The Borga transform and some applications in seismic data analysis

Todor I. Todorov and Gary F. Margrave

ABSTRACT

Signal transforms form the bases for many seismic data processing and analysis algorithms. We present the adjoint of the Gabor transform, which we call the Borga transform. The Gabor transform uses the operations of first windowing and then Fourier transform while the Borga transform reverses the order so that the window is applied in the frequency domain. The result is a real-valued time-frequency decomposition that is essentially a complete set of filter slices. When summed, the frequency slices exactly recreate the original signal.

The Borga transform can be used in a various processing steps. Since surface noise is predominantly low-frequency and high-amplitude, one can separate it from the signal in a raw shot gathers. Other types of noise can have a band-limited nature and anomalous amplitudes as well. By assuming local linear behavior of the amplitudes in a CMP NMO-corrected gathers, we can design a noise attenuation algorithm, based on Borga frequency slices. The process can lead to better results in AVO analysis and inversion. The transform can be a natural choice for time-variant spectral whitening as well. By applying an amplitude gain function to frequency slices, one can compensate for time and frequency dependant amplitude attenuation.

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