## 2 Methods  
### Different-Order Multiple Crosstalk Artifacts and Illumination Analysis  
Seismic data contain various wavefield components, such as direct waves, primaries, multiples, and refracted waves. Both primaries and multiples act as authentic reflections of the subsurface, and they convey valuable information and constitute effective signals. In this paper, we define the primaries and all-order multiples as the full-wavefield data. Figure 1 is a schematic diagram of multiple paths. \(S\) denotes the source wavelet, \(D\) denotes the downward wavefields, \(U\) denotes the upward wavefields, and the subscript \(F\) denotes forward propagation. The superscript \(i\) denotes the \((i+1)\)th-order scattering, where first-order scattering \(i=0\) corresponds to the primary wave, second-order scattering \(i=1\) is refers to first-order multiples, third-order scattering \(i=2\) refers to second-order multiples, and so on. \(d^{0}\) denotes the seismic record of primaries, \(d^{1}\) denotes the seismic record of first-order multiples, and \(d^{2}\) denotes the seismic record of second-order multiples. Primaries \(d^{0}\) are the wavefield with only one scattering event occurring in the subsurface \(S\)-\(D_{F}^{0}\)-\(U_{F}^{0}\). Multiples are wavefields that, following the primary scattering event, re-inject into the medium as virtual sources and undergo multi-order scattering. \(d^{1}\) denotes a second-order scattering event, and refers to a first-order multiple with a path of \(S\)-\(D_{F}^{0}\)-\(U_{F}^{0}\)-\(D_{F}^{1}\)-\(U_{F}^{1}\). Multiples can be divided into surface-related multiples and internal multiples based on the location of the virtual sources. For surface-related multiples, the sea surface or other free surfaces act as secondary virtual sources for incidence (red line path in Figure 1b), while the virtual source of internal multiples is a strong subsurface reflector (yellow line path in Figure 1c). Figure 1d represents the sum of the primary wave, first-order surface-related multiples, and first-order internal multiples \(d^{0}+d^{1}\). For clarity, only the first-order multiples are shown here. For ease of intuitive understanding, in Figures 1 and 2, we consider only the first-order multiples and the primary wave as the full-wavefield data to illustrate the imaging of different orders of the wavefield. Primary migration can be described as the zero-lag cross-correlation between the forward-propagating source wavelet and the primary wavefield at the receiver location:  
\[I(x)=\sum_{\omega}U_{B}^{0}(x,\omega)D_{F}^{0^{*}}(x,\omega), \tag{1}\]  
where \(D_{F}^{0^{*}}(x,\omega)\) is the complex conjugation of the primary downward forward propagation wavefield, \(U_{B}^{0}(x,\omega)\) is the primary upward backward propagation wavefield, the subscript \(B\) denotes backward propagation, \(\omega\) is the angular frequency, \(I(x)\) is the depth imaging result, and \(x\) denotes the image position. When seismic data contain both primary and multiple waves, the receiver wavefield can be written as follows:  
\[U=\sum_{i}U^{i}, \tag{2}\]  
where \(U\) is the primary and all-order multiple upward wavefield. The superscript \(i\) denotes the \((i+1)\)th-order scattering, for example, \(U^{0}\) is the primary upward wavefield, \(U^{1}\) is the first-order multiple upward wavefield, \(U^{2}\) is the second-order multiple upward wavefield, and \(U^{3}\) is the third-order multiple upward wavefield. When the receiver wavefields contain both primaries and multiples simultaneously, crosstalk artifacts arise in the primary migration algorithm. The forward propagating primary wavefield and the backward propagation primary wavefield are correct imaging (the first term in the expanded form of Equation (3)), while different orders of surface-related and internal multiples are crosstalk artifacts and represent a type of strong coherent noise (the second term in the expanded form of Equation (3)).