An Automated Method for Picking the Fundamental Mode Dispersion Curve and Reliably Estimating the Phase Velocity of This Mode in Surface Waves

Surface waves are type of seismic waves that provide valuable information from near-surface Earth structures in seismic studies, particularly non-invasive seismic surveys with geological, engineering, and earthquake engineering objectives.

One of the main challenges in surface wave analysis is the extraction of dispersion curves, which represent the relationship between the phase velocities and corresponding frequency components. Conventional methods for extracting these curves are often done manually via point-vise picking by the user, which, in addition to being time-consuming, increases the possibility of erroneous identifying of the desired dispersion mode.

In this study, an automatic method for identifying dispersion curves is presented. The method automatically finds the optimal path along the fundamental dispersion mode through intelligent search and extracts the dispersion curve. An important feature of this algorithm is its simplicity and lack of need for complex configurations, such that it can search for the dispersion curve based on the position of local energy maxima in the phase-velocity spectrum without user involvement through two different search strategies so called low-frequency search strategy and high-frequency search strategy with minimum manual adjustments. Additionally, in the low-frequency search strategy, resolution limits based on survey profile length have been incorporated as a stopping criterion for the algorithm. This condition ensures that the final dispersion curve is confined to a frequency that is physically measurable and reliable, and prevents the algorithm from deviating toward erroneous points at low frequency part. The proposed algorithm by utilizing abovementioned two strategies is capable of automatically and accurately picking of the fundamental mode dispersion curve.

The efficiency of the proposed method has been evaluated by applying on synthetic and real seismic data. According to the results obtained from synthetic data, the proposed method possesses high accuracy in automatically identifying of dispersion curves, even in the presence of severe noise. In clean (noise-free) data, the mean square error between the theoretical dispersion curve and the dispersion curve picked by the proposed method was 6.3, and the maximum relative error was 1.8%. For comparison proposes and to demonstrate the efficiency of the proposed method, an automatic peak-value picking method was also used to extract the fundamental mode dispersion curves, where the mean square error between the theoretical dispersion curve and the picked one was 161830 and the corresponding maximum relative error was 116%, indicating the significant superiority of the proposed method over automatic peak-value picking technique. Furthermore, under stronger noise conditions with a signal-to-noise ratio of -25 db, the mean square error obtained by the proposed method was 156 and the maximum relative error was 6.9%, which still maintains considerably higher accuracy compared to the automatic peak-value picking method. The proposed method can significantly reduce the runtime and improves the accuracy of dispersion curve extraction as well as shear-wave velocity distribution model estimation.