Application of minimum support constraints to seismic traveltime tomography

Traditional regularization operators used in near-surface inversion (and inversion in general) rely on low-order differential operators to minimize weighted measures of model length resulting in models which are small, flat, or smooth. In many cases, such operators may not be appropriate constraints, particularly when the causative source of a geophysical anomaly is highly localized. Since regularization is used to choose between models with equivalent data residuals, the characteristics of the operator should reflect an understanding of target structure. Compactness or minimum support constraints, originally developed within the context of potential inversion algorithms, are well suited to a variety of near-surface and environmental problems. We explore several approaches to implementing compactness constraints and apply them to both absolute and differential seismic traveltime tomography. We use the formulation developed by Portniaguine and Zhdanov [1999] as a starting point and examine the use of compactness, compact derivative, and compact laplacian constraints, operators which minimize the number of regions with non-zero values of the appropriate slowness measures. We also investigate the convergence behavior, selection of regularization parameters, and the eigen-properties of the augmented operator matrix. Such constraints hold particular promise for monitoring fluid flow processes which, unlike more general structural features, exhibit localization along hydraulically conductive features. We demonstrate the efficacy of our approach on two synthetic examples, one targeting a cavity and the second replicating a CO2 injection monitoring experiment.