QEDispInv is an open-source C++ program developed for the forward modeling and inversion of surface wave dispersion curves, accompanying this work on integrating quadratic extrema interpolation and randomized layering with multiple initial models. This toolkit encompasses the complete workflow of surface wave analysis, from dispersion curve calculation to subsurface structure inversion, designed to address the challenges of low-velocity layers (LVLs) and ``mode-kissing'' phenomena in complex geological models.
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Forward Modeling: Implements the quadratic extrema interpolation method for accurate and efficient dispersion curve computation, specifically optimized to resolve mode-kissing zones in models with LVLs. This method significantly reduces root omission rates compared to conventional approaches (e.g., CPS) while achieving substantial speed improvements (
$12.6\times$ for full-mode computation and$17.4\times$ for fundamental-mode calculation in benchmark tests). - Inversion Framework: Incorporates wavelength-constrained layering schemes that adapt to the depth-dependent resolution of surface wave data, combined with depth-zoned empirical relationships for deriving P-wave velocity and density from shear-wave velocity. The inversion process utilizes the L-BFGS-B algorithm, with statistical aggregation of results from multiple initial models to address non-uniqueness.
- Comprehensive Workflow: Supports both forward computation (dispersion curve generation) and inversion (subsurface structure recovery), validated through numerical simulations (near-surface and crustal LVL models) and real data applications (Mirandola site and USArray).
The program can be cloned from the GitHub repository:
git clone https://github.com/pan3rock/QEDispInv.git
cd QEDispInv
git submodule update --initPlease refer to the Install document for compilation instructions and dependencies.
A detailed tutorial covering step-by-step instructions for using QEDispInv, including forward
modeling setup, inversion parameter configuration, result visualization, and example walkthroughs,
is available in the Tutorial document. This tutorial is designed to help new
users quickly get started with the toolkit and explore its full functionality.
QEDispInv provides command-line interfaces for both forward and inversion modules:
- Forward Modeling: Compute dispersion curves for a given subsurface model using the quadratic extrema interpolation method.
- Inversion: Perform inversion of observed dispersion curves to derive shear-wave velocity profiles, incorporating the wavelength-constrained layering and empirical relationships described in this work.
Detailed usage examples and parameter specifications are available in the Tutorial.
If you use QEDispInv in your research, please cite this work as follows:
- Pan, L., Wang, J., & Chen, X. (2026). Surface wave dispersion curve computation and inversion: A framework integrating quadratic extrema interpolation and randomized layering with multiple initial models. Bulletin of the Seismological Society of America, 116(3), 902-922. https://doi.org/10.1785/0120250207
- Pan, L., & Chen, X. (2025). Efficient Computation of Dispersion Curves in Low‐Velocity‐Layered Half‐Spaces. Bulletin of the Seismological Society of America, 115 (4), 1381–1391. https://doi.org/10.1785/0120250003
- Pan, L., Chen, X., Wang, J., Yang, Z., & Zhang, D. (2019). Sensitivity analysis of dispersion curves of Rayleigh waves with fundamental and higher modes. Geophysical Journal International, 216(2), 1276-1303. https://doi.org/10.1093/gji/ggy479
https://github.com/pan3rock/QEDispINV
This program is released under the GNU LESSER GENERAL PUBLIC LICENSE (LGPL) to promote open science and facilitate further development in the geophysical community.