By Guust Nolet
The 1st textbook to supply an intensive advent to seismic tomography for complex scholars and examine practitioners.
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Additional resources for A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun
The polarization of an S-wave may be in the (local) plane of propagation or perpendicular to it. Is the S-velocity dependent on its polarization? 14 Why can you state that the direction of displacement of a P-wave is parallel to the ray direction? Are there different polarizations of the P-wave? 15 In a fluid µ = 0. Reduce the expressions for VP and VS for this case and compare to the acoustic velocity c. 10). Does this pressure satisfy the wave equation in a solid? If so, how fast is it propagating?
3) where ∂Lk xk − xk−1 = , ∂xk Lk ∂Lk+1 xk − xk+1 = , ∂xk Lk+1 and ∂ c¯k ∂ c¯k+1 1 ∂ck = = . ∂xk ∂xk 2 ∂xk This gives a system of equations of the form: αk xk−1 + βk xk + γk xk+1 = rk , with similar equations for yk and zk . Since it is tri-diagonal it is efficient to solve. 3) is not exactly linear, since a relocation of the nodes may change the average velocity c¯k , but it generally iterates quickly to a minimum. The coordinate changes must be orthogonalized to the local ray direction to avoid the problem of the travel time being optimized by collocating many nodes in regions of high velocity (making lower velocities invisible to the interpolation).
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 . 23) is now: u(r, ω) = A(r)eiωτ (r) . 44) Substituting this into the elastodynamic equation, and collecting all terms with ω2 : −ρAi = j ∂τ ∂τ ∂τ −(λ + µ) Aj − µ ∂xi ∂xj ∂xj 2 Ai , which is more easily interpretable in vector notation: −ρ A + (λ + µ)∇τ (∇τ · A) + µ|∇τ |2 A = 0 .