High resolution method

The high resolution frequency-wavenumber method is used on the same signals as the f-k method. The results are shown in figures 6.34(a) to 6.34(d) for array A to D, respectively. For array A, 16 signal windows were processed separately providing 16 velocity estimates by frequency band (figure 6.34(a)) while only one velocity estimate is available for arrays B and C. For array D, two windows are available and two velocity estimates are determined by frequency band (figure 6.34(d)). The average dispersion curve obtained with the f-k method is plotted for comparison, as well as the wavenumber limits deduced from the theoretical array responses.

Figure 6.34: Results of the high resolution frequency-wavenumber method applied to arrays A to D (figures (a) to (d), respectively), represented with black dots. The dispersion curve observed for frequency-wavenumber method is plotted for comparison in grey. Wavenumber limits deduced for the f-k method are also shown with the same legend as in figure 6.30.

For synthetic signals (section 6.1), the high resolution method results were consistent between each other and agreed with the ones obtained with the f-k method and even gave a better estimate of the true dispersion curve for some frequencies. For this real case, strong discrepancies are observed between the different curves for the high resolution method and between the two methods for some frequencies, even in the theoretical validity range. For instance, the velocity value measured by array A at 6.5 Hz (around 500 m/s) with the high resolution method is lower than the one measured with the same method by the other arrays (about 700 m/s). This last value is consistent with the results of the f-k method. Also an abnormal jump on the high resolution curve is observed (figure 6.34(d), array D) around 6 Hz, while the curve obtained by f-k method exhibits a regular decrease with frequency. The high resolution results for array A at high frequency seem to indicate the existence of higher modes. The uncertainty on these results is obviously too high to use this information for inversion purposes. As a conclusion, the high resolution method appears to be unable to obtain a reliable velocity estimate below 6 Hz in this case. Over 6 Hz, a good agreement is reached between the high resolution and the f-k methods in the valid frequency range of the arrays. The f-k method then appears to be more robust in the whole frequency range, with an increase of the uncertainty in the low frequency range.