Research of step-length estimation methods for full waveform inversion in time domain

ABSTRACT

Full waveform inversion (FWI) is a powerful tool for reconstructing high-resolution subsurface parameters estimated by iteratively minimising the difference between calculated and observed data. Step-length estimation is a key step in the successful implementation of the FWI algorithm. An optimal step-length value rapidly causes the FWI algorithm to reach the global minimum with reduced iterations and fewer extra forward modelling simulations during each iteration. Step-length can typically be calculated using an inexact or an exact line-search method. The backtracking line-search method (BLSM) is a typical inexact method. Initial methods of guessing the step-length and evaluation conditions determine the efficiency of a BLSM scheme. Here, we propose a quadratic extrapolation value as the initial guess in a BLSM scheme, and then compare it with other initial-guess approaches by using the first Wolfe condition to evaluate step-length values. Exact line-search methods include a parabolic fitting search method through three points (PFSM-3), a parabolic fitting search method through two points (PFSM-2) and the analytical step-length method (ASLM). To find optimal and stable step-length estimation methods for FWI, we compare four step-length estimation methods: BLSM, PFSM-3, PFSM-2 and ASLM. Numerical examples using synthetic data demonstrate that quadratic extrapolation values perform better than first-order change and adaptive values in the BLSM scheme, in terms of resolution of the reconstructed model and computational costs. Of the four step-length estimation methods, ASLM and BLSM are both efficient for noise-free data, and robust ASLM is more efficient for noisy data. However, PFSM-2 and PFSM-3 are less efficient because of low accuracy and high computational cost.

KEYWORDS:

• Full waveform inversion
• step-length estimation method
• exact line-search method
• inexact line-search method
• step-length initial-guess method

Acknowledgements

We would like to thank Daniel Köhn for the significant discussions. This research is supported financially by the R&D of Key Instruments and Technologies for Deep Resources Prospecting (the National R&D Projects for Key Scientific Instruments): grant no. ZDYZ2012-1-06 and Open Issue of Key Laboratory of Mineral Resources, Chinese Academy of Sciences: grant no. KLMR2017-17.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Xiaona Ma http://orcid.org/0000-0002-1155-6296

Additional information

Funding

This research is financially supported by the R&D of Key Instruments and Technologies for Deep Resources Prospecting (the National R&D Projects for Key Scientific Instruments): grant NO. ZDYZ2012-1-06 and Open Issue of Key Laboratory of Mineral Resources, Chinese Academy of Sciences: grant NO. KLMR2017-17.