## 2 Methods
### Different-Order Multiple Crosstalk Artifacts and Illumination Analysis
\[\begin{array}{ll}I(x)&=\sum_{\omega}U_{B}^{i}(x,\omega)D_{F}^{0^{*}}(x, \omega)\\ &=\sum_{\omega}\underbrace{\left[U_{B}^{0}(x,\omega)D_{F}^{0^{*}}(x,\omega) \right]}_{\text{correct imaging}}+\  
where \(U_{B}^{i}(x,z,\omega)\) is the upward backward propagation wavefield of the \((i+1)\)th-order scattering, that is, \(U_{B}^{0}(x,\omega)\) denotes the primary upward backward propagation wavefield, \(U_{B}^{1}(x,\omega)\) denotes the first-order multiple upward backward propagation wavefield, \(U_{B}^{2}(x,\omega)\) denotes the second-order multiple upward backward propagation wavefield, and so on.  
Figure 2: Schematic diagram of different-order wavefield imaging: (**a**) primary data with primary migration (Equation (1)); (**b**) full-wavefield data with primary migration (Equation (3)); (**c**) full-wavefield data with full-wavefield migration (Equation (4)).  
Full-wavefield migration (FWM) treats surface-related multiples and internal multiples as virtual sources in the source forward propagation process and uses the full-wavefield data containing multiples as the receiver wavefield. In accordance with the theory of controlled-order multiple migration [36], the imaging can be analytically decomposed into a composite of images generated by different orders of wavefields (Equation (4)).  
\[I(x) =\sum_{\omega}U_{B}^{i}(x,\omega)D_{F}^{\prime^{*}}(x,\omega) \tag{4}\] \[=\sum_{\omega}\underbrace{\left[U_{B}^{0}(x,\omega)D_{F}^{0^{*}} (x,\omega)\right]}_{\text{primary correct imaging}}+\sum_{\omega}\left[ \begin{array}{c}U_{B}^{1} (x,\omega)D_{F}^{1^{*}}(x,\omega)+\\ U_{B}^{2}(x,\omega)D_{F}^{2^{*}}(x,\omega)+\\ U_{B}^{3}(x,\omega)D_{F}^{3^{*}}(x,\omega)+\\ \dots\end{array} \right]}_{\text{multiple correct imaging}}\] \[+\sum_{\omega}\underbrace{\left[ \begin{array}{c}U_{B}^{1}(x, \omega)D_{F}^{0^{*}}(x,\omega)+\\ U_{B}^{2}(x,\omega)D_{F}^{0^{*}}(x,\omega)+\\ U_{B}^{3}(x,\omega)D_{F}^{0^{*}}(x,\omega)+\\ \dots\end{array} \right]}_{\text{$\omega$}}+\sum_{\omega^{\prime}}\left[ \begin{array}{c}U_{B}^{2}(x,\omega)D_{F}^{1^{*}}(x,\omega)+\dots\\ U_{B}^{3}(x,\omega)D_{F}^{2^{*}}(x,\omega)+\dots\\ U_{B}^{4}(x,\omega)D_{F}^{3^{*}}(x,\omega)+\dots\end{array} \right]}_{\text{ $\omega$}}.\]  
The source wavefields consist of the primary downward forward propagation wavefield \(D_{F}^{0}(x,\omega)\) and the multiple downward forward propagation wavefield \(D_{F}^{j}(x,\omega)(j>0)\), and the receiver wavefields consist of the primary upward backward propagation wavefield \(U_{B}^{0}(x,\omega)\) and the multiple upward backward propagation wavefield \(U_{B}^{1}(x,\omega)(i>0)\). According to the analysis of the expanded terms, Equation (4), \(U_{B}^{0}(x,\omega)D_{F}^{0^{*}}(x,\omega)\) is the correct imaging of the primary, \(\sum_{\omega}U_{B}^{i}(x,\omega)D_{F}^{i^{*}}(x,\omega)\) is the correct imaging of the multiple. All the other components are considered crosstalk artifacts. Figure 2 illustrates the crosstalk artifact and correct imaging of each order of scattering in Equations (1), (3) and (4). Figure 2a corresponds to the application of the primary migration method to the processing of the primary wave data and represents a correct image without crosstalk artefacts. Figure 2b corresponds to the primary migration method applied to the full-wavefield data, where internal multiples and surface-related multiples cause crosstalk artefacts. Figure 2c corresponds to the full-wavefield migration method applied to the full-wavefield data, resulting in correct imaging of some surface-related and internal multiples. Compared to Figure 2b, the number of correctly imaged points is increased. To analyze the crosstalk artifact and correct imaging of each order of scattering in Equations (1), (3) and (4), a full-wavefield modeling algorithm can be used to simulate different order multiples. The full-wavefield modeling algorithm (FWMOD) [43] can be used to simulate the full-wavefield data, including high-order scattering in the forward model.