# Seismic Tomography with Sparsity Constraints, at the Global and the Exploration Scale

Frederik Simons
Deptartment of Geosciences, Princeton University

Room: REC 225

Feb 26, 2014 3:30 PM EST

Seismic tomography leads to often gigantic systems of linear equations, and as data volumes increase, every effort has to be made to reduce the inversion problem to manageable size. At the same time as achieving a reduction of computational complexity, new sparsity-seeking methods should be able to give additional insight into the nature of the problem itself, and the character of the solution. Practically speaking, this means that if we are solving systems that relate data (functionals of seismograms) to model parameters (the physical properties of the Earth) through the use of sensitivity kernels (partial derivatives of the measurements with respect to the unknown Earth parameters), we have opportunities for dimensional reduction on the data, the model, and the kernel side. In this presentation I discuss strategies to make inroads on all three sides of the seismic tomographic inverse problem, using one-, two- and three-dimensional spherical wavelets, and $\ell_2$-$\ell_1$ combination misfit norms. Examples come from global tomography on the basis of finite-frequency travel time measurements, and from exploration tomography using spectral-element adjoint waveform inversion.