A dispersion analysis of a surface-wave train gives phase velocities at period and at

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Surface waves, free oscillations and seismic tomography

Problem

A dispersion analysis of a surface-wave train gives phase velocities

c = 3.50\,\mathrm{km\,s^{-1}}

at period

T = 15\,\mathrm{s}

and

c = 3.85\,\mathrm{km\,s^{-1}}

T = 25\,\mathrm{s}

. Using the group-velocity relation

U = c^2/(c + T\,\mathrm{d}c/\mathrm{d}T)

, estimate the group velocity at the mean period of

20\,\mathrm{s}

, taking

\mathrm{d}c/\mathrm{d}T

from the two measurements as a constant slope.

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