A Novel Approach to Model Surface Wave Propagation in Layered Media
Publication: Geo-Congress 2023
ABSTRACT
The fidelity of the surface wave inversion is greatly influenced by the efficiency and accuracy of the forward analysis. Existing forward modelling approaches generate only theoretically calculated dispersion curves without any information regarding the modal amplitude. The present study proposes a semi-analytical forward modelling approach to determine the dispersion image from a 1D profile similar to that produced by multichannel field data. An analytical solution is used in the horizontal direction, and finite element discretization is applied in the vertical direction. The infinitely extended elastic half-space is efficiently modelled by using perfectly matched discrete layer (PMDL) elements. The higher-order finite element discretization and the use of PMDL elements significantly reduce the computational cost. The proposed method calculates the vertical displacement responses at different receiver positions on the surface in frequency-space domain. The complex frequency-space domain response is transformed into seismogram data and velocity spectra.
Get full access to this article
View all available purchase options and get full access to this chapter.
REFERENCES
Haskell, N. A. 1953. “The dispersion of surface waves on multilayered media.” Bulletin of the Seismological Society of America, 43 (1): 17–34. Seismological Society of America (SSA). https://doi.org/10.1785/bssa0430010017.
Kausel, E. 1981. An explicit solution for the Green functions for dynamic loads in layered media.
Kausel, E. 2005. “Waves Propagation Modes: From Simple Systems to Layered Soils.” Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks, 165–202. Vienna: Springer Vienna.
Kausel, E., and J. M. Roësset. 1981. “Stiffness matrices for layered soils.” Bulletin of the Seismological Society of America, 71 (6): 1743–1761. https://doi.org/10.1785/BSSA0710061743.
Kumar, J., and T. Naskar. 2015. “Effects of site stiffness and source to receiver distance on surface wave tests׳ results.” Soil Dynamics and Earthquake Engineering, 77: 71–82. Elsevier Ltd. https://doi.org/10.1016/j.soildyn.2015.04.022.
Kumar, J., and T. Naskar. 2017a. “A fast and accurate method to compute dispersion spectra for layered media using a modified Kausel-Roësset stiffness matrix approach.” Soil Dynamics and Earthquake Engineering, 92 (September 2016): 176–182. Elsevier. https://doi.org/10.1016/j.soildyn.2016.09.042.
Kumar, J., and T. Naskar. 2017b. “Resolving phase wrapping by using sliding transform for generation of dispersion curves.” Geophysics, 82 (3): V127–V136. Society of Exploration Geophysicists. https://doi.org/10.1190/geo2016-0207.1.
Lai, C. G., M. D. Mangriotis, and G. J. Rix. 2014. “An explicit relation for the apparent phase velocity of Rayleigh waves in a vertically heterogeneous elastic half-space.” Geophysical Journal International, 199 (2): 673–687. https://doi.org/10.1093/gji/ggu283.
Naskar, T., and J. Kumar. 2017. “Predominant modes for Rayleigh wave propagation using the dynamic stiffness matrix approach.” Journal of Geophysics and Engineering, 14 (5): 1032–1041. Institute of Physics Publishing. https://doi.org/10.1088/1742-2140/aa6fe3.
Naskar, T., and J. Kumar. 2019. “A faster scheme to generate multimodal dispersion plots for Rayleigh wave propagation.” Soil Dynamics and Earthquake Engineering, 117 (December 2018): 280–287. Elsevier Ltd. https://doi.org/10.1016/j.soildyn.2018.11.024.
Naskar, T., and J. Kumar. 2022. “MATLAB codes for generating dispersion images for ground exploration using different MASW transforms.” Geophysics, 1–37. Society of Exploration Geophysicists. https://doi.org/10.1190/geo2020-0928.1.
Savadatti, S., and M. N. Guddati. 2010. “A finite element alternative to infinite elements.” Computer Methods in Applied Mechanics and Engineering, 199 (33–36): 2204–2223. https://doi.org/10.1016/j.cma.2010.03.018.
Schwab, F. A., and L. Knopoff. 1972. Fast Surface Wave and Free Mode Computations. 87–180. Elsevier.
Thomson, W. T. 1950. “Transmission of Elastic Waves through a Stratified Solid Medium.” Journal of Applied Physics, 21 (2): 89–93. https://doi.org/10.1063/1.1699629.
Tokimatsu, K., S. Tamura, and H. Kojima. 1992. “Effects of multiple modes on rayleigh wave dispersion characteristics.” Journal of Geotechnical Engineering, 118 (10): 1529–1543. American Society of Civil Engineers. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:10(1529).
Virieux, J. 1986. “P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method.” Geophysics, 51 (4): 889–901. https://doi.org/10.1190/1.1442147.
Information & Authors
Information
Published In
Geo-Congress 2023
Pages: 268 - 277
History
Published online: Mar 23, 2023
ASCE Technical Topics:
- Continuum mechanics
- Curvature
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Field tests
- Finite element method
- Geomechanics
- Geometry
- Geotechnical engineering
- Layered systems
- Mathematics
- Methodology (by type)
- Model accuracy
- Models (by type)
- Numerical methods
- Soil dynamics
- Soil mechanics
- Solid mechanics
- Surface waves
- Systems engineering
- Systems management
- Tests (by type)
- Wave propagation
- Waves (mechanics)
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.