The generic assumption for scattered light is that it is a phase noise, see for example the note by Edwige VIR-0070A-08. With scattered coupling to the main beam with a phase due to the motion of the scatterer

And then that phase noise coupling directly into the sensitivity with a flat transfer function

However, using the last night sea activity as an injection of SNEB motion, the transfer function between B7_DC and Hrec is not flat, it seems to be proportional to 1/f^2.

Up to now my assumption was that the transfer function is a simple pole at ~50Hz, due to arm cavity response. The model for that is that the scatterer on SNEB is creating power fluctuations, which are filtered by the response of the arm, and then arrive on the B1 photodiode.

To explain the 1/f^2 response, an option is to assume radiation pressure is involved. The scattered beam interfers with the main beam in the arms, this causes power fluctuation in the arms from the beat between the two, the power fluctuation pushes on the mirrors that have a 1/f^2 response to radiation pressure (the same as acting with the photon calibrator), and the motion of the mirrors is what we seen on the B1 photodiode.

In summary, the coupling of the SNEB scattered light appears to not be scattered light reaching directly the B1 photodiodes, but rather scattered light causing excess motion of the mirrors that is then sensed by the B1 photodiode.

Figure 1 shows the measured B7 to h(t) transfer function and a model with a double pole at 0.7Hz and a simple pole at 50Hz.