By Guust Nolet

This is often the 1st textbook to hide the fundamental features of the subject at a degree obtainable to scholars. whereas concentrating on functions in sturdy earth geophysics, the e-book additionally uniquely comprises tours into helioseismology, thereby highlighting the powerful affinity among the 2 fields. The e-book offers a entire advent to seismic tomography, together with the fundamental thought of wave propagation, the ray and Born approximations required for interpretation of amplitudes, and shuttle occasions and levels. It considers observational beneficial properties whereas additionally supplying sensible options for enforcing numerical types. Written through one of many leaders within the box, and containing quite a few pupil routines, this textbook is suitable for complicated undergraduate and graduate classes. it's also a useful advisor for seismology learn practitioners in geophysics and astronomy. suggestions to the workouts and accompanying tomographic software program and documentation might be accessed on-line from www.cambridge.org/9780521882446.

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**Example text**

24) which is known as the eikonal equation for the wavefront τ (r). 3), perpendicular to the surface where τ = constant (the wavefront) and therefore by definition parallel to the ray. This allows us to derive an equation for the ray geometry itself. Let dr be a ˆ tangent along the ray with length ds. Thus nˆ = dr/ds, or, using c∇τ = n: ∇τ (r) = 1 dr . c ds With n · ∇τ = dτ/ds = 1/c and d(∇τ )/ds = ∇(dτ/ds): d ds 1 dr c ds =∇ 1 c . 25). 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 .

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. When using his original surname, the spelling with one l is more appropriate.

35) with continuity of p at an interface with a jump in c. 10) are used in ray tracing applications (Chapter 3). g. Cerven´ y et al. [47] or Moser [221]) – to which we return in the next chapter – or by the perturbation methods developed by Snieder and Aldridge [331]. 7 Verify that | rˆ × p| = r sin i/c. 8 Check that the correct units for the spherical slowness are seconds/radian (s/rad). For an Earth with surface radius 6371 km, how fast does a ray travel (in km/s) with p = 637 s/rad? 9 Where along the ray path is p = r/c?