Spatial estimation of fundamental mode dispersion curves using geostatistical techniques

This paper proposes the use of geostatistical techniques to estimate dispersion curves between other known ones. To do it, we introduce two novel methodologies: the stacking method and the group-velocity mapping method. We obtain our set of group-velocity fundamental mode dispersion curves from seismic noise correlation. Consequently, we first assign their attribution point at the mid-distance between the stations used for the dispersion curves calculation. The stacking method uses the range of the omnidirectional semivariogram of a regionalized variable that quantifies the similarity between dispersion curves to stack them according to their spatial correlation. We test this technique with dispersion curves obtained in Mexico City and get a range of ∼400 m for the omnidirectional semivariogram. We also calculate directional semivariograms and observe a maximum range (∼500 m) in the NW-SE direction, agreeing with the city's spatial distribution of natural periods. On the other hand, the group-velocity mapping method uses the ordinary kriging estimator in the group velocities for all the ranges of periods to generate maps and then dispersion curves. Estimated dispersion curves retrieved from both, the stacking and the group-velocity mapping method, were compared with those obtained with the fast marching tomographic method. We also establish analogies between getting group-velocity maps with the tomographic method and with the group-velocity mapping method. Finally, we observe that the range of the omnidirectional semivariogram used in the stacking method may be related to the tomographic method resolution.