Surface-wave separation and its impact on seismic survey design

Surface waves in seismic data are often dominant and mask primaries in land or shallow-water environments. Separating them from the primaries is of great importance either for removing them as noise for reservoir imaging and characterization, or for considering them as signal for near-surface characterization. However, their complex properties, such as dispersion, multi-modality and spatial variability, make the surface-wave separation significantly challenging in processing. To address the challenges, we introduced a method of 3-D surface-wave estimation and separation using a closed-loop approach. The closed loop contains a relatively simple forward model of surface waves and adaptive subtraction of the forward-modelled surface waves from the observed surface waves, making it possible to evaluate the residual between them. In this approach, the surface-wave model is parameterized by the frequency-dependent slowness and source properties for each surface-wave mode. The optimal model parameters are estimated in an iterative way such that the residual is minimized and, consequently, this approach solves the inverse problem. Through synthetic and real data examples, we observed that this method successfully estimates and separates out the surface waves from the seismic data to consequently obtain the subsurface signals. We also observed the method's wide range of applicability to under-sampled, asymmetrically sampled, irregularly sampled and blended seismic data. This suggests the possibility of relaxing requirements for survey parameters in terms of surface-wave separation and, therefore, offers flexibility as well as potential effort reduction with respect to seismic surveys. Seismic survey design corresponds to choosing a set of survey parameters that enables imaging and amplitude-versus-offset applications of target reflectors with sufficient data quality under given economical and operational constraints. However, surface waves are often dominant in the seismic data, as already mentioned, and the effectiveness of surface-wave separation or removal significantly affects that of the subsequent steps for target reflectors. Therefore, they impose additional requirements on the survey parameters for acquisition so that those allow for effective surface-wave separation in processing. We should understand how the application of surface-wave separation affects the choice of survey parameters and the resulting data quality. For this purpose, we discussed the relationship between the survey parameters and the resulting data quality in order to find the essential types of survey parameters and their optimal values for a required data quality in the context of surface-wave separation. For 3-D seismic surveys, the relevant survey parameters are the four spatial sampling intervals and apertures of the template geometry. Two of the four spatial coordinates specify the spatial sampling of the basic subset, and two other coordinates specify the spatial redundancy of the basic subsets, i.e., the fold. The signal-to-noise ratio of the data sets after surface-wave separation serves as an attribute or measure representing the resulting data quality. We carried out a case study, applying surface-wave separation and signal-to-noise ratio estimation to several data sets with different survey parameters. The case study led us to conclude that the spatial sampling intervals of the basic subset are the essential types of survey parameters. The resulting data quality is related to the spatial sampling intervals and follows a trend curve, in which finer spatial sampling intervals improve the resulting data quality until it levels off on a plateau. The shape of this trend curve depends on the method of surface-wave separation. Given this impact of surface-wave separation on survey design, it should be included in the design, next to its intended application for reflection imaging or amplitude-versus-offset analysis. We then discussed the relationship between the survey parameters and the resulting data quality in the context of reflection imaging and amplitude-versus-offset applications. We also carried out a case study for this purpose using the so-called focal-beam method to several data sets with different survey parameters. Through the case study, we observed that the spatial sampling intervals and apertures of the basic subset are the essential types of survey parameters for reflection imaging, and that all the four spatial sampling intervals and apertures of the template geometry are essential for amplitude-versus-offset applications. A noteworthy conclusion is that suitable spatial sampling intervals for surface-wave separation also suffice for reflection imaging and amplitude-versus-offset applications. Therefore, for survey design, the spatial sampling intervals of the basic subset should be determined first for a required signal-to-noise ratio as needed for surface-wave separation. The other survey parameters should be considered next for a required resolution and pre-stack amplitude fidelity as required for reflection imaging and amplitude-versus-offset applications.