Low-Dimensional Multi-Trace Impedance Inversion in Sparse Space with Elastic Half Norm Constraint

Abstract

Recently, multi-trace impedance inversion has attracted great interest in seismic exploration because it improves the horizontal continuity and fidelity of the inversion results by exploiting the lateral structure information of the strata. However, computational inefficiency affects its practical application. Furthermore, in terms of vertical constraints on the model parameters, it only considers smooth features while ignoring sharp discontinuity features. This leads to yielding an over-smooth solution that does not accurately reflect the distribution of underground rock. To deal with the above situations, we first develop a low-dimensional multi-trace impedance inversion (LMII) framework. Inspired by compressed sensing, this framework utilizes low-dimensional measurements in sparse space containing the maximum information of the signal to construct the objective function for multi-trace inversion, which can significantly reduce the size of the inversion problem and improve the inverse efficiency. Then, we introduce the elastic half (EH) norm as a vertical constraint on the model parameters in the LMII framework and formulate a novel constrained LMII model for impedance inversion. Because the introduced EH norm takes into account both the smoothness and blockiness of rock impedance, the constrained LMII model can effectively raise the inversion accuracy of complex strata. Finally, an efficient alternating multiplier iteration algorithm is derived based on the variable splitting technique to optimize the constrained LMII model. The performance of the developed approaches is tested using synthetic and practical data, and the results prove their feasibility and superiority.