Simultaneous inversion for velocity and attenuation by waveform tomography

• Analyze the real part and the imaginary part of the gradients with respect to the velocity and the attenuation models;
• Combine the imaginary part of the gradient for attenuation and the real part of the gradient for velocity in the inversion;
• Propose an adaptive tuning factor which balances the sensitivity difference between the two parameters in each iteration.

Seismic waveform tomography can invert for the velocity and attenuation (Q− 1) variations simultaneously. For this simultaneous inversion, we propose two strategies for waveform tomography. First, we analyze the contributions of the real part and the imaginary part of the gradients, associated with the velocity and attenuation parameters respectively, and determine that the combination of the real part of the gradient subvector for the velocity parameter and the imaginary part of the gradient subvector for the attenuation parameter would produce an optimal inversion result. Second, we attempt to balance the sensitivities of the objective function to the velocity and the attenuation parameters. Considering the magnitude differences between these two-type parameters in the simultaneous inversion, we apply preliminarily a normalization to both the velocity model and the attenuation model. However, for balancing their sensitivities, we further adjust the corresponding model updates using a tuning factor. We determine this tuning parameter adaptively, based on the sensitivities of these two parameters, at each iteration. Numerical tests demonstrate the feasibility and reliability of these two strategies in full waveform inversion.