Detection of mantle plumes in the lower mantle by diffraction tomography: theory

We investigate the properties of long-period seismic waves scattered by idealized plume conduits in the lower mantle. We build a schematic, yet realistic, model of the seismic velocity and density anomalies caused by a thermal plume. We devise a method to construct realistic seismograms of P-waves scattered by this anomaly. The results show that the scattered wave takes the form of an Airy phase, which arrives after the direct P-wave, at a time that corresponds to the shortest time it takes for the P-wave to travel from the source to the plume, and from there to the station. The predicted amplitude at a long period (T≃20 s) is in the range of 1–5% of the amplitude of the direct wave. We explore the variation of the amplitude as a function of the geometrical parameters, and show that it is well explained by considering the contribution of the column of the plume in a T/4 Fresnel zone around the fastest scattered ray. We compare the amplitudes and waveforms obtained in the Rayleigh and Mie approximations, and find that, for realistic geometries, wider plumes yield a larger signal. Nevertheless, the predicted amplitudes are too small to yield a detectable signal. In the Born approximation, the image reconstruction of nearly vertical features reduces to a 2D linear inversion. We present a method, based on LSQR, to produce such images from the global set of long-period seismograms. In a companion paper [Ying Ji, H.-C. Nataf, Earth Planet. Sci. Lett., this issue], this method is applied to real data that sample the lower mantle beneath Hawaii.