Dense spatial recording patterns of three?component (3C) receivers
allow for direct wavefield decomposition through explicit calculation
of divergence and curl of the recorded elastic wavefield. Since this
approach is based upon the observation of small phase shifts, it
requires highly accurate deployment of the receiver configurations.
To study the feasibility of a recently proposed P/S?wave separation
scheme, we systematically assess the effects of position and orientation
errors of one or several geophones within the recording pattern on
technique performance.
We find that realistic deployment errors can significantly affect
estimates of the divergence and curl of particle velocity. The errors
induced by mispositioned or misoriented geophones differ for each
of the geophones that make up a pattern. Moreover, the inaccuracies
vary with the angle of incidence, potentially affecting analysis
procedures applied to the data at a later stage, such as amplitude
variation with offset (AVO). Based on a relative L1?criterion, the
position of each receiver needs to be accurate within 10% of the
length of the sides of the configuration to obtain meaningful divergence
and curl estimates. Furthermore, the output is particularly sensitive
to misorientations of geophones, requiring that the orientations
of all geophones be accurate within 2°. These observations point
to significant difficulties when applying this technique.
To alleviate this problem, we present an approach to detect and compensate
for such deployment?related inaccuracies prior to explicit P/S?wave
separation. This strategy is based on a pyramid?shaped receiver configuration
and relies on minimizing the differences between the divergence and
curl estimates calculated over the pyramid and each of the four subtetrahedra
that comprise the pyramid.