Stochastic spectral inversion for sparse-spike reflectivity by presetting the number of non-zero spikes as a prior sparsity constraint

Abstract

In this paper, presetting the number of non-zero spikes is applied as a prior sparsity constraint to implement the proposed stochastic spectral inversion for sparse-spike reflectivity. Instead of being set artificially, the preset number of non-zero spikes can be estimated directly by the selected frequency bandwidth of seismic data using the signal sampling and reconstruction theory with finite rate of innovation. Then the spectral equations of sparse-spike reflectivity can be derived in the frequency domain by adding the proposed prior sparsity constraint. Using an iterative algorithm combining very fast simulated annealing with a linear least-squares method, we can solve the spectral equations to obtain both the time locations and the amplitudes of non-zero sparse-spike reflectivity and reconstruct the sparse-spike reflectivity series. Examples using 1D synthetic data show that the proposed prior sparsity constraint can ensure that the inversion results are robust and reliable and maximize the number of the reconstructed true spikes with the minimum number of false spikes. Moreover, statistical results of stochastic spectral inversion using a thin-layer model illustrate that the proposed method has the ability of detecting the thin layers below the tuning thickness. Results using 2D synthetic data for the Marmousi2 model demonstrate that the reconstructed sparse-spike reflectivity section can preserve the lateral continuity of layers and distinguish thin beds in the sparse-layer model. The application of 2D field data confirms the validity of the proposed inversion method.