Due to non-linear effects, the swept frequency signals (sweeps) transmitted into the subsurface by vibrators are contaminated by harmonics. Upon correlation of the recorded seismograms, these harmonics lead to noise trains which are particularly disturbing in the case of down-sweeps. The method described in this paper-which can be regarded as a generalization of Sorkin's approach to the suppression of even order harmonics-allows elimination, from the final vibratory source seismogram, of harmonics of the sweep up to any desired order. It requires that not one single signal but rather a series of M signals is employed where each signal has an initial phase differing from that of the previous one of the series by the phase angle 2n/M. Prior to stacking, the seismograms generated with the different signals have to be brought into the form they would have if they had been generated with the same signal.The method seems also to be capable of reducing the correlation noise if sign-bit recording techniques are used.

The amplitude of the signal and the energy of the noise on each of at least three traces can be estimated provided that the signal has the same form (but not necessarily the same amplitude) on these traces and that the noise on any trace is correlated with neither the signal nor the noise on any other trace. This estimation of signal amplitude and noise energy can be achieved by a rather simple algorithm. The accuracy of the estimate depends, of course, on the degree to which the assumption that signal and noise on the different traces are mutually uncorrelated is actually met. The accuracy tends to improve with increasing number of traces.

Determination of impedance or velocity from a stacked seismic trace generally suffers from noise and the fact that seismic data are bandlimited. These deficiencies can frequently be alleviated by ancillary information which is often expressed more naturally in terms of probabilities than in the form of equations or inequalities. In such a situation information theory can be used to include ‘soft’information in the inversion process. The vehicle used for this purpose is the Maximum Entropy (ME) principle. The basic idea is that a prior probability distribution (pd) of the unknown parameter(s) or function(s) is converted into a posterior pd which has a larger entropy than any other pd which also accounts for the information. Since providing new information generally lowers the entropy, this means that the ME pd is as non‐committal as possible with regard to information which is not (yet) available. If the information used is correct, then the ME pd cannot be contradicted by new, also correct, data and thus represents a conservative solution to the inverse problem. In the actual implementation, the final result is, generally, not the pd itself (which may be quite broad) but rather the expectation values of the desired parameter(s) or function(s). A general problem of the ME approach is the need for a prior pd for the parameter(s) to be estimated. The approach used here for the velocity is based on an invariance criterion, which ensures that the result is the same whether velocity or slowness is estimated. Unfortunately, this criterion does not provide a unique prior pd but rather a class of functions from which a suitable one must be selected with the help of other considerations.

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.

In this second part of a two‐part work, a more robust algorithm is derived and used for the estimation of the seismic wavelet as the common signal of two or more seismic traces. It is based on the properties of the eigenvectors with zero eigenvalue of a matrix derived in the first part, whose elements are the samples of the autocorrelation functions and crosscorrelation functions of these seismic traces for a number of lags. The noise resistance of this algorithm is illustrated by means of a synthetic‐data example and then demonstrated on field data. In one field‐data example, the so‐called Euclid wavelet is compared with one derived deterministically by means of an impedance log. The other example relates three quite different Euclid wavelets determined in three different time zones on a seismic line to one another by showing that their differences can be explained by absorption.