Reconstruction of a velocity field for a 3-D advection–diffusion equation

• Published in: International journal of thermal sciences 2011-12, Vol.50 (12), p.2340-2354
• Main Authors: Dou, Yi-Xin, Han, Bo
• Format: Article
• Language: English
• Subjects: Advection-diffusion equation; Earth sciences; Earth, ocean, space; Error analysis; Errors; Evolution; Exact sciences and technology; Inverse problem; l1 data fidelity; Reconstruction; Regularization; Tectonics. Structural geology. Plate tectonics; Three dimensional; Topography; Total variation penalty term
• ISSN: 1290-0729; 1778-4166
• DOI: 10.1016/j.ijthermalsci.2011.08.002

This work deals with the reconstruction of a piecewise constant velocity field for a 3-D advection–diffusion equation. Reconstructing a velocity field often plays an important role in understanding the formation and evolution of orogenic topography. In order to suppress measurement errors and to identify sharp features, we propose a new regularization integrating an l 1 data fidelity with a total variation 1 1 Total variation is abbreviated to TV. The combination of an l 1 data fidelity and an l 2 penalty term is abbreviated to ( l 1 +  l 2). The combination of an l 2 data fidelity and TV penalty term is abbreviated to ( l 2 +  TV). The combination of an l 1 data fidelity and TV penalty term is abbreviated to ( l 1 +  TV). The combination of an l 2 data fidelity and an l 2 penalty term is abbreviated to ( l 2 +  l 2). penalty term to reconstruct a piecewise constant velocity field. For testing the performance of our proposed regularization method, we compare four different regularization methods. From numerical experiments, we can draw conclusions: (I) an l 1 data fidelity can suppress measurement errors including Gaussian noise and non-Gaussian noise; (II) a total variation penalty term has the ability to identify sharp features. ► Reconstructing a 3-D velocity field for low/high tectonic activities. ► Designing an algorithm to suppress outliers and to identify discontinuities. ► Comparing four different regularization methods.