Ormsby wavelet

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Figure. 1 Ormsby wavelet with low-cut frequency f1, low-pass frequency f2, high-pass frequency f3, and the high-cut frequency f4 at 5 Hz, 10 Hz, 40 Hz, and 45 Hz, respectively.  

Ormsby wavelets are zero-phase wavelet, featuring a controllable flat frequency content (Ryan, 1994)[1]. Rather than two side lobes, like Ricker wavelet, Ormsby wavelets have numerous side lobes which are symmetrical about a vertical line through its central peak at time zero (Fig 1). Four frequencies,  to, are needed to form an Ormsby wavelet whose frequency spectrum is the trapezoidal shape. These frequencies are f1, low-cut frequency; f2, low-pass frequency; f3, high-pass frequency; and f4, high-cut frequency. Similar to a bandpass filter, the frequency spectrum of the Ormsby wavelet is of trapezoidal shape, which maintains a stable frequency component between low-pass frequency to high pass frequency and clear-cutting beyond the low-cut frequency and high-cut frequency (Fig 2).

The amplitude A(t) of the Ormsby wavelet with low-cut frequency f1, low-pass frequency f2, high-pass frequency f3, and the high-cut frequency f4 at time t is given by,

Ormsby wavelet formula .png

Application

Figure 2. The frequency spectrum of Ormsby wavelet with low-cut frequency, low-pass frequency, high-pass frequency, and the high-cut frequency at 5 Hz, 10 Hz, 40 Hz, and 45 Hz, respectively.  

Ormsby wavelets are one of the most common-used wavelets available in regular commercially seismic software. For wavelet estimation, Ormsby wavelet works well for the data volume that has a trapezoidal frequency spectrum rather than has the spectrum with a dominant frequency. For complicate rock-soil conditions, the [[1]]Ormsby wavelet can have more flexible control on frequency domain than Ricker wavelet, which helps modeler reconstruct the seismogram that is comparable to real seismic data.  

See Also

Wavelet

Ricker Wavelet

Ormsby Wavelet

Band

Filter

External Links

Ricker, Ormsby, Klander, Butterworth – A Choice of Wavelets

Caparison of wavelet estimation methods

Understanding the Seismic Wavelet

References

  1. Ryan, H. (1994). Ricker, Ormsby; Klander, Bntterwo-A Choice of Wavelets.