Did you know that a seismograph may record an earthquake more than a minute after the rupture began—without the instrument being late or faulty? The ground sends a message through rock, and that message takes time to arrive. A student who reads the first wiggle on a graph as the moment the earthquake started is confusing the event with the arrival of evidence about the event.
Earthquake origin time is the estimated time the rupture began at its source; a seismic phase arrival time is when a particular wave, such as a P wave, reaches a particular recording station. Origin time = arrival time − modelled travel time, provided the correct phase, station clock, time standard and travel-time model are used. The arrival is read from the trace; origin time is usually inferred by combining observed arrivals with a model of where and how waves travel.
Why two clocks can both tell the truth
Imagine someone clapping at the far end of a field. You hear the sound later than the clap occurred. A seismometer and an earthquake are separated by a much more complicated pathway through Earth, but the question is similar: when did the event happen, and when did the signal arrive? A wave’s arrival is not a second earthquake. It is a delayed observation of one source event.
An earthquake begins at a subsurface point commonly described as its hypocentre or focus. The epicentre is the point on Earth’s surface above it. Different seismic phases travel along different paths and have different speeds. The fast P phase normally arrives before the slower S phase at a station. The US Geological Survey explains this explicitly in its seismograph guide and its earthquake travel-time table. The instrument’s time axis tells us when motion was detected at the station, not automatically when the rupture began deep underground.
A diagnostic that separates observation from inference
- What was observed? The P-wave and S-wave picks on a station’s recorded trace, with clock time, station identifier, units and time zone.
- What was inferred? A likely earthquake location, origin time and phase travel times using a travel-time model and several stations where available.
- What could be uncertain? A noisy phase onset, an incorrectly set station clock, a mistaken P/S label, approximate depth, an unsuitable speed model, or a timezone conversion.
- What must not be invented? A perfect arrival time between unreadable trace samples or an exact origin time unsupported by the available model and data.
Ask a learner to underline a column labelled arrival time and circle a separate column labelled origin time. If they cannot say whose clock each represents, stop before doing subtraction. Choosing the wrong quantity can produce impeccable arithmetic and a scientifically false answer.
One hand-checked reconstruction with real published model numbers
Illustrative invented classroom scenario, not a real earthquake: Use the USGS travel-time table for an earthquake at a modelled depth of 33 km and an angular source–station separation of 5.0 degrees. The published table gives the first P-wave travel time as 1 minute 12.7 seconds and the difference between S and P arrivals as 57.4 seconds. To practise, imagine a station observes the P wave at 10:01:12.7 UTC. The clock time is invented for this exercise; the travel-time values come from the source table.
Step 1: convert the P-wave travel time to one unit
1 minute 12.7 seconds means 60 + 12.7 = 72.7 seconds. Do not mistake 1:12.7 for 1.127 minutes or 112.7 seconds. The colon here separates minutes from seconds, and 12.7 is a decimal number of seconds.
Step 2: subtract travel time from the P arrival
10:01:12.7 minus 00:01:12.7 equals 10:00:00.0 UTC. This is the origin time implied by the invented arrival and the adopted USGS model. It is not an independently observed clock at the earthquake focus. We can check it in the forward direction: 10:00:00 + 72.7 seconds = 10:01:12.7.
Step 3: calculate when the S wave should arrive
The table says S arrives 57.4 seconds after P. Add this interval to the P arrival: 10:01:12.7 + 57.4 seconds = 10:02:10.1 UTC. The seconds total 70.1, which becomes 1 additional minute and 10.1 seconds. Separately, the implied S travel time is 72.7 + 57.4 = 130.1 seconds, or 2 minutes 10.1 seconds.
Step 4: perform two independent checks
First, subtract the origin from the expected S arrival: 10:02:10.1 − 10:00:00.0 = 130.1 seconds, matching the model. Second, subtract P arrival from S arrival: 10:02:10.1 − 10:01:12.7 = 57.4 seconds, matching the published S−P value. If either check fails, revisit borrowing across the minute boundary or the meaning of the column headings.
Step 5: state exactly what the calculation proves
Under the assumed 33 km depth and 5.0-degree distance travel-time model, the invented P arrival is consistent with an origin at 10:00:00 UTC and an S arrival at 10:02:10.1 UTC. It does not prove an actual event occurred then, nor that an arbitrary seismogram with similar-looking wiggles has the same depth, distance or phase picks. A model-based classroom calculation is not a reviewed earthquake catalogue solution.
P, S, origin: three useful labels, not three competing guesses
The P wave is normally the earliest prominent seismic body-wave phase at a station. S waves have different motion and arrive later along typical crustal paths. Their arrival-time difference, often written S−P, can help constrain distance from the earthquake. But the S−P interval is not the origin time. For example, our scenario’s 57.4-second S−P interval is a difference between two arrivals; its value cannot be placed on the wall clock as 10:00:57.4 without adding an appropriate reference time.
A station farther from the source usually observes a later arrival than one nearer, after accounting for varying paths and velocities. That does not mean the earthquake has a different origin time for every station. Analysts look for a modelled origin and location that jointly explain arrivals at multiple stations. The USGS Yellowstone location explainer illustrates a separate origin-time line and P/S picks on an actual recording. It is an excellent visual reminder of how the labels differ.
Common mistakes and what they reveal
- Calling the first P wiggle ‘the earthquake time’. This ignores propagation delay; repair it by drawing separate source and station clocks.
- Subtracting S−P from P arrival to estimate origin. The S−P difference is not necessarily the P travel time; consult the appropriate travel-time table or solved model.
- Reading 1 minute 12.7 seconds as 1.12 minutes. This mixes decimal and sexagesimal notation; first convert to seconds and reverse-check.
