By Guust Nolet
The 1st textbook to supply an intensive advent to seismic tomography for complicated scholars and study practitioners.
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Additional resources for A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun
Initially, all nodes are in Q with infinite travel time. † Note that the ‘path’ itself is fully prescribed by assigning to each node the preceding node along its shortest path to the source. g. Johnsonbaugh . The algorithm can be speeded up considerably by sorting the nodes in Q into a ‘heap’, which is defined as a set of N travel times Tj such that: Tj ≥ Tj/2 for 1 ≤ j/2 < j ≤ N . A heap is a comparatively fast way to find the fastest path among a set of paths without having to sort the whole set.
9 travelling from A to B, and secondary source at C on the wavefront, at a distance h from the direct path AB. Energy from C will arrive at B with a delay. If AB has length L, and C, when projected on AB is at a distance s from A, then the difference in length is: ACB − AB = s 2 + h2 + (L − s)2 + h2 − L ≈ h2 2 1 1 + s L−s , 32 Ray theory for seismic waves where we use a first-order Taylor expansion for small h/s and h/(L − s). The secondary wave will still interfere constructively with the direct arrival if the difference is less than half a wavelength λ (some prefer a stricter criterion of λ/4).
34 Ray theory for seismic waves sources – and the Green’s function for sources on that surface: (P2 (r, ω)δ(r − r1 ))d3 r = P2 (r1 , ω) V 1 nˆ · [P2 (r, ω)∇G(r, ω; r1 ) − G(r, ω; r1 )∇P2 (r, ω)] d2 r . 53) is not very efficient since it would force us to compute the Green’s function for many different source locations r1 if we wish to know P2 at those locations. 51) shows, however, that we only need source at the surface S if we exchange r and r1 in the expressions for G. 53) is unnecessarily cumbersome.
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