Understanding total variation regularization: Why can it recover dipping structures?

Abstract

Many geological features of scientific and/or economic interest have structural orientations that are neither horizontal nor vertical. Being able to recover such dipping structures from geophysical inversions is, therefore, important. Different regularization strategies have been proposed to help recover dipping structures. One notable example is total variation. However, there seems to be a lack of understanding within the geophysical community regarding why total variation regularization allows dipping structures to be recovered, whereas L₁ norm regularization does not. In this paper, we compare these two regularization strategies from an optimization point of view using two simple block models. We also perform three-dimensional inversions using a synthetic example and a field data example involving gravity gradient data to demonstrate the resolving power of total variation in potential field data inversion.