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Title: Reflection coefficient of a fractional reflector

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Abstract: In seismology and in oil exploration, the diffraction or refraction of sound by an interface where there is a jump of sound velocity, formulae are well known. However, little is known when the velocity is continuous and has a jump in one of its derivatives (even a fractional one)

This talk defines and give an estimate for the reflection $R$ coefficient for solutions of the Helmholtz equation听(\Delta u -c^{-2}(1+l(((x_{1})_+^{\alpha}))\partial^2_{t^2}u=0听that is $e^{-i\omega t+ ik_2x_2+i\sqrt{\frac{\omega^2}{c^2}-k_2^2}x_1}+R.e^{-i\omega t+ ik_2x_2-i\sqrt{\frac{\omega^2}{c^2}-k_2^2}x_1}$ for $x_1<0$ and $Tu^{>}$ for $x_1>0$.

This passes through the precise definition of an 'outgoing at infinity wave' u^{>} and its precise expression, using the limiting absorption principle. The leading order term of R is a Fourier multiplier, whose principal symbol will be given.

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Meeting ID: 831 1853 9851

Passcode: 215516

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