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

By Guust Nolet

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

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Extra resources for A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun

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Use the given example forstar subroutine. Plot the paths from a node near the centre to all other nodes in the model. Compare the computed travel times with the theoretically correct ones. 4 Extend the forward star routine to include more nodes, further away from the source, and repeat the calculations of the previous problem. 5 Adapt subroutine forstar, such that the velocity increases linearly with one of the coordinate axes. Repeat the calculations from the previous problem for the new model and plot.

Explain why we may interpret the solution as a plane wave in ˆ the direction given by the unit vector n. 18). Explain why the amplitude has to diminish as 1/r to conserve energy (Hint: energy is proportional to the square of the pressure amplitude). For a wave in a two-dimensional membrane, how does the amplitude vary with r? 5 The ray approximation What if the medium is not homogeneous? 11) numerically. ). 12). 22) where f (ω) now denotes the spectrum of the source. 62). 21). At location r = (x1 , x2 , x3 ) let us denote the delay by τ (r): P (r, t) = A(r)δ[t − τ (r)] .

7. A sketch of the assumption that O(∂ui /∂xj ) O(∂µ/∂xj ), or ka 1 introduce an elastic Earth. To reduce the large number of elastic variables cij kl we usually assume that the elastic properties of the Earth are not dependent on the orientation of the rock. In such an isotropic Earth the elasticity tensor involves only two constants, the bulk modulus κ and the shear modulus µ: 2 cij kl = κ − µ δij δkl + µ(δik δj l + δil δj k ) . 39) A wave with a spatial dependence u ∼ eikx will have derivatives ∂u/∂x ∼ ku.

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