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Summary: Applying compactness constraints to differential traveltime tomography
Jonathan B. Ajo-Franklin1
, Burke J. Minsley1
, and Thomas M. Daley2
ABSTRACT
Tomographic imaging problems are typically ill-posed and of-
ten require the use of regularization techniques to guarantee a sta-
ble solution. Minimization of a weighted norm of model length
is one commonly used secondary constraint. Tikhonov methods
exploit low-order differential operators to select for solutions
that are small, flat, or smooth in one or more dimensions. This
class of regularizing functionals may not always be appropriate,
particularly in cases where the anomaly being imaged is generat-
ed by a nonsmooth spatial process. Time-lapse imaging of flow-
induced velocity anomalies is one such case; flow features are of-
ten characterized by spatial compactness or connectivity. By per-
forming inversions on differenced arrival time data, the proper-
ties of the time-lapse feature can be directly constrained. We de-
velop a differential traveltime tomography algorithm which
selects for compact solutions, i.e., models with a minimum area
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