Download PDF by Barry Saltzman, Renata Dmowska: Advances in Geophysics, Vol. 43

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By Barry Saltzman, Renata Dmowska

ISBN-10: 0120188430

ISBN-13: 9780120188437

This sequence presents a venue for longer stories of present advances in geophysics. Written at a degree available to graduate scholars, the articles serve to expand wisdom of varied fields and will be worthy in classes and seminars.

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Expression (63) does not contain any approximation since A is a generic function of x and to. To obtain the approximation of the classic ray theory we have to expand the amplitude vector in a series of inverse powers of to oo A(x, Xo, to) - S(to) Z Ai(x, Xo)to -i , (64) i=O where S(to) is the FT of the source time function. x0) u(x, to) = S(to)A0(x, x0) ~/J (x, x0) (65) and represents an approximation of the solution of the wave equation valid only at high frequencies, when the higher terms can be neglected in (65).

The wavefield diffracted in medium M' from interface S, separating M and M', can be described as a radiation generated by secondary sources distributed along the interface. Therefore the wavefield in P can be described as f V(P) - Vo(P) 4- Js cr(Q)G(P, Q)dQ, (58) where er(Q) is a density function of the source that represents the force of the wavefield diffracted from point Q, and G(P, Q) is the wavefield generated in P by a unit source placed in Q (it is also known as the Green function). Analogously, the diffracted wavefield in P' is f V'(P') = JsCr'(Q)G'(P ', Q)dQ, (59) where G' is the Green function of M'.

5, surface waves (fundamental and first few higher modes) represent the longest and strongest portion of a seismic signal generated from an earthquake. These waves constitute the dominant part of the seismogram and thus supply the data with the most favorable signal/noise ratio. , 1998), and for seismic hazard studies, with engineering implications (see Sect. 5). Surface waves cannot be modelled easily with methods based on ray theory, because of computational problems: it is not a theoretical limitation but a practical one.

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Advances in Geophysics, Vol. 43 by Barry Saltzman, Renata Dmowska

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