### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 1aPA8. Computation of transient Green's functions through plane interfaces.

**Carsten Draeger
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Didier Cassereau
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*Lab. Ondes et Acoustique, Universite Paris 7, E.S.P.C.I., 10 rue Vauquelin,
75231 Paris Cedex 05, France
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This work studies the acoustical field generated by a point source after
reflection or transmission by a plane interface. There are two classical
approaches to calculate such transient Green's functions, using either a Laplace
or a Fourier transform over time. However, the second approach involves
numerical integrations that are difficult to carry out because of singularities
of the integrand. It is shown that it is possible to avoid this difficulty using
an excitation in the form of a temporal Lorentz function of variable width,
introducing several judicious variable changes and finally deforming the
integration path in the complex plane. By developing the expression of the
transmission/reflection coefficient into Taylor's series around suitable points,
it is even possible to carry out a piecewise integration analytically, therefore
resulting in an approximate expression of the acoustical field as a function of
space and time. Since this expression turns out to be in a closed form, it can
be evaluated fast and even be manipulated later on.