I. Introduction
Seismic impedance inversion is extensively used in reservoir prediction. There are mainly two kinds of impedance inversion methods: traditional methods and machine learning-based (ML-based) methods. Recursive inversion [1], trace integration [2], and constrained sparse spike inversion (CSSI) [3] are the traditional methods that have strong interpretability. ML-based methods [4] train models to learn the mapping from seismic data to impedance data. ML-based methods [5] always have strong nonlinear learning ability and can make full use of real data and synthetic data to learn a mapping from seismic data to impedance data. ML-based methods are end-to-end learning approaches and present poor interpretability. Artificial neural networks (ANNs) [6], [7] and convolutional neural networks (CNN) [8] have been proposed to perform impedance inversion. CNN has shown great potential in predicting acoustic impedance (AI), but its performance drops when applied to the training dataset with the presence of various source wavelet frequencies. Moreover, Biswas et al. [9] proposed a physics-guided CNN to perform the prestack inversion. ML algorithms require varieties of labeled data to guarantee the performance. Alfarraj and Regib [10] proposed semisupervised CNN to utilize the unlabeled data. The closed-loop CNN network proposed by Wang et al. [11] consists of a seismic forward network and an impedance inversion network so that the unlabeled data can be applied during the training process. Based on the closed-loop structure, bilateral filtering is further combined to constrain the spatial continuity of the inversion results [12]. In addition, Wang et al. [13] proposed to use a cycle-consistent generative adversarial network to improve the impedance inversion results.