Optimum arrival-time estimation in exploration seismology

Estimation of the arrival time of a primary seismic layer reflection is formulated as a radar/sonar problem of optimum processing in the presence of colored noise. In this application, the colored noise is considered to be reverberation noise, the sum of all undesired arrivals. The performance of the optimum processor represents an upper bound for any other processor which seeks to perform the same task. Estimation and detection performance bounds are computed for the optimum processor. A primary distinction between this method and others used to date is that an explicit model of earth attenuation has been postulated and employed in the derivation of the processor: deep return are recoverable in the presence of shallow, for instance, because the deep returns have been more severely filtered by the earth.