Euclid and the art of wavelet estimation, Part I: Basic algorithm for noise-free data

An algorithm borrowed from polynomial algebra for finding the common factors of two or more polynomials can be used to find the wavelet that several seismic traces have in common. In the implementation described in this first part of a two‐part work, a matrix is constructed from the autocorrelations and crosscorrelations of these seismic traces. The number of zero eigenvalues of this matrix is equal to the number of samples of the wavelet, and the eigenvectors associated with these eigenvalues are related to the reflection coefficients. The method, which works well if the noise is not too high, is illustrated by means of a synthetic example. Part II of this two‐part work shows how this method is affected by noise and gives field‐data examples.