Applying Compactness Constraints to Differential Traveltime Tomography
Name
Franklin_compactness_ERL2007.pdf
Size
793.5 KB
Format
Adobe PDF
Checksum (MD5)
838d47825eac23adc4d2fb44b35cc5a0
Author(s)
Ajo-Franklin, Jonathan B.
Minsley, Burke J.
Daley, Thomas M.
Date Issued
2007
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;2007-06
Abstract
Tomographic imaging problems are typically ill-posed and often require the use of regularization techniques
to guarantee a stable 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 generated by
a non-smooth spatial process. Timelapse imaging of flow-induced velocity anomalies is one such case;
flow features are often characterized by spatial compactness or connectivity. By performing inversions
on differenced arrival time data, the properties of the timelapse feature can be directly constrained. We
develop a differential traveltime tomography algorithm which selects for compact solutions i.e. models
with a minimum area of support, through application of model-space iteratively reweighted least squares.
Our technique is an adaptation of minimum support regularization methods previously explored within
the potential theory community. We compare our inversion algorithm to the results obtained by traditional
Tikhonov regularization for two simple synthetic models; one including several sharp localized
anomalies and a second with smoother features. We use a more complicated synthetic test case based on
multiphase flow results to illustrate the efficacy of compactness constraints for contaminant infiltration
imaging. We conclude by applying the algorithm to a CO[subscript 2] sequestration monitoring dataset acquired
at the Frio pilot site. We observe that in cases where the assumption of a localized anomaly is correct,
the addition of compactness constraints improves image quality by reducing tomographic artifacts and
spatial smearing of target features.
Persistent DSpace Link
