Measuring surface wave phase velocities beneath small broad-band arrays: tests of an improved algorithm and application to the French Alps

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The local measurement of dispersion curves of intermediate-period surface waves is particularly difficult because of the long wavelengths involved. We suggest an improved procedure for measuring dispersion curves using small-aperture broad-band arrays. The method is based on the hypotheses of plane incoming waves and that averaging over a set of events with a good backazimuth distribution will suppress the effects of diffraction outside the array. None of the elements of the processing are new in themselves, but each step is optimized so we can obtain a reliable dispersion curve with a well-defined uncertainty. The method is based on the inversion for the slowness vector at each event and frequency using time delays between pairs of stations, where the time delays Δt are obtained by frequency-domain Wiener filtering. The interstation distance projected on to the slowness vector (D) is then calculated. The final dispersion curve is found by, at each frequency, calculating the inverse of the slope of the best-fitting line of all (D, Δt) points. To test the algorithm, it is applied to synthetic seismograms of fundamental mode Rayleigh waves in different configurations: (1) the sum of several incident waves; (2) an array located next to or above a crustal thickening; and (3) added white noise, using regular and irregular backazimuth distributions. In each case, a circular array of 23 km diameter and composed of six stations is used. The algorithm is stable over a large range of wavelengths (between half and a tenth of the array size), depending on the configuration. The situations of several, simultaneously incoming waves or neighbouring heterogeneities are well handled and the inferred dispersion curve corresponds to that of the underlying medium. Above a strong lateral heterogeneity, the inferred dispersion curve corresponds to that of the underlying medium up to wavelengths of eight times the array size in the configuration considered, but further work is needed to better understand the limits under which the obtained dispersion curve is not biased. In the case of 5 per cent spectral amplitude white noise, the dispersion curve is also stable for wavelengths up to approximately eight times the array size, but this limit depends of course strongly on the noise level. The method is finally applied to data from two arrays in the French Alps located 50 km apart. It is possible to measure the dispersion curves up to wavelengths approximately ten times bigger than the array diameter. The difference in the dispersion curves is compatible with a crustal and lithospheric thickening under the Alps. However, the observed errors are large, which result in severe limits on the interpretation in terms of lithospheric structure. Longer recording periods may help to reduce the errors. Otherwise the algorithm is likely to be of use mainly in areas where the lateral variations outside the array are smaller than those of the French Alps.