaries and multiples overlap. Recently, a new approach for surface-related multiple removal was proposed: the estimation of primaries by sparse inversion (EPSI), which is based on a full waveform inversion approach. EPSI is based on the same primary-multiple model as surface-related multiple elimination (SRME) and does not require a subsurface model. In contrast to SRME, EPSI estimates the primaries as unknowns in a multidimensional inversion process rather than a subtraction process.The multidimensional primary impulse responses are parameterized by band-limited spikes, which are estimated such that they, along with their corresponding multiples, match the input data. An interesting aspect of the EPSI method is that it produces a residual, which is the part of the input data not explained by primaries and multiples. This residual can be analyzed and may provide useful information on the primary estimation process. Furthermore, it has been demonstrated that EPSI is also capable of reconstructing the missing near offsets from the multiples. The proposed method is applied to a field data set with moderate water depth, where it is demonstrated that the results are comparable with SRME. This data set is used to illustrate the residual. For a shallow-water field data set, it is shown that EPSI gives a better result than the standard SRME result caused by EPSI's capability to reconstruct the missing near offsets.

Accurate removal of surface-related multiples remains a challenge in many cases. To overcome typical inaccuracies in current multiple-removal techniques, we have developed a new primary-estimation method: estimation of primaries by sparse inversion (EPSI). EPSI is based on the same primary-multiple model as surface-related multiple elimination (SRME) and also requires no subsurface model. Unlike SRME, EPSI estimates the primaries as unknowns in a multidimensional inversion process rather than in a subtraction process. Furthermore, it does not depend on interpolated missing near-offset data because it can reconstruct missing data simultaneously. Sparseness plays a key role in the new primary-estimation procedure. The method was tested on 2D synthetic data.