INVERSE CONVOLUTION FILTERS

Abstract

The difficult problem of trying to locate stratigraphic traps with the reflection seismograph would be simplified (at least in good record areas) if it were possible to perform the inverse of the reflection process, i.e., to “divide out” the reflection wavelet of which the record is composed, leaving only the impulses representing the reflection coefficients. This process has been discussed by Robinson under the title “predictive decomposition,” but his approach requires that the basic composition wavelet be a one‐sided, damped, minimum‐phase time function. Most seismic wavelets which we observe or are accustomed to working with (e.g. the symmetric Ricker wavelet) are not of this class. The purpose of this paper is to discuss a digital computer approach to the problem. Finite, bounded inverse filter functions are obtained which will reduce seismic wave forms to best approximations to the unit impulse in the least squares sense. The degree of approximation obtained depends upon the time length of the inverse filter. Inverse filter functions of moderate length produce approximate unit impulses whose breadths are 50 percent or less than those of the original wavelets. Hence, these filters will increase resolution well beyond the practical limits of instrumental filters. Their effectiveness is more or less sensitive to variations in the peak frequency and shape of the composition wavelet, and to interference, depending upon individual conditions. Although this sensitivity problem can be solved to some extent through the proper design of the inverse filter, it is aggravated by the usual lack of knowledge about the form of the composition wavelet.