The constant Q theory describes in frequency domain that the seismic wave amplitude attenuation linearly increases with respect to frequencies. We present a simple generalized time-domain wave equation to precisely simulate such linear attenuation. The key idea is to represent the wavefield by a complex-valued function which is the Hilbert transform of the physical wavefield. The proposed complex-valued wave equation (CWE) has four advantages. First, the CWE is in the time domain and thus suitable for 3D seismic simulations; second, the amplitudes computed from the CWE attenuate precisely linear to frequencies; third, the CWE could be easily converted to two different CWEs to describe dispersion-only and dissipation-only phenomena; and last, the CWE could be easily implemented by simply converting arrays from real to complex values in many existing time-domain computer algorithms. For verification, numerical solutions from CWE are compared with analytical solutions, and nearly perfect matching between these two solutions is obtained. We also extend these CWEs to be applied for heterogeneous media and the results are verified by nonstationary operator Fourier Integral method.
Presentation Date: Wednesday, October 14, 2020
Session Start Time: 1:50 PM
Presentation Time: 1:50 PM
Presentation Type: Oral