## 1 Introduction  
Elastic seismic wavefields contain different wave modes, such as converted, P-, and S-waves, and therefore ERTM can provide multi-wave imaging results including PP, PS, SP and SS depth images [1; 2], which is helpful to effectively reduce the ambiguity of multi-component seismic data interpretation. Because the cross-correlation imaging calculation of coupled P- and S-wave modes will bring about some crosstalk artifacts in imaging results [3; 4], ERTM usually requires one to accurately separate the different wave modes from the coupled elastic seismic wavefields before utilizing the cross-correlation imaging conditions [5; 6]. There are three frequently used methods to achieve the separation and decomposition of P- and S-wave modes from the coupled elastic seismic wavefields. The first approach is the Helmholtz decomposition algorithm which can be theoretically regarded as applying the divergence and curl operators to, respectively, obtain the decoupled P- and S-wave modes from the coupled elastic seismic wavefields [7; 8], but it has two serious deficiencies which will affect the multi-wave imaging accuracy of ERTM: one is that it will seriously damage the amplitude and phase characteristics of the decoupled P- and S-wave modes [9; 10], and the other is that the corresponding PS and SP images will suffer from polarity reversals [11]. The second approach is the vector decomposition algorithm based on the decoupled elastic wave equations which can effectively simulate the decoupled vector P- and S-wave modes for a given elastic model at different times by discretely solving these decoupled wave equations [12; 13; 14; 15; 16; 17], but it can only obtain the good vector decomposition results of different wave modes when this elastic model is sufficiently smoothed, because adopting the true elastic models to model the decomposed vector P- and S-wave modes will give rise to obvious artifacts at the strong reflectors when using these decoupled elastic wave equations [3; 17; 18]. The third approach is the vector decomposition algorithm in the wavenumber domain which can effectively preserve all the components of the decoupled vector P- and S-wave modes and has its advantages in terms of amplitude and phase accuracy [19; 20], but its computational efficiency is poor because of the extra forward and inverse Fourier transforms. Although these above conventional approaches can achieve the separation and decomposition of P- and S-wave modes to a certain extent, they are usually dependent on accurate elastic model parameters and certain prior conditions and therefore have obvious limitations in practical application. In recent years, the application of deep learning methods [21] in the fields of geophysics and applied geophysics has received great attention and promising achievements, such as detecting faults [22; 23], classifying facies [24; 25], attenuating noise [26; 27], picking first arrivals [28; 29], building velocity models [30; 31] and reconstructing seismic data [32; 33]. Inspired by deep learning methods, some scholars have proposed many effective separation and decomposition methods of P- and S-wave modes from the coupled elastic seismic wavefields based on different neural networks, such as multi-task learning [34], convolutional neural networks (CNNs) [35; 36], generative adversarial networks (GANs) [37; 38] and deep convolutional neural networks (DCNNs) [39], and these methods are intelligent data-driven algorithms for the separation and decomposition of P- and S-wave modes which are not dependent on elastic model parameters and certain prior conditions. However, these above methods mainly use the corresponding neural networks to separate two decoupled scalar P- and S-wave modes from the coupled elastic seismic wavefields, and therefore cannot obtain all the horizontal and vertical components of the decomposed vector P- and S-wave modes.