P/S wavefield separation in the presence of statics
Peter W. Cary
Existing wavefield separation techniques for 4C ocean-bottom cable data are formulated with the assumption that the earth is essentially one-dimensional at the sea-bottom; i.e. the equations assume that the sea floor is flat and that the medium properties of the ocean bottom are homogeneous. These assumptions are often violated. For example, shear-wave receiver statics often exist, which are an indication of rapid variation in shear velocity within a wavelength along the sea floor. It would appear, therefore, that a method that accounts for a heterogeneous sea floor is needed. However, this is only true if the analysis is performed on common-shot gathers. Performing the decomposition on common-receiver gathers is a simple solution to this problem. All traces in the receiver gather are subject to the same S-wave and P-wave receiver static, so the sea-floor appears to be homogeneous in this domain. It is necessary to perform the analysis on a common-shot gather only if the spatial sampling within each common-receiver gather is coarse enough to cause data aliasing. This is often the case in land 2D acquisition, where the source interval is usually several times larger than the receiver interval. A technique for performing the wavefield separation on shot gathers in this situation is presented here. The approach assumes that a homogeneous layer exists below the heterogeneous near-surface layer that causes the statics. Localized ray-tracing is used to model the upgoing wave propagation through the heterogeneous layer to each receiver. The forward modeling equations are inverted in order to resolve the plane-wave components of the P and S wavefields at a fixed depth below the heterogeneous layer. The near-surface medium properties, as well as the different geophone component response functions, are required input parameters to this decomposition.