Toward optimal spatial filters for demultiple and wavefield splitting of ocean‐bottom seismic data

Abstract

Suppressing the receiver‐side sea‐surface ghost with its accompanying water‐layer reverberations in multicomponent sea‐floor data can be performed in both the frequency–wavenumber and the frequency–space domains. Similarly, separation of ocean‐bottom seismic (OBS) data into upgoing P‐ and S‐mode responses can be formulated in both domains. The frequency–space domain algorithms can be attractive when the sea‐floor medium has lateral velocity variations or the data are irregularly sampled along the sea floor, which requires that the data be processed with local, compact decomposition filters having optimal angular (wavenumber) response.By deriving the frequency–space domain formulas, we find an exact representation for the demultipled pressure response. This formula involves filter convolutions over the data, with filters having a long spatial impulse response. The filtering can be approximated in the wavenumber domain by, for example, power series, Chebyshev polynonomial fitting, Pade approximants, or continued fraction expansions. The filters must then be Fourier transformed back to the frequency–space domain, where the resulting filter is convolved with the data. The implies that the demultipled OBS data must be computed by numerical solution of a differential equation.Alternatively, the spatial filtering can be formulated as a filter design problem, where the filtering is performed by an optimal filter. This latter formulation can to some extent handle local variations in the medium properties along the sea floor, and it does not require solving a differential equation for the multiple suppressed pressure.