Summary
Without considering intrinsic attenuation, reverse time migration (RTM) in lossy media may produce unfocused migration images, because of the amplitude loss and velocity dispersion in the recorded data caused by Q. We use a constant Q viscoelastic equation for source and receiver extrapolations. Two fractional Laplacian operators introduce velocity dispersion and amplitude loss effects, respectively, for each wave mode. Velocity dispersion and amplitude loss can be separated. To compensate the Q effect, we reverse the sign of the amplitude loss operator, and keep the sign of velocity dispersion operator unchanged, during receiver extrapolations. Boundary-valuebased viscoelastic source wavefield reconstruction shows that this Q-compensation strategy can compensate the amplitude loss and avoid phase distortion. The source-normalized crosscorrelation imaging condition is applied. Two numerical examples show that, with Q compensation, structures are better focused at the correct positions, and with more energy.
Introduction
Multi-parameter imaging in viscous media is of growing interest (Prieux, et al., 2013). For viscoelastic media, energy absorption and intrinsic velocity dispersion affects the amplitude and travel time of the wavefield. For seismic imaging in viscous media, without considering Q, migrated images will not be well focused (Zhang et al., 2010; Zhu et al., 2014), because of the amplitude loss along the propagation path, and from the phase distortion.
One approach to compensate the Q effects is in the data domain. A simple and straightforward method is by applying an inverse Q filter to the seismograms (Hargreaves and Calvert, 1991). Inverse Q filtering is based on a 1-D assumption; it is not applicable to Q compensation in complicated media. Since seismic attenuation affects waveforms during propagation, it is more natural and accurate to compensate the Q effects during wavefield extrapolation, by modifying the wavefield propagators.
To include Q effects in source and receiver wavefield extrapolations, two categories of viscous wave equations are widely used. The first is based on the generalized standard linear solid model (e.g. Carcione et al., 1988). Memory variables are introduced to address the computation of the convolutional kernel in the stress-strain constitutive relations, and thus introduce the Q effects. For viscoelastic RTM, Deng and McMechan (2008) proposed to reverse the sign of memory variables, during receiver extrapolation, to compensate the amplitude loss.
