Adaptive wavelength-dependent dispersion curve extraction

Surface wave-based non-destructive site characterization techniques are often considered approximate at best. The lack of accuracy can be attributed to the ill-posed nature of the inversion, the inability to clearly identify and separate different propagating modes, and the erroneous extraction of dispersion data. Traditionally, modal curves are extracted by manually locating a few key points on the dispersion image and applying a velocity band to identify the regions with maximum energy. This approach often fails if modal curves feature complex silhouettes or exhibit rapid changes in velocity. Moreover, extensive human intervention makes the entire process laborious and time-consuming. Automated methods primarily rely on the global maximum modal energy, which is effective only for the predominant mode. Machine learning-based curve-extraction approaches work well only for synthetic data and fail miserably in real-world tests. The paper introduces a computationally efficient adaptive wavelength-dependent empirical formula to sequentially search for the maximum energy of modal curves. With predefined approximate starting and ending locations on the dispersion image, it can automatically extract multi-modal curves with precision. Dispersion curves extracted from the published synthetic and field data are compared against state-of-the-art practices, including Geopsy, popular commercial software, and recently published machine learning techniques. The proposed technique performed exceptionally well in diverse scenarios and produced negligible root mean square error compared to the true modal curves. The execution of the entire process takes less than a second. The developed formula will significantly enhance the accuracy of dispersion curve extraction and facilitate the efficient processing of vast amounts of survey data.