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Incident and Diffracted Waves
Generalized Ray Integrals
Inverse Fourier Transform of the
acoustic waves applying asymptotic boundary condition branch cut branch points Cagniard method chapter circular cylinder complex t plane condition of Eq contour corresponding creep waves cylindrical surface diffracted ray diffracted waves dimensional problem direct incident waves equation evaluate exists a stationary function F(t function g function g^(u,0 Hankel function hard cylinder imaginary u axis integral transform integration path inverse Fourier transform inverse transformation lit zone multivalued function negative real obtain phase function point source Poisson summation formula positive real quadrant ray integrals ray parameter ray path reach the receiver real axis real time variable real u axis reflected ray reflected wave saddle point scattered waves shadow zone shown in Fig simultaneous transformation slip stream soft cylinder Sommerfeld-Watson Transformation Sound Pulses spherical stationary point thesis three dimensional Total wave field transformation of Eq transient acoustic transient waves ucos ucosh vz/c wave front x-y plane