- Mixing UTC and local timestamps. Use one explicitly named time standard before subtraction. Convert presentation times only after the scientific timeline is consistent.
- Assuming the largest amplitude marks the first arrival. Later phases may produce larger motions. Read the onset and phase label, not merely the tallest wiggle.
- Interpreting a rounded catalogue timestamp as a perfectly measured instant. Real origin times have estimation uncertainty and can be revised as additional observations are processed.
A learner’s quick self-test
Before calculating, cover the origin-time column in a diagram and ask: ‘What can I actually see? What is the station’s clock showing? Do I know a valid travel time?’ A pupil who can say ‘I see an arrival at 10:01:12.7, but I need a model to infer the earlier origin’ has crossed the important conceptual gap even before attempting arithmetic.
Next ask whether a single P arrival determines one unique origin without the distance or depth. It generally does not: a later origin with a short travel time or an earlier origin with a longer one could generate the same arrival time. That is why multi-station observations, identifiable phases and suitable seismic models matter.
A four-stage practice progression
Stage one: complete an already-modelled example
Give the student an origin time of 09:20:00 UTC and a modelled P travel time of 50 seconds. Ask for the P arrival. Answer: 09:20:50 UTC. Then suppose the S travel time is 89 seconds. The S arrival is 09:21:29 UTC and S−P is 39 seconds. This is a deliberately invented, arithmetic-only example. Its purpose is to rehearse the time relationship without pretending the travel times fit a particular real Earth model.
Stage two: reverse the relationship
Provide a P arrival of 14:22:30 UTC and an explicitly supplied P travel time of 90 seconds. The inferred origin is 14:21:00 UTC. Check by adding 90 seconds again. If a learner incorrectly answers 14:23:… they are adding rather than subtracting a propagation delay. Ask them to explain why a signal cannot ordinarily reach a distant receiver before the source event.
Stage three: use a tiny two-station table
Create two fictional stations observing the same source. At station A, P arrival is 12:05:20 with a stipulated travel time of 80 seconds. At station B, arrival is 12:05:45 with a stipulated travel time of 105 seconds. Both independently imply 12:04:00 as the origin. Deliberately change station B’s supplied arrival to 12:05:48 and ask what happened: its inferred origin becomes 12:04:03, three seconds later. The difference could be observational or model error; do not silently choose either story without evidence.
Stage four: transfer to an unfamiliar trace or report
Present an accessible USGS seismogram or catalogue with distinct arrival, origin and depth information. Ask students to annotate what is directly reported, what is model-based and what precision the source actually provides. They should first describe the evidence, then calculate only where the required assumptions and values are supplied. If the worksheet omits a travel-time model, a correct answer may be ‘the origin cannot be uniquely determined from this information alone’.
What should a parent or teacher actually look for?
Ask the pupil to draw a two-point timeline: ‘rupture starts at source’ and ‘P wave recorded at station’. The space between points represents travel time. Then change the arrival time in an invented example while keeping travel time fixed and ask what origin follows. This simple variation reveals whether the student understands the relationship or has memorised a formula mechanically.
A teacher can track improvement by scoring three separate abilities: correct classification of origin versus arrival; accurate clock-time arithmetic; and honest statement of assumptions or missing data. For instance, in an illustrative record only, a pupil might classify 4/5 labels correctly, compute 2/3 time differences correctly and identify the missing-model limitation on 1/2 scenarios. The next practice is targeted to the second and third skills, rather than prescribing another generic hour of revision.
Use realistic caution with safety-related earthquake reports. This is an educational interpretation exercise, not an early-warning service. Do not infer an earthquake location, shaking intensity or personal safety advice from these simplified calculations.
Important limitations and scientific context
Earth is not a uniform medium. Seismic velocities and ray paths change with depth and composition. The 5.0-degree and 33 km USGS reference row provides a modelled comparison, not a universal travel time for every event at that distance. Real picks can be noisy and station clocks may have problems; the arrival–origin fit may include residuals. An automatically estimated earthquake origin may later be revised after analyst review. When a task needs scientific precision, use the original source’s reported depth, location, uncertainties, time zone and model conventions.
Frequently asked questions
Is the origin time the same as the time the strongest shaking occurred?
Not necessarily. Origin time refers to the beginning of rupture. Stronger later shaking at a station may be associated with later wave phases, source processes and local site effects.
Why is P usually recorded before S?
P waves propagate faster than S waves along ordinary comparable paths through solid Earth. Their differing arrivals support phase recognition and distance estimation, although real paths and waveforms can be complicated.
Can S−P be used directly as P travel time?
No. S−P is the interval between S and P arrivals, whereas P travel time is measured from origin to the P arrival. A specified model is needed to connect them.
What if the station recorded in local time?
Identify the date, time zone and any daylight-saving convention, then convert all relevant timestamps to a consistent standard such as UTC before doing arithmetic. Do not combine labels from different clocks uncritically.
What if the arrival onset is too noisy to pick to the tenth of a second?
Record the uncertainty or use the source’s reported precision. A calculated decimal place should not be treated as direct evidence the instrument resolved that instant perfectly.
Does a later P arrival at another station mean there were two earthquakes?
No. Stations at different locations can record waves from the same event at different times. Distinguish station arrival data from the catalogue’s common event origin.
Keep learning: evidence before interpretation
The lesson connects to honest timing when a stopwatch resets and to elapsed time across midnight. For further Earth science, see earthquakes, seismic waves and risk. Explore the eduKate Education learning hub; the diagnosis-first tutorial reference shows why independent checking is part of lasting understanding.
The core aim
A science learner should become able to say, ‘This is when the event started; this is when the evidence reached the observer; here is how a model connects them.’ That sentence prevents a surprising number of calculation and interpretation errors. More importantly, it trains a habit useful beyond seismology: respect the distance between an event and its measurement.