The Duration-distance Relationship and Average Envelope Shapes of Small Kamchatka Earthquakes

Average envelope shapes (mean square amplitude time histories) of small earthquakes represent a convenient basis for the construction of semi-empirical stochastic ‘‘Green’s functions,’’ needed for prediction of future strong ground motion. At the same time, they provide crucial evidence for verification of the theories of scattering of high-frequency seismic waves in the lithosphere. To determine such shapes in the Kamchatka region we use the records of near (R = 50–200 km) shallow earthquakes located around the broadband station PET. On these records, we select the S-wave group and determine its root-mean-square duration Trms, separately for each of the five octave frequency bands. We determine the empirical Trms vs. distance dependence and find it to be very close to a linear one. At the reference distance R = 100 km, average Trms decreases from 5.4 sec for the 0.75 Hz band to 3.9 sec for the 12 Hz band. To analyze average envelopes, we assume that the functional form of the envelope shape function is independent of distance, and stretch each of the observed envelopes along the time axis so as to reduce it to a fixed distance. Through averaging of these envelopes we obtain characteristic envelope shape functions. We qualitatively analyze these shapes and find that around the peak they are close to the shapes expected for a medium with power-law inhomogeneity spectrum, with the spectral exponent 3.5–4. From onset-topeak delay times we derive the values of transport mean free path and of scattering Q for a set of distances.