Beyond fixed thresholds: trend surface modeling of geochemical anomalies in the Shadan porphyry gold–copper deposit, eastern Iran

The Shadan porphyry Au–Cu deposit in eastern Iran has undergone significant erosion, yielding mostly low-grade surface geochemical signatures and a mixture of porphyry- and epithermal-style mineralization. Under such conditions, conventional contouring with a single threshold fails to resolve geochemical anomalies reliably. To overcome this limitation, we applied six trend surface functions-linear, quadratic, cubic polynomials, spline, logistic, and Fourier—to lithogeochemical data (480 rock samples) and generated corresponding trend and residual maps for Au and Cu. Model performance was evaluated against the mineralization production index (derived from 20,111 drill-core assays from 93 boreholes) and the mapped geology. Results show that spline, Fourier, and logistic functions most effectively capture the mineralization trend, while their residual maps amplify anomaly intensity and areal extent by roughly two- to three-fold, improving delineation of mineralized zones. Simpler first- and second-order polynomials are adequate for straightforward mineralization patterns, whereas cubic polynomials and logistic functions provide greater accuracy in moderately complex settings. For multi-stage and telescope mineralization systems such as Shadan, spline and Fourier models are the most suitable. These findings demonstrate that trend–residual decomposition provides a more robust alternative to fixed-threshold mapping for anomaly-background separation in porphyry exploration.