Depth mismatches between well logs acquired in different runs (e.g., electrical wireline logging (EWL) versus logging while drilling (LWD)) impede stratigraphic correlation and bias reservoir property estimation. Existing alignment methods, such as maximum cross-correlation (MaxCC), are fast but generally assume near-uniform shifts and can be noise-sensitive, whereas dynamic time warping (DTW) can accommodate nonlinear discrepancies but is computationally heavier than global-shift methods and less interpretable. We present a semi-automated Fast Walsh–Hadamard Transform (FWHT) workflow that enhances step-like responses associated with lithological transitions, quantifies boundary evidence via a Walsh Boundary Index (WBI), and uses matched boundary pairs as control points to construct a monotone, piecewise-linear depth-warping function that maps LWD depths onto an EWL reference.“Semi-automated” denotes that, once the log channels and the user-specified cutoff C and WBI threshold τ are defined, all remaining steps are automatic and deterministic. The method is applied to normalized EWL–LWD datasets containing gamma ray (GR), bulk density (RHOB), neutron porosity (NPHI), and compressional sonic slowness (DTC) logs. FWHT increases the slice-averaged Pearson correlation r (mean across logs) from 0.079 to 0.574 and reduces the Euclidean distance e from 1.863 to 0.964; the MaxCC baseline achieves a similar mean correlation (0.595) but a higher distance (1.008), consistent with its global-shift assumption. A constrained global DTW baseline achieves higher similarity ( r = 0.878; e = 0.632), but does so via dense pointwise warping that is less interpretable and can introduce locally nonuniform distortions. Scalability is evaluated on 89 GR log pairs from the Norwegian Continental Shelf: mean Pearson correlation r increases from 0.367 (unaligned) to 0.851 with FWHT (excluding 5 NA pairs), compared with 0.860 using MaxCC. With a uniform threshold ( τ = 0.08 ) , MaxCC performs better in 45 cases, FWHT in 29, and 15 are comparable. Across the evaluated wells, FWHT shows the largest performance gains relative to global-shift methods in intervals exhibiting depth-dependent (nonlinear) misalignment. Overall, the FWHT framework provides an interpretable and computationally efficient approach for boundary-controlled, nonlinear well-log depth alignment.
Acharya et al. (Mon,) studied this question.