An automatic algorithm for surface wave dispersion curve picking based on Hessian matrix attributes

A new automatic method for dispersion curve picking based on Hessian matrix attributes is proposed, on which, an algorithm is developed in this paper. The algorithm is based on dispersion power spectra transformed from surface waves. It fulfills the automatic picking of the surface wave dispersion curves from the fundamental to high orders, by ridge searching and extraction, ridge line segment connection, dispersion curve selecting and order sorting. The algorithm does not have to rely on model training and there is no manual interaction requirement. This inherent efficiency advantage of the algorithm provides an efficient tool for surface wave dispersion curve picking for large projects such as oil and gas exploration. The algorithm is tested using two conceptual models. On the synthetic data of the test models, surface wave dispersion curves up to the 8th order are successfully picked, which shows the excellent picking ability of the method. Further comparative experiments show that the algorithm is superior to other methods in terms of picking accuracy, completeness, anti-noise performance and computation efficiency. In order to evaluate the practicability of the algorithm, we applied it to surface wave data from an industrial prospecting project. Three dispersion curves, including the fundamental order, first order and second order, are successfully obtained. The dispersion curve inversion result matches perfectly with the vertical seismic profile. This application case verified the effectiveness and practicability of the algorithm.