Reflection waveform inversion (RWI) and its alternative - joint full waveform inversion (JFWI), are powerful tools for improving initial velocity model building beyond the diving-wave penetration depth. Such approaches rely on the scale separation between the smooth background model controlling the kinematics and the model perturbation characterizing the rapid local variations. The key difficulty in RWI and JFWI is the intensive computational cost introduced by alternating between the background velocity update and the model perturbation reconstruction. To update the background model at each step, a number of iterations are generally required to accurately reconstruct the model perturbation such that the alternating workflow becomes prohibitively expensive. To get rid of this computational intensity, we combine RWI or JFWI with efficient impedance waveform inversion which introduces the approximate inverse preconditioner. This approximate inverse approach contains only wave-equation-based operators and is formulated in the time domain.


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