AbstractIn the mathematical theory of seismic signal detection and parameter estimation given, the seismic measurements are assumed to consist of a sum of signals corrupted by additive Gaussian white noise uncorrelated to the signals. Each signal is assumed to consist of a signal pulse multiplied by a space‐dependent amplitude function and with a space‐dependent arrival time. The signal pulse, amplitude, and arrival time are estimated by the method of maximum likelihood.For this signal‐and‐noise model, the maximum likelihood method is equivalent to the method of least squares which will be shown to correspond to using the signal energy as coherency measure. The semblance coefficient is equal to the signal energy divided by the measurement energy. For this signal model we get a more general form of the semblance coefficient which reduces to the usual expression in the case of a constant signal amplitude function.The signal pulse, amplitude, and arrival time can be estimated by a simple iterative algorithm. The effectiveness of the algorithm on seismic field data is demon