A frequency-decomposed nonstationary convolutional model for amplitude-versus-angle-and-frequency forward waveform modeling in attenuative media

Abstract

The conventional convolutional model (CCM) is widely applied to generate synthetic seismic data for numerous applications including amplitude variation with offset forward modeling, seismic well tie, and inversion. This approach assumes frequency-independent reflection coefficients and time-invariant seismic wavelets in laterally homogeneous elastic media. We have extended CCM to heterogeneous poroelastic media in which reflection coefficients are frequency dependent and the seismic wave is attenuated as it propagates. First, we decompose the seismic wavelet into monofrequency components through the Fourier transform. Then, to account for the attenuation effects at the reflection interfaces, we multiply the frequency-dependent reflection coefficients series with an attenuation function of frequency-variant quality factor [Formula: see text]. Finally, we convolve this product results with a monofrequency wavelet and sum all of the frequencies together to obtain the synthetic seismograms. The advantage of the proposed frequency-decomposed nonstationary convolutional model is that it takes into account the effects of attenuation on the wave reflections and propagation in attenuative media. In addition, it uses the frequency-dependent [Formula: see text] instead of the constant [Formula: see text] that is used by the traditional nonstationary convolutional model. The technique has been applied to amplitude-versus-angle-and-frequency forward waveform modeling in attenuative media, and it shows good agreement between synthetic and real data on seismic well ties.