Tomographic resolution of ray and finite-frequency methods: a membrane-wave investigation

The purpose of this study is to evaluate the resolution potential of current finite-frequency approaches to tomography, and to do that in a framework similar to that of global scale seismology. According to our current knowledge and understanding, the only way to do this is by constructing a large set of 'ground-truth' synthetic data computed numerically (spectral elements, finite differences, etc.), and then to invert them using the various available linearized techniques. Specifically, we address the problem of using surface wave data to map phase-velocity distributions. Our investigation is strictly valid for the propagation of elastic waves on a spherical, heterogeneous membrane, and a good analogue for the propagation of surface waves within the outermost layers of the Earth. This amounts to drastically reducing the computational expense, with a certain loss of accuracy if very short-wavelength features of a strongly heterogeneous Earth are to be modelled. Our analysis suggests that a single-scattering finite-frequency approach to tomography, with sensitivity kernels computed via the adjoint method, is significantly more powerful than ray-theoretical methods, as a tool to image the fine structure of the Earth.