Full waveform inversion based on time-integral-damping wavefield

• Published in: Journal of applied geophysics Vol. 163; pp. 84 - 95
• Main Authors: Chen, Sheng-Chang, Chen, Guo-Xin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2019
• Subjects: Cycle-skipping; Full waveform inversion; Integral wavefield; Time damping; Wave propagation; Integral wavefield; Full waveform inversion; Wave propagation; Time damping; Cycle-skipping
• ISSN: 0926-9851; 1879-1859
• DOI: 10.1016/j.jappgeo.2019.02.019

Full waveform inversion is a highly nonlinear inverse problem. Without an accurate initial model, it is difficult to obtain a global optimal solution because of cycle-skipping. In this paper we combine the Nth-order time integral and time-damping to avoid cycle-skipping and obtain the global optimal solution. Firstly, we define a numerical operator-- ‘Nth-order time integral’ –which can enhance the low frequency information in seismic data. We introduce a Nth-order time integral operator into the wave equation and derive the propagation equation of Nth-order time integral scattered wavefield. Using the adjoint state method, we obtain a full waveform inversion method based on an integral wavefield. In the Nth-order time integral method, a high order time integral is used to make low-frequency components become dominant so we can recover the long-wavelength background structure of the model; then the order of the time integral is reduced to reconstruct the high-frequency information of the model. Secondly, we introduce a time-damping factor into the objective function of full waveform inversion to realize inversion in a shallow-to-deep manner. Finally, we combine these two approaches and develop a multi-scale localized method: Nth-order time Integral and time-damping FWI (InteTD). In the numerical experiments, we apply the InteTD to the Marmousi model and SEG/EAGE Overthrust model by using a low-cut source (frequency components below 4 Hz were truncated). Seismic data with random noise is used to test the noise-resistant property of the InteTD. The results of the numerical test demonstrated the effectiveness of this method. •The integral wavefield is utilized to efficiently utilize the low frequency components contained in the seismic data.•Based on the recursive idea in mathematics, the time damping factor is used to realize the inversion in the shallow-to-deep way.•The integral and time-damping are combined to develop a multi-scale localized method to deal with the more realistic case when seismic data does not have low-frequency components.