Summary
Sparse-Spike Deconvolution (SSD) is a commonly used seismic deconvolution method for reflectivity inversion and acoustic impedance inversion. However, when applying it to multi-dimensional seismic data on a trace-by-trace basis or to seismic data with complex structure, the conventional methods may show lateral instability and the quality may be compromised in the presence of noise and wavelet estimation error. To address these problems, we present a new seismic SSD method based on Toeplitz-Sparse Matrix Factorization (TSMF). Assuming the convolution model, a constant source wavelet, and the sparse reflectivity, a seismic profile can be considered as a matrix that is the product of a Toeplitz wavelet matrix and a sparse reflectivity matrix. Consequently, we propose a new TSMF algorithm to deconvolve the seismic matrix into source wavelet and reflectivity by alternatively solving two inversion sub-problems, one is related to the wavelet matrix that has a Toeplitz structure and the other is related to the sparse reflectivity matrix. Tests on synthetic and field seismic data demonstrate the validity of the proposed method.
Introduction
Introduction
According to the convolutional model, a seismogram trace y(t) can be modeledas
[equation]
where '*' means convolution, w(t) is the source wavelet, r(t) contains the reflectivity coefficients of the subsurface, and n(t) is the noise. From equation (1), we can see that the recorded seismic trace always bears the source wavelet, which smears adjacent events and reduces the resolution of the seismic image. Seismic deconvolution is an inverse problem for removing the source wavelet from a recorded seismic trace. In the ideal case, after deconvolution the true seismic reflectivity is recovered. In reality, because the source wavelet is always band-limited, the inverse problem is ill-posed, and requires regularization to achieve stable results. Since the bigger seismic reflectivity coefficients are the main contributors of seismic acoustic impedance, and they are usually sparse in time, sparsity is usually taken as a regularization constraint for reflectivity inversion. Using this constraint leads to a methodology called Sparse-Spike Deconvolution (SSD) method (Nguyen, 2008; Latimer et al., 2000). The main objective of SSD is to provide a significant increase in the bandwidth content from band-limited seismic observations, so that its result has high resolution and is suitable for acoustic impedance inversion.
