LAUSR

Abstract 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.