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impedance and surface waves |
Look out for a pedantic post. Reason 1 - There are a lot of ways to think of it, but we mathematically separate the waves into surface waves - Love & Rayleigh varieties, and body waves, P & S. The surface waves require a surface to propagate, and diminish exponentially with depth. A 100s surface Rayleigh wave, for example, only has much motion in the top 100 km. As the surface waves spread over a surface, which spreads the waves linearly with time, their energy per unit area diminishes linearly with time and distance, and the amplitude decays with the square root of distance. The body waves expand over a sphere, whose surface grows as time squared or distance squared, and the amplitude therefor decays inversely with distance. This is ignoring damping and dispersion. This is a long way of saying the body waves decay more rapidly than the surface waves with distance, and so the surface waves dominate the long-period motions at a distance of more than a few source depths, and the surface waves are weak more than a wavelength or so below the surface. Reason 2 - The impedance is the seismic velocity times the density, and for a given energy input, motion is proportional to the inverse of the impedance (if I remember correctly). So whether there is a surface or not, if the density goes down and the seismic velocity goes down, the amplitude of the waves goes up. Because of the soft, less dense material at the surface, waves can be many times bigger there. Just above an earthquake, reason 2 dominates, far from the quake, reason 1 is more important. Probably more than you wanted to read, and then there's the free surface correction, sometimes another factor of two. Follow Ups: ● Re: impedance and surface waves - Mike Williams in Arroyo Grande 06:44:30 - 8/7/2007 (72352) (2) ● John-Ignore my "Additional Question" - Mike Williams in Arroyo Grande 10:18:48 - 8/7/2007 (72354) (0) ● more on impedance and surface waves - John Vidale 08:54:19 - 8/7/2007 (72353) (0) |
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