Exact line search method for using the L1-norm misfit function in full waveform inversion
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Key Laboratory of Mineral Resources, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China ([email protected]) Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China Institute of Geophysics, China Earthquake Administration, Beijing 100081, China The Third Institute of China Electronics Technology Corporation, Beijing 100015, China
Received: January 15, 2020; Revised: July 7, 2020; Accepted: September 4, 2020
ABSTRACT Full waveform inversion (FWI) is a non-linear inverse problem that can be sensitive to noise. The tolerance of the noise-interference characteristics depends on the types of misfit functions. To date, different misfit functions, such as the least-squares norm (L2), the least-absolute-value norm (L1), and combinations of the two (e.g., the Huber and hybrid criteria), have been applied to FWI. The L2 norm is highly sensitive to nonGaussian errors in the data and gives rise to high-amplitude artifacts in reconstructed models. For non-Gaussian noise data, the L1 norm and the Huber and hybrid criteria always reliably reconstruct models. However, the Huber and hybrid criteria require tedious error investigations to estimate their threshold criterion. Thus, the L1 norm is adopted here to improve the anti-noise ability of the FWI. The step length is closely related to the misfit function, and an optimal step-length estimation method can rapidly make the FWI algorithm reach the global minimum, with a reduced number of iterations and fewer extra forward modeling simulations during each iteration. The step length can usually be obtained using the exact or inexact line search method. Generally, the exact line search method is faster than the inexact one. Therefore, we derived an exact line search method for the L1 norm in the FWI process. Its effectiveness was tested using noise-free data from Overthrust and the SEG/EAGE salt models. The results demonstrate that this method can recover high-resolution velocity models with low computational costs. Numerical tests using the synthetic Overthrust model contaminated by strong noise were used to further validate the robustness of this exact line search method. K e y w o r d s : full waveform inversion, L1 misfit function, exact line search method
1. INTRODUCTION At present, geophysicists are interested in applying full waveform inversion (FWI) to describe subsurface geological structures, evaluate soil properties, and characterize energy Stud. Geophys. Geod., 64 (2020), DOI: 10.1007/s11200-020-0904-5, in print © 2020 Inst. Geophys. CAS, Prague
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reservoirs. FWI makes full use of the dynamic and kinematic information in the data, so it can yield a high-resolution geometric picture of the target structures and preferable model parameters (e.g., velocity, density, and quality factor). Lailly (1983) and Tarantola (1984) solved the seismic waveform inversion using reverse time migration in the time domain. Ever since, FWI has been extensively studied using similar back-propagation techn
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