### Society of Exploration Geophysicists conference abstract

Dalton, D.R. and Yedlin, M.J. "Exact Time-Domain Solutions for
Acoustic Diffraction by a Half Plane",
presented at the 58th Annual (1988) SEG
(Society of Exploration Geophysicists) Meeting in Anaheim.
We derive an exact time-domain solution for scattering of acoustic
waves by a half plane by inverse Fourier transforming the
frequency-domain integral solution. The solution consists 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 (G.O.) 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.
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.