Models and Fréchet kernels for frequency-(in)dependent Q

We present a new method for the modelling of frequency-dependent and frequency-independent Q in time-domain seismic wave propagation. Unlike previous approaches, attenuation models are constructed such that Q as a function of position in the Earth appears explicitly as a parameter in the equations of motion. This feature facilitates the derivation of Fréchet kernels for Q using adjoint techniques. Being simple products of the forward strain field and the adjoint memory variables, these kernels can be computed with no additional cost, compared to Fréchet kernels for elastic properties. The same holds for Fréchet kernels for the power-law exponent of frequency-dependent Q, that we derive as well. To illustrate our developments, we present examples from regional- and global-scale time-domain wave propagation.