TY - JOUR
T1 - Acoustic propagation operators for pressure waves on an arbitrarily curved surface in a homogeneous medium
AU - Sun, Yimin
AU - Verschuur, Eric
AU - van Borselen, Roald
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
U2 - 10.1016/j.jappgeo.2017.11.007
DO - 10.1016/j.jappgeo.2017.11.007
M3 - Article
SN - 0926-9851
VL - 150
SP - 314
EP - 324
JO - Journal of Applied Geophysics
JF - Journal of Applied Geophysics
ER -