Elastic and anelastic adjoint tomography with Fréchet and full Hessian kernels

Summary The elastic and anelastic structures of the Earth offer fundamental constraints for understanding its physical chemical properties. Deciphering small variations in velocity amplitude seismic waves can be challenging. Advanced approaches such as full-waveform inversion (FWI) useful. We re-write Fréchet kernel expression Fichtner & van Driel (2014) using displacement-stress formulation. then derive full Hessian viscoelastic In these formulations, kernels are computed by forward strain a shift adjoint strain. This is complementary to Q expressions that explicit velocity-stress To reduce disk space I/O requirements computing kernels, on fly, while combination on-the-fly approach (Xie et al., 2021) with parsimonious storage method (Komatitsch 2016). Applications tomography presented two synthetic 2D models, including an idealised model rectangular anomalies approximates subduction zone, one 3D geometry. calculation approximately doubles computationally cost per iteration inversion; however, reduced number iterations fewer frequency stages required achieve same level convergence make it overall less expensive than classical L-BFGS FWI tested models. find use provides comparable results improved models stage up 0.5 Hz. Given computational expense calculation, not advantageous inversions at this time until further improvements made. For model, similar image quality 0.1 observe rate comparison higher stage, Hz 0.2 Hz, we speculate may more Finally, perform simultaneously work re-derived which about 1/3 when compared additionally defined source. recovered smeared investigation frequencies remains challenging requires work. used other purposes instance resolution analysis addition inversions.