For far-field wave-motion response to a point dynamic dislocation source, the temporal and spatial features of the source mechanism are characterized, respectively, by two factors, i.e., a source time function for dislocation growth and a combination of nine couples of impulse forces that is equivalent to the final dislocation. The mathematical representation for each of the couples, referred to as spatial couples, is a couple of impulses acting in opposing directions with an infinitesimal separation distance or, in the limit, by the derivative of the impulse with respect to the separation-distance parameter. This study proposes a temporal-spatial pulse representation for the nine couples, referred to as temporal-spatial couples, and subsequently for the dislocation source modeling. Each temporal-spatial couple consists of two impulses acting in opposite directions with both an infinitesimal separation distance and an infinitesimal time delay. By examining dynamite source modeling, this study shows that the proposed representation can intrinsically integrate the spatial and temporal features of the dislocation sources from the response point of view. This study also shows an example of a point, shear-slip seismic source modeling using traditional and proposed pulse representations for far-field wave motion. Discussion is finally provided for the implications of the proposed representation in broad applications.
Concept and Fundamentals of Temporal-Spatial Pulse Representation for Dislocation Source Modeling
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, March 3, 2004; final revision, July 13, 2004. Associated Editor: Z. Suo. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Journal of Applied Mechanics, Department of Mechanical and Environmental Engineering, University of California - Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Ruichong Zhang, R. (January 27, 2005). "Concept and Fundamentals of Temporal-Spatial Pulse Representation for Dislocation Source Modeling ." ASME. J. Appl. Mech. November 2004; 71(6): 887–893. https://doi.org/10.1115/1.1855316
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