Arrival time determination using iterative signal reconstruction from the phase of the cross spectrum

A situation encountered in such applications as seismics, ocean acoustics, radar, sonar and others, is that of an unknown wavelet propagating nondispersively in a reverberatory or multipath environment. Two receivers placed in such an environment will each record the arrival of this wavelet numerous times and each time with a different attenuation factor. In this paper, we demonstrate that if 1) there is no noise, 2) the interreceiver delays are distinct, and 3) the arrival sequence at each receiver has no zero phase convolutional component, then the arrival times and attenuation factors at each receiver can be determined as well as the wavelet itself. We show this via the construction of a finite length sequence whose phase equals that of the cross spectrum of the two received signals. This reconstructed signal, under the conditions above, can then be "inverted" to recover the desired arrival time and attenuation information at each receiver. An example using synthetically generated data is provided.