By Guust Nolet
The 1st textbook to supply an intensive creation to seismic tomography for complicated scholars and study practitioners.
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Extra info for A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun
X ∼ µ/a. If ka 1, we may neglect the spatial derivatives of the elastic parameters. 7). 40) ∂uj ∂ui ∂ µ + ∂xj ∂xi ∂xj . 41) Or, in vector notation, writing ∇u for ∂ui /∂xj and ∇uT for its transpose ∂uj /∂xi : − ρω2 u = ∇(λ∇ · u) + ∇ · [µ(∇u + ∇uT )] . 42) For the purpose of this book it is sufficient to define the correlation distance as the distance over which a parameter still looks smooth. e. if the variations in elastic properties are smooth: − ρω2 ui = λ j ∂ 2 uj ∂ +µ ∂xi ∂xj ∂xj ∂uj ∂ui + ∂xj ∂xi .
35) with continuity of p at an interface with a jump in c. 10) are used in ray tracing applications (Chapter 3). g. Cerven´ y et al.  or Moser ) – to which we return in the next chapter – or by the perturbation methods developed by Snieder and Aldridge . 7 Verify that | rˆ × p| = r sin i/c. 8 Check that the correct units for the spherical slowness are seconds/radian (s/rad). For an Earth with surface radius 6371 km, how fast does a ray travel (in km/s) with p = 637 s/rad? 9 Where along the ray path is p = r/c?
The wavefields resulting from these point sources are by definition Green’s functions: P1 ≡ G(r, ω; r1 ) and P2 ≡ G(r, ω; r2 ). 49) immediately gives an important result, the reciprocity relation: G(r2 , ω; r1 )eiωt2 = G(r1 , ω; r2 )eiωt1 . 51) An even simpler symmetry becomes evident if we choose t1 = t2 . The time delays t1 and t2 are added as phases in the spectra of G through the exponentials, and not directly evident in the notation we adopt for G in the spectral domain. 65): G(r2 , t − t2 ; r1 , t1 ) = G(r1 , t − t1 ; r2 , t2 ).