TY - JOUR

T1 - Linear wavefield optimization using a modified source

AU - Alkhalifah, Tariq Ali

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: I thank KAUST for its support. I also thank the SWAG group for many useful discussions. I especially thank Chao Song for many fruitful exchanges. I also thank the assistant editor, Mohammad Akbar Zuberi and an anonymous reviewer for their help in reviewing the paper.

PY - 2020/5/9

Y1 - 2020/5/9

N2 - Recorded seismic data are sensitive to the Earth's elastic properties, and thus, they carry information of such properties in their waveforms. The sensitivity of such waveforms to the properties is nonlinear causing all kinds of difficulties to the inversion of such properties. Inverting directly for the components forming the wave equation, which includes the wave equation operator (or its perturbation), and the wavefield, as independent parameters enhances the convexity of the inverse problem. The optimization in this case is provided by an objective function that maximizes the data fitting and the wave equation fidelity, simultaneously. To enhance the practicality and efficiency of the optimization, I recast the velocity perturbations as secondary sources in a modified source function, and invert for the wavefield and the modified source function, as independent parameters. The optimization in this case corresponds to a linear problem. The inverted functions can be used directly to extract the velocity perturbation. Unlike gradient methods, this optimization problem is free of the Born approximation limitations in the update, including single scattering and cross talk that may arise for example in the case of multi sources. These specific features are shown for a simple synthetic example, as well as the Marmousi model.

AB - Recorded seismic data are sensitive to the Earth's elastic properties, and thus, they carry information of such properties in their waveforms. The sensitivity of such waveforms to the properties is nonlinear causing all kinds of difficulties to the inversion of such properties. Inverting directly for the components forming the wave equation, which includes the wave equation operator (or its perturbation), and the wavefield, as independent parameters enhances the convexity of the inverse problem. The optimization in this case is provided by an objective function that maximizes the data fitting and the wave equation fidelity, simultaneously. To enhance the practicality and efficiency of the optimization, I recast the velocity perturbations as secondary sources in a modified source function, and invert for the wavefield and the modified source function, as independent parameters. The optimization in this case corresponds to a linear problem. The inverted functions can be used directly to extract the velocity perturbation. Unlike gradient methods, this optimization problem is free of the Born approximation limitations in the update, including single scattering and cross talk that may arise for example in the case of multi sources. These specific features are shown for a simple synthetic example, as well as the Marmousi model.

UR - http://hdl.handle.net/10754/665352

UR - http://global-sci.org/intro/article_detail/cicp/16837.html

UR - http://www.scopus.com/inward/record.url?scp=85091309301&partnerID=8YFLogxK

U2 - 10.4208/CICP.OA-2018-0144

DO - 10.4208/CICP.OA-2018-0144

M3 - Article

SN - 1991-7120

VL - 28

SP - 276

EP - 296

JO - Communications in Computational Physics

JF - Communications in Computational Physics

IS - 1

ER -