A KALMAN FILTER APPROACH TO THE DECONVOLUTION OF SEISMIC SIGNALS

Abstract

It is common practice to model a reflection seismogram as a convolution of the reflectivity function of the earth and an energy waveform referred to as the seismic wavelet. The objective of the deconvolution technique described here is to extract the reflectivity function from the reflection seismogram. The most common approach to deconvolution has been the design of inverse filters based on Wiener filter theory. Some of the disadvantages of the inverse filter approach may be overcome by using a state variable representation of the earth’s reflectivity function and the seismic signal generating process. The problem is formulated in discrete state variable form to facilitate digital computer processing of digitized seismic signals. The discrete form of the Kalman filter is then used to generate an estimate of the reflectivity function. The principal advantages of this technique are its capability for handling continually time‐varying models, its adaptability to a large class of models, its suitability for either single or multi‐channel processing, and its potentially high‐resolution capabilities. Examples based on both synthetic and field seismic data illustrate the feasibility of the method.