Power-law frequency-dependent Q simulations in viscoacoustic media using decoupled fractional Laplacians

Quantifying seismic attenuation of wave propagation in the Earth’s interior is essential for studying subsurface structures. Previous approaches for attenuation simulations (e.g., the standard linear solid and the fractional derivative model) are mainly based on the frequency-independent quality factor Q assumption. However, seismic attenuation in high-temperature and high-pressure regions usually exhibits power-law frequency-dependent Q characteristics. To simulate this Q effect in attenuative media, we derive a new viscoacoustic wave equation with decoupled fractional Laplacians in the time domain. Unlike the existing methods using relaxation functions to fit the power-law relationship in a specific frequency band, our proposed equation is directly derived from the approximated complex modulus, which explicitly involves the reference quality factor and fractional exponent parameters. Furthermore, this equation contains two fractional Laplacians, which can easily simulate decoupled amplitude dissipation and phase distortion effects, making it amenable to Q-compensated reverse-time migration. In the implementation, a Taylor-series expansion and a pseudo-spectral method are introduced to solve the fractional Laplacians with variable fractional exponents. Numerical experiments demonstrate the effectiveness of the proposed method for power-law frequency-dependent Q simulations. As a forward-modeling engine, our derived viscoacoustic wave equation is a good supplement to the current Q simulation methods and it could be applied in many seismic applications, including Q-compensated reverse time migration and full-waveform inversion.