= Solution
Nearby events observed at the same station share most of their propagation path, so common model and station errors cancel in differential arrival times. Waveform <cross-correlation> can also determine their relative timing more precisely than separate onset picks. <Double-difference earthquake relocation> fits
$$
(t_{ik}-t_{jk})_{\rm obs}-[T_k(\mathbf x_i)-T_k(\mathbf x_j)]
$$
along with the difference in origin times. \b[The relative cluster geometry can be precise while the entire cluster remains displaced.] Absolute anchoring still needs a well-calibrated <velocity> model or a source of known position.<A Double-difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California by F. Waldhauser and W. Ellsworth>[2000, method and common-path rationale]{ref}
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