Nonlinear multichannel impedance inversion by total-variation regularization

The analysis of acoustic impedance (AI) allows for the mapping of seismic reflection data to lithology, and hence it plays an important role in the interpretation of poststack seismic data. The AI is obtainable from the inversion of the earth reflectivity series. Efficient deconvolution methods have been developed for recovering the reflectivity series from band-limited poststack data, which are multiple free, zero offset, and migrated. However, calculation of the AI from the reflectivity, when considering the spatial correlation of the impedance parameters, demands the solution of a constrained nonlinear inverse problem. Two efficient algorithms are proposed for solving the nonlinear impedance problem in multichannel form with the total-variation (TV) constraint to recover impedance maps with blocky structures. The first uses the continuous earth model for reflectivity, which allows linearizing the problem in the logarithm domain. The second uses the discrete (layered) earth model for reflectivity. In this case, a nonlinear problem is solved in the original domain. The main properties of the algorithms, which are built based on the split-Bregman technique and the discrete cosine transform are as follows: (1) They are multichannel inversion procedures, so they respect the spatial and temporal correlation of the data, (2) they impose the TV constraint on the parameters to generate blocky structures, (3) they are fast such that a large 3D impedance model with a blocky structure can be recovered easily on a personal computer, and (4) the computational complexities of both algorithms are the same. Numerical tests using simulated 2D data obtained froma benchmarkMarmousi model and also 2D and 3D field data confirmed that the proposed algorithm generates more accurate with higher resolution impedance models compared with the conventional methods.