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For surface stations at similar distances, the travel-time derivatives with respect to depth can be small or nearly equal. Their arrival-time shifts are then difficult to distinguish from a common change in earthquake origin time. A deeper source can be paired with an earlier origin. Nearby stations, broad distance coverage, and depth-sensitive phases help separate the two parameters.

An earthquake origin time is the estimated onset time of rupture. Predicted arrivals add this time to a propagation travel time; an uncertain origin time therefore couples to uncertain source depth in some station geometries.

For two phases travelling the same path length $R$ at constant wave speeds $v_A>v_B$, let $r=v_A/v_B>1$, $t_A=t_0+R/v_A$ and $\Delta t=t_B-t_A$. ThenThe intercept of this geometric relation is earthquake origin time $t_0$ and its slope is $1/(r-1)$.

A common station clock offset $c_i$ added to both phase arrivals cancels from $\Delta t$, but remains in $t_A$. Ordinary linear regression can then estimate the relation under zero-mean offsets uncorrelated with the true delays. A common systematic clock bias instead shifts the intercept, and unrestricted fixed station offsets destroy identifiability of the speed ratio.

Phase-specific arrival-picking errors are a different issue. If independent errors ${\epsilon }_A,{\epsilon }_B$ affect the two picks, the predictor error is ${\epsilon }_B-{\epsilon }_A$ and the response error contains ${\epsilon }_A$. Their covariance is $-\mathrm{var}({\epsilon }_A)$, so even individually unbiased picks do not produce an ordinary regression with error-free predictor and independent response noise. A justified errors-in-variables model or a joint arrival-time likelihood must account for that shared measurement error. More stations alone do not remove this structural bias.

Identify the event and pick calibrated P wave and, where available, S wave arrivals at stations of known position. Associate each pick with a seismic phase and uncertainty. An earthquake location by arrival times fitsfor the three hypocentre coordinates and earthquake origin time, using travel times from a specified velocity model. A grid search can initialize iterative weighted least squares or a probabilistic inversion. Station coverage must constrain depth as well as horizontal position; merely having four observations does not ensure a well-conditioned solution.

Errors include uncertain or misidentified onsets, clock and station-coordinate errors, wrong velocities or neglected three-dimensional structure, poor azimuthal coverage, inadequate station distances and depth–origin-time tradeoffs. Examine residual patterns and resolution, not only the minimum residual. A small formal covariance within a wrong velocity model can accompany a systematically biased hypocentre.

The northern station is closer, under comparable P wave and S wave paths through the same velocity model. In the actual Figure 4 the northern P and S pulses are separated by about 6 s, whereas the southern separation is roughly 8–8.5 s. The S–P time removes the unknown earthquake origin time:Both northern pulses also occur earlier on the shared absolute clock, consistent with the smaller distance. Earlier arrival alone would not be sufficient if clocks or velocity models differed.

For reproducible graph readings, the northern positive-to-negative zero crossings are approximately $13.3\mathrm{s}$ for P and $19.3\mathrm{s}$ for S; the southern crossings are approximately $16.7\mathrm{s}$ and $25.0\mathrm{s}$. These are convenient corresponding pulse landmarks, not sharply defined first-break onsets. The first visible motion begins earlier: approximately 12 s and 18 s in the north, and 14–15 s and 22–23 s in the south, depending on the amplitude threshold. The horizontal axis is seconds since midnight on 1 January 2000, not elapsed time since rupture initiation.

The time for a specified seismic phase to propagate along its ray. Arrival time additionally includes earthquake origin time; those quantities must not be interchanged on an absolute-clock seismogram.

The delay between corresponding S wave and P wave arrivals. For a common uniform path of length $r$, $\Delta t=r(1/V_s-1/V_p)$, cancelling earthquake origin time. Matched phase identification and an appropriate velocity model are needed to infer distance.