Seismic sparse-spike deconvolution using toeplitz-sparse matrix factorization

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.