Improvement Of Multichannel Seismic Data Through Application Of The Median Concept

ABSTRACT Different types of median filters can be used in order to improve multichannel seismic data, particularly at the stacking stage in processing. Four different applications of the median concept will be described and discussed. The most direct application is the Simple Median Stack (SMS), i.e. to use as output the median value of the input amplitudes at each reflection time. The Extended Median Stack (EMS) is a sort of generalized version of the SMS by which it is possible to exclude an optional amount of the input amplitudes that are most different from the median value. A more novel use of the median concept is the Weighted Median Stack (WMS). The WMS method if based upon a rather long median filter consisting of a small number of elements. The implicit weighting which is purely statistical in nature, is due to edge effects that occur when the filter is applied. By shifting the traces around before filtering the maximum weight may be given to for example the far offset traces. The fourth method is the Iterative Median Stack (IMS). This method, which also includes a strong element of weighting, consists of a repeated use of a comparatively long median filter combined with a gradual shortening of the filter after each iteration. The number of amplitudes will also be reduced after each filter operation, and the final result will be one discrete amplitude. Examples of how the seismic data can benefit from the application of these methods will be shown. INTRODUCTION A major part of the signal-to-noise improvement in seismic data processing is due to the stacking procedure. However, in many case the normal straight summation of assumed equivalent seismic traces is not the optimum way of improving the seismic data. Allthough this simple procedure is rather robust, the methods sensitivity to strong sporadic noise and/or sometimes insufficient ability to attenuate coherent noise, represents serious limitations. Instead of direct summation the median concept may be applied in several different ways to try to increase the signal to noise ratio even further. We will first clarify what we mean by the median. This is best explained by a simple numerical example. Let a set of discrete input amplitudes be given by the number sequence 6, 1, 4, 25, 7. After sorting this set according to increasing amplitude we get the sequence 1, 4, 6, 7, 25. The median (or median value) is now found in the middle position. Hence, the output of a 5-element median filter applied to this input sequence would be 6. Median filters have been used in many different areas, examples are in electrical engineering, speech processing and in picture processing. The most attractive property have been the ability of such filters to eliminate impulses or spikes while at the same time retaining sharp stepwise changes, provided such changes have a certain duration. The more usual linear filters cannot completely eliminate spikes or their effect, and they also tend to smooth the data in an often unwanted manner.