Geological investigations use quantitative skills: converting between map distance and real distance using the scale, calculating rates (of deposition, erosion or plate movement) from an amount and a time, reading and plotting graphs and gradients, and handling data with means, ranges and percentages; the distance to an earthquake epicentre can be estimated from the gap between P-wave and S-wave arrivals, and rates and ages are calculated using simple formulae and the half-life idea.

What this dot point is asking

Eduqas wants you to apply quantitative skills to geological investigations: converting between map distance and real distance using the scale, calculating rates (of deposition, erosion or plate movement) from an amount and a time, reading and plotting graphs and gradients, and handling data (means, ranges and percentages). Two geology-specific calculations matter: estimating the distance to an earthquake epicentre from the P-wave and S-wave arrival gap, and using simple formulae and the half-life idea for rates and ages. These embedded maths skills carry marks across both components.

The answer

Using the map scale

A map scale tells you how map distance relates to real distance. A scale of $1{:}50\,000$ means $1$ unit on the map equals $50\,000$ units on the ground, so $1$ cm on the map is $50\,000$ cm $= 0.5$ km in reality.

To convert, multiply the map distance by the scale factor, then convert the units:

For example, $4$ cm on a $1{:}50\,000$ map is $4 \times 50\,000 = 200\,000$ cm $= 2$ km on the ground. The same idea, in reverse, lets you measure a real distance off a map.

Calculating rates

A rate is an amount of change divided by the time it took:

This single formula covers the geological rates Eduqas asks about:

• Deposition rate = thickness of sediment divided by time (for example mm per year).
• Erosion rate = thickness or volume removed divided by time.
• Plate movement rate = distance moved divided by time (for example mm or cm per year).

The key skills are choosing the right formula, converting units consistently (metres to millimetres, years to the unit asked for), and giving the unit with the answer.

Reading graphs and gradients

Many geological data are presented as graphs (for example a travel-time graph, or grain size against depth). You need to:

• read values off the axes accurately;
• plot points correctly and draw a line of best fit where appropriate;
• find a gradient (the steepness, change in $y$ divided by change in $x$), which often represents a rate.

Handling data

Field and lab data are summarised with simple statistics:

• the mean (add the values, divide by how many) for an average;
• the range (largest minus smallest) for the spread;
• percentages and percentage change for proportions and how much something has changed.

These let you compare sites or samples objectively.

The epicentre distance from P and S waves

The signature geology calculation uses seismic waves. P-waves travel faster than S-waves, so they arrive first, and the gap between the two arrivals grows with distance from the earthquake. A standard travel-time graph converts the P-S gap into a distance to the station. Because one distance gives only a circle (not a direction), three stations are needed; the three distance-circles intersect at the epicentre.

Ages from half-life

Ages in years come from the half-life idea: a radioactive parent decays to a daughter at a fixed rate, so the parent-to-daughter ratio gives the number of half-lives, and multiplying by the half-life gives the age. (The detail is in the geochronology dot point; here it is one of the standard quantitative tools.)

Examples in context

Example 1. Estimating uplift. If a marine bed now sits $200$ m above sea level and is $2$ million years old, the average uplift rate is $\frac{200\,000 \text{ mm}}{2\,000\,000 \text{ years}} = 0.1$ mm/year, the same amount-over-time method applied to uplift.

Example 2. A travel-time graph in the exam. Component 2 may give a travel-time graph and several stations' P-S gaps, asking you to read each distance and explain how three of them pin the epicentre, a direct test of this skill.

Try this

Q1. On a $1{:}25\,000$ map, $1$ cm represents how much real distance? [1 mark]

• Cue. $25\,000$ cm $= 250$ m ($0.25$ km).

Q2. A cliff retreats $50$ m in $200$ years. Calculate the average rate of erosion in metres per year. [2 marks]

• Cue. $\text{rate} = \frac{50 \text{ m}}{200 \text{ years}} = 0.25$ m/year.

Q3. State why the gap between P-wave and S-wave arrivals can be used to find the distance to an earthquake. [1 mark]

• Cue. P-waves are faster and arrive first, and the gap to the slower S-wave grows with distance, so its size gives the distance.