How serious is the nonlinear effect on traveltime delays predicted by sensitivity kernels
Wenjun Xu, Xiao‐Bi Xie · 2009
Sensitivity kernels are used in travel-time tomography and waveform inversion for its obvious advantages in matching wave-motion theory rather than ray theory. However, there still remain some concerns regarding its accuracy and when the small-perturbation theory will break down. We investigate these questions using numerical simulations. Sensitivity kernels calculated in the background model and based on the linear scattering theory are used to predict the traveltime delay caused by the velocity perturbations. On the other hand, the traveltime differences between the background and the perturbed velocity models are directly calculated from the synthetic seismograms generated by the finite-difference method. The predicted traveltime delays are compared to these direct measurements and the results are used to judge the accuracy of the linear theory. Velocity models with perturbations of different scales or different perturbation values are used to conduct the tests. Our results show that extending the scale or increasing the amplitude of the velocity perturbations or both can affect the precision of the traveltime sensitivity kernel. These factors also complicate waveforms of synthetic seismograms as well as the shape of the sensitivity kernels in the perturbed velocity model. Nevertheless, within a large range of velocity perturbations, the sensitivity kernels based on linear theory still give reasonably accurate traveltime delay, indicating the linearization plus iteration method is still effective under reasonably large velocity perturbations.