ESSAI D'ANALYSE DE TRACES SISMIQUES*
Authors: KUNETZ G. 
Published: April 2006

Abstract

Comparison of synthetic seismograms with field records has shown, that, under favorable circumstances, a large part of what is present on the latter may be ascribed to direct or multiple reflections due to velocity contrasts as they appear on a nearby velocity log.

Therefore it does not seem unreasonable to submit good field records to a series of transformations, inverse to those which lead from a velocity log to the synthetic seismogram, with the purpose of getting somewhat more detailed and more accurate information on the variation of velocities with depth.

The main difficulty in this kind of problem is generally the lack of stability of the results, i.e. the great influence on the final outcome of even small and unavoidable inaccuracies in the data or in the assumptions.

For this reason a theoretical case has first been examined, where both the data and the physical hypotheses, as well as the final result were perfectly well known,—as this allows estimation and if necessary improvement in the stability of the method employed.

Thus the successive steps of the inverse procedure, leading from a filtered synthetic record with multiples back to the initial velocity log are briefly discussed and the results obtained are shown.

Two main stages are distinguished:

—suppression of the effect of filtering, called “deconvolution”

—discrimination between direct and multiple reflection, called “analysis”.

For the former stage, the largely unknown filtering effect of the earth has also to be taken into account. First the way of deducing the total filtering effect from the filtered record itself is examined; second (a certain shape of the “signal”, the impulsional response of this filter, being assumed) an inverse filter is calculated ensuring a compromise between a good recovery of the original impulse and a minimum amplification of noise.

A complete example of the results of the inverse procedure is given, in the case of a filtered synthetic record without multiples. The only data, supposedly known, were the sampled ordinates of this record, drawn on the usual scale of a field record. Good correlation was nevertheless found between the output of the inverse filtering and the original impulsional record. Integration yielded a pseudo‐velocity as a function of time, showing again good agreement with the true velocities, except for their absolute values. If, in addition, check‐shot data are supposedly available, these pseudo‐velocities can be tied in, and a second integration yields the values of depth in function of time.

The analysis itself, discrimination of direct and multiple reflection, starts by a step by step reversal of the recurrent procedure used for introducing multiple reflections (p. 4 ref. 3). The rapidly increasing accumulation of errors, due to the noise on the record and to the approximate nature of the physical assumptions, is partially accounted for by a continous readjusting of the results obtained. Nevertheless, if this method allows, as shown by a last example, a very satisfactory analysis of a rather noisy synthetic record, it is still too unstable to be applied to field records. An alternative method of successive approximations is finally outlined.

As a conclusion, the necessarily approximate nature of the solutions of these problems is stressed. If some of the methods presented are still too theoretical, others have already been applied with success to field records.