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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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In the overburden layer the wave fields are expanded in terms of cylindrical waves. Within the anomaly, spherical wave functions are used. Relationships between both sets of expansion coefficients are obtained from the boundary conditions by applying Green's theorem. The solution method is well-known as the null-field or T-matrix approach (see Martin (1982), Kristensson and Strom (1978) and Bostrom and Karlsson (1984». In Section 4, the relationships for both sets of expansion coefficients are transformed to one infinite system of algebraic equations for the expansion coefficients of the pressure field in the sphere.

With respect to w. are performed by using the FFT algorithm. using frequency values w = (j-l)6w-iy. e. Nyquist sampling is applied to obtain a trace of length T). The Fourier transforms are smoothly truncated. using the tapering function Rew - 0 {I + cos(( 0 -Q 1)~)} for 0 1 ( Rew ( O2 , 2 1 For the frequency dependent part few) of the source. we have chosen the Fourier transform of the pulse function i ~~ {I + cos(t~~ ~)}. 0 ( t ( 2~. In Figs. 2a-c the results are displayed for a model with velocity contrasts only.

64:917. 5. , 1982, Acoustic scattering and radiation problems, and the null-field method. Wave Motion, 4:391. (t) J received at the jth geophone station as the convolution of the impulse response of the earth g .. (t) with a seismic wavelet 1J Sl' (t), plus some un- correlated noise n .. (t) : 1J f giJ'('rls i (t - T)dT + n .. (t) 1J (1) o In this equation gij(t) is regavded as the response the jth geophone station would measure in the absence of any noise, if a perfect impulse were emitted at the ith source position at time t = O.

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