Simultaneous Imaging of Velocity and Attenuation Perturbations from Seismic Data Is Nearly Impossible

We generated synthetic reflection data for the constant-density visco-acoustic wave equation in the Born approximation. Perturbations in velocity and attenuation that have rapid variations on small length scales create reflections. In the frequency domain, a single complex-valued model parameter that depends on subsurface position describes both. Its real part is related to the classic reflectivity, its imaginary part also involves attenuation variations. When we applied a weighted Hilbert transform in the depth coordinate to our scattering model, we obtained almost the same synthetic data for scatterers with small dip. This means that, in practice, it will be impossible to simultaneously determine the real and imaginary part of the scattering parameters by linearized inversion without imposing additional constraints.