Inversion gradients for acoustic VTI wavefield tomography

Vladimir Li, Hui Wang, Ilya Tsvankin, Esteban Díaz, Tariq Ali Alkhalifah

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a generalized pseudospectral operator based on a separable approximation for the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified image-power objective functions. We also obtain the gradient expressions for a data-domain objective function that can more easily incorporate borehole information necessary for stable VTI velocity analysis. These gradients are similar to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations but the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show the potential advantages of the modified image-power objective function in estimating the anellipticity parameter η.
Original languageEnglish (US)
Pages (from-to)WA55-WA65
Number of pages1
Issue number4
StatePublished - Jun 7 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank Paul Fowler, Jorg Schleicher, and the A(nisotropy)- and i(maging)-Teams at CWP for fruitful discussions. We also thank associate editor Igor Ravve and reviewers Alexey Stovas, Jiubing Cheng, and Junzhe Sun for their helpful comments. This work was supported by the Consortium Project on Seismic Inverse Methods for Complex Structures at CWP and the competitive research funding from King Abdullah University of Science and Technology (KAUST). The reproducible numeric examples in this paper are generated with the Madagascar open-source software package (Fomel et al., 2013a) freely available from


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