127 Each sliding window is flattened into a feature vector, and the full set of n windows forms the structured data matrix #= ⎣ ⎢ ⎢ ⎡ (!"(#" ( ⋮$"⎦ ⎥ ⎥ ⎤ ∈ℝ$×&, 1=2' ×2( Each row corresponds to one sliding window, and the known deposit corresponds to one specific row of #, denoted by index 4, which serves as the reference signature against which all other windows are compared. In the multivariate case, co-located sliding windows are extracted simultaneously from all geophysical grids so that the sampled windows retain both spatial context and cross-variable relationships. Spatial principal component analysis is then applied in pixel space, where the features are window pixels rather than distinct geophysical variables. After column-wise standardization, #5 )* = #)* −7* 8* , #5 =9:" where 7* and 8* are the column-wise mean and standard deviation, respectively. For constant features, 8* is set to 1 to avoid division by zero. In this decomposition, : contains the spatial loadings and 9 contains the PCA scores, which quantify how strongly each window expresses the retained spatial patterns. Only the first ; retained components are used in the similarity calculation, where ; is chosen as the smallest number of principal components (PC) that still provides an adequate representation of the deposit signature. Deposit-specific weights are then derived from the deposit scores, 2+ = <,# + = < . -/! ,# -, >=1,…,;, so that components expressed more strongly by the deposit contribute more to the comparison. Similarity is then computed from the difference between the score vector of each window and that of the deposit, Δ ),+ =Z),+ −Z,,+, 4) # =C2+ . +/! Δ),+ # , 4) =D4) #. Windows with smaller 4) are therefore those whose multiscale spatial patterns most closely reproduce the deposit signature. Ranking all windows by increasing 4) produces the similarity map used for regional targeting. Where other known deposits are available, the ranked predictions are validated against them using cumulative footprint recovery, counting unique overlap area so that overlapping prediction windows within the same deposit are not counted more than once, and recording the first rank at which a test deposit reaches a minimum coverage threshold of 50%. 4. RESULTS Case 1. Paulo Afonso: Univariate TMI After sampling the TMI grid with overlapping sliding windows and projecting the windows into the sPCA space (Figure ), the deposit signature was progressively reconstructed using an increasing number of retained components. The dominant TMI dipole pattern emerged clearly in the first components and became progressively more complete as additional components were included (Figure 2). By K = 17, the reconstruction captured the main geometry and internal spatial variations of the deposit, while later components contributed only minor refinements and noise. This value was therefore selected as a suitable balance between retaining the essential deposit signature and avoiding the inclusion of weak higher-order components.
RkJQdWJsaXNoZXIy MTM0Mzk2