THE COMPLETE EXTENSION OF THE BIOT-TOLSTOI SOLUTION TO THE DENSITY CONTRAST WEDGE WITH SAMPLE CALCULATIONS

The Biot-Tolstoy exact time-domain solution for the three-dimensional impulse response of an impenetrable wedge is extended to accommodate t he isovelocity or density-contrast wedge. Fourier transformation of th e time and axial variables, along with a Kantorovich-Lebedev transform applied to the cylindrical radial coordinate, leads to a solution in terms of residue series. When the wedge angle is a rational fraction o f pi, the residue series can be reduced to a finite sum which is evalu ated for some special cases. The total pressure field consists of geom etrical acoustics contributions, as predicted by Snell's laws, plus a modified version of the Biot-Tolstoy diffraction field. (C) 1997 Acous tical Society of America.