P/S separation of OBS data by inversion in a homogeneous medium

Discussion and conclusion

The more the homogeneous medium parameters used in the inversion differ from the true medium parameters in which the receivers were placed, the less accurate is the reconstructed wavefield in the proximity of the receivers. This in turn means that the spatial derivatives will differ from the true derivatives, and thus the separation of P-waves from S-waves will be less reliable. However, given the typical length of seismic waves in exploration geophysics, and the spatial oversampling used in finite-difference modeling, the inaccuracy in medium parameters for which this separation method can still function reliably is quite large.

The locations of virtual sources in relation to the receivers determine what wavenumbers can be reconstructed. In order to accurately recreate all wavenumbers in the data, the virtual-sources must be placed in a configuration that enables the generation of those wavenumbers. For land data, the implication is that virtual-sources should be placed below the receivers. For OBS data, this should mean that virtual-sources must be placed above and below the receivers. However, such a configuration drastically increases the null-space of the inversion, and the results (not shown here) are very noisy and inaccurately reconstructed P and S sections.

I am currently investigating two possible avenues for implementing the inversion successfully on OBS data. The first possibility is to run the inversion twice: once with virtual-sources below the receivers, and once with virtual-sources above. The shear waves propagate upward only, and will be reconstructed by the upgoing inversion. As can be seen from Figures 14(a) and 14(d), the downgoing P-waves are reconstructed with opposite polarity when the virtual-sources are below the receivers. Likewise, the upgoing P-waves will be reconstructed with an opposite polarity when the virtual-sources are above the receivers. By comparing the polarity reversals to the observed hydrophone data, it is possible to gauge which P events are improperly reconstructed. I am searching for a way to introduce the hydrophone data as a constraint to the objective function, so that the polarity reversal attribute can be used to guide the inversion.

The second possibility is to have the virtual-sources below the receivers, but use a reflecting upper boundary, thereby recreating the downgoing waves generated by reflections off the sea surface. This configuration is not trivial to implement, since there is an important condition that has to be met: The free surface should not generate a mode conversion. If it does, downgoing shear waves will be present in the reconstructed displacement fields, and such waves definitely do not exist in OBS data.

One way of preventing a mode conversion from the free upper boundary is to use a medium with no shear strength. The possible configuration then is a line of receivers placed in a medium with parameters approximating those of the sea bottom. Above these receivers the medium will be water. Effectively, a homogeneous elastic medium underlying a homogeneous acoustic medium. The added value such a configuration may give is not only in the enabling of reconstruction of downgoing P-waves, but also in the possibility of reconstructing the surface waves.

P/S separation of OBS data by inversion in a homogeneous medium