Array measurements adapted to the number of available sensors: Theoretical and practical approach for ESAC method

• Implementation of an N-receiver positions array by a set of M stations (M < N)
• Practical guidelines to implement the proposed methodology
• Implementation of any array layout with at least 2 stations
• Implementation of dense arrays by only increasing the total recording time

Array measurements of ambient noise have become a useful technique to estimate the surface wave dispersion curves and subsequently the subsurface elastic parameters that characterize the studied soil. One of the logistical handicaps associated with this kind of measurements is the requirement of several stations recording at the same time, which limits their applicability in the case of research groups without enough infrastructure resources. In this paper, we describe the theoretical basis of the ESAC method and we deduce how the number of stations needed to implement any array layout can be reduced to only two stations. In this way, we propose a new methodology to implement an N stations array layout by using only M stations (M < N), which will be recording in different positions of the original prearranged N stations geometry at different times. We also provide some practical guidelines to implement the proposed approach and we show different examples where the obtained results confirm the theoretical foundations. Thus, the study carried out reflects that we can use a minimum of 2 stations to deploy any array layout originally designed for higher number of sensors.