基于二进小波变换自适应Kalman滤波反褶积

Adaptive Kalman Filtering Deconvolution Based on Dyadic Wavelet Transform

本文提出了基于二进小波变换自适应Kalman滤波反褶积 (AKFD)新方法 .它抛弃了传统预测反褶积对信号平稳性的假设 ,克服了提高分辨率反而明显降低信噪比的矛盾 ,其较好地压缩反射波形 ,但噪声并没有明显提高 ,所以具有很好的抗噪性能 .在小波域进行的AKFD压制假反射比在时间域AKFD好 ,此外 ,该方法具有对信号分频进行AKFD的特性 ,增强了Kalman滤波的自适应性 ,所以在小波域下的分辨率明显比在时域内高 .同时 ,该方法克服了在时域内进行的AKFD抬升低频成份的缺陷 .

A new approach of adaptive Kalman filtering deconvolution (AKFD) is developed based on dyadic wavelet transforms. The technique discards the assumption of signals stationarity in predictive deconvolution, and overcomes the problem of improving resolution at the price of substantially decreasing signal-to-noise rate (SNR). The technique can well compress the reflection waveforms, but the noises are not lifted in substance. So it has a better ability of noise tolerance. Suppressing false reflections in dyadic wavelet transform domain is better than by applying AKFD in the time domain. In addition, since the technique also has the characteristic of adaptive Kalman filtering in every band for a signal respectively, it enhances the adaptation of Kalman filtering, and the resolution is obvious higher than that in the time domain. At the same time, the technique also overcomes the drawback of increasing the low-frequency component of AKFD in the time domain. Numerical models and real seismic data indicate that the technique has obvious effect.