By Chris Chapman
Featuring a complete advent to the propagation of high-frequency body-waves in elastodynamics, this quantity develops the speculation of seismic wave propagation in acoustic, elastic and anisotropic media to permit seismic waves to be modelled in advanced, life like three-d Earth types. The booklet is a textual content for graduate classes in theoretical seismology, and a reference for all educational and commercial seismologists utilizing numerical modelling tools. workouts and recommendations for extra interpreting are incorporated in each one bankruptcy.
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Extra info for Fundamentals of Seismic Wave Propagation
2 except for a velocity decrease). 7, wavefronts from a point source in a model with a velocity increase are illustrated. 2 A point source 15 z zS reflection direct head (a) z1 transmission x (b) Fig. 7. Wavefronts at a plane interface with a velocity increase. 6, with the extra head wave indicated by a dashed-dotted line. The partial and total reflection are shown dashed. Wavefronts at four times are shown: before the direct wave reaches the interface; and before, at and after the critical angle is reached.
It can also be proved geometrically. 3 Travel-time function in layered media 19 z dX x θ c dT θ p p + dp Fig. 10. Two rays with parameters p and p + d p, extra range dX and extra ray length c dT . 10). The extra length of ray is c dT and the extra range dX . 14). A useful function is τ ( p, z) = T ( p, z) − p X ( p, z) = q dz. 11). 15) is known as the tau-p curve, or the intercept time (or sometimes the delay time although this is open to confusion). 15), it is straightforward to prove that dτ = −X.
The depth, range, slowness and times axes are to a common scale in the sub-figures. 4 Types of ray and travel-time results z 27 c c2 z2 c1 x p direct c1−1 partial reflection total reflection c2−1 head wave c2−1 X p X c1−1 c2−1 T c1−1 τ 28 Basic wave propagation If the source and receiver are not at the same depth, then the direct ray has the same form as the reflection. 19, where we have assumed c2 < c1 so no head wave exists. 18. Analytic examples of these rays are easily generated for a homogeneous layered model.
Fundamentals of Seismic Wave Propagation by Chris Chapman