By Guust Nolet

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

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

**Example text**

It is not difficult to transform the system to a first-order system by 22 Ray theory for seismic waves defining the slowness vector p: 1 dr . 27) . 27), are often said to be in ‘canonical form’, after the Greek κανων or ‘rule’. 6 Show that the elements of the vector p are equal to the direction cosines γi ≡ xi /r of the ray path scaled by the velocity c. 6 Ray solutions in layered and spherical systems In a medium with horizontal stratification, where c(x, y, z) = c(z), we may without loss of generality choose our x-axis in the direction of propagation.

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). This region is called the ‘Fresnel zone’. This criterion defines an ellipse with a maximum h at the centre where s = L/2 and where 2h2 /L ≤ λ/2 or 1√ h= λL .

In the case of horizontal layering the subscript x on px is usually omitted. The horizontal slowness p is measured in s/m or s/km. The constant p is also known as the ‘ray parameter’. At an interface with a jump in c, the slowness p remains constant, which implies a jump in the incidence angle i (refraction). 4b we see that dT = dx sin i/c or dT . 30) Though commonly spelled as Snell’s law, the law was discovered by Willebrord Snel van Royen (1580–1626), a Dutch mathematician who latinized his name to Snellius.