Christophe Zaroli

Toward Seeing the Earth's Interior Through Unbiased Tomographic Lenses

Geophysical tomographic studies traditionally exploit linear, damped least squares inversion methods. We demonstrate that the resulting models can be locally biased toward lower or higher amplitudes in regions of poor data illumination, potentially causing physical misinterpretations. For example, we show that global model S40RTS is locally biased toward higher amplitudes below isolated receivers where raypaths are quasi-vertical, such as on Hawaii. This leads to questions on the apparent low-velocity structure interpreted as the Hawaii hot spot. We prove that a linear Backus-Gilbert inversion scheme can bring the Earth’s interior into focus through unbiased tomographic lenses, as its model estimates are constrained to be averages over the true model. It also efficiently computes the full generalized inverse required to infer both model resolution and its covariance, enabling quantitative interpretations of tomographic models.

Conjugate gradient based acceleration for inverse problems

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite precision arithmetic) the exact solution after a finite number of iterations. It is thus well suited for many types of inverse problems. On the other hand, the method requires the computation of the gradient. Here difficulty can arise, since the functional of interest to the given inverse problem may not be differentiable. In this paper, we review two approaches to deal with this situation: iteratively reweighted least squares and convolution smoothing. We apply the methods to a more generalized, two parameter penalty functional. We show advantages of the proposed algorithms using examples from a geotomographical application and for synthetically constructed multi-scale reconstruction and regularization parameter estimation.