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Obliquely incident wave propagation across rock joints with virtual wave source method

Zhu, J. B. and Zhao, J. (2013) Obliquely incident wave propagation across rock joints with virtual wave source method. Journal of Applied Geophysics, 88 . pp. 23-30. ISSN 0926-9851.

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Due to the presence of joints, waves are greatly attenuated when propagating across rock masses. Zhu et al. (2011) (Normally incident wave propagation across a joint set with virtual wave source method. J. Appl. Geophys.73, 283–288.) studied normally incident wave propagation across a joint set with the virtual wave source method (VWSM). The introduced VWSM has merits in some aspects, especially the capability of separating differently arriving transmitted waves. However, normal wave incidence is only the special case for wave incidence with arbitrary incident angles. Obliquely incident wave propagation across a joint set is more complicated than normally incident wave propagation due to wave transformation at the joints. As a continuation of the previous paper, this work is extended to analytically study obliquely incident wave propagation across joints with VWSM. Complete theoretical reflection and transmission coefficients across single joint described by displacement discontinuity model are derived through plane wave analysis. The superposition of P wave and S wave is for the first time mathematically expressed and studied. The VWSM is verified through comparison with the propagation matrix method. Through extensive parametric studies on wave transmission across single and multiple parallel joints, it is shown that transmitted wave energy is mainly constrained in the transmitted wave of the same type as the incident wave. And with increasing joint stiffness, the transmission coefficients across single joint increases except those whose wave type is different from the incident wave. The amplitude of superposed transmitted wave for P wave incidence increases with incident angle, which is coincident with field observations. Both joint spacing and number of joints have significant effects on transmission coefficients. We find that when joint spacing is sufficiently large, the transmission coefficient is no longer a constant as the normally incident wave propagation case (Zhu et al., 2011). And when joints are very closely spaced, wave attenuation depends little on the number of joints, which is different from the conclusions from equivalent medium method.

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Additional Information:© 2012 Elsevier B.V. Received 1 May 2011; Accepted 7 October 2012; Available online 13 October 2012. We wish to thank Dr. Gaofeng Zhao for the help in implementing our method into Matlab. Dr. Xiaobao Zhao and Dr. Jianchun Li are acknowledged for their useful discussions and innovative ideas. We would like to acknowledge the two anonymous reviewers and the Editor, Professor Klaus Holliger, for their constructive comments. This research is financially supported by the Swiss National Science Foundation (200021–116536).
Funding AgencyGrant Number
Swiss National Science Foundation (SNSF)200021-116536
Subject Keywords:Oblique wave incidence; Virtual wave source method; Rock joints; Superposed wave; Displacement discontinuity model
Record Number:CaltechAUTHORS:20130214-103845331
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Official Citation:J.B. Zhu, J. Zhao, Obliquely incident wave propagation across rock joints with virtual wave source method, Journal of Applied Geophysics, Volume 88, January 2013, Pages 23-30, ISSN 0926-9851, 10.1016/j.jappgeo.2012.10.002.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36925
Deposited By: Tony Diaz
Deposited On:14 Feb 2013 23:11
Last Modified:03 Oct 2019 04:42

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