The following question appeared in UPSC IFS 2020 Geology Optional exam:

## Q) Discuss how the depth of a fold can be calculated. Enlist the assumptions in the calculation. (Marks = 15)

This question has left students wondering – what is the ‘Depth of a Fold?’ Is it related to the amplitude or is it something entirely different? Here we provide the explanation of this term, how to calculate it and what are the assumptions involved.

**The depth of a fold is not to be confused with amplitude. **

The **amplitude** is measured by taking half the distance along the axial plane from one anticlinal hinge to the surface enveloping the two adjoining synclinal hinges (or vice versa), namely, the distance along the axial plane from the median surface to the hinge. A train of folds may fold a surface periodically or non-periodically.

**DEPTH OF A FOLD:**

The depth of a fold is the distance between a local datum (eg. sea level) and the detachment at the base of the folded sequence. Detachment is a faulting process in which a large rock mass, usually sedimentary, becomes detached from the rocks beneath and independently moves laterally a great distance, which is typically measured in miles.

Depth of the fold may be known from seismic reflection profiles or borehole litholog data. In the absence of such data, a commonly used method is **depth-to-detachment calculation**

### Excess area method:

- Classically, the excess-area method derived by Chamberlin has been used to estimate the depth of detachment beneath a fold.
- This method is based on the area-conservation principle.
- It predicts that the depth of the fold equals the excess area beneath a particular horizon uplifted above the revional divide by the shortening undergone by this horizon.

- Shortening displacement, D, on the lower detachment produces deformation an uplift of an excess area, S, above the regional elevation (the datum).
- Assuming constant area, the excess area is:
**S = Dh**

- If we also assume that the bed length remained constant during deformation, then
**D = L**_{0}-L_{1}

- Where
**L**= curved-bed (original) length,_{0}**L**= straight-line length_{1}

- This gives:
**h = S/(L**_{0}-L_{1})

### Assumptions in excess area method

- It is assumed that no material enters or leaves the ends of the cross-section.
- The bed length is assumed to be constant.
- The area is assumed to be constant, neither gained (such as by extension fracturing) nor lost (such as by pressure solution)
- The original regional elevation of a horizon is assumed to be known, because it may be shifted vertically from its original level by deformation.
- The reference horizon and the lower detachment are assumed to be parallel,

If the aforementioned assumptions are not met the depth of the fold estimated by the excess area method might not be correct.

### Further modifications/improvements

Some modifications can be applied to the original method to find depth to detachment if L0 and L1 are not known. For example, we could calculate excess area of multiple beds rather than a single bed and use the slope to estimate the depth of the fold.