Download A Breviary of Seismic Tomography: Imaging the Interior of by Guust Nolet PDF

March 28, 2017 | Waves Wave Mechanics | By admin | 0 Comments

By Guust Nolet

The 1st textbook to supply an in depth creation to seismic tomography for complicated scholars and study practitioners.

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Additional info for A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun

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If the perturbed ray is computed for a spherically symmetric Earth model, this greatly improves the efficiency of the calculations. from A to B, so the perturbation in T is: B B 1 1 nˆ · dr + nˆ · dδr c c A A B B 1 dr(s) dδr(s) 1 = nˆ · ds + nˆ · ds . δ c ds c ds A A δT = δ We insert δ(1/c) = δr · ∇(1/c) in the first integral, integrate the second one by parts and use nˆ = dr/ds: B δT = δr · ∇ A 1 c − d ds 1 dr c ds ds , where the end contributions disappear because we impose that the ray starts at A and ends at B so that δrA = δrB = 0.

This is usually called an ‘equivalent force’. Alternatively, we can model the source as the divergence of a stress tensor, the ‘stress glut’ : fi = j ∂j ij . Outside of the source region we may set fi = 0 (we shall do this often without explicitly specifying this condition). The frequency domain solution for homogeneous media is obtained by assuming a harmonic time dependence of the 18 Ray theory for seismic waves form P (r, t) = P (r, ω)eiωt :† c2 ∇ 2 P + ω2 P = 0 . 3) that the solution to the wave equation is given by any wave of the form g(x − ct).

Another important shortcoming is that effects of wave diffraction are not modelled by rays; we return to this in Chapter 7. 8 Rays in an isotropic, elastic Earth The acoustic case was easy to handle because the equations only deal with a scalar quantity, the pressure P . 8 Rays in an isotropic, elastic Earth 27 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 00000000000000000000000000000 11111111111111111111111111111 11111111111111111111111111111 00000000000000000000000000000 2 π /k 111111111111111111111111111 000000000000000000000000000 a Fig.

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