## 3 Results
### Synthetic Seismic Data  
We use an implementation of the wavenumber integration method called OASES [40] to generate synthetic seismic data corresponding to the velocity models shown in Figure 3. We model the vertical particle displacement for a 120 m-long line with geophones spaced 1 m apart and an impulsive source.  
Figure 4a-c show synthetic seismic gathers corresponding to the velocity profiles for T0, T1, and T3 of Figure 3. We observe significant differences between the various gathers, and the complexity of the data increases as the temperature variability with depth increases. For T0, only two events are visible: a non-dispersive strong event travelling at approximately 1450 m/s, which is the fundamental mode of the surface wave (A), and one weaker non-dispersive event travelling at approximately 2700 m/s, which is the direct P-wave (B). The seismic gathers for T1 and T3 are more difficult to interpret, so in addition to the seismic gathers showed here, we make use of computed group velocities and modeling of separate modes of surface waves (as done in normal mode summation [41]). For T1, dispersive waves dominate the wavefield. This includes a wide fan-shaped event with group velocities ranging from approximately 200 m/s to 1450 m/s (C), which is associated with the fundamental mode of the surface wave, and a narrower fan-shaped event with group velocities ranging from approximately 500 m/s to 850 m/s (D), which is the first higher mode. Also for T3, dispersive events dominate the wavefield. The lower fan-shaped event (E) has group velocities ranging from approximately 200 m/s to 1450 m/s, and is the fundamental mode of the surface wave. Amplitudes are particularly high at a group velocity of approximately 380 m/s, which we attribute to the fundamental mode being dispersive at low frequencies, but becoming non-dispersive and correspondingly have a constant group velocity of 380 m/s at higher frequencies. The weaker fan-shaped event (F) is the first higher mode of surface wave with group velocities ranging from 380 m/s to 1000 m/s.  
Figure 4d-f show the corresponding FV-spectra, with theoretical modal curves computed from the input models overlaid on the spectra for easier mode identification. Just as with the seismic gathers, there are significant differences between the various models. For T0, the peak in the FV-spectrum appears at fairly constant phase velocities of around 1450 m/s for all frequencies, corresponding with the non-dispersive event observed in Figure 4a. T1 and T3 have similar and constant phase velocities of about 380 m/s at frequencies \(>\)120 Hz, but at frequencies between approximately 63 and 120 Hz, phase velocities are higher for T1 than T3. By comparing the FV-spectra with the modal curves, the spectrum  
peak for T0 corresponds well with the fundamental mode at all frequencies. For T1, it corresponds well with the fundamental mode below 31 Hz and above 63 Hz, and with the first higher mode from 31 to 63 Hz. We observe a weak fundamental mode between 31 and 63 Hz as well, but the first higher mode is dominant. For T3, the modal curves correspond well with the strong fundamental mode in most of the frequency range displayed here, while the first higher mode is dominant in a narrow frequency range of approximately 20 to 30 Hz. We also observe two weak higher modes starting at approximately 60 Hz and 110 Hz, respectively. At low frequencies for all models, we find energy at phase velocities higher than the S-wave velocity in the lower half space, which cannot be normal mode Rayleigh waves and, therefore, we interpret these as leaky wave modes.