Seismic data deconvolution using Kalman filter based on a new system model

Seismic resolution plays an important role in geologic interpretation and reservoir prediction. To improve the vertical resolution of a seismic image, we have developed a new Kalman filter system model for seismic deconvolution. Similar to the conventional Kalman filter model for seismic deconvolution, our new Kalman model is also based on the common viewpoint that a reflected seismic record can be regarded as a convolution of a seismic wavelet with a reflection coefficient series. The new model uses a reversed seismic wavelet to slide across a reflectivity function to achieve the convolution result, instead of using a reversed reflectivity function to slide across a seismic wavelet in the conventional Kalman filter model. A simpler state equation for the new model is achieved, and the number of parameters to select is fewer than the conventional. Furthermore, the number of parameters can be reduced to only one by a theoretical demonstration for stationary noisy signals, which decreases the requirement for multiple parameters selection in the conventional model. The practical selection for this parameter should be a compromise between resolution improvement and noise amplification. Experimental results in the time and frequency domains on synthetic and field seismic records revealed that the Kalman filter based on the new model has the advantages of a higher resolution and peak signal-to-noise ratio (PS/N) than the conventional Kalman filter for stationary and nonstationary signals, and it works similarly to the Wiener filter for stationary signals, and it is superior to the Wiener filter in resolution and PS/N for nonstationary signals. The Kalman filter based on the new model can be applied to seismic resolution improvement.