Seismic reflection waveform inversion based on Gauss–Newton optimization

Abstract

Abstract Owing to the lack of long-offset signals and effective low-frequency components, it is extremely difficult for classical full-waveform inversion (FWI) to obtain the long-wavelength components of medium and deep elastic parameter models. Considering ray theory, reflection traveltime tomography is restricted by resolution, and the reflection waveform inversion (RWI) method of the wave equation, and its practicability, has received greater attention. However, previous studies into RWI have primarily used first-order optimization methods, in which convergence and resolution still need substantial improvement. Based on the second-order optimization inversion theory, we deduced the reflection wave-sensitive kernel, objective function gradient and Hessian operator of background and perturbation model. Additionally, we revealed the de-fuzzification effect of the Hessian matrix on the gradient of inversion and the working mechanism of background velocity updating on direction optimization and inversion resolution improvement. Experiments on the SEG/EAGE overthrust model showed that an RWI with the Gauss–Newton method using an approximate Hessian matrix significantly improved convergence and wide-spectrum modeling capability compared with the conjugate gradient method. On the streamer seismic data of the East China Sea, the second-order optimization RWI method surpassed the commonly used reflection traveltime tomography based on pre-stack depth migration. In addition, the RTM of inversion model can depict the complex fault system in the Changjiang sag with a high resolution, which improves the imaging quality of the deep basement.