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An earthquake centroid is an effective average location of seismic moment release. It differs from the hypocenter, where rupture starts, and can depend on the source representation and observations. An associated centroid time similarly averages release rather than marking its first instant.

Arrival-time location estimates a hypocenter and origin time by comparing picked phase arrivals with predicted travel times. Linearization gives residual changes $\delta t_i=\delta t_0+\nabla T_i\cdot \delta \mathbf{x}$. Poorly distinct derivative columns cause tradeoffs, while incorrect wave speeds or phase labels cause systematic bias even with many stations.

In a homogeneous medium with surface stations along coordinate $x$, an hypocenter at horizontal position $x_0$ and depth $z_0>0$ has straight-ray distance $R=\sqrt{(x-x_0{)}^2+z_0^2}$. For two phases along that path, set $K=1/v_B-1/v_A>0$. Their arrival delay satisfieswith $A=K^2$, $B=-2K^2{x}_0$ and $C=K^2(x_0^2+z_0^2)$. Completing the square yieldsThe ratio of intercept to curvature gives squared depth only after centering at the fitted vertex: $(\Delta t{)}^2=A(x-x_0{)}^2+A{z}_0^2$. The raw uncentered ratio $C/A$ includes $x_0^2$ and generally overestimates squared depth.

The fitted curvature also determines $K=\sqrt{A}$, but it does not separately identify both wave speeds. Shared clock offsets cancel in the interphase delay, while a wrong homogeneous velocity model or phase-picking errors still affect the result. Squaring noisy delays changes their error probability distribution; practical inference should model that transformation or fit the unsquared delay relation directly.

The epicenter is the projection of an earthquake's hypocenter onto the surface directly above it.

The hypocenter is the point where an earthquake rupture starts, rather than necessarily the centroid of its eventual slip distribution.

Distance from an earthquake hypocenter to a receiver. In a uniform velocity model it is the straight ray-path length; in layered material an interphase delay instead constrains a model-dependent path.

Use the northern S–P time, approximately $\Delta t_N=6\mathrm{s}$, rather than multiplying an absolute-clock arrival by a wave speed. For common approximately straight paths,No numerical crustal velocities are specified in Q3. If the usual illustrative crustal values $V_p=6.0\mathrm{km}{\mathrm{s}}^{-1}$ and $V_s=3.5\mathrm{km}{\mathrm{s}}^{-1}$ are adopted, the distance isThese assumed crustal speeds are unrelated to Q1's offshore layer values. They are representative rather than measurements of the Swiss column; the British Geological Survey gives broad typical crustal ranges of 5–7 km/s for P waves and 3–4 km/s for S waves.^[ref]

Using the corresponding northern central pulse times gives an effective source time near $13.3-50.4/6\simeq 4.9\mathrm{s}$ after midnight, and the S estimate is the same to graph accuracy. The southern central landmarks similarly give a distance near 70 km and an effective source time near 5 s. That consistency supports the example, but pulse landmarks need not mark the rupture's true onset. $D_N$ is a source-to-station path or hypocentral distance in the uniform-speed approximation. An epicentral distance additionally needs the hypocenter depth; it cannot simply be equated to 50 km for an unknown depth.