In this book, we adopt the following notational conventions: tensors are represented by bold calligraphic letters, such as \(\mathcal {T}\) ; matrices are represented by bold uppercase letters, such as \( T \) ; vectors are represented by bold lowercase letters, such as \(\textbf{t}\) ; and scalars are represented by lowercase letters, such as t, as illustrated in Fig. 2.1. Our focus is on real-valued third-order seismic data tensors in the space \(\mathbb {R}^{N_x \times N_y \times N_t}\) , as depicted in Fig. 2.2. The indices i, j, and k are used to denote the x-line, y-line, and time dimensions of a tensor, respectively, where \(i \in [N_x]\) , \(j \in [N_y]\) , and \(k \in [N_t]\) , with [N] representing the set \({1,2, \ldots , N}\) . For a given tensor \(\mathcal {T}~\in \mathbb {R}^{N_x \times N_y \times N_t}\) , the (i, j, k)-th element is written as \(\mathcal {T}(i, j, k)\) , or more compactly as \(\mathcal {T}_{ijk}\) . The i-th horizontal and j-th lateral slices are denoted by \(\mathcal {T}(i, :, :)\) and \(\mathcal {T}(:, j, :)\) , respectively. The k-th frontal slice is represented by \(\mathcal {T}(:, :, k)\) , or concisely as \(\mathcal {T}^{(k)}\) .