On the singularity index and the unfolding of the diffraction catastrophes |
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| Institution: | 1. School of Engineering, RMIT University, GPO Box 2476, Melbourne, Victoria 3001, Australia;2. Centre for Environmental Sustainability and Remediation, RMIT University, Victoria, Australia;3. CDM Smith, Richmond, Victoria, Australia;4. Australian Contaminated Land Consultants Association, Victoria, Australia;5. Centre for Applied Sciences, EPA Victoria, Victoria, Australia;6. School of Science, RMIT University, Victoria, Australia;1. School of Earth Sciences and Engineering, Sun Yat-sen University, Guangzhou 510275, China;2. Guangdong Provincial Key Laboratory of Geological Process and Mineral Resource Exploration, Guangzhou 510275, China;3. Guangdong Provincial Key Lab of Geodynamics and Geohazards, Guangzhou 510275, China;4. Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519000, China;1. College of Earth Science, Chengdu University of Technology, Chengdu 610059, China;2. Key Laboratory of Geoscience Spatial Information Technology of Ministry of Land and Resources (Chengdu University of Technology), Chengdu 610059, China;3. State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan 430074, China |
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| Abstract: | The caustics of high-frequency wave propagation may be classified using catastrophe theory. The wavefield in the vicinity of any caustic is described by the corresponding diffraction catastrophe. The singularity index, β, is a measure of the rate at which such a wavefield diverges as ω→∞ at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point β also describes a balance between two different measures of the unfolding of the wavefield in each control direction, β = σnϱn. The indices σn and ϱn describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter. |
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