GNGTS 2015 - Atti del 34° Convegno Nazionale

the reliability of such result we can investigate how the final pseudo-section depends on the imputed data. Of course, since this is not an inversion, a traditional definition of “sensitivity” is neither possible nor applicable. To achieve the result in this context, we define “sensitivity to the data” the normalized number of contributions per block. Since the velocity value in each squared block is obtained by averaging multiple contributions, the most the contributions, the most reliable will be the result. The sensitivity corresponding to the pseudo-section of Fig. 2a is shown in Fig. 2c, while Fig. 2b shows a schematic example on how different receiving pairs contribute to the final Vs interpretation and to its sensitivity pattern. The depth, to which lateral heterogeneity is correctly retrieved, is roughly L/3, where L is the array length. Beyond this depth, a result can still be retrieved but, since only distant receivers are involved, the interpreted velocity values are spread horizontally and their exact location under the array is lost. 3-D approach. A relevant number of factors come into play when a three dimensional (3- D) subsurface is considered, for instance, near-foundation soils in urban areas. The presence of localized V S variations such as the foundation itself, heterogeneities due to excavations and successive replenishments, sewers, fuel tanks, surface velocity inversions due to artificial pavements, or even tree roots, makes up a severe and challenging 3-D subsurface. Furthermore, since the space available at the surface may be insufficient, receivers must be placed keeping into account both the accessibility of the specific site and the need to record a dataset with sufficient wavenumber coverage. In practice, to tackle the 3-D Vs subsoil reconstruction challenge a method for the elaboration of surface waves recordings unbound from both a rigid field geometry and from the 1D assumption would be highly desirable. To extend the approach to the three dimensional world, since SW spreading from a point source is cylindrical, we can still use the procedure reported in Eqs. 1-4 under the assumption that the angle α between R 1 and R 2 is small enough. This enables to link the portion of the cylindrical shell defined by R 1 and R 2 and the angle α = R 1 SR 2 (i.e. a portion of the target volume) to the COP obtained for the receiver pair under investigation. Note that the strategy to obtain the COP and its extension to 3-D may represent a very promising strategy for the 3-D inversion of the data. The assembly process is still performed using the COP�� �������� �� ��� ��� �������� ������ ��� ’s relative to all the receiver pairs, all the sources and multiple shots but the 3-D subsurface is now discretized in cubic blocks where the value of the velocity is calculated according to Eqs. 3, 4a and 4b. The result is a 3-D pseudo-volume of V S where the velocity values are most properly retrieved to a depth roughly equal to L/3, where L is the maximum distance between the two farthest receivers. In the 3-D case with arbitrarily located sources and receivers, it is of course not possible to filter the COP using a frequency-velocity transform, as is allowed by several (usually 24, at least) regularly spaced traces, and this can potentially enable for artifacts introduction. The only constraint we can impose is based on the energy produced by each single shot (5) where, for each pair, is the energy transferred by the most energetic harmonic. For this reason, the 3-D sensitivity with respect to the data is the main tool not only to judge the reliability of the result at any location ( x,y,z ) but also to have an indication about the spectral accuracy in terms of wavenumber coverage. Finally, Fig. 3 shows a three dimensional survey where the signals recorded at 24 vertical, 4.5 Hz proper frequency geophones and produced by 21 different sources where used to characterize the subsurface under the foundations of a residential building, with particular emphasis to one of its corners, where a settlement occurred. The obtained Vs (Fig. 3a) also presents anomalies due to the sewer system and as expected, a lowering of the shear velocity under the investigated corner where the walls presented some cracks, probably connected to the degradation of the supportive function of the foundation soil. 86 GNGTS 2015 S essione 3.2