### Surveys in Geophysics abstract

Dalton, D.R. and Yedlin, M.J. (1989) "Exact Time-Domain Solutions for Acoustic Diffraction by a Half
Plane", Surveys in Geophysics 10, 305-330. This was also published in the book: Aspects of Seismic
Reflection Data Processing, ed. R. Marschall (Prakla-Seismos).
We derive exact time-domain solutions for scattering of acoustic waves
by a half plane by inverse Fourier transforming the frequency-domain
integral solutions. The solutions consist of a direct term, a
reflected term and two diffraction terms. The diffracting edge induces
step function discontinuities in the direct and reflected terms at two
shadow boundaries. At each boundary, the associated diffraction term
reaches a maximum amplitude of half the geometrical optics term and
has a signum function discontinuity so that the total field remains
continuous. We evaluate solutions for practical point source
configurations by numerically convolving the impulse diffraction
responses with a wavelet. We solve the associated problems of
convolution with a singular, truncated diffraction operator by
analytically derived correction techniques. We produce a zero-offset
section and compare it to a Kirchhoff integral solution.
Our exact diffraction hyperbola exhibits noticeable asymmetry, with
higher amplitudes on the reflector side of the edge. Near the apex of
the hyperbola the Kirchhoff solution approximates the exact
diffraction term symmetric in amplitude about the reflection shadow
boundary, but omits the other low amplitude term
necessary to ensure continuity at the direct shadow boundary.