Teleseismic Wave-equation Reflection Tomography Using Free Surface Reflected Phases

Abstract. Reverse-time migration (RTM) of teleseismic converted and free-surface reflected phases has been successful in helping to constrain the structure of the crust and upper mantle, but its accuracy is to a large extent determined by the background velocity model used in the underlying wave propagation. To this end, we develop a technique for RTM based wave-equation reflection tomography in order to improve this velocity model and hence the image of the discontinuities in the subsurface. RTM-based reflection tomography belongs to a class of methods that judge the fitness of a smooth velocity model using the redundancy in reflection data. The redundancy can be characterized by the range of the single scattering operator modeling the relevant scattered phases in the data. The range of such operators can be determined by so-called annihilators. However, due to the sparsity and irregular distribution of teleseismic sources, it is unlikely that the data will be sufficient to warrant a proper application of these annihilators. In order to accommodate the sparse distribution of sources and irregular array design in teleseismic studies, we turn towards a source-profile scheme for reflection tomography. Instead of extended image annihilation, we determine the accuracy of the tomographic velocity model by using a weighted image correlation power norm. We compare pairs of images obtained from each teleseismic source by crosscorrelation. We look for a suitable background model by penalizing the correlation power away from zero “depth”. The total correlation power between images is then used as the error function and the smooth velocity model is iteratively optimized. We base our inversion scheme on the adjoint state method, and henceforth relate a perturbation in the background velocity model to a perturbation in the image correlation power norm. We present the method and a proof-of-concept with 2D synthetic data.