Dip, strike and true thickness: the definition and measurement of true dip, apparent dip, dip direction and strike with a compass-clinometer; structure contours; the calculation of the true (perpendicular) and vertical thickness of a bed from its outcrop width and dip using trigonometry; the distinction between vertical and true thickness; and the rule of Vs for outcrops crossing valleys.

What this dot point is asking

Eduqas wants you to define and measure the orientation of a tilted bed (true dip, apparent dip, dip direction and strike) with a compass-clinometer, to understand structure contours, and to calculate the true thickness of a bed from its outcrop width and dip using trigonometry, distinguishing the true (perpendicular) thickness from the vertical thickness. You also apply the rule of Vs to read the dip of a bed whose outcrop crosses a valley. These are practical skills tested directly in Components 1 and 3, and they involve real trig you must be able to do under exam conditions.

The answer

True dip, apparent dip, dip direction and strike

The true dip is the steepest line you can draw down the plane; the strike is horizontal and runs across the plane at $90^{\circ}$ to the dip. An apparent dip, measured in any direction other than straight down the dip, is always less than the true dip, because no direction across the plane is steeper than the true dip, and along the strike itself the dip is zero. Orientation is recorded as the dip amount and direction, for example "$30^{\circ}$ towards $135^{\circ}$", measured with a compass-clinometer (the compass reads the strike or dip direction, the clinometer reads the dip angle).

Structure contours

A structure contour is a line joining points of equal height (elevation) on a particular geological surface (such as the top of a bed), exactly as a topographic contour joins points of equal ground height. Evenly spaced, parallel structure contours show a planar bed dipping uniformly; the spacing gives the dip (closely spaced means a steep dip), and the contours run parallel to the strike, with dip down the steepest direction across them. Structure contours let you predict the depth of a bed at any point and where it will outcrop.

The rule of Vs

Where an inclined bed crosses a valley, its outcrop bends into a V on the map. The V points in the direction the bed dips (for the usual case of a bed dipping less steeply than the valley gradient). The rule lets you read the dip direction from the outcrop pattern without a dip arrow:

• A horizontal bed follows the contours (its outcrop runs parallel to them).
• A vertical bed runs straight across, ignoring the valley.
• An inclined bed Vs across the valley, the V pointing down-dip.

True thickness from outcrop width (flat ground)

The true thickness of a bed is measured perpendicular to the bedding, not across the ground, so a dipping bed's true thickness is less than its horizontal outcrop width. For a bed measured horizontally across its outcrop at right angles to the strike on flat ground:

where $t$ is the true (perpendicular) thickness, $w$ is the horizontal outcrop width and $\delta$ is the dip. This comes from the right-angled triangle in which the true thickness is the side opposite the dip angle.

Vertical versus true thickness

The vertical thickness is the depth of the bed measured straight down (for example down a borehole), and it is not the same as the true thickness. For a bed measured vertically:

where $v$ is the vertical thickness and $\delta$ is the dip; here the true thickness is the side adjacent to the dip angle. A vertical line cuts a dipping bed obliquely, so the vertical thickness is larger than the true thickness, and multiplying by $\cos\delta$ projects it onto the perpendicular. The two cases use different trig functions, so identify whether the measurement is horizontal ($t = w\sin\delta$) or vertical ($t = v\cos\delta$) before you start.

Examples in context

Example 1. Estimating a reservoir's thickness. Calculating the true thickness of a dipping reservoir sandstone from its outcrop width and dip ($t = w\sin\delta$) gives the real stratigraphic thickness needed to estimate the rock volume and so the hydrocarbon or water it could hold; using the outcrop width directly would over-estimate it.

Example 2. Apparent dip in a quarry face. A bed seen in a quarry face that runs obliquely to the strike appears to dip more gently than its true dip; recognising this as an apparent dip prevents under-estimating the true dip from an oblique exposure, a common Component 3 trap.

Try this

Q1. Define the strike of a bed and state its angular relationship to the dip. [2 marks]

• Cue. The compass direction of a horizontal line on the bedding plane; it lies at right angles ($90^{\circ}$) to the true dip.

Q2. A bed dips at $40^{\circ}$ and its horizontal outcrop width (at right angles to strike, flat ground) is $30\ \mathrm{m}$. Calculate the true thickness. [2 marks]

• Cue. $t = w\sin\delta = 30 \times \sin 40^{\circ} \approx 30 \times 0.643 \approx 19.3\ \mathrm{m}$.

Q3. Using the rule of Vs, state the dip direction of a bed whose outcrop Vs upstream (up-valley) where it crosses a valley. [1 mark]

• Cue. The bed dips upstream (up the valley), because the V points in the direction of dip.