Multifrequency viscoacoustic modeling and inversion

Modeling and inversion for seismic wavefields that include the attenuation and phase dispersion effects of Q can be implemented in the space-frequency domain. The viscoacoustic wave equation is solved by the moment method. Absorbing boundary conditions are implemented by reducing Q and adjusting the complex velocity (to reduce Q-dependent reflectivity) in a zone around the edges of the model grid. Nonlinear inversion is performed using iterative linearized inversions. The residual wavefield at a single frequency is back projected, using an anticausal Green's function, along the viscoacoustic wavepath in an estimate of the model, to get updated velocity and Q distributions. The model obtained from data at one frequency becomes input to inversion at the next higher frequency. Velocity and Q are inverted simultaneously as they are interdependent. Both modeling and inversion algorithms are successfully tested with synthetic examples; data at two or three frequencies are sufficient to produce reliable images from noise-free synthetic data.