When Is Source Information Worth Retaining? Evidence-Gated Selective Transfer for Sparse Geothermal Profiles

Sparse geothermal temperature logs often leave long depth intervals unobserved, making profile reconstruction difficult when only a few target measurements are available. Target-only methods avoid cross-well mismatch, but sparse anchors often constrain the large-scale trend more strongly than the nonlinear structure inside a wide gap. Source-assisted methods can recover some of that structure from other wells, but only when source and target profiles are sufficiently compatible. With few target anchors, transfer can be selected too optimistically if the same observations are used both to calibrate a source correction and to judge its reliability. We introduce Evidence-Gated Selective Transfer (ESGT), which separates these two roles. Geometry-matched inner pseudo-gaps estimate the correction magnitude, outer held-out anchor blocks evaluate the calibrated correction without reusing their labels, and a detrended source-target shape statistic provides an additional compatibility check. The source correction is retained only when these signals support transfer; otherwise, ESGT uses a target-only reconstruction. We evaluate ESGT under controlled structural shifts and on measured geothermal profiles, with additional report-derived profiles prepared through lightweight multimodal indexing. Across the controlled scenarios, ESGT reduces RMSE from 0.876 for the strongest selective baseline to 0.822 while substantially reducing harmful transfer under source-target mismatch. On the Montana field data, it achieves an RMSE of $0.370^{\circ }$C. Separating calibration from retention is most useful when source relevance varies across targets.