Application of a method to determine S and P wave velocities from surface waves data analysis in presence of sharp lateral variations

Introduction. �eismic surface waves are �ecoming a leading method to estimate �-wave velocit� (V�) through dispersion curve (DC) extraction and inversion (�occo et al., 2010). �occo et al. (2017) showed that a relationship �etween wavelength and depth (W/D) of surface waves can �e determined and used to directl� transform the DC into the time-average V� model, avoiding the inversion process. �urface waves are usuall� considered unsuita�le for estimating P-wave velocit� (VP), or Poisson’s ratio, due to the low sensitivit� of dispersion curve to these parameters (Nazarian,1984). �occo and Comina (2017) found that this W/D relationship is sensitive to Poisson’s ratio. A method was therefore developed to determine also the time average VP �� using the W/D relationship. �hese methods are ro�ust in terms of accurac� and efficient in terms of computational cost. �he� can �e applied to a set of dispersion curves over a seismic line to provide a pseudo 2D time-average V� and VP model along the line. �he methods require a reference DC and its associated V� profile to get the W/D relationship. However, using a unique reference curve for the whole line �ecomes pro�lematic when sharp lateral variations or zones with different velocities are present. In this work, a hierarchical clustering algorithm is developed to select ensem�les of DCs within a uniform zone that can �e interpreted using the same reference DC. �hen, reference W/D relationships are estimated in each uniform zone and com�ined with DCs to determine time-average V� and VP models over the whole area. In the following, the clustering method is first �riefl� explained, then, the application of the method to field data from a test site (CNR in �urin) is shown and discussed. Methodology. A hierarchical clustering method has �een used to group the DCs. In hierarchical clustering, there is no need to set a predefined num�er of clusters, this is a great advantage since we want a method a�le to identif� uniform zones without knowing a priori the expected lateral varia�ilit� of the area. �he result of hierarchical clustering is a dendrogram which shows the nested grouping of o�servations and similarit� levels at which grouping change (Maimon and Rokach, 2000). Hierarchical methods can �e divided into two su�groups (Maimon and Rokach, 2000): i) agglomerative a �ottom up approach in which ever� o�servation is considered a cluster and similar clusters are identified and merged together to make �igger clusters� ii) divisive a top down approach in which the o�servations all start in a single cluster and at each step the� are removed from the cluster to create a new cluster or join other clusters. �ests on s�nthetic and real data showed that agglomerative and divisive methods have similar performances for our purpose. We selected agglomerative clustering �ecause it makes the process tracking easier. A measure of dissimilarit� is needed to merge the clusters. �his is usuall� achieved �� appropriate metric and linkage criterion. Euclidean distance is used here to determine the metric �etween two dispersion curves: