Elastic Born modeling in an ocean-bottom node acquisition scenario

PZ summation

PZ summation involves summing the pressure data recorded by the hydrophone data with the vertical particle velocity data recorded by the geophone, with some scaling factor:

$$U (z_r) = \frac{1}{2} \left[ P(z_r) - \beta V_z (z_r) \right] ,$$

$$D (z_r) = \frac{1}{2} \left[ P(z_r) + \beta V_z (z_r) \right] ,$$ (1)

where $P$ is the pressure data, $V_z$ is the vertical particle velocity, $U$ is the upgoing data, $D$ is the downgoing data and $z_r$ is the receiver depth. $\beta$ is a scaling factor, which can be defined in several ways. Amundsen (1993) does the separation in the $f-k$ domain, and uses $\beta = \frac {\rho \omega}{k_z}$ , where $k_z = \sqrt {\frac {\omega^2}{v^2} - k^2_x -k^2_y}$ , and $\rho$ is the density. Alternately in the $t-x$ space, the scaling can be determined by the ratio of the direct arrival's amplitude on the hydrophone and vertical geophone components at various offsets.

As mentioned above, this method assumes that all energy is pressure wave energy, and therefore everything recorded by the hydrophone has its counterpart in the geophone data, with either positive polarity (upgoing) or negative polarity (downgoing). Shear waves, on the other hand, can only propagate upwards, since they are generated by mode conversions in the subsurface. They can have a very different polarity upon reaching the sea bed, which can change differently with offset in comparison to the P-wave polarity. Running PZ summation on data that contains significant shear wave energy (or indeed - significant amounts of anything that is not pure P body waves) introduces events into the separated data fields, which will be construed by later processing steps as either upgoing or downgoing P-wave energy.

Elastic Born modeling in an ocean-bottom node acquisition scenario