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In the three-dimensional Earth, a network identifies P- and S-wave arrivals and fits source coordinates $(x_0,y_0,z_0)$ and origin time $t_0$ using a travel-time model. Time differences constrain path lengths without requiring a common absolute clock zero; calibrated absolute times then fix the origin time. Real inversions trace refracted rays through a layered or heterogeneous velocity model and use many stations, azimuths, and phases, rather than literal circles at fixed wave speed. Residuals and the sensitivity matrix quantify uncertainty and expose poor station geometry or a poor velocity model.

Depth and origin time are often the weakest pair, especially for a shallow event observed by distant surface stations. In the homogeneous example,If the depth sensitivities are small or nearly alike across the network, a deeper source's longer travel time can be offset by an earlier origin time. In contrast, horizontal displacement often gives opposite-sign residuals on opposite sides of an event and is better constrained by good azimuthal coverage. Nearby stations and depth-sensitive reflected phases can break the earthquake depth–origin-time trade-off; the ranking is not universal for every network or event depth.