Block-diagonal Approximate Hessian for Preconditioning in Full Waveform Inversion

We present a preconditioner for the non-linear conjugate gradient method in time-domain multi-parameter full-waveform inversion. The proposed preconditioner is a block-diagonal approximation of the Hessian, constructed with second-order time-domain adjoint techniques. Working in the time domain ensures the applicability to large-scale 3D problems. The preconditioner efficiently compensates the extreme values of Fréchet kernels near sources and receivers, thereby accelerating convergence in less densely covered regions. To assess the efficiency of the preconditioned conjugate-gradient optimisation with respect to the standard conjugate-gradient method, we consider a layered model with two elliptical inclusions. Our numerical results show that the preconditioned method yields more accurate inversion results, especially for the shear velocity model. In addition, convergence accelerated significantly while the extra computational cost is limited to four wave field simulations per multi-scale step.