Geophysical Attenuation Models
Geophysical attenuation models are mathematical descriptions of how seismic waves ought to attenuate in the earth’s crust, given the known properties of the crust. Portions of these mathematical descriptions can be adapted to be used in attenuation relations.
Attenuation relations present the results of analyzing strong motion data in showing how large the ground motions are expected to be for a certain earthquake magnitude and a certain distance from the earthquake.
Usually the attenuation relations are obtained by a statistical process called regression. Given a specified mathematical equation, regression determines parameters for that equation. In some cases, regression is used to determine the remaining parameters when the other parameters are given by geophysical attenuation models.
Then, given a magnitude, a distance, and a geologic site condition, the equation given the average value of the ground motion expected.
For a future earthquake, the actual ground motion will not be that average value, but rather a value in some uncertainty range around that average value. The regression also gives an estimate of that uncertainty range.
The adjustment for geological site condition is sometimes determined by regression, but also sometimes determined by physical models of the soil column effect.