Abstract
The numerical solution of the Helmholtz equation is examined for a separated source and receiver over a model having a single planar interface. Expressions describing the construction and reconstruction of acoustical wave fields are derived in terms of Green’s functions. Their relation to the Fourier transform is briefly discussed. Three simple Green’s functions—free space, free surface, and rigid surface—are used to test the relative accuracy of the respective weighting factors by comparing the numerically calculated field for a simple model to a field obtained analytically by application of rigorous diffraction theory. The main purpose of this paper is to study the behavior of the total response (amplitude and phase) for models in which the aperture is not sufficiently sampled (e.g., close to half the wavelength). The degree of distortion in the response due to spatial undersampling is unacceptable for all three Green’s functions. A modified weighting factor relative to the free‐space Green’s function is introduced, which effectively reduces the degree of distortion in the total response under the same sampling condition. The importance of this finding to exploration geophysics in the construction of the synthetic seismograms by application of the Huygen’s principle and in seismic migration will be demonstrated.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
