Target-oriented wave-equation inversion

Alejandro A. Valenciano, Biondo Biondi, and Antoine Guitton

valencia@sep.stanford.edu, biondo@sep.stanford.edu, antoine@sep.stanford.edu

ABSTRACT

A target-oriented strategy can be applied to estimate the wave-equation least-squares inverse image ($\hat {\bf m}$) by explicitly computing the Hessian ($\bf H$). The least-squares inverse image is obtained as the solution, using a conjugate gradient algorithm, of a non-stationary least-squares filtering problem ${\bf H} \hat{{\bf m}}={\bf m}_{mig}$ (where ${\bf m}_{mig}$ is the migration image, and the rows of the Hessian are non-stationary filters). This approach allows us to perform the number of iterations necessary to achieve the convergence, by exploiting the sparsity and structure of the Hessian matrix. The results on a constant velocity model and a model with a velocity Gaussian anomaly show the validity of the method.