High frequency fall-off of source spectra using Q-free spectra estimation

Abstract

A broadband seismogram may be represented by a convolution of source time function, the propagation operator and the scattering/attenuation operator. As the propagation operator is frequency-independent, and the scattering/attenuation effect may be described by a Q-factor depending on frequency via Q ⁻¹=Q ⁻¹₁ +(Q ₂ ω)⁻¹, considering a combination of the displacement spectra, the source spectra may directly be estimated, in which the contribution of the Q-value may be eliminated automatically. Using this algorithm, the near-source broadband seismograms of five aftershocks of the 1988 Lancang-Gengma, Yunnan Province, China earthquake were processed. The results for the M _L=3.0 and M _L=3.5 aftershocks show that for the same earthquake, similar high-frequency fall-off may be obtained from different recording stations. The result for the M _S=6.7 aftershock shows that consistent source parameters may be gotten from different seismic stations. The parameters estimated also agree with the results obtained by empirical Green’s function approach. The high-frequency spectra of the aftershocks exhibit a typical f ^−γ fall-off. For the M _L=3.0 aftershock, γ≈3; for the M _S=6.7 and M _L=4.0 aftershocks, γ≈2; and for the M _L=3.5 and M _L=3.0 aftershocks, γ≈2.5. The corner frequency of the M _S=6.7 aftershock indicates that it has a small source dimension, implying that it may come from the rupture of a small but strong barrier.