Sparsity-promoting multi-parameter pseudoinverse Born inversion in acoustic media

Least-squares reverse-time migration has become the method of choice for quantitative seismic imaging. The main drawback of such scheme is that it requires many migration/modeling cycles. The convergence of least-squares reverse-time migration can be accelerated by using a suitable preconditioner. In the context of extended domain in a variable density acoustic media, the pseudoinverse Born operator is the recommended preconditioner, providing quantitative results within a single iteration. This method consists of two steps: application of the pseudoinverse Born operator, and inversion of two parameters using an efficient weighted least-squares approach based on the Radon transform. As expected, cross-talk artifacts are generated in the second step due to limited acquisition. We present a variable density pseudoinverse Born operator constrained with the ℓ1-norm for each model parameter to suppress the artifacts. The fast iterative shrinkage-thresholding algorithm is used to carry out the optimization problem. In classical iterative least-squares migration, the ℓ1-norm constraints would affect the whole imaging process. As the imaging method is split into two steps, only the Radon transform part is modified, where no wave-based operators are involved. Through numerical experiments, we verify the robustness of the proposed method against different migration artifacts including the parameter cross-talk, interfaces with abrupt truncations, sparse shot acquisition geometry, noisy data and high contrast complex structures.