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Pd is the peak amplitude of displacement in the first three seconds after the arrival of the P wave. We investigated the attenuation of Pd with the hypocentral distance R in southern California as a function of magnitude M , and obtained the following relationship: log ( P d ) = −3.463 + 0.729 × M − 1.374 × log ( R ) ± 0.305. Given an earthquake location determined by the P ‐wave arrival times at stations close to the epicenter, this relationship can be used to define a so‐called “ Pd magnitude” of earthquakes. Our result shows that for earthquakes in southern California the Pd magnitudes agree with the catalog magnitudes with a standard deviation of 0.18 for events less than magnitude 6.5. Therefore, Pd is a robust measurement for estimating the magnitudes of earthquakes and has practical application in earthquake early warning systems.
Wu et al. (Tue,) studied this question.