16 - Seismic wave propagation

Summary

Preamble

The consideration of elastic waves in this chapter is a preliminary to their use in Chapter 17 to study the internal structure of the Earth, but also an extension to the discussion of elasticity in Chapter 10. Virtually all the information that we have on the elasticity of the Earth is obtained from observations of seismic waves. Tidal deformation (Section 8.2) and the period of the Chandler wobble (Section 7.3) give supplementary data that extend to low frequencies, but lack the detail and precision of seismology. In the full context of the subject, seismological observations can be considered to extend to zero frequency if the static strains of earthquake displacements are included, but the lower limit of seismic wave frequencies is 3 × 10^{− 4} Hz, the 54 minute period of the ₀S₂ mode of free oscillation. At the other end of the scale, waves with frequencies of order 1 Hz are recorded at observatories remote from the earthquakes that generate them; for more local studies, and especially in exploration seismology, much higher frequencies are used. With this wide frequency range it is necessary to recognize a slight frequency dependence of elasticity and consequent dispersion of elastic waves (Section 10.7). Without an allowance for this there is a small, but noticeable, discrepancy between models of the Earth derived from high-frequency body waves (Section 16.2) and free oscillations (Section 16.6).