Waveform Inversion of the Teleseismic Wavefield

The issue of seismic inversion/imaging can be generalized to find the velocity perturbation field that provides the best explanation for seismic data. Theoretically, migration is the first iteration in the inversion process, not the solution that minimizes the RMS error between observed and model-predicted wavefield. Waveform inversion, however, seeks to find the true perturbation field by directly solving the partial differential wave equations. When the wavefield is densely sampled, waveform inversion has been proven to be able to image sub-wavelength scale structure. Recent developments in passive seismic observations make it possible to apply imaging techniques developed for petroleum exploration, such as waveform tomography, to investigate crustal and mantle structures. We have been attempting to apply this technique to the teleseismic wavefield. Here we start with the relative simple 2D SH-wave case with reflection source-receiver geometry to target the core-mantle boundary (CMB) region. Many studies suggest that the lowermost several hundreds of kilometers of Earth's mantle, the D" layer is complicated and heterogeneous in terms of seismic structure. D" heterogeneities cover a wide range of scales that vary from a few kilometers to a few thousands of kilometers laterally and tenths to tens of percents in intensity. The D" layer also has very different 1D velocity structure. Different techniques have been used to study these very different structures. It is thus very interesting to see whether we can use teleseismic S and ScS waveforms to image these heterogeneities. The partial differential SH wave equation is parameterized in the discrete frequency-space domain. Inversion is performed iteratively to minimize the misfit between observed and model-predicted waveforms using a local descent algorithm. Iteration is employed at discrete frequencies, moving from low to high to mitigate the nonlinearity of the problem. The teleseismic wavefield is approximated by a plane wave input. A rectangular model with 200 by 100 grid points is used in our synthetic tests. The flattened iasp91 model is used as the background velocity model. The teleseismic S and ScS usually have dominant frequencies lower than 0.5 Hz, corresponding to a wavelength of 15 km. We used a rotated finite-difference operator which allows modeling the wavefield with 4 grid points per wavelength. Thus with the above model parameters we can cover a D" area of 750 km by 375 km. A variety of 2D velocity models that are characterized by small sub-wavelength scatterers, horizontally lying slabs and vertically ascending plumes with varying velocity contrasts have been tested. Both 1D and travel time tomography generated 2D models have been employed as the starting model. In all the cases especially with travel time based 2D starting model, the input models are very well recovered.