geology · structural
Cross Section Vertical Exaggeration
VE = Horizontal Scale Denominator / Vertical Scale Denominator
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Inputs
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Description
Computes the vertical exaggeration of a geologic cross section — the ratio between its vertical and horizontal scales — from the denominators of the section's horizontal and vertical representative-fraction scales (1:N). Cross sections are routinely drawn with the vertical scale exaggerated relative to the horizontal scale so that thin beds and subtle structural relief remain visible at a workable horizontal scale; this calculator makes the resulting exaggeration factor explicit so it can be reported alongside the section, as good drafting practice requires.
Variables
| Symbol | Unit | Description |
|---|---|---|
| VE | — | Vertical Exaggeration |
| Nh | — | The denominator N of the cross-section's horizontal representative fraction scale (1:N) — e.g. enter 24000 for a 1:24,000 horizontal scale. |
| Nv | — | The denominator N of the cross-section's vertical representative fraction scale (1:N) — e.g. enter 2400 for a 1:2,400 vertical scale. A smaller vertical denominator than the horizontal one (as here) is what produces a vertically exaggerated section. |
Assumptions
- Both the horizontal and vertical scales are true representative fractions (1:N, consistent units on both sides) — not a bar scale or verbal scale that would need converting first.
- The same length unit (e.g. both in feet, or both in meters) underlies both the horizontal and vertical scale denominators — mixing unit systems between the two inputs will silently produce an incorrect exaggeration factor.
- The cross section uses a single, uniform vertical exaggeration throughout — it is not a section with a variable or broken vertical scale.
Limitations
- Reports the exaggeration factor only — it does not itself correct or annotate a drawn section; always label a cross section's own vertical exaggeration directly on the figure, as required by standard drafting and publication practice.
- Does not warn about the interpretive consequences of a high exaggeration factor beyond a simple threshold flag — vertical exaggeration increases apparent dips, distorts fault angles, and inflates the apparent cross-sectional area of rock bodies, all of which can mislead a reader who is not told the exaggeration factor used.
- The VE = VS/HS relationship is elementary, uncontroversial representative-fraction arithmetic, corroborated across multiple independent sources this session (Wikipedia's dedicated Vertical exaggeration article, directly fetched, including its own worked example; AAPG Wiki's Cross section page; a Carleton SERC geology teaching module) — but a dedicated structural-geology academic PDF found this session (L.B. Railsback, railsback.org) returned unreadable/corrupted content when fetched and was not independently verified. Given the formula's simplicity this is a low-severity gap, but disclosed explicitly rather than silently omitted, per this discipline's established pattern.
Use Cases
- → Reporting exaggeration on a drafted cross section: Compute and label the correct vertical exaggeration factor on a hand- or software-drafted geologic cross section, as standard practice requires.
- → Comparing sections drawn at different scales: Check whether two cross sections from different sources or vintages use the same vertical exaggeration before visually comparing dips or structural relief between them.
- → Choosing a vertical scale for a new section: Given a required horizontal scale and a target exaggeration factor (e.g. the conventional order-of-magnitude increase), back into the vertical scale denominator needed to achieve it.
Related Calculations
Region Notes
Global
A vertical exaggeration on the order of 10x (one order of magnitude beyond the horizontal scale) is a common convention for regional cross sections showing gently-dipping strata, but always confirm the specific exaggeration used in any published or client-supplied section rather than assuming this convention — unlabeled or inconsistently-exaggerated sections are a persistent source of misread dip and structural relief in practice.
References
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