Seismic tomography has revealed the Elastic structure of Earth's mantle at long wavelength resolution. Using classical imaging techniques, it is increasingly difficult to surpass this resolution because it is tied to the distribution of stations and sources on the Earth. In my thesis, I use a statistical approach to examine the effects of smaller, unresolved heterogeneities, and demonstrate a novel method to infer their properties from the wavefield.
I approach this problem through the following steps:
a) To obtain an idea about the strength of small scale structure in Earth's mantle, I examine given tomographic models statistically. I find that the distribution of mantle heterogeneities is difficult to describe using a simple model spectrum (e.g. power-law decay). Multiple dominant heterogeneity scales can be seen that are associated with the different physical processes that shape the Earth. Regional high resolution models indicate the presence of equally strong heterogeneities at smaller scales than at the larger globally resolved ones.
b) I then present a method that can be used to generate realisations of random models with fixed, depth-dependent statistics in the sphere.
c) In combined tomographic and statistical model realisations, I numerically compute the wavefield and examine the development of a coda and extrinsic attenuation. Both effects are relatively weak, compared to the unperturbed wavefield. In our models, scattering contributes less than 2-4\% to the total observed attenuation. From seismogram energy in the coda, we can distinguish between models with different small scale complexity. Because scattering attenuation and coda are weak and linearly related to the model covariance of the statistical scatterers, they can likely be described using single scattering theory.
d) I explore a method to employ single scattering theory (Born) kernels to image not only seismic velocities, as is common in tomographic inversions, but also the local covariance function of the model. In this approach, small features that cannot be localized in a typical tomographic inversion due to an insufficient source/receiver distribution, can be examined through the model covariance function. This technique can be seen as a combination of well-known large scale, long period tomographic and small scale, short period statistical modeling.