Estimation of velocity function parameters in unconsolidated sands using semblance velocity analysis

To properly understand seismic wave propagation in unconsolidated sand layers, it is important to estimate the parameters of their continuous velocity-depth functions. This study proposes a procedure to estimate the V ₀ and k parameters of a specific velocity function, where V ₀ is the direct P-wave velocity at the ground surface and k is the velocity gradient. The V ₀ and k parameters are generally independent of each other. However, it is possible to relate them numerically because both depend strongly on the porosity (φ{symbol}) and water saturation (S _w). The proposed procedure starts by tabulating V ₀ and k for 0.05 ≤ φ{symbol} ≤ 0.5 sampled at Δφ{symbol} = 0.05 and S _w = 0.6, so that only V ₀ is needed for fitting. Then, time-distance (T-X) type curves of the direct arrival are calculated for the corresponding values of V ₀ and k parameters values. The type curves are fitted then to the observed shot gather through a modification of the classic semblance velocity analysis method. Once the best-fit V ₀ value is found, the corresponding k, φ{symbol}, and S _w values are picked from a V ₀-k-φ{symbol} lookup table. The procedure is applied on synthetic shot gathers with various amounts of additive Gaussian random noise. Results show that the method is robust and tolerant to low to moderate amounts of noise.