By Frederic L. Lizzi, D. Jackson Coleman, Jack Driller (auth.), A. J. Berkhout, J. Ridder, L. F. van der Wal (eds.)
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Since the sound waves travel from the shot to the receiver by a variety of paths, leaving the shot in many different directions, the convolution implies that the seismic wavelet produced by the shot is the same in all these directions. This is achieved if the wavefield of the shot has spherical symmetry. Ideally we should like our seismic wavelet to be a perfect Dirac pulse 6 (t), and to have no noise, for then x. (t) would be equal to J gij(t). In the real world we cannot ignore the noise and will also have to deal with a bandlimited seismic wavelet.
R, J 36 J (13 ) the outward normal on Sj with respect to V2. /, J v. J a Re v. uation (14) is simplified by expanding the outgoing spherical waves <1>0;) in terms of cylindrical waves. 149) from BenMenahem and Singh's publication (1981), we find 1 vI h I - v I h (1+ Bl e + (1B2 e = S(k,w), (19) a) a) where S(k,w) = _1_ I: ex 1; 4> (k) 2~v2 n=O n n n ' (20) with 4> n (k) = 12n+l i- n e -v (d-h) 2 p n (21) 37 Equation (15) is simplified if its left-hand side is multiplied by a spherical harmonic function Ymn • and integrated over the surface of a sphere in V3.
Armour, E. P. , "Human Cancer Treatment with Ultrasound," IEEE Trans. on Sonics and UltrasoniCS, SU-31, 444-456, 1984. , "A Strategy for Localized Chemotherapy of Tumors Using Ultrasonic Hyperthermia," Ultrasound in Medicine and Biology, 5 :95, 1979. , "Studies of Thermal Injury," Archives of Pathology, 5:489-502, 1947. , Miller, M. , "Biological Effects of Ultrasound," J. Bio. Physics, 2: 173-192, 1974. , "Effects of Ultrasound on Excised Bovine Lenses," Graefe Arch. , 139:301-322, 1938. , Purnell, E.
Acoustical Imaging by Frederic L. Lizzi, D. Jackson Coleman, Jack Driller (auth.), A. J. Berkhout, J. Ridder, L. F. van der Wal (eds.)