Noise attenuation by the S transform
EXISTENCE of random noise is one of the problematic topic in the processing and interpretation of seismic data. Like the analysis of the NMO velocity, migration operator and deconvolution has a lot of destructive efforts. On the other way the information gathered on the seismic records and geophysical data are multi-scales. This is because of nature of seismic studies since seismic waves lose their high frequently altitudes gradually because of the penetration in the earth, and their frequency range, on the other word, their scale will change.
To study these data it is necessary to apply mathematics which can satisfy multi-scaled data .With the S transform we can get the time frequency distribution of seismic and geophysical data. The S transform, which is introduced in this correspondence, is an extension of the ideas of the continuous wavelet transform (CWT), and is based on a moving and scalable localizing Gaussian window. It is shown here to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum .These advantages of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates .This by itself is a base to design an Adaptive- weighted filter for noise attenuation .On this article we probe ability of adaptive- weighted filter. We will show by synthetic example that this filter is the effective way to decrease the noise with the low signal to noise ratio .This transform can be used to design other filters for noise attenuation in the other geophysical data.