Viscoelastic wave propagation for nearly constant Q transverse isotropy

Constant Q, also called frequency-independent Q, is a phenomenological assumption often used in practice for dissipative wave propagation in both forward and inverse seismic modelling. A constant Q dissipative model generally results in a temporal convolution-type wave equation, which is computationally costly to solve by a time-domain numerical modelling method. In this paper, we use the recently proposed weighting function method to derive the nearly constant Q wave equations in differential form for viscoelastic transversely isotropic media. These wave equations explicitly involve specified Q parameters, which is convenient for time-domain waveform modelling and inversion. As numerical examples, we analyse the nearly constant Q behaviour of the proposed model, nearly constant Q wave reflection and wave propagation in a heterogeneous case.