# Filter effects on waveshape

Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 7 221 - 252 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem

Figure 7.12a illustrates filter effects. Evaluate the characteristics of (a) low-frequency cut, (b) high-frequency cut, (c) bandwidth, and (d) filter slope on (i) time delay to a point that could be timed reliably, (ii) apparent polarity, and (iii) ringing. The conclusions can be generalized for filters of other design types.

### Background

Minimum phase is discussed in Sheriff and Geldart, 1995, Sections 9.4 and 15.5.6.

### Solution

The first three columns in Figure 7.12a illustrate the effect of increasing the low-frequency cut and the last three columns do the same for the high-frequency cut. Broadly speaking, (i) as low frequencies are increasingly removed, the wavelet becomes more ringy (oscillatory) and energy shifts later in the wavelet; (ii) as high frequencies are removed, the pulse is lengthened without adding more cycles; (iii) as the filter slope increases, the energy is pushed later in the wavelet, resulting in pulse shape changes as evidenced by decreased ratios of first trough to first peak amplitudes.

Figure 7.12a  Impulse response of minimum-phase filters. In the last column, ${\displaystyle \infty }$ means that high-cut filters were not used (“out”). The filter passbands are given above.
1. Importance of low-frequency cut on
1. time-delay: the backward drift of energy means that the first pickable point may be shifted to later time;
2. apparent polarity: the backward energy drift also means a weaker first half-cycle, increasing the chance of missing it and picking the next half-cycle with reversed polarity;
3. ringing: increases ringing.
2. Importance of high-frequency cut on
1. time delay: lengthening the pulse delays the first pickable point;
2. apparent polarity: no appreciable effect;
3. ringing: no appreciable effect.
3. Importance of bandwidth: the 6–60 Hz passband is roughly 3.5 octaves, the 6–30 Hz is 2.5 octaves, the 18–60 Hz is 1.5 octaves;
1. time delay: with narrower bandwidth, energy shifts backward within the wavelet, making it more difficult to pick early cycles, thus increasing time delays;
2. apparent polarity: the same effect increases the likelihood of mistaking wavelet polarity;
3. ringing: ringing increases with narrower bandwidth.
4. Importance of filter slope on
1. time delay: increasing slope increases the delay;
2. polarity: since the ratio of amplitudes of the first peak to the first trough changes, apparent polarity can be affected;
3. ringing: increases ringing.