By Guust Nolet
The 1st textbook to supply an in depth creation 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
46) define the velocities of compressional or P-waves and shear or S-waves in the Earth. 14). 13 How can you show that the direction of displacement of S-waves is perpendicular to the ray? 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.
3). 3) with a perturbation in the gravity force. This we shall ignore here. 3) we have three equations, one for each direction, but nine unknowns (three displacements ui and the six independent elements of the symmetric tensor σj i ). 3) by introducing empirical laws that relate stress to displacement. Such laws can be very complicated, but are greatly simplified when we ignore the hysteresis caused by anelastic effects and when we confine ourselves to very small displacements. In that case the medium deforms approximately linearly with the applied stress.
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 ). 52) tells us that we can switch source and receiver and record the same signal, with the same delay and amplitude, no matter how heterogeneous the transmitting medium is.
A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun by Guust Nolet