Wave Equation-based Teleseismic Full-waveform Tomography Method

We develop a new time-space optimized symplectic(TSOS)method for numerically solving elastic wave equations in heterogeneous isotropic media.We use the phase-preserving symplectic partitioned Runge–Kutta method to evaluate the time derivatives and optimized explicit finite-difference(FD)schemes to discretize the space derivatives.The averaged medium scheme is introduced into the TSOS method to further increase its capability of dealing with heterogeneous media.We also match the boundary-modified scheme for implementing freesurface boundary conditions and the auxiliary differential equation-perfectly matched layer(ADE-PML)non-reflecting boundaries with the TSOS method.A comparison of the TSOS method with analytical solutions and standard FD schemes indicates that the waveform generated by the TSOS method is more similar to the analytic solution and has smaller error than other FD methods,which illustrates the efficiency and accuracy of the TSOS method.Subsequently,we focus on the calculation of synthetic seismograms for teleseismic P-or S-waves entering and propagating in the local heterogeneous region of interest.To improve the computational efficiency,we successfully combine the TSOS method with the frequency-wavenumber(FK)method and apply the ADE-PML to absorb the scattered waves caused by the regional heterogeneity.The TSOS-FK hybrid method is benchmarked against semi-analytical solutions provided by the FK method for a 1-D layered model.Several numerical experiments,including a vertical cross-section of the Chinese capital area crustal model,illustrate that the TSOS-FK hybrid method works well for modelling waves propagating in complex heterogeneous media and remains stable for long-time computation.These numerical examples also show that the TSOS-FK method can tackle the converted and scattered waves of the teleseismic plane waves caused by local heterogeneity.Thus,the TS OS and TSOS-FK methods proposed in this study present an essential tool for the joint inversion of local,regional,and teleseismic waveform data.We then apply the TSOS-FK hybrid method to full waveform inversion of teleseismic waveforms.The adjoint techniques are used to compute the gradient of the misfit function.We implement a non-linear CG method to iteratively improve the model.Multiscale strategies are introduced to mitigate the nonlinearity of full waveform inversion and speed up its convergence.Several synthetic imaging experiments,including velocity anomalies in the crust or subduction zones in the mantle,are shown to demonstrate the promising capabilities of adjoint tomography based on TSOS-FK hybrid method.Furthermore,the high-resolution joint inversion of local,regional,and teleseismic waveform data is expectable in the future,using our proposed TSOS and TSOS-FK as forward-modelling tools.