Question

Match the semi-variogram shape with the model name and the property.

• A. P→III→E,; Q→II→F,; R→IV→E,; S→I→G
• B. P→II→F,; Q→I→G,; R→III→E,; S→IV→E
• C. P→IV→G,; Q→III→F,; R→II→E,; S→I→E
• D. P→II→E,; Q→I→E,; R→III→F,; S→IV→G

Hint:

Spherical models reach the sill at a finite distance, exponential models approach it slowly, Gaussian curves are smoothest at the origin, and pure nugget has no spatial structure.

Answer 1

The Correct Option is A

A semi-variogram $\gamma(h)$ describes how spatial variability changes with lag distance $h$. Each model has a characteristic shape and sill-behavior: \begin{itemize} \item Pure nugget (I) — reaches sill instantaneously (G) \item Exponential (II) — reaches sill asymptotically (F) \item Spherical (III) — reaches sill at finite range (E) \item Gaussian (IV) — smooth, asymptotic with faster initial growth \end{itemize} Step 1: Match shapes P, Q, R, S. Shape P: Shows a curve that reaches sill at a finite distance → spherical model (III) → property E.
Shape Q: Shows a smooth, gradually rising curve reaching sill asymptotically → exponential (II) → property F.
Shape R: Very smooth near origin, steeper growth, typical Gaussian → Gaussian (IV) → property E (finite sill behavior shown).
Shape S: Flat at all lags → pure nugget (I) → reaches sill instantly (G).
Step 2: Combine matches: \[ P \rightarrow III \rightarrow E,\quad Q \rightarrow II \rightarrow F,\quad R \rightarrow IV \rightarrow E,\quad S \rightarrow I \rightarrow G. \] This matches option (A).
Final Answer: (A)