# Application of full waveform inversion algorithms to seismic data lacking low-frequency information from a simple starting model

Hyunggu Jun^{1}

^{4}Jungkyun Shin

^{2}Changsoo Shin

^{3}

^{1} Korea Institute of Ocean Science and Technology, 787, Haean-ro, Snagnok-gu, Ansan, Gyeonggi-do 15627, Korea.

^{2} Korea Institute of Geoscience and Mineral Resources, 905, Yeongilman-daero, Buk-gu, Pohang 37559, Korea.

^{3} Seoul National University, Department of Energy Systems Engineering, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea.

^{4} Corresponding author. Email: hgjun1026@kiost.ac.kr

*Exploration Geophysics* - https://doi.org/10.1071/EG17007

Submitted: 17 January 2017 Accepted: 20 May 2017 Published online: 21 July 2017

## Abstract

Full waveform inversion (FWI) is a method that is used to reconstruct velocity models of the subsurface. However, this approach suffers from the local minimum problem during optimisation procedures. The local minimum problem is caused by several issues (e.g. lack of low-frequency information and an inaccurate starting model), which can create obstacles to the practical application of FWI with real field data. We applied a 4-phase FWI in a sequential manner to obtain the correct velocity model when a dataset lacks low-frequency information and the starting velocity model is inaccurate. The first phase is Laplace-domain FWI, which inverts the large-scale velocity model. The second phase is Laplace-Fourier-domain FWI, which generates a large- to mid-scale velocity model. The third phase is a frequency-domain FWI that uses a logarithmic wavefield; the inverted velocity becomes more accurate during this step. The fourth phase is a conventional frequency-domain FWI, which generates an improved velocity model with correct values. The detailed methods of applying each FWI phase are explained, and the proposed method is validated via numerical tests with a SEG/EAGE salt synthetic dataset and Gulf of Mexico field dataset. The numerical tests show that the 4-phase FWI inverts the velocity correctly despite the lack of low-frequency information and an inaccurate starting velocity model both in synthetic data and field data.

**Key words:** 2D, acoustic, frequency, full waveform inversion, Laplace.

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