Acoustic propagation operators for pressure waves on an arbitrarily curved surface in a homogeneous medium
| Autor: | Yimin Sun, Roald van Borselen, Eric Verschuur |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
010504 meteorology & atmospheric sciences Helmholtz equation Mathematical analysis Spherical cap 010502 geochemistry & geophysics Curvature 01 natural sciences symbols.namesake Geophysics Planar Classical mechanics Homogeneous Acoustic propagation symbols Acoustic wave equation Rayleigh scattering 0105 earth and related environmental sciences |
| Zdroj: | Journal of Applied Geophysics. 150:314-324 |
| ISSN: | 0926-9851 |
| DOI: | 10.1016/j.jappgeo.2017.11.007 |
| Popis: | The Rayleigh integral solution of the acoustic Helmholtz equation in a homogeneous medium can only be applied when the integral surface is a planar surface, while in reality almost all surfaces where pressure waves are measured exhibit some curvature. In this paper we derive a theoretically rigorous way of building propagation operators for pressure waves on an arbitrarily curved surface. Our theory is still based upon the Rayleigh integral, but it resorts to matrix inversion to overcome the limitations faced by the Rayleigh integral. Three examples are used to demonstrate the correctness of our theory – propagation of pressure waves acquired on an arbitrarily curved surface to a planar surface, on an arbitrarily curved surface to another arbitrarily curved surface, and on a spherical cap to a planar surface, and results agree well with the analytical solutions. The generalization of our method for particle velocities and the calculation cost of our method are also discussed. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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