[DSRP Evidence](https://dsrpevidence.org/)

# Semi-automated bed boundary detection and log alignment using fast Walsh–Hadamard transform

## Details

**Authors** Sushil Acharya, Karl Fabian, Anis Yazidi, Kjetil Westeng

**Year** 2026

**Publisher** Frontiers in Earth Science

**Kind of work** article

**Discipline** Geology

**Secondary disciplines** Data Science

**Applied** false

[Read it at the publisher](https://doi.org/10.3389/feart.2026.1736164) 
10.3389/feart.2026.1736164

## In authors' words

### Abstract

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. The method is applied to normalized EWL–LWD datasets containing gamma ray, bulk density, neutron porosity, and compressional sonic slowness logs. FWHT increases the slice-averaged Pearson correlation from 0.079 to 0.574 and reduces the Euclidean distance from 1.863 to 0.964. Scalability is evaluated on 89 GR log pairs from the Norwegian Continental Shelf: mean Pearson correlation increases from 0.367 (unaligned) to 0.851 with FWHT. Overall, the FWHT framework provides an interpretable and computationally efficient approach for boundary-controlled, nonlinear well-log depth alignment.

### What they set out to do (purpose)

To develop an interpretable, computationally efficient method for detecting stratigraphic bed boundaries and using them to align depth-mismatched well logs from different drilling runs.

### Who or what was studied (sample)

Normalized electrical wireline logging and logging-while-drilling log pairs (gamma ray, bulk density, neutron porosity, sonic slowness) from a Norwegian Continental Shelf well, plus a batch of 89 gamma-ray log pairs from the same region.

### How they did it (methods)

A semi-automated Fast Walsh–Hadamard Transform workflow enhances step-like log responses at lithological transitions, quantifies boundary evidence with a Walsh Boundary Index, and uses matched boundary pairs as control points for a monotone piecewise-linear depth-warping function, benchmarked against maximum cross-correlation and dynamic time warping baselines.

### What they found (results)

The Walsh-Hadamard boundary-detection method raised mean log-to-log correlation from 0.367 to 0.851 across 89 well-log pairs, performing comparably to established alignment baselines while remaining more interpretable.

## Commentary

### In short

The finding shows that reliably distinguishing bed boundaries in one signal lets otherwise mismatched records of the same underlying whole be reconciled into a single coherent depth framework.

**Patterns it shows** D, S

**Added** 2026-09-28

**How to cite this** Sushil Acharya, Karl Fabian, Anis Yazidi, Kjetil Westeng (2026). Semi-automated bed boundary detection and log alignment using fast Walsh–Hadamard transform. Frontiers in Earth Science.