Blind deconvolution technique for de-noising of non-stationary seismic signals using DWT

Discrete wavelet transform is an effective tool to disintegrate the time variant seismic data in time-frequency manner. This work incorporates the wavelet transform in the blind deconvolution technique to deal with the inherent non-stationarity present in seismic data and to improve the SNR of seismic data. Time varying nature of seismic data is the result of a depth varying character of seismic source wavelet (where high frequency components of the source wavelet get absorbs due to increasing heat gradient with depth) convolved with the non Gaussian distributed earth reflectivity in presence of additive Gaussian, color Gaussian noise. Seismic signal can thus be considered as a result of multiple subsystems with different constraints based on time-frequency localization convolved with input signal. Techniques based on stationarity assumptions are not effective in modeling the time variance character of source with depth. In this work we apply the discrete wavelet transform (DWT) to decompose the seismic data into different time-frequency signals. Denoising based on soft thresholding is applied to get the shrinkage effect of wavelet coefficients. Combination of blind deconvolution technique mixed with the discrete wavelet transform gives the best result in terms of reducing the noise and improving the resolution of seismic data with time. Denoising based on soft thresholding gives optimal minimum means square value, low convolutional noise and also low maximum distortion value than hard thresholding.