Estimation of average shear V_sz and compressional V_pzwaves velocities using wavelength-depth relation obtained from surface waves analysis

Shear wave velocity (ܸ௦) and its average based on travel time from the surface to a depth of 30 m, is known as (ܸ௦ଷ଴) are often used in engineering projects to determine soil parameters, evaluate the dynamic properties of the soil and classify it. This quantity is directly related to the important property of soil and rock, i.e., their shear strength. The average shear wave velocity is used in geotechnics to assess soil liquefaction and in earthquake engineering to determine soil period, site amplification coefficient, and determination of attenuation. Usually, the average shear wave velocity is obtained from shear wave refraction survey, PS logging or from shear wave velocity profile obtained by inversion of experimental dispersion curve of surface waves. Surface wave analysis is one of the methods for estimating the profile of shear wave velocity, but inverting of dispersion curve is a time-consuming part of this process and also, the inverse problem has a non-unique solution. This becomes more evident when the goal is to determine a two- or three-dimensional shear wave velocity model. This study provides a method to estimate directly the average shear wave velocity (ܸ௦௭) as well as the average compressional wave velocity (ܸ௣௭) from dispersion curves of surface waves without the need to invert the dispersion curves. For this purpose, we need to exploit the relation between surface wave wavelength and investigation depth. Estimating the wavelength-depth relationship requires access to a shear wave velocity model (a reference model) in the study area, which can be obtained from well data, refraction seismic profiles, or by inverting one of the experimental surface wave dispersion curves. The ܸ௦௭ is then estimated directly from dispersion curve using the wavelength-depth relationship. In addition, due to the dependence of the value of ܸ௦௭ to Poisson's ratio and the sensitivity of the estimated wavelength-depth relationship to this ratio, we estimate the Poisson's ratio profile and average compressional velocity (ܸ௣௭) for the study area, from the ܸ௦௭. For a given range of Poisson's ratio values, theoretical dispersion curves of the synthetic earth models are determined by forward modeling. Then using these dispersion curves and estimated average shear wave velocity of the model, the wavelength-depth relationship corresponding to each Poisson's ratio is determined. In the next step by comparing experimental and estimated wavelength-depth relationships, one can estimate the Poisson's ratio at each depth. Then the average compressional wave velocity (ܸ௣௭) is estimated using the ܸ௦௭ and the Poisson's ratios. We evaluated the performance of the proposed method by applying on both real MASW seismic data set from USA and synthetic seismic data. The synthetic data collected over synthetic earth model and showed that the average shear and compression waves velocities are estimated with uncertainty of less than 10% in layered earth model with very large lateral variations in shear and compression waves velocities. According to the results, the proposed method can be used to take the non-destructive advantages of the surface wave method in engineering, geotechnical, and earthquake engineering projects to get the average shear wave velocity ܸ௦௭.