Seismic wave amplitude attenuates with distance from the source due to geometric spreading, which differs fundamentally between body waves (propagating through the 3D volume of the Earth) and surface waves (propagating along the roughly 2D surface of the Earth). Body wave energy spreads over an expanding spherical wavefront, while surface wave energy spreads over an expanding cylindrical wavefront.
For body waves, energy spreads over the surface area of an expanding sphere (proportional to r²), so amplitude (proportional to sqrt(energy)) decreases as 1/r. For...
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