Based on the convolutional model, a seismic trace is the convolution of seismic source wavelet and reflection coefficient series of the earth. Seismic source wavelet estimation is one of the most important stages in processing and interpretation of seismic data. Accurate estimation of wavelet increases the efficiency of the deconvolution and temporal resolution of seismic data. On the other hand, the most important stage of seismic data interpretation is the inversion of seismic data to seismic impedance. The quality of inversion depends on the correlation of synthetic and real seismic traces in the well position. With increased accuracy in estimating source wavelet, the correlation increases.
Different methods have been introduced for estimating seismic source wavelet, such as homomorphic deconvolution, least squares method, autoregressive method and Hopfield neural network method.
In this paper, we used frequency behavior of reflection coefficient series and seismic source wavelet, and then attenuated the effect of reflection coefficient series of the earth from seismic trace and estimated the seismic source wavelet. The amplitude spectrum of reflection coefficients series behaves as a signal with high frequency content, whereas the amplitude spectrum of seismic source wavelet behaves as a signal with low frequency content.
So, the amplitude spectrum of the trace is the product of two high frequency signals (amplitude spectrum of reflection coefficient series) and low frequency signal (amplitude spectrum of seismic wavelet). Therefore, we can consider the amplitude spectrum of the reflection series as a noise and the amplitude spectrum of the wavelet as a signal.
Most of the denoising methods attenuate the additive noise from signals. In our case, the noise is the multiplicative type. We used the logarithm operator to convert the multiplicative type of noise to be additive. Now, we can estimate the seismic wavelet by denoising the logarithm of the amplitude spectrum of seismic trace.
In this paper, we used three different denoising methods, discrete wavelet transform, empirical mode decomposition and time – frequency peak filtering to denoise the logarithm of the amplitude spectrum of seismic trace.
The efficiency of the above- mentioned three denoising methods to estimate the seismic source wavelet are tested on both synthetic and real seismic data. The obtained results show that the three introduced methods estimate the seismic source wavelet accurately. As can be seen from the results, the estimated wavelets by EMD and TFPF methods have higher accuracy than that of the DWT method.
)