IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i11p1884-d437575.html
   My bibliography  Save this article

Surface Motion of a Half-Space Containing an Elliptical-Arc Canyon under Incident SH Waves

Author

Listed:
  • Hui Qi

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Fuqing Chu

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Jing Guo

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

  • Runjie Yang

    (College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China)

Abstract

The existence of local terrain has a great influence on the scattering and diffraction of seismic waves. The wave function expansion method is a commonly used method for studying terrain effects, because it can reveal the physical process of wave scattering and verify the accuracy of numerical methods. An exact, analytical solution of two-dimensional scattering of plane SH (shear-horizontal) waves by an elliptical-arc canyon on the surface of the elastic half-space is proposed by using the wave function expansion method. The problem of transforming wave functions in multi-ellipse coordinate systems was solved by using the extra-domain Mathieu function addition theorem, and the steady-state solution of the SH wave scattering problem of elliptical-arc depression terrain was reduced to the solution of simple infinite algebra equations. The numerical results of the solution are obtained by truncating the infinite equation. The accuracy of the proposed solution is verified by comparing the results obtained when the elliptical arc-shaped depression is degraded into a semi-ellipsoidal depression or even a semi-circular depression with previous results. Complicated effects of the canyon depth-to-span ratio, elliptical axis ratio, and incident angle on ground motion are shown by the numerical results for typical cases.

Suggested Citation

  • Hui Qi & Fuqing Chu & Jing Guo & Runjie Yang, 2020. "Surface Motion of a Half-Space Containing an Elliptical-Arc Canyon under Incident SH Waves," Mathematics, MDPI, vol. 8(11), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1884-:d:437575
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/11/1884/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/11/1884/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1884-:d:437575. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.