scholarly journals Approximate Separability of Green's Function for High Frequency Helmholtz Equations

2014 ◽  
Author(s):  
Bjoern Engquist ◽  
Hongkai Zhao
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
High Frequency ◽  
Helmholtz Equations

scholarly journals Asymptotic high-frequency Green's function for a planar phased sectoral array of dipoles

Radio Science ◽  
2000 ◽  
Vol 35 (2) ◽  
pp. 579-593 ◽  
Author(s):  
F. Capolino ◽  
S. Maci ◽  
L. B. Felsen
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
High Frequency

Fast Huygens’ sweeping methods for multiarrival Green’s functions of Helmholtz equations in the high-frequency regime

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. T91-T100 ◽  
Author(s):  
Jianliang Qian ◽  
Songting Luo ◽  
Robert Burridge
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Finite Difference Methods ◽  
Fixed Number ◽  
Point Sources ◽  
Helmholtz Equations ◽  
Frequency Regime ◽  
First Arrival

Multiarrival Green’s functions are essential in seismic modeling, migration, and inversion. Huygens-Kirchhoff (HK) integrals provide a bridge to integrate locally valid first-arrival Green’s functions into a globally valid multiarrival Green’s function. We have designed robust and accurate finite-difference methods to compute first-arrival traveltimes and amplitudes, so that first-arrival Green’s functions can be constructed rapidly. We adapted a fast butterfly algorithm to evaluate discretized HK integrals. The resulting fast Huygens’ sweeping method has the following unique features: (1) it precomputes a set of local traveltime and amplitude tables, (2) it automatically takes care of caustics, (3) it constructs Green’s functions of the Helmholtz equation for arbitrary frequencies and for many point sources, and (4) for a fixed number of points per wavelength, it constructs each Green’s function in nearly optimal complexity [Formula: see text] in terms of the total number of mesh points [Formula: see text], where the prefactor of the complexity only depends on the specified accuracy, and is independent of the frequency. The 2D and 3D examples revealed the performance of the method.

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