True-amplitude linearized waveform inversion with the quasi-elastic wave equation

Zongcai Feng, Gerard T. Schuster

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We present a quasi-elastic wave equation as a function of the pressure variable, which can accurately model PP reflections with elastic amplitude variation with offset effects under the first-order Born approximation. The kinematic part of the quasi-elastic wave equation accurately models the propagation of P waves, whereas the virtual-source part, which models the amplitudes of reflections, is a function of the perturbations of density and Lamé parameters [Formula: see text] and [Formula: see text]. The quasi-elastic wave equation generates a scattering radiation pattern that is exactly the same as that for the elastic wave equation, and only requires the solution of two acoustic wave equations for each shot gather. This means that the quasi-elastic wave equation can be used for true-amplitude linearized waveform inversion (also known as least-squares reverse time migration) of elastic PP reflections, in which the corresponding misfit gradients are with respect to the perturbations of density and the P- and S-wave impedances. The perturbations of elastic parameters are iteratively updated by minimizing the [Formula: see text]-norm of the difference between the recorded PP reflections and the predicted pressure data modeled from the quasi-elastic wave equation. Numerical tests on synthetic and field data indicate that true-amplitude linearized waveform inversion using the quasi-elastic wave equation can account for the elastic PP amplitudes and provide a robust estimate of the perturbations of P- and S-wave impedances and, in some cases, the density. In addition, true-amplitude linearized waveform inversion provides images with a wider bandwidth and fewer artifacts because the PP amplitudes are accurately explained. We also determine the 2D scalar quasi-elastic wave equation for P-SV reflections and the 3D vector equation for PS reflections.
Original languageEnglish (US)
Pages (from-to)R827-R844
Number of pages1
Issue number6
StatePublished - Jul 19 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research is supported by the King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. We are grateful to the sponsors of the Center for Subsurface Imaging and Modeling Consortium for their financial support. For computer time, this research used the resources of the Supercomputing Laboratory at KAUST and the IT Research Computing Group. We thank them for providing the computational resources required for carrying out this work.


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