By Armand Wirgin (eds.)
ISBN-10: 321183320X
ISBN-13: 9783211833209
ISBN-10: 3709124867
ISBN-13: 9783709124864
This ebook offers an up to date presentation of a vast variety of up to date difficulties in inverse scattering concerning acoustic, elastic and electromagnetic waves. Descriptions can be given of conventional (but nonetheless in use and topic to on-going advancements) and newer equipment for selecting both: a) the homogenized fabric parameters of (spatially) unbounded or bounded heterogeneous media, or b) the precise composition (spatial distribution of the fabric parameters) of unbounded or bounded heterogeneous media, or c) the positioning, form, orientation and fabric features of an item embedded in a wellcharacterized homogeneous, homogenized or heterogeneous unbounded or bounded medium, through inversion of mirrored, transmitted or scattered spatiotemporal recorded waveforms caused by the propagation of probe radiation in the medium.
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Additional info for Wavefield Inversion
Example text
L21) are never zero. 121) are written as G. Dassios 46 f (r · r')n- 2kfn (r') F(r') ds(r') s2 = 1 n-2k+ 1 J fn (r') F(r') ds(r') s2 2 "" ( 2 -m)! x Yf (r) 5(n- 2k) + (n-2k+1)(n-2k+3) L.... (2+m)! m=-2 f Yf (r') fn (r') F(r') ds(r') s2 9(n- k)(n- 2k- 2) +--------------------(n- 2k + 1)(n- 2k + 3)(n- 2k + 5) 4 X "" L.... m=-4 4 ( - m)! (4+m)! Yf (r) f Yf (r') fn (r') F(r') ds(r') + ... l23) s2 for n=even, and f (r · r')n- 2kfn(r') F(r') ds(r') sz 3 ~ (1-m)! y 1m (r) = n- 2k + 2 L.... (I+ m)! m=-1 JYt (r') fn (r') F(r') ds(r') 82 3 + "" (3-m)!
This contradicts our initial assumption that a80 =1 . Hence, Dp is nonsingular. 138) is a consequence of the geometrical assumption that the surface of the scatterer does not pass through the origin, which has been chosen to be the point with respect to which the surface is star shape. The steps that lead to the reconstruction of the surface of the scatterer from a knowledge of the low-frequency far field pattern, are the following (i) Expand the scattering amplitude in powers of the wave number.
158) states that the time rate of change of the elastic energy density is balanced by the spatial power flux. 159) where the square of the norm of the dyadic is defined as the sum of the squares of its components. 160) 25 Energy Functionals in Scattering Theory and Inversion The power flux in the direction is surface an Jn· P ds = rolm an. 161) an. 162) where ap, ag are the amplitudes of the longitudinal and the transverse waves respectively, and b is orthogonal to the propagation vector k. P r~oo 5 c~ Igr(r) 2 +c~ ~I ge(r) ro 2 cpap + c 5 a 5 k.