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Open AccessArticle

A MATLAB Package for Calculating Partial Derivatives of Surface-Wave Dispersion Curves by a Reduced Delta Matrix Method

Research Institute of Petroleum Exploration & Development, Lanzhou 730030, China
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Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(23), 5214; https://doi.org/10.3390/app9235214
Received: 26 October 2019 / Revised: 26 November 2019 / Accepted: 27 November 2019 / Published: 30 November 2019
(This article belongs to the Special Issue Surface Waves for Monitoring of Materials at Different Scales)
Various surface-wave exploration methods have become increasingly important tools in investigating the properties of subsurface structures. Inversion of the experimental dispersion curves is generally an indispensable component of these methods. Accurate and reliable calculation of partial derivatives of surface-wave dispersion curves with respect to parameters of subsurface layers is critical to the success of these approaches if the linearized inversion strategies are adopted. Here we present an open-source MATLAB package, named SWPD (Surface Wave Partial Derivative), for modeling surface-wave (both Rayleigh- and Love-wave) dispersion curves (both phase and group velocity) and particularly for computing their partial derivatives with high precision. The package is able to compute partial derivatives of phase velocity and of Love-wave group velocity analytically based on the combined use of the reduced delta matrix theory and the implicit function theorem. For partial derivatives of Rayleigh-wave group velocity, a hemi-analytical method is presented, which analytically calculates all the first-order partial differentiations and approximates the mixed second-order partial differentiation term with a central difference scheme. We provide examples to demonstrate the effectiveness of this package, and demo scripts are also provided for users to reproduce all results of this paper and thus to become familiar with the package as quickly as possible. View Full-Text
Keywords: phase velocity; group velocity; surface waves; love waves; rayleigh waves; partial derivatives; dispersion curves; open-source code; MATLAB package phase velocity; group velocity; surface waves; love waves; rayleigh waves; partial derivatives; dispersion curves; open-source code; MATLAB package
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Wu, D.; Wang, X.; Su, Q.; Zhang, T. A MATLAB Package for Calculating Partial Derivatives of Surface-Wave Dispersion Curves by a Reduced Delta Matrix Method. Appl. Sci. 2019, 9, 5214.

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