Relative acoustic impedance inversion via Toeplitz-Sparse Matrix Factorization

We propose a new relative acoustic impedance inversion method based on Toeplitz-Sparse Matrix Factorization (TSMF), to address the problems of lateral continuity, wavelet estimation error and the effect of noise in the inversion. This method transforms the Toeplitz-Sparse Matrix Factorization of a seismic profile into two subproblems. One takes the elements of the Toeplitz wavelet matrix as parameters to be inverted for, and will be solved by Fused Lasso, which guarantees that the wavelet has compact support and is smooth. The other takes the elements of the sparse reflectivity matrix as parameters to be inverted for, and will be solved by fast iterative shrinkage-thresholding algorithm (FISTA) with backtracking, which makes it easy to choose the parameter for the objective function. The seismic profile can be simultaneously deconvolved into a Toeplitz wavelet matrix and a sparse reflectivity matrix by alternatively solving the above two sub-problems. Then the high resolution relative acoustic impedance can be achieved by recursive inversion using the deconvolved reflectivity matrix. The high resolution acoustic impedance can also be achieved by adding the low-frequency components derived from the well to the relative acoustic impedance. Tests on the synthetic seismic data from the Marmousi2 model and a section of field seismic data demonstrate that the proposed method can effectively derive the relative acoustic impedance from band-limited data with appropriate resolution and lateral coherence, even when the initially estimated wavelet is inaccurate and the seismic data are contaminated by noise.