*Analysis of discrepancies between Preferred and authors’ BP1 models *

Following submission of blind interpretations by all participants (step BP1), a Preferred layered-earth model and geological data were released by the Committee for purposes of reanalysis and discussion (step BP4). Fig. 4 shows modeled dispersion curves for five modes of Rayleigh-wave propagation for both the Preferred model and the authors’ step BP1 model. Two strong discrepancies are obvious: (a) the R0 mode for 10-40 Hz on the Preferred model is close to half the values shown for the authors’ BP1 model, and (b) For frequencies 0.4-1.5 Hz the BP1 model has larger differences between phase velocities for the R0 and Re modes than does the Preferred model.

The differences between the two models are also evident in Fig. 5 which shows examples of observed SPAC spectra together with spectra modeled using the Re dispersion curve for the Preferred and the BP1 models. Fig. 5a uses an example of data from the S array, station separation 10 m, and shows a standard deviation of 0.14 for the best fit of observed and BP1 model spectra at frequencies 2-38 Hz. The equivalent standard deviation for the Preferred model is 0.24. Fig. 5b shows similarly using the LL array, station separation 277 m; for the frequency band of 0.5-2.5 Hz the corresponding standard deviations are 0.06 (BP1) and 1.7 (Preferred).

Fig. 6a shows Vs logs for the upper 40 m of the Preferred and our BP1 models. Geological data is provided from a borehole of depth 39 m, located close to station LL5 (see Fig. 1a, and also Oyo, 2020). The borehole has also been logged with P and S-wave velocities but the velocity values and ratio between P and S-wave values appear anomalous; those downhole P and S-wave values appear to have been incorporated in the Preferred model and may therefore explain discrepancy (a) above.

*Detection of a near-surface low velocity layer*

The geological log in Fig. 6b shows a layer of sand-silt at depth 20 to 29 m. This zone also shows as a relatively soft layer in the standard penetration test (SPT) log in Fig. 6b, underlain by harder gravels (from Oyo, 2020). Comparing this geological and SPT data with our BP1 interpreted Vs profile, we see an affirmative correlation of an interpreted low-velocity layer (LVL), estimated to be 14-25 m depth, and underlain by a significant Vs contrast estimated at 25 m depth. These values however are about 20% shallower than boundaries shown in the geological and SPT logs.

The result relating to the prediction and subsequent affirmation of existence of the LVL when using the method of MMSPAC, are consistent with the discussion of the LVL challenge provided in Asten and Hayashi (2018). The Preferred model does not show existence of the LVL.

*Detection of a major V*s velocity contrast at 580+ m

Fig. 6c compares interpreted models for Vs to a depth of 800 m for the Preferred model and the authors’ BP1 model. Both models show a major increase in Vs at depth (580 m and 750 m respectively). This velocity contrast is significant in that it is the principal cause of the 0.4 Hz peak in HVSR data, noted in Fig. 1c.

*Achievable bandwidth for interpretation*

The direct fitting of observed and model SPAC spectrum enabled use of passive seismic data over the frequency range 0.5 to 38 Hz. Of the remaining 27 submissions of BP1 interpretations, one showed a maximum usable frequency with passive data of 30 Hz, and four showed a maximum of 20 Hz. Eight submissions used active-source data to achieve an equivalent or higher maximum frequency for data inversion to a Vs profile.

*Reduction of bias in V*s profiles via use of Rayleigh wave effective mode

There is some indication that use of Rayleigh effective-mode modeling reduces bias in estimates of the Vs profile. Fig. 6c shows the authors’ best-fit Vs model to depth 800 m when limiting phase velocity models to the Rayleigh fundamental mode only. The Vs profile is obviously biased to higher velocities in this case; quantitatively we compute Vs300 = 584 m/s and 655 m/s respectively for the effective-mode and the fundamental mode interpretations.

The results of the blind trial step BP1 for all participants are summarized graphically by Blind Project Committee (2021). There are 28 submissions and simple inspection shows four submissions can be excluded due to very large deviations from the Preferred model; 19 of the remaining 24 submissions show the submitted Vs profile clearly biased towards higher Vs values compared with the Preferred model over the depth interval 100-500m. The remaining five submissions (including the authors’ BP1 model) show some overlap with the preferred model over this depth interval.

Depths 100-500 m correspond approximately to frequencies 0.8-2 Hz when using the Rayleigh wave depth sensitivity guideline of a half-wavelength, and as shown in Fig. 4b it is this frequency band which shows the effective mode shifted to phase velocities higher than the fundamental mode. This argument is qualitative in nature, but it allows us to propose the hypothesis that inversion of phase velocity dispersion data using fundamental-mode modeling only, may be a cause of bias of interpreted Vs profiles to higher velocities than those present in the real earth. The hypothesis may be tested quantitatively when tabular data for all submitted Vs profiles together with details of modelling algorithms used, becomes available.