Retrieving both the impedance contrast and background velocity: A global strategy for the seismic reflection problem

Recorded seismic reflection waveforms contain information as to the small‐scale variations of impedance and the large‐scale variations of velocity. This information can be retrieved by minimizing the misfit between the recorded waveforms and synthetic seismograms as a function of the model parameters. Because of the different physical characters of the velocity and the impedance, we update these parameters in an alternating fashion, which amounts to a relaxation approach to the minimization of the waveform misfit. As far as the impedance is concerned, this minimization can be performed efficiently using gradient algorithms. For the inversion for seismic velocities, gradient methods do not work nearly as well; therefore, we use different minimization methods for determining impedances and velocities. However, the determination of the impedance and the determination of the velocity are strongly coupled; relaxation is most effective when this coupling is as weak as possible. Weak coupling can be achieved par...