Scaling properties of corner frequencies of Kamchatka earthquakes

Scaling properties of earthquake populations bear the major information on the physics of the source process of an earthquake. To determine scaling properties, source spectra of more than 400 earthquakes of Kamchatka were determined in a frequency range 0.1–30 Hz using materials of digital registration of PET station, and characteristic frequencies of earthquakes were estimated. The range of magnitudes is 4–6.5, the range of distances is 80–220 km. To enable reduction of a spectrum to the source, attenuation properties of the medium around PET were determined beforehand. It is revealed that source spectra show several corner (characteristic) frequencies: f _c1, f _c2 and f _c3; where the spectral trend changes: from f ⁰ to f ^?1, from f ^?1 to f ^?2, and from f ^?2 to f ^?3, respectively. Although in some cases f _c1 ≈ f _c2 in agreement with the usual ω^?2 spectral model, the main part of spectra has more complicated character. For a large part of the studied earthquakes a source-controlled upper cutoff of acceleration spectrum, or corner frequency f _c3, is observed. This is an important fact, as the existence of f _c3 (source-controlled f _max) is not recognized in the bulk of the seismological literature. For f _c1, the observed scaling agrees with the usual hypothesis of similarity of the earthquake sources of different size (magnitude); it is close to f _c1 ～ M ₀ ^?1/3 , where M ₀ is seismic moment. For f _c2, scaling is close to f _c2 ～ M ₀ ^?0.17 ～ f _c1 ^0.5 , that indicates an expressed violation of similarity. For f _c3, scaling is close to f _c2 ～ M ₀ ^?0.08 ～ f _c1 ^0.25 , so that similarity is broken even sharper in this case. Hypotheses about possible causes of the observed scaling are discussed.