# Multi-scale full waveform inversion for areas with irregular surface topography in an auxiliary coordinate system

Yingming Qu^{1}

^{3}Zhenchun Li

^{1}Jianping Huang

^{1}Jinli Li

^{2}

^{1} School of Geosciences, China University of Petroleum, Qingdao 266580, China.

^{2} Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences, Langfang 065000, China.

^{3} Corresponding author. Email: qu_geophysics@yahoo.com

*Exploration Geophysics* - https://doi.org/10.1071/EG16037

Submitted: 12 March 2016 Accepted: 16 October 2016 Published online: 24 November 2016

## Abstract

For land exploration areas with irregular surface topography, there are many challenges and problems for full waveform inversion (FWI); for example, which type of wave equation should be used to calculate high-accuracy seismic wavefields, how to deal with diffraction of irregular surface topography, what initial velocity model should be utilised to improve the inversion accuracy and how to enhance the computational efficiency of iterative FWI. Aiming at these difficulties, we first simulate the seismic waves with the first-order acoustic wave equation in an auxiliary coordinate system, which easily describes irregular surface topography. Then, we apply this wavefield simulation frame to FWI to improve inversion quality of near-surface regions with strong elevation and velocity variation. Furthermore, to enhance the robustness and computational efficiency, a time-domain multi-scale decomposition method based on the Wiener filter and an optimised encoding strategy are introduced to the proposed inversion frame, and are critical to promoting the practical application of our method. Typical numerical tests prove that the proposed method can obtain more accurate inversion results than the traditional time-domain FWI.

**Key words:** auxiliary coordinate system, full waveform inversion, irregular surface topography, multi-scale decomposition, optimised encoding technology.

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