Kirchhoff–Helmholtz integral

The Kirchhoff–Helmholtz integral combines the Helmholtz equation with the Kirchhoff integral theorem^[1] to produce a method applicable to acoustics,^[2] seismology^[3] and other disciplines involving wave propagation.

It states that the sound pressure is completely determined within a volume free of sources, if sound pressure and velocity are determined in all points on its surface.

{\boldsymbol {P}}(w,z)=\iint _{dA}\left(G(w,z\vert z'){\frac {\partial }{\partial n}}P(w,z')-P(w,z'){\frac {\partial }{\partial n}}G(w,z\vert z')\right)dz'

References

^ Kurt Heutschi (2013-01-25), Acoustics I: sound field calculations (PDF)
^ Oleg A. Godin (August 1998), "The Kirchhoff–Helmholtz integral theorem and related identities for waves in an inhomogeneous moving fluid", Journal of the Acoustical Society of America, 99 (4): 2468–2500, doi:10.1121/1.415524
^ Patricia Scott; Don Helmberger (1983), Applications of the Kirchhoff-Helmholtz integral to problems in seismology

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[1] Kurt Heutschi (2013-01-25), Acoustics I: sound field calculations (PDF)

[2] Oleg A. Godin (August 1998), "The Kirchhoff–Helmholtz integral theorem and related identities for waves in an inhomogeneous moving fluid", Journal of the Acoustical Society of America, 99 (4): 2468–2500, doi:10.1121/1.415524

[3] Patricia Scott; Don Helmberger (1983), Applications of the Kirchhoff-Helmholtz integral to problems in seismology

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