How to fit a nested variogram

Can you estimate the range and sill of nested structures just by inspecting a variogram, without interactive fitting or trial and error?

🤔 To some extent, yes.

By observing where the experimental variogram changes its behavior, you can often identify inflection points.

Each inflection point marks where a shorter-range structure reaches its range, where that component’s contribution to spatial correlation levels off.

✅ That gives you the range of the first structure.❌ But not its sill.

At that first range, the variogram value equals:

This is sometimes referred to as the apparent sill of the first structure, though the term can be ambiguous, as “apparent” may carry different meanings in other contexts.

It’s often clearer to focus on inflection points instead of “apparent sills” because:

👉 They are visually identifiable and reproducible.

👉 They reduce subjective interpretation between analysts.

👉 They represent independent characteristics of the experimental curve, whereas model parameters (ranges and sills) are interdependent.

For example, adjusting the second structure’s range or sill often requires re-tuning the first to maintain a good fit.

Inflection points alone won’t define the full model, but they provide a solid, objective foundation for fitting nested variograms.

From there, parameter estimation can proceed analytically or with the help of interactive tools that refine the model to best match the experimental data.