# Difference between revisions of "Klauder filter"

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A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time ''t'' = 0 ms. | A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time ''t'' = 0 ms. | ||

− | The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency ''f''<sub> | + | The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency ''f''<sub>lower</sub> (perhaps 2–8 Hz), its upper frequency ''f''<sub>upper</sub> (often about 100–200 Hz), and its duration ''T'', commonly about 6–12 s. |

:<math>A(t) = \mathrm{Re} \left[ \frac{\sin (\pi k t (T-t)}{\pi k t \mathrm{e}^{2 \pi \mathrm{i} f_0 t} } \right] </math> | :<math>A(t) = \mathrm{Re} \left[ \frac{\sin (\pi k t (T-t)}{\pi k t \mathrm{e}^{2 \pi \mathrm{i} f_0 t} } \right] </math> | ||

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where ''k'' is the rate of change of frequency with time: | where ''k'' is the rate of change of frequency with time: | ||

− | :<math>k = \frac{f_\mathrm{ | + | :<math>k = \frac{f_\mathrm{upper} - f_\mathrm{lower}}{T} \ </math> |

and ''f''<sub>0</sub> is the mid-frequency of the bandwidth: | and ''f''<sub>0</sub> is the mid-frequency of the bandwidth: | ||

− | :<math>f_0 = \frac{f_\mathrm{ | + | :<math>f_0 = \frac{f_\mathrm{upper} + f_\mathrm{lower}}{2} \ </math> |

Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side. | Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side. | ||

+ | |||

+ | ==See also== | ||

+ | * [[Ricker wavelet]] | ||

+ | * [[Butterworth filter]] | ||

+ | * [[Ormsby filter]] | ||

==References== | ==References== |

## Latest revision as of 00:06, 27 February 2014

A common type of synthetic wavelet in reflection seismology. It is zero-phase, and symmetrical about time *t* = 0 ms.

The Klauder wavelet 'represents the autocorrelation of a linearly swept frequency-modulated sinuusoidal signal used in Vibroseis' (Ryan 1994). It is defined by its lower frequency *f*_{lower} (perhaps 2–8 Hz), its upper frequency *f*_{upper} (often about 100–200 Hz), and its duration *T*, commonly about 6–12 s.

where *k* is the rate of change of frequency with time:

and *f*_{0} is the mid-frequency of the bandwidth:

Klauder-filtered wavelets have several sidelobes, unlike Ricker wavelets which only have two, one either side.

## See also

## References

- Ryan, 1994. A choice of wavelets. CSEG Recorder September 1994.

## External links

- Klauder wavelet — Sheriff's Encyclopedic Dictionary

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